@article{cui_2024, title={Bus Admittance Matrix Revisited: Performance Challenges on Modern Computers}, url={https://doi.org/10.1109/OAJPE.2024.3366117}, DOI={10.1109/OAJPE.2024.3366117}, abstractNote={Bus admittance matrix is widely used in power engineering for network modeling. Being highly sparse, it requires fewer CPU operations when used for calculations. Meanwhile, sparse matrix calculations involve numerous indexing and scalar operations, which are unfavorable to modern processors. Without using the admittance matrix, nodal power injections and the corresponding sparse Jacobian can be computed by an element-wise method, which consists of a highly regular, vectorized evaluation step and a reduction step. This paper revisits the computational performance of the admittance matrix-based method, in terms of power injection and Jacobian matrix calculation, by comparing it with the element-wise method. Case studies show that the admittance matrix method is generally slower than the element-wise method for grid test cases with thousands to hundreds of thousands of buses, especially on CPUs with support for wide vector instructions. This paper also analyzes the impact of the width of vector instructions and memory speed to predict the trend for future computers.}, journal={IEEE Open Access Journal of Power and Energy}, author={Cui, Hantao}, year={2024} }
 @article{wang_li_fang_wang_cui_zhang_she_2024, title={Electric Vehicles Charging Time Constrained Deliverable Provision of Secondary Frequency Regulation}, url={https://doi.org/10.1109/TSG.2024.3356948}, DOI={10.1109/TSG.2024.3356948}, abstractNote={Aggregation of electric vehicles (EVs) is a promising technique for providing secondary frequency regulation (SFR) in highly renewable energy-penetrated power systems. Equipped with energy storage devices, EV aggregation can provide reliable SFR. However, the main challenge is to guarantee reliable intra-interval SFR capacities and inter-interval delivery following the automatic generation control (AGC) signal. Furthermore, aggregated EV SFR provision will be further complicated by the EV charging time anxiety because SFR provision might extend EV’s charging time. This paper proposes a deliverable EV SFR provision with a charging-time-constrained control strategy. First, a charging-time-constrained EV aggregation is proposed to address the uncertainty of EV capacity based on the state-space model considering the charging-time restriction of EV owners. Second, a real-time economic dispatch and time domain simulation (RTED-TDS) cosimulation framework is proposed to verify financial results and the dynamic performance of the EV SFR provision. Last, the proposed charging time-constrained EV aggregation is validated on the IEEE 39-bus system. The results demonstrate that with charging time-constrained EV aggregation, the dynamic performance of the system can be improved with a marginal increase in total cost. More importantly, the charging time constraint can be respected in the proposed SFR provision of the EV aggregation.}, journal={IEEE Transactions on Smart Grid}, author={Wang, Jinning and Li, Fangxing and Fang, Xin and Wang, Wenbo and Cui, Hantao and Zhang, Qiwei and She, Buxin}, year={2024} }
 @article{she_li_cui_shuai_oboreh-snapps_bo_praisuwanna_wang_tolbert_2024, title={Inverter PQ Control With Trajectory Tracking Capability for Microgrids Based on Physics-Informed Reinforcement Learning}, url={https://doi.org/10.1109/TSG.2023.3277330}, DOI={10.1109/TSG.2023.3277330}, abstractNote={The increasing penetration of inverter-based resources (IBRs) calls for an advanced active and reactive power (PQ) control strategy in microgrids. To enhance the controllability and flexibility of the IBRs, this paper proposed an adaptive PQ control method with trajectory tracking capability, combining model-based analysis, physics-informed reinforcement learning (RL), and power hardware-in-the-loop (HIL) experiments. First, model-based analysis proves that there exists an adaptive proportional-integral controller with time-varying gains that can ensure any exponential PQ output trajectory of IBRs. These gains consist of a constant factor and an exponentially decaying factor, which are then obtained using a model-free deep reinforcement learning approach known as the twin delayed deeper deterministic policy gradient. With the model-based derivation, the learning space of the RL agent is narrowed down from a function space to a real space, which reduces the training complexity significantly. Finally, the proposed method is verified through numerical simulation in MATLAB-Simulink and power HIL experiments in the CURENT center.With the physics-informed learning method, exponential response time constants can be freely assigned to IBRs, and they can follow any predefined trajectory without complicated gain tuning.}, journal={IEEE Transactions on Smart Grid}, author={She, Buxin and Li, Fangxing and Cui, Hantao and Shuai, Hang and Oboreh-Snapps, Oroghene and Bo, Rui and Praisuwanna, Nattapat and Wang, Jingxin and Tolbert, Leon M.}, year={2024}, month={Jan} }
 @article{she_liu_qiu_cui_praisuwanna_wang_tolbert_li_2024, title={Systematic Controller Design for Inverter-Based Microgrids With Certified Large-Signal Stability and Domain of Attraction}, url={https://doi.org/10.1109/TSG.2023.3330705}, DOI={10.1109/TSG.2023.3330705}, abstractNote={Inverter-based resources (IBRs) introduce fast dynamics and high non-linearities to microgrids, degrading their stability and complicating the design of effective controllers. To address the arising vulnerability and non-linearities, this paper presents a systematic controller design approach that ensures large-signal stability and domain of attraction (DOA) for islanded microgrids. First, the nonlinear electromagnetic transient model of inverter-based microgrids is developed in the rotating dq reference frame, which is then transformed to a homogeneous-like system with nonlinear terms acting as superimposed parameter uncertainties. Next, the stability conditions, including certified stability, certified DOA, and their combination, are derived to rigorously guarantee a designated range to be a subset of DOA. The designated region is customized and flexible enough to cover microgrids' normal or emergency operational ranges, such as low- and high-voltage ride-through (L/HVRT) conditions. Then, a systematic method for identifying the candidate control parameter set is developed by integrating the analytical stability conditions. This approach is further exemplified in the droop controller design to improve microgrid stability and resilience. Finally, the proposed systematic controller design is verified through numerical simulation and power hardware-in-the-loop experiments to ensure large-signal stability and DOA of microgrids in emergency L/HVRT conditions.}, journal={IEEE Transactions on Smart Grid}, author={She, Buxin and Liu, Jianzhe and Qiu, Feng and Cui, Hantao and Praisuwanna, Nattapat and Wang, Jingxin and Tolbert, Leon M. and Li, Fangxing}, year={2024} }
 @article{she_li_cui_wang_zhang_bo_2024, title={Virtual Inertia Scheduling (VIS) for Real-Time Economic Dispatch of IBR-Penetrated Power Systems}, url={https://doi.org/10.1109/TSTE.2023.3319307}, DOI={10.1109/TSTE.2023.3319307}, abstractNote={A new concept called virtual inertia scheduling (VIS) is proposed to efficiently handle the increasing penetration of inverter-based resources (IBRs) in power systems. VIS is an inertia management framework that targets security-constrained and economy-oriented inertia scheduling and generation dispatch with a large scale of renewable generations. Specifically, it determines the appropriate power setpoint and reserved capacity of synchronous generators and IBRs, as well as the control modes and control parameters of IBRs to provide secure and cost-effective inertia support. First, a uniform system model is employed to quantify the frequency dynamics of IBR-penetrated power systems after disturbances. Leveraging this model, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> -domain and time-domain analytical responses of IBRs with inertia support capability are derived. Then, VIS-based real-time economic dispatch (VIS-RTED) is formulated to minimize generation and reserve costs, with full consideration of dynamic frequency constraints and the derived inertia support reserve constraints. The virtual inertia and damping of IBRs are formulated as decision variables. A deep learning-assisted linearization approach is further employed to address the non-linearity of dynamic constraints. Finally, VIS-RTED is demonstrated on a two-machine system and a modified IEEE 39-bus system. A full-order time-domain simulation is performed to verify the scheduling results.}, journal={IEEE Transactions on Sustainable Energy}, author={She, Buxin and Li, Fangxing and Cui, Hantao and Wang, Jinning and Zhang, Qiwei and Bo, Rui}, year={2024}, month={Apr} }
 @article{oboreh-snapps_she_fahad_chen_kimball_li_cui_bo_2024, title={Virtual Synchronous Generator Control Using Twin Delayed Deep Deterministic Policy Gradient Method}, url={https://doi.org/10.1109/TEC.2023.3309955}, DOI={10.1109/TEC.2023.3309955}, abstractNote={This paper presents a data-driven approach that adaptively tunes the parameters of a virtual synchronous generator to achieve optimal frequency response against disturbances. In the proposed approach, the control variables, namely, the virtual moment of inertia and damping factor, are transformed into actions of a reinforcement learning agent. Different from the state-of-the-art methods, the proposed study introduces the settling time parameter as one of the observations in addition to the frequency and rate of change of frequency (RoCoF). In the reward function, preset indices are considered to simultaneously ensure bounded frequency deviation, low RoCoF, fast response, and quick settling time. To maximize the reward, this study employs the Twin-Delayed Deep Deterministic Policy Gradient (TD3) algorithm. TD3 has an exceptional capacity for learning optimal policies and is free of overestimation bias, which may lead to suboptimal policies. Finally, numerical validation in MATLAB/Simulink and real-time simulation using RTDS confirm the superiority of the proposed method over other adaptive tuning methods.}, journal={IEEE Transactions on Energy Conversion}, author={Oboreh-Snapps, Oroghene and She, Buxin and Fahad, Shah and Chen, Haotian and Kimball, Jonathan and Li, Fangxing and Cui, Hantao and Bo, Rui}, year={2024} }
 @article{she_li_cui_wang_min_oboreh-snapps_bo_2023, title={Decentralized and Coordinated V-f Control for Islanded Microgrids Considering DER Inadequacy and Demand Control}, url={https://doi.org/10.1109/TEC.2023.3258919}, DOI={10.1109/TEC.2023.3258919}, abstractNote={This paper proposes a decentralized and coordinated voltage and frequency (Vf) control framework for islanded microgrids, with full consideration of the limited capacity of distributed energy resources (DERs) and Vf dependent load. First, the concept of DER inadequacy is illustrated with the challenges it poses. Then, a decentralized and coordinated control framework is proposed to regulate the output of inverter based generations and reallocate limited DER capacity for Vf control. The control framework is composed of a power regulator and a Vf regulator, which generates the supplementary signals for the primary controller. The power regulator regulates the output of grid forming inverters according to the real time capacity constraints of DERs, while the Vf regulator improves the Vf deviation by leveraging the load sensitivity to Vf. Next, the static feasibility and small signal stability of the proposed method are rigorously proven through mathematical formulation and eigenvalue analysis. Finally, a MATLAB Simulink simulation demonstrates the functionalities of the control framework. A few goals are fulfilled within the decentralized and coordinated framework, such as making the best use of limited DERs capacity, enhancing the DC side stability of inverter based generations, and reducing involuntary load shedding.}, journal={IEEE Transactions on Energy Conversion}, author={She, Buxin and Li, Fangxing and Cui, Hantao and Wang, Jinning and Min, Liang and Oboreh-Snapps, Oroghene and Bo, Rui}, year={2023} }
 @article{cui_konstantinopoulos_osipov_wang_li_tomsovic_chow_2023, title={Disturbance Propagation in Power Grids With High Converter Penetration}, url={https://doi.org/10.1109/JPROC.2022.3173813}, DOI={10.1109/JPROC.2022.3173813}, abstractNote={High penetration of converter-interfaced renewable energy resources will significantly change the swing dynamics between synchronous generators (SGs) in future power systems. This article examines the impact of high converter penetration on wave-like disturbance propagation arising from sudden generator and load losses in radial (1-D) and meshed (2-D) power systems. To keep the uniformity assumption as converters are introduced, the rating of each SG is decreased with a converter resource making up for the reduction. Numerical simulations demonstrate that as the penetration level of constant-power grid-following (GFL) converters increases, the speed of disturbance propagation increases due to the reduced system inertia. Naturally, converters with the capabilities to positively respond to disturbances would in turn reduce the propagation speed. Analytical studies based on continuum models are presented for the 2-D system with SGs and constant-power GFL converters in order to visualize the disturbance propagation and validate numerical simulations based on differential-algebraic equations. In addition, fast active power control of converters can slow down the electromechanical wave (EMW) propagation and even contain it. These concepts are illustrated on the idealized radial and meshed systems and a reduced model of the U.S. eastern interconnection.}, journal={Proceedings of the IEEE}, author={Cui, Hantao and Konstantinopoulos, Stavros and Osipov, Denis and Wang, Jinning and Li, Fangxing and Tomsovic, Kevin L. and Chow, Joe H.}, year={2023}, month={Jul} }
 @article{she_li_cui_zhang_bo_2023, title={Fusion of Microgrid Control With Model-Free Reinforcement Learning: Review and Vision}, url={https://doi.org/10.1109/TSG.2022.3222323}, DOI={10.1109/TSG.2022.3222323}, abstractNote={Challenges and opportunities coexist in microgrids as a result of emerging large-scale distributed energy resources (DERs) and advanced control techniques. In this paper, a comprehensive review of microgrid control is presented with its fusion of model-free reinforcement learning (MFRL). A high-level research map of microgrid control is developed from six distinct perspectives, followed by bottom-level modularized control blocks illustrating the configurations of grid-following (GFL) and grid-forming (GFM) inverters. Then, mainstream MFRL algorithms are introduced with an explanation of how MFRL can be integrated into the existing control framework. Next, the application guideline of MFRL is summarized with a discussion of three fusing approaches, i.e., model identification and parameter tuning, supplementary signal generation, and controller substitution, with the existing control framework. Finally, the fundamental challenges associated with adopting MFRL in microgrid control and corresponding insights for addressing these concerns are fully discussed.}, journal={IEEE Transactions on Smart Grid}, author={She, Buxin and Li, Fangxing and Cui, Hantao and Zhang, Jingqiu and Bo, Rui}, year={2023}, month={Jul} }
 @article{han_hu_cui_chen_quan_wu_2022, title={An optimal bidding and scheduling method for load service entities considering demand response uncertainty}, url={https://doi.org/10.1016/j.apenergy.2022.120167}, DOI={10.1016/j.apenergy.2022.120167}, abstractNote={With the rapid development of demand-side management technologies, load serving entities (LSEs) may offer demand response (DR) programs to improve the flexibility of power system operation. Reliable load aggregation is critical for LSEs to improve profits in electricity markets. Due to the uncertainty, the actual aggregated response of loads obtained by conventional aggregation methods can experience significant deviations from the bidding value, making it difficult for LSEs to develop an optimal bidding and scheduling strategy. In this paper, a bi-level scheduling model is proposed to maximize the net revenue of the LSE from optimal DR bidding and energy storage systems ESS scheduling by considering the impacts of the uncertainty of demand response. An online learning method is adopted to improve aggregation reliability. Additionally, the net profit for LSEs can be raised by strategically switching ESS between two modes, namely, energy arbitrage and deviation mitigation. With Karush–Kuhn–Tucker (KKT) optimality condition-based decoupling and piecewise linearization applied, this bi-level optimization model can be reformulated and converted into a mixed-integer linear programming (MILP) problem. The effectiveness and advantages of the proposed method are verified in a modified IEEE RTS-24 bus system.}, journal={Applied Energy}, author={Han, Rushuai and Hu, Qinran and Cui, Hantao and Chen, Tao and Quan, Xiangjun and Wu, Zaijun}, year={2022}, month={Dec} }
 @article{cui_li_cui_bu_shi_2022, title={Data-Driven Joint Voltage Stability Assessment Considering Load Uncertainty: A Variational Bayes Inference Integrated With Multi-CNNs}, url={https://doi.org/10.1109/TPWRS.2021.3111151}, DOI={10.1109/TPWRS.2021.3111151}, abstractNote={Few studies have focused on assessing the transient and steady-state voltage stability status of dynamic systems simultaneously. This motivated us to propose a new concept referred to as joint voltage stability assessment (JVSA). Towards this end, this paper proposes a novel data-driven JVSA method considering load uncertainty. It combines multiple convolutional neural networks (multi-CNNs) and a novel variational Bayes (VB) inference for better JVSA accuracy. First, the multi-CNN model is utilized to fast estimate the maximum voltage deviations during the transient and steady-state process. Uncertain load scenarios and system topology under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -1 contingency with are chosen as inputs of each CNN model. Second, estimated voltage deviations are put into the VB inference to automatically infer the transient and steady-state voltage stability status. To validate its effectiveness, numerical simulations are performed on the modified WECC 179-bus system by comparing with benchmark algorithms. It is demonstrated that the proposed data-driven JVSA method is more accurate and faster than the conventional VSA method.}, journal={IEEE Transactions on Power Systems}, author={Cui, Mingjian and Li, Fangxing and Cui, Hantao and Bu, Siqi and Shi, Di}, year={2022}, month={May} }
 @article{zhang_cui_liu_qiu_hong_yao_li_2022, title={Encoding Frequency Constraints in Preventive Unit Commitment Using Deep Learning With Region-of-Interest Active Sampling}, url={https://doi.org/10.1109/TPWRS.2021.3110881}, DOI={10.1109/TPWRS.2021.3110881}, abstractNote={With the increasing penetration of renewable energy, frequency response and its security are of significant concerns for reliable power system operations. Frequency-constrained unit commitment (FCUC) is proposed to address this challenge. Despite existing efforts in modeling frequency characteristics in unit commitment (UC), current strategies can only handle oversimplified low-order frequency response models and do not consider wide-range operating conditions. This paper presents a generic data-driven framework for FCUC under high renewable penetration. Deep neural networks (DNNs) are trained to predict the frequency response using real data or high-fidelity simulation data. Next, the DNN is reformulated as a set of mixed-integer linear constraints to be incorporated into the ordinary UC formulation. In the data generation phase, all possible power injections are considered, and a region-of-interest active sampling is proposed to include power injection samples with frequency nadirs closer to the UFLC threshold, which enhances the accuracy of frequency constraints in FCUC. The proposed FCUC is investigated on the IEEE 39-bus system. Then, a full-order dynamic model simulation using PSS/E verifies the effectiveness of FCUC in frequency-secure generator commitments.}, journal={IEEE Transactions on Power Systems}, author={Zhang, Yichen and Cui, Hantao and Liu, Jianzhe and Qiu, Feng and Hong, Tianqi and Yao, Rui and Li, Fangxing}, year={2022}, month={May} }
 @article{cui_zhang_tomsovic_li_2022, title={Power electronics‐interfaced cyber‐physical power systems: A review on modeling, simulation, and cybersecurity}, url={https://doi.org/10.1002/wene.448}, DOI={10.1002/wene.448}, abstractNote={Abstract We present the review of two interlinked challenges in modern electric power systems: the transformation to a cyber‐physical system, and the integration of power electronics‐interfaced renewables. Electric power systems are being modernized with the integration of power electronics‐interfaced devices (PEID) and communication‐enabled cyber‐applications. This paper reviews the concepts, studies, and testbeds for cyber‐physical power systems (CPPS), as well as the modeling of power electronics‐based devices for physical power system stability simulations. The CPPS concept is introduced in the National Institute of Standard Technology framework for cyber‐physical systems, with an emphasis on CPPS subsystems. For the physical subsystem, PEID components are generalized into the primary source and the grid interface, while controllers are generalized as a reference generator and a reference tracker. Next, the cybersecurity research objectives are summarized, followed by a categorization of CPPS studies. Further, testbed techniques for integrating communication networks with power system simulation are reviewed. Also, challenges and future directions in the area of CPPS are discussed. This article is categorized under: Energy Infrastructure > Systems and Infrastructure}, journal={WIREs Energy and Environment}, author={Cui, Hantao and Zhang, Yichen and Tomsovic, Kevin L. and Li, Fangxing}, year={2022}, month={Nov} }
 @article{wang_fang_cui_li_liu_overbye_2022, title={Transmission-and-Distribution Dynamic Co-Simulation Framework for Distributed Energy Resource Frequency Response}, url={https://doi.org/10.1109/TSG.2021.3118292}, DOI={10.1109/TSG.2021.3118292}, abstractNote={The rapid deployment of distributed energy resources (DERs) in distribution networks has made it challenging to balance the transmission system and stabilize frequency. DERs have the ability to provide frequency regulation services; however, existing frequency dynamic simulation tools—which were developed mainly for the transmission system—lack the capability to simulate distribution network dynamics with high penetrations of DERs. Although electromagnetic transient simulation tools can simulate distribution network dynamics, the computation efficiency limits their use for large-scale transmission-and-distribution (T&D) co-simulation. This paper presents an efficient open-source T&D dynamic co-simulation framework for DER frequency response based on the HELICS platform and off-the-shelf T&D simulators. The challenge of synchronizing the simulation between the transmission network and the DERs in the distribution network is solved through the detailed modeling of DERs in frequency dynamic models while DER power flow models are also preserved in the distribution networks, thereby respecting local voltage constraints when dispatching DER power for frequency response. DER frequency response (primary and secondary) is simulated in case studies to validate the proposed framework. Last, the accuracy of the proposed co-simulation model is benchmarked, and a large T&D system simulation (2k transmission and 1M distribution nodes) is presented to demonstrate the efficiency and effectiveness of the overall framework.}, journal={IEEE Transactions on Smart Grid}, author={Wang, Wenbo and Fang, Xin and Cui, Hantao and Li, Fangxing and Liu, Yijing and Overbye, Thomas J.}, year={2022}, month={Jan} }
 @article{fang_cui_du_li_kang_2021, title={Characteristics of locational uncertainty marginal price for correlated uncertainties of variable renewable generation and demands}, volume={282}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85096196557&partnerID=MN8TOARS}, DOI={10.1016/j.apenergy.2020.116064}, abstractNote={With the rapid increase of variable renewable energy sources in power systems, how to manage and price the uncertainty of renewable resources’ power outputs is becoming an urgent issue. Current market designs considering the uncertainties are mainly based on the probabilistic scenario set of demand and renewable energy resources power outputs. This consideration makes market designs vulnerable to three significant challenges when put into practice. First, the accurate probability distribution of renewable generation is hard to obtain in real-time. Second, it is challenging to clear the market timely with many scenarios to guarantee accuracy. Third, generation cost recovery cannot be guaranteed for some scenarios. To overcome these challenges, this paper proposes a locational uncertainty marginal price model to price the uncertainty explicitly based on a scenario-free stochastic market-clearing model. Instead of using the probabilistic scenario set, the uncertainty of renewable energy sources and loads is modeled with distributionally-robust chance constraints. The correlation of uncertainties can be endogenously modeled in both the market-clearing and the locational uncertainty marginal price formation. Furthermore, this paper proves that generation cost recovery, revenue adequacy, and partial market equilibrium can be achieved using the locational uncertainty marginal price model. Numerical results from both the small and large systems simulations validate that the generation cost recovery is maintained no matter the generation participates in uncertainty mitigation or not. The transmission congestion surplus is also allocated appropriately among loads, renewable energy sources, and financial transmission right owners.}, journal={Applied Energy}, author={Fang, X. and Cui, H. and Du, E. and Li, F. and Kang, C.}, year={2021} }
 @article{cui_li_fang_2021, title={Effective Parallelism for Equation and Jacobian Evaluation in Large-Scale Power Flow Calculation}, volume={36}, url={https://doi.org/10.1109/TPWRS.2021.3073591}, DOI={10.1109/TPWRS.2021.3073591}, abstractNote={This letter investigates parallelism approaches for equation and Jacobian evaluations in large-scale power flow calculation. Two levels of parallelism are proposed and analyzed: inter-model parallelism, which evaluates models in parallel, and intra-model parallelism, which evaluates calculations within each model in parallel. Parallelism techniques such as multi-threading and single instruction multiple data (SIMD) vectorization are discussed, implemented, and benchmarked as six calculation workflows. Case studies on the 70,000-bus synthetic grid show that equation evaluations can be accelerated by ten times, and the overall Newton power flow advances the state of the art by 20%.}, number={5}, journal={IEEE Transactions on Power Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Cui, Hantao and Li, Fangxing and Fang, Xin}, year={2021}, month={Sep}, pages={4872–4875} }
 @article{zhang_cui_liu_qiu_hong_yao_li_2021, title={Encoding frequency constraints in preventive unit commitment using deep learning with region-of-interest active sampling}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85102166143&partnerID=MN8TOARS}, journal={arXiv}, author={Zhang, Y. and Cui, H. and Liu, J. and Qiu, F. and Hong, T. and Yao, R. and Li, F.}, year={2021} }
 @article{cui_li_tomsovic_2021, title={Hybrid Symbolic-Numeric Framework for Power System Modeling and Analysis}, volume={36}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85101756791&partnerID=MN8TOARS}, DOI={10.1109/TPWRS.2020.3017019}, abstractNote={With the recent proliferation of open-source packages for computing, power system differential-algebraic equation (DAE) modeling and simulation are being revisited to reduce the programming efforts. Existing open-source tools require manual efforts to develop code for numerical equations, sparse Jacobians, and discontinuous components. This paper proposes a hybrid symbolic-numeric framework, exemplified by an open-source Python-based library ANDES, which consists of a symbolic layer for descriptive modeling and a numeric layer for vector-based numerical computation. This method enables the implementation of DAE models by mixing and matching modeling components, through which models are described. In the framework, a rich set of discontinuous components and standard transfer function blocks are provided besides essential modeling elements for rapid modeling. ANDES can automatically generate robust and fast numerical simulation code, as well as and high-quality documentation. Case studies present a) two implementations of turbine governor model TGOV1, b) power flow computation time break down for MATPOWER systems, c) validation of time-domain simulation with commercial software using three test systems with a variety of models, and d) the full eigenvalue analysis for Kundur's system. Validation shows that ANDES closely matches the commercial tool DSATools for power flow, time-domain simulation, and eigenvalue analysis.}, number={2}, journal={IEEE Transactions on Power Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Cui, Hantao and Li, Fangxing and Tomsovic, Kevin}, year={2021}, pages={1373–1384} }
 @article{zhang_li_cui_bo_ren_2021, title={Market-Level Defense against FDIA and a New LMP-Disguising Attack Strategy in Real-Time Market Operations}, volume={36}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85101736232&partnerID=MN8TOARS}, DOI={10.1109/TPWRS.2020.3020870}, abstractNote={Traditional cyberattack strategies on the electricity market only consider bypassing bad data detections. However, our analysis shows that experienced market operators can detect abnormal locational marginal prices (LMPs) under the traditional attack model during real-time (RT) operations, because such attack model ignores the characteristics of the LMP itself and leads to price spikes that can be an easy-to-detect signal of abnormality. A detection approach based on the concept of critical load level (CLL) is used to help operators identify risky periods when operators would be prone to overlooking abnormal LMPs. During safe periods, the abnormal LMPs are identified according to the operator's experience, while in risky CLL intervals, a N-x cyber contingency analysis is proposed to help independent system operators (ISOs) detect abnormal LMPs. Further, this paper constructs a new type of cyberattack strategy capable of not only bypassing bad data detection in the state estimation stage but also disguising the compromised LMPs as regular LMPs to avoid market operators' alerts in a realistic scenario wherein the attacker has imperfect information on system topology. Finally, the proposed analysis method and the attack strategy are evaluated through numerical studies on the PJM 5-bus system and the IEEE 118-bus system.}, number={2}, journal={IEEE Transactions on Power Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Zhang, Qiwei and Li, Fangxing and Cui, Hantao and Bo, Rui and Ren, Lingyu}, year={2021}, pages={1419–1431} }
 @article{feng_shi_cui_li_2021, title={Optimal power allocation strategy for black start in VSC-MTDC systems considering dynamic impacts}, volume={193}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85100142384&partnerID=MN8TOARS}, DOI={10.1016/j.epsr.2021.107023}, abstractNote={The ability of voltage source converters (VSCs) to restore blackout grid has been widely accepted based on their abilities in flexible and independent power control. However, the traditional literature only studied the case of a two-terminal hybrid system in which all required black start (BS) power is provided by a single healthy AC grid. Meanwhile, the dynamic changes at the sending end, including AC grid and converter, are not considered. In this paper, an optimal power allocation strategy is proposed to perform BS in the VSC-based multi-terminal direct current (VSC-MTDC) systems. The new strategy ensures that all the healthy AC grids can cooperate to transfer BS power together to the blackout grid. Thus, each grid only needs to provide a proportion of the required power. Furthermore, since the grids and converters in practical VSC-MTDC projects are generally limited to small sizes, the capacities together with main dynamic characteristics are also considered in the new strategy. By reasonably setting the optimization objective and constraints, the overall dynamic impacts can be significantly reduced, and the stability of AC grids and converters can be guaranteed. Finally, the comparison tests on a typical four-terminal system verify the feasibility and effectiveness of the proposed method.}, journal={Electric Power Systems Research}, author={Feng, Wei and Shi, Qingxin and Cui, Hantao and Li, Fangxing}, year={2021} }
 @article{wang_fang_cui_li_2021, title={Transmission-and-distribution frequency dynamic co-simulation framework for distributed energy resources frequency response}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85101158830&partnerID=MN8TOARS}, journal={arXiv}, author={Wang, W. and Fang, X. and Cui, H. and Li, F.}, year={2021} }
 @article{li_tomsovic_cui_2020, title={A Large-Scale Testbed as a Virtual Power Grid: For Closed-Loop Controls in Research and Testing}, volume={18}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85081046437&partnerID=MN8TOARS}, DOI={10.1109/MPE.2019.2959054}, abstractNote={The electric power grid is undergoing unprecedented modernization toward higher reliability, higher efficiency, and lower cost through the integration of renewable energy, wide-area monitoring, and advanced control technology. This integration is making the transmission grid overwhelmingly complex to understand and model to apply new control or actuation technologies. This calls for a fast-prototyping platform for research and testing under the new transmission technology paradigm. Such a platform should be highly integrated, closed loop, and capable of mimicking a real power grid for testing new controls or algorithms. However, traditional software simulation packages usually perform specific tasks such as dynamic simulation or state estimation but lack the capability of providing an integrated closed-loop platform.}, number={2}, journal={IEEE Power and Energy Magazine}, author={Li, F. and Tomsovic, K. and Cui, H.}, year={2020}, pages={60–68} }
 @article{lackner_osipov_cui_chow_2020, title={A Privacy-Preserving Distributed Wide-Area Automatic Generation Control Scheme}, volume={8}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85097841333&partnerID=MN8TOARS}, DOI={10.1109/ACCESS.2020.3040883}, abstractNote={The increased penetration of renewable resources has made frequency regulation and generation control growing concerns for power system operators. Due to the variability of renewable resources and the reduced inertia leading to the deterioration of system frequency response, many balancing areas expect a need to increase their regulation services and non-spinning reserves. This also increases the total cost of system operation and may elevate location marginal energy prices. This article addresses the scheduling of energy interchange between balancing areas, in light of optimizing regulation services in the entire interconnected power system. A control architecture is defined to extend the existing area control error concept to allow more cooperation between interconnected balancing areas. In this scheme, regulation services from different balancing areas can be pooled such that a loss of generation in one control area can utilize regulation services from multiple areas resulting in a more economic dispatch of generation resources. The effectiveness of the wide-area control scheme is demonstrated in a large-scale testbed for two power systems with high renewable penetration.}, journal={IEEE Access}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Lackner, Christoph and Osipov, Denis and Cui, Hantao and Chow, Joe H.}, year={2020}, pages={212699–212708} }
 @article{zhai_sun_cui_hu_li_2020, title={Adjustable loads control and stochastic stability analysis for multi-energy generation system based on Markov model}, volume={32}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85062676155&partnerID=MN8TOARS}, DOI={10.1007/s00521-019-04120-0}, number={6}, journal={Neural Computing and Applications}, author={Zhai, S. and Sun, Y. and Cui, H. and Hu, Y. and Li, Z.}, year={2020}, pages={1517–1529} }
 @article{li_jiang_yuan_cui_li_li_jia_2020, title={An eigensystem realization algorithm based data-driven approach for extracting electromechanical oscillation dynamic patterns from synchrophasor measurements in bulk power grids}, volume={116}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85072184535&partnerID=MN8TOARS}, DOI={10.1016/j.ijepes.2019.105549}, abstractNote={In power systems, electromechanical oscillatory dynamics, dominant modes, mode shapes, participation factors and coherent groups of generators are all important modal parameters. Most of the existing measurement-based methods focus on estimating one or two aspects among dominant modes, mode shapes, participation factors, and coherent groups. Nevertheless, none of existing methods explore all the four aspects from synchrophasor measurements at the same time. In this work, an eigensystem realization algorithm (ERA) based data-driven approach is developed to estimate dominant modes, mode shapes, participation factors and coherent groups from synchrophasor measurements in a holistic framework. In the proposed approach, the reduced power system dynamic model is first estimated by ERA from multichannel synchrophasor measurements. Then, based on the estimated power system dynamic model, electromechanical oscillation modes, corresponding mode shapes and the left eigenvalue vectors are solved. Next, using the solved mode shapes and left eigenvalue vectors, the participation factors of the generators associated with the electromechanical oscillation modes are calculated. Further, the direction cosines among the generators representing coherent strength of generators are calculated by using the achieved mode shapes. Finally, in accordance with the calculated direction cosines, the coherent generators are then identified. The proposed approach is demonstrated with the simulation data of the 16-machine, 68-bus test system and the field Phasor Measurement Units (PMUs) data collected in Liaoning Electric Power Grid. The results demonstrate that the proposed data-driven approach captures dominant modes, mode shapes, participation factors, and coherent groups of generators from synchrophasor measurements with high accuracy and efficiency.}, journal={International Journal of Electrical Power and Energy Systems}, author={Li, X. and Jiang, T. and Yuan, H. and Cui, H. and Li, F. and Li, G. and Jia, H.}, year={2020} }
 @article{li_jiang_liu_bai_cui_li_2020, title={Bootstrap-based confidence interval estimation for thermal security region of bulk power grid}, volume={115}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85070973046&partnerID=MN8TOARS}, DOI={10.1016/j.ijepes.2019.105498}, abstractNote={Thermal security region (TSR) is a powerful tool for monitoring and controlling the thermal security of bulk power grid with high penetration of renewable energy. One of the major challenges of TSR in practical application is to obtain the exact analytical expression of the TSR boundary (TSRB) because TSRB is a nonlinear hypersurface described by an implicit function. For this reason, the TSRB is usually approximated by hyperplane instead of getting the exact analytical expression. Traditionally, the coefficients of the hyperplane are estimated with a set of original TSRB points using least square estimation (LSE). However, LSE is a point estimation method, which is incapable of evaluating the quality of the estimation. In addition, the accuracy and computational efficiency of the hyperplane approximation are influenced by the number of TSRB points significantly. In this paper, a bootstrap based confidence interval estimation is proposed to estimate not only the coefficients of TSRB approximation hyperplane, but also the standard deviations and confidence intervals of the coefficients for evaluating the quality and reliability of the approximation results. First, empirical distribution functions (EDFs) of the coefficients of TSRB approximation hyperplane are approximated from a set of original TSRB points by using residual resampling bootstrap method. Then, the EDFs of the coefficients are employed to estimate the coefficients of the approximation hyperplane. Meanwhile, the standard deviations and confidence intervals of the estimated coefficients of the hyperplanes are also calculated for evaluating the quality and reliability of the approximation. The proposed approach is tested on the China Southern Power Grid (CSG). Results of simulations validate the accuracy and efficiency of the proposed approach in approximating the TSRB.}, journal={International Journal of Electrical Power and Energy Systems}, author={Li, X. and Jiang, T. and Liu, G. and Bai, L. and Cui, H. and Li, F.}, year={2020} }
 @article{cui_li_tomsovic_2020, title={Cyber‐physical system testbed for power system monitoring and wide‐area control verification}, volume={2}, url={https://doi.org/10.1049/iet-esi.2019.0084}, DOI={10.1049/iet-esi.2019.0084}, abstractNote={IET Energy Systems IntegrationVolume 2, Issue 1 p. 32-39 Research ArticleOpen Access Cyber-physical system testbed for power system monitoring and wide-area control verification Hantao Cui, orcid.org/0000-0002-4259-5925 Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this authorFangxing Li, Corresponding Author fli6@utk.edu Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this authorKevin Tomsovic, Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this author Hantao Cui, orcid.org/0000-0002-4259-5925 Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this authorFangxing Li, Corresponding Author fli6@utk.edu Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this authorKevin Tomsovic, Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this author First published: 07 February 2020 https://doi.org/10.1049/iet-esi.2019.0084Citations: 5AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract The electric power system is intrinsically a cyber-physical system (CPS) with power flowing inthe physical system and information flowing in the cyber-network. Testbeds arecrucial for understanding the cyber-physical interactions and provideenvironments for prototyping novel applications. This study proposes afour-layer architecture for CPS testbeds with emphases on communication networkemulation and networked physical components. A configurable software-definednetwork is employed to bridge physical components with wide-area applicationsfor closed-loop control. In order to distribute physically coupled devices intomultiple software simulations, this study proposes a data broker setup based ona distributed messaging environment to achieve low-latency data streaming. Thedecoupled design with data streaming allows for building testbed components asmodules and running them in a distributed manner. Case studies verify the databroker setup for low-latency sensing and actuation, as well as the communicationemulation setup for the desired network latency. Also illustrated is a replayattack scenario using synchrophasors in the Western Electricity CoordinatingCouncil (WECC) 181-bus system for demonstrating the closed-loop cyber-physicalsimulation capability of the testbed. 1 Introduction Modern electric power systems are facing new challenges and opportunities due to the increasing level of renewable energy. Traditional vertically integrated utilities are being deregulated, and information sharing between system operators is becoming common. Power system control paradigms are shifting from the traditional, local control dominated scheme to the modern, wide-area synchrophasor data assisted controls [1]. Due to the intertwined nature of the physical and cyber components, the testing of emerging applications needs to be done in environments that can characterise both the physical system and the cyber network. Testbeds serve as platforms for conducting rigid yet replicable tests and verification of new controls and applications. Traditional testing approaches involve computer simulation and physical hardware emulation with an emphasis on physical systems, where most of the closed-loop controllers are local. For example, analogue simulators, electromagnetic transient programs, transient stability programs [2-4], and digital real-time simulators belong to this category. These tools are still broadly utilised for modelling the physical system in testbeds. More recently, the growing interest in modelling power system wide-area monitoring, control, and cybersecurity requires the integration of communication networks ('network' hereafter). A global event-driven co-simulation framework is described in [5] for wide-area measurement and control schemes. A cyber-physical system (CPS) testbed is proposed in [6] for intrusion detection in power systems. A toolkit for security research on CPS networks is proposed in [7] to connect CPS software and hardware for studying cyber attacks and defences. The architecture and studies of the PowerCyber testbed for substation cybersecurity are described in [8]. An integrated testbed, SURE, for security and resilience for general CPS is described in [9]. Related wide-area applications in cyber-physical power system testbeds [10-13] can be categorised based on their focus, such as hardware-in-the-loop (HIL) device verification [14, 15], Supervisory Control and Data Acquisition (SCADA) [16], wide-area monitoring, protection, and control (WAMPAC) [17-21], and cyber-security studies [22-26]. In particular, Hardware Testbed, a converter-based power system HIL emulation platform, is proposed in [27]. In [28], real-time digital simulator and CompactRIO are applied for microgrid testing. A testbed for WAMPAC is proposed in [29] with inverter-based power system emulation, protection devices, and communication in the loop. In [21] a multi-agent testbed is proposed with a focus on resilience improvement. In [20], an offline co-simulation of electromagnetic transients with network emulators is proposed and implemented. Based on the tightness of the coupling of the simulation, measurement, control, and communication, the above work can be further categorised into three types: full integration, co-simulation, and hybrid. The full-integration approach, such as iTesla in [30], aims to develop and simulate all the pieces in a unified tool, which is accurate but requires extensive expertise for implementation. The co-simulation approach aims to glue pieces together using a co-simulation middleware, such as the Hierarchical Engine for Large-scale Infrastructure Co-Simulation (HELICS) in [31], which is agnostic of the linked pieces. This approach is easy to extend and multi-domain applicable, but it leaves the consistency check and validation to the user. Our work applies a hybrid approach by allowing for the modules to be developed independently but coupled for closed-loop simulation and control through defined data interfaces. Moreover, the modelling accuracy of the interactions between the physical system andcommunication networks is crucial for the fidelity of testing results. For example, in a testbed where the power grid simulation accepts control signals from over thenetwork, the network topology, bandwidth, and latency become crucial and cannot beneglected. However, none of the existing research has evaluated the accuracy orproposed any solution for improvement. In addition, testbeds need to be structuredto provide convenient data interfaces for integrating the control under test, whichmay be developed separated from other software pieces. This paper focuses on building a CPS testbed, which is built on top of an earlier version of the CURENT large-scale testbed (LTB) [32], for accurately modelling the low-latency data acquisition and latency-embedded communication networks for monitoring and closed-loop controls in power systems. Distributed software pieces representing the physical system, monitoring, energy management system (EMS), and measurement-based control system (MBCS) are organised into four-layer software architecture. This paper also proposes the data broker setup to stream data between applications and networked physical devices with low latency. In the proposed testbed, networked physical devices modelled by distributed software programs can exchange data through the low-latency distributed messaging channels, while wide-area applications can communicate over the highly configurable emulated Internet Protocol (IP) network. Compared with recent work on power system testbeds, for example, [20, 21, 26], our proposed testbed is focused on the integration of large-scale power system simulation with cyber networks for wide-area control and is unique in providing both low-latency data streaming and network emulation. The rest of this paper is organised as follows. Section 2 introduces the four-layer software architecture and presents detailed descriptions of each layer. Section 3 proposes the distributed messaging environment and the data broker setup for low-latency data streaming between the physical system layer and the networked physical devices layer. Section 4 presents case studies for data streaming latency analysis and closed-loop CPS control. Section 5 draws the conclusions. 2 Testbed architecture design 2.1 Overview Generally speaking, a cyber-physical testbed for power systems should consist of at least a physical system, a communication network, and network applications. Our testbed follows the concept but adds a layer for the so-called 'networked physical components'. The overall architecture of our testbed is shown in Fig. 1. From the bottom up, the physical system layer runs simulations to characterise power system dynamics. The networked physical component layer models measurement devices and actuators that are equipped with communication capability and, in the meantime, interact with the physical system. The communication network emulation layer creates software-defined networks (SDN) for data transmission. The application layer consists of both power system applications and cyber-network applications. Figure 1Open in figure viewerPowerPoint Architecture of the proposed cyber-physical power system testbed Instead of developing a monolithic architecture, the testbed leverages existing tools by integrating them into a modular architecture. A module is a self-contained set of routines designed to complete a specified task. For example, a physical system layer may be composed of one conventional power system simulator, and a state estimation routine may become a module in the application layer. Modules are decoupled, which means one module is developed individually and executed asynchronously with the rest of the testbed. The layered and decoupled testbed has the following advantages: (a) existing code and tools can be reused; (b) modules of similar functionality can be interchangeable; (c) data interfaces can be clearly designed; and (d) modules can be distributed to multiple processors or machines and executed in parallel. 2.2 Physical power system layer The physical power system layer runs computational routines to simulate the characteristics of the physical power grid. The main components in power grids include generators, transformers, transmission lines, capacitors, and loads. The time scale for power system simulations may vary from microseconds to hours, depending on the type of problem. The testbed focuses on extended-term transient stability analysis (– s) using positive-sequence phasor-domain models. By assuming a balanced network, ignoring transmission line transients, and considering the positive symmetric component, the stability-type simulation tools sufficient for large-scale electro-mechanical transient studies and short-term economic studies with less computation. The physical layer simulators can be adapted from existing tools, either open- or closed-source, as long as data interfaces and execution control interfaces are provided. The physical layer provides application program interfaces for loading power system data, sending raw simulation data to the networked components, and receiving control commands from the networked components. In addition, the simulator module also has to provide the simulation time for synchronisation. The testbed interfaces to two open-source simulators (ANDES [33] and GridDyn [34]) and a commercial real-time simulator (ePHASORsim) for different testing purposes. 2.3 Networked components layer The networked components layer proposed in this paper aims at modelling monitoring and actuationdevices that are attached to the physical power system andcommunication-capable. Examples of networked components include synchrophasors, remote telemetry units, and actuators that can be controlled remotely. Suchdevices are not part of typical power system simulators due to the complexity ofnetworking features. However, their critical roles in wide-area monitoring andcontrol require explicit and accurate modelling. Networked devices in the testbed can be hardware or software. A more familiar example is that a hardware phasor measurement unit (PMU) can be attached to the analogue signal outputs of a real-time simulator in order to measure the states in the simulated system. This example can be implemented purely in software so that the PMU acquires data from a running simulation software tool, embeds noises, errors, and latency, and then packages data in the IEEE C37.118–2011 format for streaming. Using software for simulating networked components is appealing due to low costs and simplicity. Interactions between networked components and the physical system, however, require a messaging service for sending and receiving data rapidly amongst distributed software pieces. Details of the proposed messaging service will be discussed in Section 4. 2.4 Network emulation layer The network emulation layer utilises SDN-based network emulation software for creating internet protocol-based communication networks. The IP-based network is composed of hosts, links, switches, routers, and network controllers. SDN provides flexibility for configuring arbitrary networks using these components to emulate large-scale physical networks. Parameters for the components such as link bandwidth and routing algorithms are configurable, and physical network interfaces can be mapped to the emulated network. In the testbed, communication networks linking the networked components layer with the application layer can be defined based on actual or proposed topology. One can create a PMU data streaming network by connecting PMUs and phasor data concentrators (PDCs) to switches using links with different latency. Software-based networked components and applications can run on virtual environments or containers that are provided by or connected to the network emulator. Hardware-based components can be plugged into the physical network interfaces for access. 2.5 Application layer The application layer is a collection of power system applications, such as the EMS, MBCS, and network applications, including traffic monitoring and cyber-attack defence. Power system applications and some network applications are modules for specific routines while communicating over the network. Other applications may directly interact with the SDN controller. Specifically, among power system applications, EMS and MBCS are two different sets of modules differentiated by their functionality and execution time horizon. EMS modules are generally considered as steady-state calculations [35], while the MBCS modules are mostly developed for enhancing stability and resiliency. Regardless of functionality differences, the EMS and MBCS in the testbed software implementation can follow the same program structure. Several EMS and MBCS methodologies have been implemented in the proposed testbed. For example, a two-stage, robust dynamic state estimator [36] has been integrated for estimating static and dynamic states from SCADA and PMU data. Remedial action schemes [37], such as a controlled system separation scheme [38] and guaranteed frequency response [39, 40] has been implemented as a remedial action scheme for the large-scale Western Electricity Coordinating Council (WECC) test system. Also, a wide-area damping control allocation algorithm [41] and frequency control frameworks [42, 43] have also been implemented. The above are examples to prove that the LTB is designed for fast prototyping and validation of research methodologies. 3 Data streaming for distributed layers 3.1 Distributed messaging environment The four-layer architecture proposed in Section 2 involves distributed software and hardware modules, between which rapid data exchange, are required. This issue exists in most distributed simulation or co-simulation environment. If a distributed simulation only involves two pieces of programs, ad-hoc data exchange may be programmed based on the scenario. In a more complex testbed, data exchange is needed between multiple modules. For example, the physical system simulator may need to send the calculated states to multiple PMU simulators and, in the meantime, check for a control signal from substation simulators. To address the difficulty in managing multi-party data streaming in a rapid manner, the Distributed Messaging Environment (DIME) is proposed and implemented. The DIME has a server/client architecture and implements several routines for distributed messaging. The DIME server can connect to a Transmission Control Protocol (TCP), User Diagram Protocol (UDP), or a Unix Inter-Process Communication (IPC). A DIME client can assign itself a name and connect it to the server. Clients are able to query the names of connected clients and perform one-to-one or one-to-many messaging. When a message is received by the server, it will enter the queue for the recipient. A client is able to retrieve the first item in the queue by synchronising with the DIME server, which will de-queue the sent data. In addition, the DIME server is transparent to its clients. The differences between DIME and SDN are listed as follows: (i) DIME relies on an existing IP-based network for data streaming ifworking in the TCP or UDP mode, while SDN creates an IP-basednetwork itself inside a Linux operating system. (ii) DIME has no control over the network configuration where thedata is sent, while SDN can control the network topology andparameters that affect how the data is sent. (iii) DIME is for sending information between two modules where, inreality, the info is immediately available (via hardware). Forexample, the PMU will obtain the measurement locally and almostinstantaneously. However, to implement this in the testbed, we needto connect two modules and stream the 'measurement' data. Incontrast, the network represented by the SDN is always present inreality. The proposed DIME allows for decoupling simulation, data acquisition, and actuation processes on multiple computers. In the testbed, data acquisitionand actuation programs may run in virtual hosts (VHs) created in emulatedenvironments on the same machine as the network emulator. Physical systemsimulation is a heavy-loading number-crunching process that occupies the centralprocessor for a long time. The DIME opens up the possibility of running thesimulation on a dedicated machine, which is connected to the network emulationmachine with data acquisition and actuation. 3.2 Data broker for the applications layer Care needs to be taken when using DIME over a network with link latency. Ideally, in the above example, the simulation computer may be plugged into the emulated network and use TCP/IP based DIME for messaging. If link latency is emulated, however, the latency between DIME clients will double, which is an undesired situation and will result in system errors. This issue is illustrated in Fig. 2. In this setup, delivering power system states from the simulator to the PMU at Virtual Host 1 will bear a latency of 5 ms. This latency should have kicked in only for wide-area data transmission. Therefore, the delay from the simulator to the PMU, or in general, the delay between the physical layer and networked component layer, must be eliminated. Figure 2Open in figure viewerPowerPoint Double communication latency issue when the DIME exchanges data between the simulator and virtual hosts The proposed approach for avoiding the double latency issue and achieve low-latency distributed messaging introduces a data broker program and an IPC-based DIME. As illustrated in Fig. 3, the simulator is connected to a separate switch where a host for the data broker is connected. The data broker instantiates two DIME clients, one connected to the simulator over TCP/IP and the other one connected to the IPC-based DIME, and relays data from one client to the other. In addition, networked components running at other virtual hosts are also connected to the IPC-based DIME. Since that (a) IPC protocol is implemented using file systems, which can be treated as instantaneous, and (b) there is no latency on the link between the simulator and the switch, the distributed messaging between the simulator and networked components can achieve low latency. Figure 3Open in figure viewerPowerPoint Proposed low-latency distributed messaging setup using two DIME servers and a data broker The proposed approach can be extended to systems with networked components running on dedicated hardware rather than on virtual hosts. For example, there are cases when prototyping a PMU simulator on a Raspberry Pi micro-computer is needed. An additional physical network switch can be added between the simulator and the emulator. The Raspberry Pi will connect its on-board network interface to the switch and run DIME client over TCP/IP, and then use a USB-based Ethernet adapter to connect to the network emulator. Clearly, this setup achieves low-latency distributed messaging between the simulator and the PMU simulator on hardware. 3.3 Closing the loops The last feature to emphasise is the closed-loop simulation capability, which differentiates the testbed from a conventional open-loop environment. Control loops modelled in the testbed include local control loops and wide-area measurement-based loops. Local controllers are mostly modelled in the physical system simulator, whereas wide-area controllers are implemented as applications connected to the network since communication must be addressed in wide-area control to make it highly practical. Data-driven applications in wide-area control loops usually have incoming paths from PMUs and outgoing paths to actuators. The incoming paths are established between PMUs and a PDC program, behind which the data-driven application resides. The outgoing paths are established between the application and actuators, to which the control signals should be sent, using substation communication protocols such as the International Electrotechnical Commission (IEC) Standard 61850. The execution of the closed-loop simulation and testing are described in Table 1. First, processes for the four layers will be started in the given sequence, which will naturally handle the dependency of layers. Then, the initialisation loops will be executed for each module and between layers. Next, after the initialisation, the main loops of the processes will run to generate, exchange and process data until the end of the simulation. Table 1. Execution workflow for the cyber-physical testbed (a) Start processes for (i) Communication network emulation (ii) DIME servers and the data broker (iii) Applications running on virtual hosts (iv) Networked components and (v) Physical power system simulator (b) Initialisation for (i) Self-initialisation of modules (ii) Between networked components and the simulator, and (iii) Between applications and networked components (c) Execute processes for (i) The simulator, at each integration step, (1) send variable values to networked components, and (2) receive control signals from networked components. (ii) Networked components, upon receiving data, Perform input and output operations as programmed. (iii) Applications, upon receiving data, Perform computation and communication as programmed. (d) Exit when (i) all module processes have finished, or (ii) any global unrecoverable error occurred. 3.4 Open-source implementation The following open-source tools and libraries are utilised: ZeroMQ: the backend for the DIME server and client. Mininet: the backend for the network emulation layer. PyPMU: the backend for IEEE C37.118 PMU data streaming. In addition, the authors have developed and released on Github the following open-source tools: ANDES: ANother Dynamic Energy system Simulator. It works for simulating the physical power grid. LTBNet: Network emulator for PMU data streaming. It includes a networked component, MiniPMU, which can connect to ANDES and stream PMU data. 4 Case study 4.1 Verification of rapid data acquisition This section presents case studies for verifying the proposed rapid data acquisition using the DIME and data broker. The setup of the case study involves the physical system layer and networked components layer and is distributed onto two computers. The setup for the scenario is similar to Fig. 3. Computer 1 represents the physical system layer using the power system simulation tool, ANDES, and establishes a DIME server at tcp://192.168.1.200. Computer 2 represents the networked components layer and part of the network emulation layer by executing a network emulation program, inside which one network switch and a virtual host is created. A PMU simulator runs on the virtual host and connects to a local DIME server at ipc:///tmp/dime. Computer 2 also runs the data broker program for relaying data between the two DIME servers. Lastly, Computer 1 is plugged into Computer 2 using an RJ45 Ethernet cable. In terms of the data volume, we consider measurements on a bus, including , namely, voltage magnitude, voltage phase, injection current magnitude, injection current phase, and frequency, respectively. Thus, for each time step, the simulator will send a group of five variables to the PMU through the switch and the data broker. The round-trip time between the sender and receiver is measured for 5000 random samples. The measured one-way latency, which is equal to half of the loop-back time, is scatter plotted in Fig. 4, along with the linear regression results. Figure 4Open in figure viewerPowerPoint Measured latency of the proposed data broker It can be observed that the latency of the distributed messaging between the simulator and the PMU runs stably around 1 ms. This latency includes the networking time and double serial/de-serialisation time in the DIME. It is worth mentioning that it is simpler to measure the round-trip time by the sender than to measure the difference by the receiver because the latter involves synchronising the clocks of the two computers. If compared with the double communication network latency without the data broker, the proposed method has significantly reduced the time for data acquisition and can be considered as having low latency. The scalability of the proposed approach is also illustrated in Fig. 5. Consider an increase in the data volume from five measurements to 500 with a step of five. Results show that the proposed method scales well in the range. Figure 5Open in figure viewerPowerPoint Measured latency as the number of measurements increase 4.2 Verification of the communication network latency Next, the SDN-based communication network emulation is verified for the accuracy of communication latency. Two scenarios are examined, including a small test system with three hosts, two network switches, and four links, and a proposed communication network for WECC. The topology of Scenario 1 is illustrated in Fig. 6. In the network emulator, two switches, two VHs, and three links with the noted latency are created. A physical computer is connected to a physical network interface, which is connected to Switch 1 using a latency-free link. The theoretical latency is 7 ms between H1 and H2, 12 ms between H1 and PC, and 15 ms between H2 and PC. The latency is measured by a server/client socket connection over TCP, and the results are plotted in Fig. 7, which shows the observed latency matches the theoretical values well. Note that the first connection may take longer due to the address resolute protocol (ARP) for querying the media access control (MAC) address. Once the ARP caches the MAC, the time reflects the actual latency. Figure 6Open in figure viewerPowerPoint Simple communication network topology for measuring delays Figure 7Open in figure viewerPowerPoint latency in the simple emulated communication network Then, a network topology for the WECC system is used to examine the emulated latency. The communication network topology shown in Fig. 8 contains 15 balancing regions. Multiple hosts are created in each region to resemble PMU substations (green circles) and a regional PDC (purple circles). PMUs and the PDC in each region are connected to a regional network switch (solid red circles), and the switches are interconnected to form the network for WECC wide-area data streaming. The latency in the network is configured as follows: (i) 10 ms between a PMU and a switch. Figure 8Open in figure viewerPowerPoint Emulated communication network topology for WECC (ii) 5 ms between a PDC and a switch. (iii) 15 ms between two regional switches. The latency of the following scenarios is measured: (i) Between a PMU and a PDC in the LADWP region. (ii) Between the two PDCs in AESO and SRP. For Scenario 2, the path compute}, number={1}, journal={IET Energy Systems Integration}, publisher={Institution of Engineering and Technology (IET)}, author={Cui, Hantao and Li, Fangxing and Tomsovic, Kevin}, year={2020}, month={Mar}, pages={32–39} }
 @article{cui_li_fang_2020, title={Effective parallelism for equation and jacobian evaluation in power flow calculation}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85098610575&partnerID=MN8TOARS}, journal={arXiv}, author={Cui, H. and Li, F. and Fang, X.}, year={2020} }
 @article{cui_li_tomsovic_2020, title={Hybrid Symbolic-Numeric Library for Power System Modeling and Analysis}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093447204&partnerID=MN8TOARS}, journal={arXiv}, author={Cui, H. and Li, F. and Tomsovic, K.}, year={2020} }
 @article{mass-matrix differential-algebraic equation formulation for transient stability simulation_2020, year={2020}, month={Aug} }
 @article{cui_li_chow_2020, title={Mass-matrix differential-algebraic equation formulation for transient stability simulation}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85095547228&partnerID=MN8TOARS}, journal={arXiv}, author={Cui, H. and Li, F. and Chow, J.H.}, year={2020} }
 @article{cui_zhang_milano_li_2020, title={On the Modeling and Simulation of Anti-Windup Proportional-Integral Controller}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85095510499&partnerID=MN8TOARS}, journal={arXiv}, author={Cui, H. and Zhang, Y. and Milano, F. and Li, F.}, year={2020} }
 @inproceedings{feng_cui_shi_li_yuan_dai_liu_2020, title={Sequential State Estimation Containing the Operating Limits for VSC MTDC System}, volume={2020-October}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85099126205&partnerID=MN8TOARS}, DOI={10.1109/TD39804.2020.9300004}, abstractNote={This paper proposes an improved sequential state estimation method containing the operating limits for VSC MTDC (voltage source converter, multiple-terminal direct current) system. As a fully controlled quick-response power equipment, VSC has a set of strict restrictions to ensure safe operation. However, the conventional SE (state estimation) approach presents challenges when the concerned VSC works on the boundaries. Thus, the SE results may be outside the limits because of dealing with measurement errors. To avoid this problem, the operating limits are considered in the process of SE. First, the safe operating range of VSC are analyzed and drawn in details based on basic state variables. Furthermore, the check of limit violation is implemented inside the sequential method. Once the violation is detected, the corresponding parameter will be set as the boundary value and regarded as high-weighted pseudo-measurement for the following calculation loop. Thus, the accuracy and reasonability of SE can be guaranteed. The proposed method is programmed and tested in MATLAB to show the feasibility and satisfactory efficiency.}, booktitle={Proceedings of the IEEE Power Engineering Society Transmission and Distribution Conference}, author={Feng, W. and Cui, H. and Shi, Q. and Li, F. and Yuan, C. and Dai, R. and Liu, G.}, year={2020} }
 @inproceedings{feng_shi_cui_li_yuan_dai_liu_2020, title={Using Lagrangian Relaxation to Include Operating Limits of VSC-MTDC System for State Estimation}, volume={2020-August}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85099120701&partnerID=MN8TOARS}, DOI={10.1109/PESGM41954.2020.9281457}, abstractNote={This paper proposes an improved state estimation (SE) method by combining Lagrangian relaxation and WLS (weighted least square) such that the operating limits of voltage sourced converter based multi-terminal direct current (VSC-MTDC) system are considered. Taking advantage of the fast-regulating ability of pulse-width modulation (PWM), the operating range of the converter is strictly restricted within limits. In addition, when the limits violate, the new control strategy can be executed in a very short time to ensure safe operation. However, the conventional SE approaches, which rely on global optimization, may fail to tackle the operating limits due to the different measurement errors of AC and DC grids. To improve the accuracy of SE for VSC-MTDC system, an improved SE method is proposed with three main contributions. First, the operating limits, together with the regulations, are analyzed in detail. Then, a violation-checking procedure is implemented inside the Sequential Method. Finally, once the violated estimations are detected, the corresponding equality constraints which represent the precise operating points are added in WLS and solved by Lagrangian relaxation. The accuracy and efficiency of the proposed method are tested on two typical systems with different control parameters.}, booktitle={IEEE Power and Energy Society General Meeting}, author={Feng, W. and Shi, Q. and Cui, H. and Li, F. and Yuan, C. and Dai, R. and Liu, G.}, year={2020} }
 @article{gan_zheng_cui_2019, title={A two-stage model for capacity planning of centralized charging station and ordered discharging}, volume={37}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85074534486&partnerID=MN8TOARS}, DOI={10.3233/JIFS-179321}, abstractNote={In this paper, in the so-called centralized charging and unified distribution mode, a two-stage optimization model is proposed for capacity planning and ordered discharging strategies of centralized charging stations considering the peak-shaving effects. Firstly, the operating states of battery pa ck are analyzed at each moment by combining with distribution modes, then the first stage planning is processed, that is, by taking the numbers of battery pack and generators as the control variables, the mathematical model aiming at minimizing the construction cost of centralized charging stations can be solved by Simulated Annealing Particle Swarm Optimization (SAPSO). Next, in the second stage planning, in order to maximize the peaking effect of the centralized charging station, the cost function aiming at minimizing load variance is proposed, and the discharge power of each time can be obtained by using yalmip toolbox. Finally, simulation results are provided to verify the effectiveness and usefulness of the proposed optimization model.}, number={4}, journal={Journal of Intelligent and Fuzzy Systems}, author={Gan, H. and Zheng, C. and Cui, H.}, year={2019}, pages={4837–4846} }
 @inproceedings{cui_li_2019, title={ANDES: A Python-Based Cyber-Physical Power System Simulation Tool}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85061787107&partnerID=MN8TOARS}, DOI={10.1109/NAPS.2018.8600596}, abstractNote={This paper introduces the design and implementation of a Python-based software package for cyber-physical power system research called Andes. Andes is developed in an attempt to bridge the gap between the traditional power system analysis and the fast-growing needs for cybersecurity studies. First, the architecture design is proposed to accommodate for power grid prototyping, communication network set up, and the interactions between the two. Design considerations are discussed from the research and development perspective. Examples are shown using Andes for modeling, monitoring, and visualization of cyber-physical power system studies.}, booktitle={2018 North American Power Symposium, NAPS 2018}, author={Cui, H. and Li, F.}, year={2019} }
 @article{tu_zhou_cui_li_2019, title={An Equivalent Aggregated Model of Large-Scale Flexible Loads for Load Scheduling}, volume={7}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85073632942&partnerID=MN8TOARS}, DOI={10.1109/ACCESS.2019.2944233}, abstractNote={The popularity of smart applications enables the large-scale integration of flexible loads to power systems, which poses a considerable challenge to system scheduling. Focusing on scheduling optimization with large-scale flexible loads, this paper proposes the equivalent aggregated method for flexible loads, which converts a large number of flexible loads into a few equivalent models to participate in system scheduling. In order to establish the equivalent model, flexible loads are grouped based on their parameters such that loads with the same or similar parameters are clustered into the same group. Then, the equivalent model for each group is established, a proof of the equivalence relationship between the original model and the equivalent model is provided, and the upper bound of equivalence deviations is estimated. The whole equivalent aggregated model is expressed as the sum of equivalent models of all groups. Afterwards, a new approach of applying the equivalent aggregated model to system scheduling is proposed. Case studies show that the equivalent aggregated model can effectively schedule large-scale flexible loads to shave the peak and fill the valley, with small equivalent deviations and fast calculation speed. This validates the proposed model and demonstrates its promising applications to large-scale load scheduling.}, journal={IEEE Access}, author={Tu, J. and Zhou, M. and Cui, H. and Li, F.}, year={2019}, pages={143431–143444} }
 @inproceedings{yen_cui_tomsovic_2019, title={CXSparse-Based Differential Algebraic Equation Framework for Power System Simulation}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85061842231&partnerID=MN8TOARS}, DOI={10.1109/NAPS.2018.8600601}, abstractNote={Simulation is the major approach in power system studies for prototyping new devices, evaluating new scenarios, and implementing new controls. Such a simulator relies on a framework for the dynamic memory management of internal variables. Our work presents a C-based framework that significantly reduces overhead with reduced object conversion and improved matrix storage techniques. Optimized sparse matrix add and set methods take advantage of indexing characteristics of power system equations, avoiding reconstruction of matrices within the framework if possible. Evaluation of the proposed methods substantiates the efficiency and utility of our framework in a differential algebraic equation solver.}, booktitle={2018 North American Power Symposium, NAPS 2018}, author={Yen, A. and Cui, H. and Tomsovic, K.}, year={2019} }
 @article{li_cui_li_2019, title={Distribution network power loss analysis considering uncertainties in distributed generations}, volume={11}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85062824348&partnerID=MN8TOARS}, DOI={10.3390/su11051311}, abstractNote={Distribution network loss analysis is crucial for the economic operation in residential distribution networks. The increasing level of distributed generation (DG) has considerably improved the overall sustainability but raised the uncertainty in system losses and exacerbated voltage profiles. This paper presents a nodal distribution loss analysis approach in which the losses induced by loads and DGs are calculated recursively. In order to characterize the uncertainty, the Latin hypercube sampling (LHS)-based approach is presented for obtaining DG output samples. Further, the LHS-based sampling and loss analysis methods are combined into a proposed stochastic framework for loss analysis, which takes into account the DG output uncertainty. Case studies on a 36-bus radial distribution network verified the stochastic loss analysis method. Compared with the simple random sampling method, the proposed LHS-based stochastic loss analysis method can reach the same accuracy level for nodal voltages and losses more efficiently.}, number={5}, journal={Sustainability (Switzerland)}, publisher={MDPI AG}, author={Li, Hongmei and Cui, Hantao and Li, Chunjie}, year={2019}, pages={1311} }
 @article{fang_cui_yuan_tan_jiang_2019, title={Distributionally-robust chance constrained and interval optimization for integrated electricity and natural gas systems optimal power flow with wind uncertainties}, volume={252}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85066756221&partnerID=MN8TOARS}, DOI={10.1016/j.apenergy.2019.113420}, abstractNote={With increasing penetrations of gas-fired generation in power systems because of reducing gas prices and emissions regulations, the interdependent and coordinated operation of integrated electricity and natural gas systems (IEGSs) is becoming an urgent research topic. Meanwhile, the significantly increasing deployment of wind power necessitates that IEGSs operation considers wind power output uncertainty. How to model the impact of wind power uncertainty on IEGSs power and gas flows dispatch is challenging. In this paper, a hybrid distributionally-robust chance-constrained and interval optimization (DRCC-IO) based model is proposed to consider the influence of wind power uncertainty and its spatial-temporal correlation on IEGSs operation. First, the DRCC-OPF model is proposed to obtain reliable economic dispatch solutions for the electricity network considering the wind power forecast errors. The spatial-temporal correlation of the wind power plant (WPP) forecasts is considered with a sparse correlation covariance matrix. Then, the interval optimization (IO) model is used to model the impacts of the power variations of gas-fired units on the natural gas network. Finally, the proposed model considers the impacts of wind power uncertainty on both the electricity and natural gas networks. Case studies performed on a six-bus power system coupled with a seven-node gas system and an IEEE 118-bus power system with a 14-node gas system verify the effectiveness of the proposed method to improve system security and reduce costs of the IEGSs. The robustness of the wind power forecast errors can be controlled in the proposed model to trade off the security and costs of the IEGSs.}, journal={Applied Energy}, publisher={Elsevier BV}, author={Fang, Xin and Cui, Hantao and Yuan, Haoyu and Tan, Jin and Jiang, Tao}, year={2019}, pages={113420} }
 @article{sun_zhai_cui_nan_wang_2019, title={Frequency regulation strategy for private EVs participating in integrated power system of REs considering adaptive Markov transition probability}, volume={173}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85065235837&partnerID=MN8TOARS}, DOI={10.1016/j.epsr.2019.04.007}, abstractNote={The active power imbalance caused by renewable energies (REs) and loads is usually viewed as a main reason for the grid frequency variation. Private electric vehicles (EVs) participating in integrated power system frequency regulation of REs has great realistic significance, the bidirectional wireless power transfer system for EVs is analyzed in this paper, a fuzzy adaptive PI controller is proposed to achieve the charge and discharge control of EVs at any power value. Then a Markov model with adaptive Markov transition probability is developed to analyze the stochastic distribution of EVs. Considering the basic travel demands of the owners and the EV battery state of charge (SOC), a new advanced frequency regulation strategy is further proposed, and the regulation ability of EVs is quantitatively described. Finally, the effectiveness of the proposed frequency regulation strategy is verified by simulation results.}, journal={Electric Power Systems Research}, author={Sun, Y. and Zhai, S. and Cui, H. and Nan, D. and Wang, K.}, year={2019}, pages={291–301} }
 @article{chen_li_feng_wei_cui_liu_2019, title={Reliability assessment method of composite power system with wind farms and its application in capacity credit evaluation of wind farms}, volume={166}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85054457310&partnerID=MN8TOARS}, DOI={10.1016/j.epsr.2018.09.023}, abstractNote={This paper presents a non-sequential Monte Carlo Simulation (MCS)-based method for the reliability assessment of composite power system with wind farms (WFs). A multistate probability table and its corresponding Spearman’s rank correlation coefficient (SRCC) are combined to represent the power outputs of WFs, which makes the multistate model of WFs compatible with the non-sequential MCS while considering the dependence among power outputs of WFs. By constructing a system state array with encoding conversion, a state merging technique is proposed, which significantly reduces the number of system states to be evaluated. In addition, the parallel computing technique is employed to accelerate the contingency analysis for the merged system states. Furthermore, the capacity credit (CC) of WFs considering both wind power correlation and transmission network constraints is evaluated based on the proposed reliability assessment method. Finally, the effectiveness of the proposed reliability assessment method and its application in the CC evaluation are demonstrated using extensive numerical studies on several modified test systems.}, journal={Electric Power Systems Research}, author={Chen, F. and Li, F. and Feng, W. and Wei, Z. and Cui, H. and Liu, H.}, year={2019}, pages={73–82} }
 @article{zhu_han_gao_shi_cui_zu_2018, title={A Multi-Stage Optimization Approach for Active Distribution Network Scheduling Considering Coordinated Electrical Vehicle Charging Strategy}, volume={6}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85052907226&partnerID=MN8TOARS}, DOI={10.1109/ACCESS.2018.2868606}, abstractNote={The increasing integration of renewable resources and electric vehicles (EVs) presents new requirements for the construction of a current distribution network. As an alternative of conventional distribution network, active distribution network (ADN) has gained more interest for its flexibility and interactivity. However, the unpredictable behavior of ADN participants from source-side, network-side, and demand-side brings more challenges on ADN dispatch. Thus, it is urged to design an ADN optimal scheduling approach that can comprehensively regulate the ADN participants’ behavior. In this paper, an ADN performance assessment system is first established to provide a quantitative analysis on ADN’s scheduling in terms of active controllability, active manageability, and active economy, respectively. Then, according to the ADN assessment system, a multi-stage optimal scheduling approach for ADN considering coordinated EV charging strategy is proposed. It is able to not only smooth the fluctuations caused by the integration of intermittent power sources and EVs but also reconfigure the network topology. Therefore, this approach can be applied to day-ahead dispatches to help operators effectively manage the ADN. Simulation results verify the correctness and effectiveness of the proposed approach.}, journal={IEEE Access}, author={Zhu, X. and Han, H. and Gao, S. and Shi, Q. and Cui, H. and Zu, G.}, year={2018}, pages={50117–50130} }
 @article{han_cui_gao_shi_fan_wu_2018, title={A Remedial Strategic Scheduling Model for Load Serving Entities Considering the Interaction between Grid-Level Energy Storage and Virtual Power Plants}, volume={11}, url={https://doi.org/10.3390/en11092420}, DOI={10.3390/en11092420}, abstractNote={More renewable energy resources have been connected to the grid with the promotion of global energy strategies, which presents new opportunities for the current electricity market. However, the growing integration of renewable energy also brings more challenges, such as power system reliability and the participants’ marketable behavior. Thus, how to coordinate integrated renewable resources in the electricity market environment has gained increasing interest. In this paper, a bilevel bidding model for load serving entities (LSEs) considering grid-level energy storage (ES) and virtual power plant (VPP) is established in the day-ahead (DA) market. Then, the model is extended by considering contingencies in the intraday (ID) market. Also, according to the extended bidding model, a remedial strategic rescheduling approach for LSE’s daily profit is proposed. It provides a quantitative assessment of LSE’s loss reduction based on contingency forecasting, which can be applied to the power system dispatch to help LSEs deal with coming contingencies. Simulation results verify the correctness and effectiveness of the proposed method.}, number={9}, journal={Energies}, publisher={MDPI AG}, author={Han, Haiteng and Cui, Hantao and Gao, Shan and Shi, Qingxin and Fan, Anjie and Wu, Chen}, year={2018}, month={Sep}, pages={2420} }
 @article{yuan_li_cui_lu_shi_wang_2018, title={A measurement-based VSI for voltage dependent loads using angle difference between tangent lines of load and PV curves}, volume={160}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85041929472&partnerID=MN8TOARS}, DOI={10.1016/j.epsr.2018.01.021}, abstractNote={In this short communication, a generic measurement-based voltage stability indicator (VSI) is presented with voltage dependent load models incorporated. It uses the angle difference between the tangent lines of the load characteristic curve and the PV curve. Based on the Thevenin equivalent estimated from the measurements, the proposed VSI can be easily applied to both the ZIP and the exponential load models. Time domain simulation results on both load models demonstrate that the proposed VSI accurately indicates voltage instability and outperforms a conventional VSI which is based on a constant power load model.}, journal={Electric Power Systems Research}, author={Yuan, H. and Li, F. and Cui, H. and Lu, X. and Shi, D. and Wang, Z.}, year={2018}, pages={13–16} }
 @inproceedings{li_tomsovic_cui_2018, title={An integrated testbed for power system monitoring, modeling, control and actuation}, volume={2018}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85081048929&partnerID=MN8TOARS}, DOI={10.1049/cp.2018.1735}, number={CP757}, booktitle={IET Conference Publications}, author={Li, F. and Tomsovic, K. and Cui, H.}, year={2018} }
 @article{shi_li_cui_2018, title={Analytical method to aggregate multi-machine SFR model with applications in power system dynamic studies}, volume={33}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85045295433&partnerID=MN8TOARS}, DOI={10.1109/TPWRS.2018.2824823}, abstractNote={The system frequency response (SFR) model describes the average network frequency response after a disturbance and has been applied to a wide variety of dynamic studies. However, the traditional literature does not provide a generic, analytical method for obtaining the SFR model parameters when the system contains multiple generators; instead, a numerical simulation-based approach or the operators' experience is the common practice to obtain an aggregated model. In this paper, an analytical method is proposed for aggregating the multi-machine SFR model into a single-machine model. The verification study indicates that the proposed aggregated SFR model can accurately represent the multi-machine SFR model. Furthermore, the detailed system simulation illustrates that the SFR model can also accurately represent the average frequency response of large systems for power system dynamic studies. Finally, three applications of the proposed method are explored, with system frequency control, frequency stability, and dynamic model reduction. The results show the method is promising with broad potential applications.}, number={6}, journal={IEEE Transactions on Power Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Shi, Qingxin and Li, Fangxing and Cui, Hantao}, year={2018}, pages={6355–6367} }
 @article{cui_li_fang_chen_wang_2018, title={Bilevel Arbitrage Potential Evaluation for Grid-Scale Energy Storage Considering Wind Power and LMP Smoothing Effect}, volume={9}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85030769512&partnerID=MN8TOARS}, DOI={10.1109/TSTE.2017.2758378}, abstractNote={This paper deals with extended-term energy storage (ES) arbitrage problems to maximize the annual revenue in deregulated power systems with high-penetration wind power. The conventional ES arbitrage model takes the locational marginal prices (LMP) as an input and is unable to account for the impacts of ES operations on system LMPs. This paper proposes a bilevel ES arbitrage model, where the upper level maximizes the ES arbitrage revenue and the lower level simulates the market clearing process considering wind power and ES. The bilevel model is formulated as a mathematical program with equilibrium constraints) and then recast into a mixed-integer linear programming using strong duality theory. Wind power fluctuations are characterized by the GARCH forecast model and the forecast error is modeled by forecast-bin-based Beta distributions. Case studies are performed on a modified PJM 5-bus system and an IEEE 118-bus system with a weekly time horizon over an annual term to show the validity of the proposed bilevel model. The results from the conventional model and the bilevel model are compared under different ES power and energy ratings, and also various load and wind penetration levels.}, number={2}, journal={IEEE Transactions on Sustainable Energy}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Cui, Hantao and Li, Fangxing and Fang, Xin and Chen, Hao and Wang, Honggang}, year={2018}, pages={707–718} }
 @inproceedings{cui_li_yuan_2018, title={Control and limit enforcements for VSC multi-terminal HVDC in newton power flow}, volume={2018-January}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85044220873&partnerID=MN8TOARS}, DOI={10.1109/PESGM.2017.8274242}, abstractNote={This paper proposes a novel method to automatically enforce controls and limits for Voltage Source Converter (VSC) based multi-terminal HVDC in the Newton power flow iteration process. A general VSC MT-HVDC model with primary PQ or PV control and secondary voltage control is formulated. Both the dependent and independent variables are included in the propose formulation so that the algebraic variables of the VSC MT-HVDC are adjusted simultaneously. The proposed method also maintains the number of equations and the dimension of the Jacobian matrix unchanged so that, when a limit is reached and a control is released, the Jacobian needs no re-factorization. Simulations on the IEEE 14-bus and Polish 9241-bus systems are performed to demonstrate the effectiveness of the method.}, booktitle={IEEE Power and Energy Society General Meeting}, author={Cui, H. and Li, F. and Yuan, H.}, year={2018}, pages={1–5} }
 @article{cui_li_tomsovic_wang_azim_lu_yuan_2018, title={Cyber-physical testbed for power system wide-area measurement-based control using open-source software}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094539887&partnerID=MN8TOARS}, journal={arXiv}, author={Cui, H. and Li, F.F. and Tomsovic, K. and Wang, S. and Azim, R. and Lu, Y. and Yuan, H.}, year={2018} }
 @article{fang_hodge_bai_cui_li_2018, title={Mean-Variance Optimization-Based Energy Storage Scheduling Considering Day-Ahead and Real-Time LMP Uncertainties}, volume={33}, url={https://doi.org/10.1109/TPWRS.2018.2852951}, DOI={10.1109/TPWRS.2018.2852951}, abstractNote={In this letter, a new mean-variance optimization-based energy storage scheduling method is proposed with the consideration of both day-ahead (DA) and real-time (RT) energy markets price uncertainties. It considers the locational marginal price (LMP) forecast uncertainties in DA and RT markets. The energy storage arbitrage risk associated with the LMP forecast uncertainty is explicitly modeled through the variance component in the objective function. The quadratic term of this variance is transformed into a second-order cone constraint using the charging and discharging power complementarity of the energy storage system. Finally, the proposed model is formulated as a mixed-integer conic programming problem. Numerical case studies demonstrate the effectiveness of the proposed model for energy storage scheduling considering price uncertainty.}, number={6}, journal={IEEE Transactions on Power Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Fang, Xin and Hodge, Bri-Mathias and Bai, Linquan and Cui, Hantao and Li, Fangxing}, year={2018}, month={Nov}, pages={7292–7295} }
 @article{li_cui_jiang_xu_jia_li_2018, title={Multichannel continuous wavelet transform approach to estimate electromechanical oscillation modes, mode shapes and coherent groups from synchrophasors in bulk power grids}, volume={96}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85031740378&partnerID=MN8TOARS}, DOI={10.1016/j.ijepes.2017.09.043}, abstractNote={Continuous Wavelet Transform (CWT) is a traditional single-channel method to estimate the dominant mode from measurements, but it is rarely applied to estimate mode shapes and coherent generators. On the other hand, estimation accuracy of traditional CWT is significantly affected by the observability of oscillations. This paper develops a multichannel CWT which is based on multichannel measurements and is less observability constrained so as to estimate not only dominant modes, but also mode shapes and coherent generators. First, wavelet power spectrum (WPS) is applied to wavelet coefficient matrices (WCMs) of multichannel measurements obtained by CWT to detect the critical scale ranges associated with the dominate modes. Then, the WCMs with the same scales in the detected ranges extracted from the raw WCMs are used to estimate the dominant modes and mode shapes. Meanwhile, the measurements that only contains the information of dominant modes are reformed by inverse CWT to detect the coherent groups of generators using direction cosines. The proposed approach is applied and evaluated with the simulation data from the 16-generator 68-bus test system and field measurements from Phasor Measurement Units (PMUs) in China Southern Power Grid (CSG). Results show that the proposed approach is accurate and efficient in estimating dominant modes, mode shapes and coherent groups of generators from synchrophasor measurements.}, journal={International Journal of Electrical Power and Energy Systems}, author={Li, X. and Cui, H. and Jiang, T. and Xu, Y. and Jia, H. and Li, F.}, year={2018}, pages={222–237} }
 @article{cui_li_yuan_2017, title={Control and limit enforcements for vsc multi-Terminal hvdc in newton power flow}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85095104686&partnerID=MN8TOARS}, journal={arXiv}, author={Cui, H. and Li, F. and Yuan, H.}, year={2017} }
 @article{li_li_yuan_cui_hu_2017, title={GPU-Based Fast Decoupled Power Flow with Preconditioned Iterative Solver and Inexact Newton Method}, volume={32}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85021285156&partnerID=MN8TOARS}, DOI={10.1109/TPWRS.2016.2618889}, abstractNote={Power flow is the most fundamental computation in power system analysis. Traditionally, the linear solution in power flow is solved by a direct method like LU decomposition on a CPU platform. However, the serial nature of the LU-based direct method is the main obstacle for parallelization and scalability. In contrast, iterative solvers, as alternatives to direct solvers, are generally more scalable with better parallelism. This study presents a fast decouple power flow (FDPF) algorithm with a graphic processing unit (GPU)-based preconditioned conjugate gradient iterative solver. In addition, the Inexact Newton method is integrated to further improve the GPU-based parallel computing performance for solving FDPF. The results show that the GPU-based FDPF maintains the same precision and convergence as the original CPU-based FDPF, while providing considerable performance improvement for several large-scale systems. The proposed GPU-based FDPF with the Inexact Newton method gives a speedup of 2.86 times for a system with over 10 000 buses if compared with traditional FDPF, both implemented based on MATLAB. This demonstrates the promising potential of the proposed FDPF computation using a preconditioned iterative solver under GPU architecture.}, number={4}, journal={IEEE Transactions on Power Systems}, author={Li, X. and Li, F. and Yuan, H. and Cui, H. and Hu, Q.}, year={2017}, pages={2695–2703} }
 @article{li_zhang_jiang_chen_bai_cui_li_2017, title={Optimal dispatch strategy for integrated energy systems with CCHP and wind power}, volume={192}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84994515770&partnerID=MN8TOARS}, DOI={10.1016/j.apenergy.2016.08.139}, abstractNote={With the increasing installed capacity of wind power and the interdependencies among multiple energy sectors, optimal operation of integrated energy systems (IES) with combined cooling, heating and power (CCHP) is becoming more important. This paper proposes an optimal dispatch strategy for IES with CCHP and wind power. Natural gas system is modeled and its security constraints are integrated into the optimal dispatch model. The gas shift factor (GSFgas) matrix for natural gas system is derived to quantify the impact of gas supply and load at each node on the gas flow through the pipelines so that the pipeline flow equation is linearized. The objective function of the optimization model is to minimize the total operation cost of IES. Then the model is transformed into mixed integer linear programming (MILP) formulation to improve the computation efficiency. Numerical case studies conducted demonstrate the lower operation cost of the proposed model facilitating wind power integration.}, journal={Applied Energy}, author={Li, G. and Zhang, R. and Jiang, T. and Chen, H. and Bai, L. and Cui, H. and Li, X.}, year={2017}, pages={408–419} }
 @article{gao_liu_cui_wang_2017, title={Probabilistic Load Flow Analysis Using Randomized Quasi-Monte Carlo Sampling and Johnson Transformation}, volume={143}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85030478474&partnerID=MN8TOARS}, DOI={10.1061/(ASCE)EY.1943-7897.0000497}, abstractNote={As the fastest growing type of renewable generation, wind power integration has been widely studied to address both the environmental and the energy concerns. The intermittent and stochastic features of wind power, however, cause remarkable uncertainty in operations, resulting in high complexity in system state analysis. It is desirable to evaluate the system conditions as precisely and efficiently as possible. To handle this problem, this paper proposes a novel probabilistic load flow approach by combining randomized quasi–Monte Carlo (RQMC) sampling with Johnson transformation to achieve satisfying accuracy within a low time consumption. For efficient and sufficient sampling, the low discrepancy sequence is scrambled in a fully random strategy, forming the RQMC sampling approach. Furthermore, considering the distribution characteristics and correlation features of wind energy, the Johnson translation system is introduced. Tests on the wind-integrated IEEE 118-bus system and the French high-voltage transmission network show that the proposed approach is able to achieve satisfactory accuracy and efficiency. Different wind profile models, including Weibull distribution and the historical measurements–based probability density functions, can be precisely handled.}, number={6}, journal={Journal of Energy Engineering}, author={Gao, S. and Liu, Y. and Cui, H. and Wang, S.}, year={2017} }
 @article{jiang_bai_yuan_jia_li_cui_2017, title={QV interaction evaluation and pilot voltage-reactive power coupling area partitioning in bulk power systems}, volume={11}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85019250001&partnerID=MN8TOARS}, DOI={10.1049/iet-smt.2016.0232}, abstractNote={IET Science, Measurement & TechnologyVolume 11, Issue 3 p. 270-278 Research ArticleFree Access QV interaction evaluation and pilot voltage-reactive power coupling area partitioning in bulk power systems Tao Jiang, Tao Jiang Department of Electrical Engineering, Northeast Electric Power University, Jilin, 132012 People's Republic of ChinaSearch for more papers by this authorLinquan Bai, Linquan Bai Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this authorHaoyu Yuan, Haoyu Yuan Peak Reliability, Loveland, CO, 80538 USASearch for more papers by this authorHongjie Jia, Corresponding Author Hongjie Jia hjjia@tju.edu.cn Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, 300072 People's Republic of ChinaSearch for more papers by this authorFangxing Li, Fangxing Li Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this authorHantao Cui, Hantao Cui Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this author Tao Jiang, Tao Jiang Department of Electrical Engineering, Northeast Electric Power University, Jilin, 132012 People's Republic of ChinaSearch for more papers by this authorLinquan Bai, Linquan Bai Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this authorHaoyu Yuan, Haoyu Yuan Peak Reliability, Loveland, CO, 80538 USASearch for more papers by this authorHongjie Jia, Corresponding Author Hongjie Jia hjjia@tju.edu.cn Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, 300072 People's Republic of ChinaSearch for more papers by this authorFangxing Li, Fangxing Li Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this authorHantao Cui, Hantao Cui Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996 USASearch for more papers by this author First published: 01 May 2017 https://doi.org/10.1049/iet-smt.2016.0232Citations: 4AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study presents a novel methodology to evaluate the QV interactions among buses and to partition the pilot voltage-reactive power coupling areas (VRPCAs) using relative gain (RG). According to the concept of a multi-input multi-output system, the QV coupling RG is first calculated based on the QV matrix, which is extracted from power flow Jacobian matrix, to evaluate the QV interactions among different buses and then to determine the VRPCAs. The voltage stability critical buses are first identified through a modified loading margin. For each critical bus, the other buses that have strong QV coupling are detected via the cross RG and are clustered into a VRPCA piloted by the corresponding critical bus. New England 39-bus system and Polish power system are used to test the performance of the proposed approach. Simulation results verify the effectiveness of the proposed approach in evaluating the QV interactions and partitioning the VRPCAs. 1 Introduction The intermittency of renewable generation resources (such as wind, solar, tide, etc.) increases the complexity of efficient and stable operation of the power systems [1-4]. In particular, voltage control strategies adopted by system operators are usually based on the layering and zoning regulation principle, of which the effectiveness heavily relies on the voltage control areas partitioning [5-9]. An effective voltage control areas partitioning strategy can improve the system stability and security and reduce the risk of voltage instability as well [10-12]. Therefore, it is of great significance to explore the methods for partitioning voltage control areas. At present, voltage control areas are mainly determined by using electrical distance, cluster analysis, or a combination of the both methods based on power flow Jacobian matrix. In [13], the degree of voltage coupling among nodes was defined based on P-Q decoupled power flow Jacobian matrix. Meanwhile, the concept of electrical distance was proposed for the purpose of voltage control areas partitioning [13]. In [14], a hierarchical classification algorithm was employed to determine the voltage control areas based on the concept of electrical distance proposed in [13]. Then, a localised competitive market was designed for reactive power ancillary services in each individual voltage control area [14]. In [15], to overcome the disadvantages of the reduced order matrix which cannot reflect the couplings between active power, reactive power, and voltage angles, voltage control areas were partitioned based on the sensitivity of full rank Newton–Raphoson power flow Jacobian matrix. Based on electrical distances and clustering analysis, a multi-attribute hybrid method for partitioning a power system into voltage control areas and zones was presented in [16] using graph partitioning algorithm in combination with an evolutionary computational algorithm. The effectiveness of this method was verified in the Polish power grid. In [17, 18], the load nodes were mapped into a space formed by generator nodes according to the sensitivity in quasi steady state. In such space, the electrical distance was defined, base on which the voltage/reactive power areas were partitioned using clustering algorithm. Furthermore, an automatic voltage control software for online adaptive weak voltage stability areas partitioning was developed and applied in the China Southern Power Grid [19], State Grid Corporation of China and PJM interconnection system [20, 21]. For the determined voltage control areas, the optimal reactive power dispatch (ORPD) [22] was further developed to maintain the voltage magnitudes of all the buses within desired margins (usually 5% around the nominal voltage). In [23, 24], genetic algorithm was used to optimise the operations of reactive resources in order to regulate voltage and avoid voltage violations in Hydro-Québec network. In [25], an expert system based optimal power flow was proposed to dispatch the reactive power to keep voltage magnitudes at the most desired state. In [26], biogeography based optimisation was employed to readjust and determine the optimal power reference settings of the system operator such that the voltage magnitudes can be maintained within acceptable limits. In [27], a chaotic krill herd algorithm was presented to solve the ORPD problem to maintain the voltage magnitudes within the defined 5% margin. In addition, particle swarm optimisation [28, 29], chance-constrained optimisation [30], bacteria foraging-optimisation [31], distributed subgradient algorithm [32], receding-horizon multi-step optimisation [33] and distributed model predictive control [34] were applied to dispatch reactive power to maintain the voltage magnitudes of all buses in the power systems within acceptable values. Among various methods above, it is concluded that the fundamental idea of voltage control strategies is to inject reactive power to the buses that contribute most to the voltage stability of the studied area. To measure the voltage couplings, a novel relative gain (RG) based approach was proposed in [35] for identifying the voltage stability critical injection region (VSCIR). However, the proposed RG-based approach was based on the power system impedance matrix which only represents the influence of the system topology on voltage coupling. To address the aforementioned issues, this paper develops the RG in power systems by using QV matrix derived from the power flow Jacobian matrix to evaluate the QV interactions among buses and further partition the voltage-reactive power coupling areas (VRPCAs). In the proposed approach, the coupled single-port model is introduced, based on which, voltage stability index (VSI) is calculated to identify the voltage stability critical buses (pilot buses). Then, the RGs between pilot buses and other buses are calculated to identify the buses that are tightly coupled with pilot buses in the aspect of Volt-VAR interaction. Moreover, the VRPCAs are partitioned according to the RGs and pilot buses. Finally, the effectiveness and practicality of the proposed approach are verified on the New England 39-bus system and Polish power grid. The rest of paper is organised as follows: in Section 2, the RG calculation based on QV matrix is presented, and the proposed voltage control area partitioning method is proposed based on RG. In Section 3, the effectiveness of the proposed approach is demonstrated by the case studies on the New England 39-bus system and Polish power system. Section 4 concludes this paper. 2 VRPCA partitioning based on RG RG is a powerful tool for evaluating the interactions among decentralised controllers in multi-input multi-output (MIMO) systems to determine tightly coupled input–output pairs for decoupling the interactions among multiple controllers [36]. In [37, 38], RG was applied in power systems to detect dominant oscillation modes, select suitable control inputs, and place power system stabilisers. In this work, RG is further employed to assess the QV interactions among buses to determine the VRPCAs. 2.1 Relative gain RG was first developed as a new steady state measure of interaction for multivariable process control and later extended to the frequency domain [37-40]. Since RG can offer similar information about the system behaviour as modal analysis but brings less computational burden than modal analysis, RG is considered as an alternative to the modal analysis for systematic application in bulk power system studies [37-39]. The definition, calculation and properties of RG are briefly introduced in this section. Definition of RG: Let a typical multivariable MIMO system in Fig. 1 be defined by a matrix equation y = G(s)u, where the system has m inputs and n outputs. The RG rij for a given input uj and output yi is defined as a ratio between the open-loop gain and the closed-loop gain, hence, the representation of RG rij can be expressed as [37] (1) where (Δuk = 0, k≠j) means all open-loop outputs, shown in Fig. 1a; (Δyk = 0, k≠i) means control pair uk→yk is controlled and the rest have ideal control performance, shown in Fig. 1b. rii is called auto-relative gain (ARG) and rij (i≠j) is called cross-relative gain (CRG). Fig 1Open in figure viewerPowerPoint MIMO system (a) Open-loop control system, (b) Closed-loop control system Since the open-loop gain and the closed-loop gain of the input–output pair are the components of G(s) and 1/(G−1(s))T, respectively, then (1) can be rewritten as [37-39] (2) Calculation of RG: According to (1) and (2), the RG matrix for the MIMO system in Fig. 1 ℜ can be represented as (3) where ⊗ is Hadamard product, it denotes element-by-element multiplication. Properties of RG: Unlike [37, 38], which applied RG to PMUs placement and optimal selection of control input signals, the RG is employed in this work to evaluate QV interactions among the buses to determine VRPCAs. The properties of RG for this purpose are summarised as follows [35, 39, 41]: RG depends only on plant model and not on the controller, it is hence calculated for the open loop system. RG is independent on the input and the output scaling. The sum of elements in each row or column of RG equals to 1. If the CRG is 0, the pair of buses has no QV coupling. If the CRG rij is 1, there is an independent QV coupling for the pair of buses and both of these buses have no QV interactions with other buses. If the CRG is less than 0, the pair of buses has strong QV coupling. Without loss of generality, taking a two-input two-output system as an example, the transfer function of the control system can be expressed as: (4) where gij is a component of transfer function matrix. If Δy2 = 0, Δy1 in (4) can be represented as: (5) Assuming Δu2 = 0, Δy1 in (4) can be obtained. (6) According to the definition of RG, (5) and (6), the ARG r11 can be obtained as (7). r11 reflects the influence of other pairs on the control pair u1→y1. (7) Similarly, r12, r21 and r22 obtained from (4) are represented as follows (8) According to (7) and (8), the RG matrix in (4) can be expressed as (9) 2.2 Evaluate the QV interaction using RG In electric power network, the typical quasi-steady-state system model for voltage stability analysis can be described as a differential algebraic equation set in the following form. (10) where x is the vector of state variables, s is the vector of injected active power and reactive power, and y is the vector of algebraic variables which are the voltages amplitudes V and phases θ in power systems. Linearising (10) at an equilibrium point, the linearised model of (10) is expressed as follows. (11) Assuming , Δs can be expressed as Δs = JacoΔy, then Jaco can be calculated as (12) Since s = [P, Q] and y = [V, θ], Δs = JacoΔy can be described in detail as follows. (13) where Jaco is power flow Jacobian matrix in electric power network. Supposing ΔP = 0, ΔQ can be expressed as (14) The detailed representation of (14) is (15) where subscript G and L denote PV and PQ buses, respectively. Define JVQ as the inverse matrix of JQV. From (15), ΔV can be solved as below. (16) In practical power systems, VG and QL are independent system parameters, while QG and VL are dependent system parameters. Hence, VG and QL can be regarded as inputs and QG and VL as outputs. Consequently, the QV model derived from (16) can be cast as (17) where J1, J2, J3 and J4 are (18) The QV model in (17) is actually a MIMO system wherein [ΔQG; ΔVL] is output vector, [ΔVG; ΔQL] is input vector and J is transfer function matrix. According to the definition and calculation of RG, the RG matrix ℜ for the QV model described in (17) can be expressed as (19). (19) Similar to RG in control systems to analyse the interactions among multiple control loops, RG matrix ℜ in here is employed to assess the QV interactions among the buses in electrical power network for partitioning VRPCAs. 2.3 Identify voltage pilot buses based on coupled single-port model To determine the VRPCA, the first step is to identify voltage stability critical buses in electrical power network as the pilot buses. Several VSIs have been investigated to assess the system voltage stability, such as loading margin [42], L-index [43, 44], voltage sensitivity factor [45], singular values [46], voltage instability proximity index [47], tangent vector index [48], voltage controllability index [49], etc. In this paper, the loading margin of each load bus based on a coupled single-port model [50] is employed to detect the voltage critical buses. In electrical power network, coupled single-port models are described in [50]. In each coupled single-port model, the voltage and power of load bus i should follow Kirchoff's voltage law as (20): (20) where zeq,i = req,i + jxeq,i, the detailed calculation of zeq,i is referred to [26], VLi, PLi, and QLi are voltage, active power and reactive power of load bus i, respectively. The loading margin λi can be incorporated into (20) to reformulate nodal power balance of load bus i as (λi + 1)(PLi + jQLi). As λi reaching maximum corresponds to |VLi|2 having a unique solution, the maximum loading margin of load bus i can be solved as (21). (21) The buses with small loading margins will be identified as voltage stability critical buses. The weakest bus, which is the load bus with the smallest loading margin, represents the voltage stability of the whole system. However, the Thevenin equivalent parameters of coupled single-port models are calculated based on the assumption that all loads increase proportionally. If the impedance of the coupled single-port model varies with the load changes, the calculated loading margin at each load bus will be inaccurate. To address this challenge, a mitigation factor using reactive power response factor (RPRF) defined in [51] is employed to adjust the Thevenin equivalent impedance of the existing coupled single-port model to calculate loading margins with respect to any load variations. Through this modified coupled-single port model, the loading margins for load buses can be calculated, and the voltage stability weak buses can be identified. From PMUs or EMS, the direction of load variation di(k) and RPRF of electrical power network ri(k) at each load bus can be updated in real-time. (22) where k is the time interval. With di(k) and ri(k), the proposed mitigation factor αi can be calculated according to the following equation. (23) where (24) The impedance zeq,i can be updated as αizeq,i with mitigation factor αi. The Thevenin equivalent parameters of the modified coupled single-port model can be expressed as [50]: (25) Substituting (25) to (21), loading margin of each load bus can be calculated based on the modified coupled single-port model. Thus, enhanced VSI can be achieved. According to this VSI, the voltage stability pilot buses can be identified. 2.4 Partition the VRPCAs The proposed loading margin introduced in Section 2.3 is a fundamental index of voltage stability, which is defined as the amount of additional load in a specific direction of load increase that would lead to a voltage collapse. According to [13-35], there exists a VRPCA with strong QV coupling among the voltage stability pilot buses in the network. Therefore, the VRPCA that is strongly coupled with the pilot bus can be determined. According to the VRPCA, the voltage stability of the network can be improved via coordinated control of the reactive power injection in the VRPCA. Thus, it is of great significance to determine the VRPCAs that have tight QV coupling relationships with pilot buses. According to the characteristics of RG in Section 2.1, the principles of partitioning VRPCA using CRG are described as follows: Utilise voltage stability pilot buses to select the corresponding row of the RG matrix ℜ. Identify the QV coupling strength between the voltage stability pilot bus and other buses according to the properties of CRG. All the buses that are strongly coupled with the pilot bus are partitioned into one VRPCA. Following this principle, several primary VRPCAs are partitioned with multiple voltage stability pilot buses. Merge VRPCAs, define boundaries of VRPCAs and assign isolated buses. If the pilot buses in several individual VRPCAs have strong interactive effects, these VRPCAs should be merged into one VRPCA. The buses that are strongly coupled with multiple pilot buses are regarded as the boundary buses. The boundary buses may belong to multiple VRPCAs. In order to assign the boundary buses to a rational VRPCA, the corresponding column of RG matrix is employed according to the properties of RG. The boundary bus will be assigned to the VRPCAs whose pilot bus has the strongest coupling with the boundary bus. Similarly, the isolated buses are assigned to the coupling area whose pilot bus has stronger coupling. 2.5 Implementation framework The implementation framework of the proposed wide-area VRPCA partitioning method is described in Fig. 2. As shown in Fig. 2, the overall framework of the proposed approach consists of Block 1, Block 2, and Block 3, whose functions are summarised as follows. Block 1: calculate all the coupled single-port models and mitigation factors of the electrical power network, then update Thevenin equivalent parameters of the modified coupled single-port models to obtain loading margin at each bus to identify voltage stability critical buses. Block 2: solve the dynamic/steady power flow Jacobian matrix to form RG matrix of electric power network. Block 3: determine VRPCAs based on the critical buses and their strong Volt-VAR coupled buses. Fig 2Open in figure viewerPowerPoint Flowchart of evaluating QV interactions and partitioning QV coupling areas It should be noted that Block 1 and Block 2 are parallel processes in the implementation of the proposed method. 3 Case studies In this section, New England 39-bus system and Polish power system are used to evaluate the performance of the proposed approach and its applicability in bulk power systems. 3.1 NewEngland-39 Detailed description of NewEngland-39 test system is available in [52]. In order to fully test the effectiveness and accuracy of the proposed approach in evaluating the QV interactions among the buses and partitioning the VRPCAs, modal analysis and the three scenarios are considered: Scenario 1: The system operates under normal conditions (base case). Scenario 2: base case with the load of bus 15 increased 9 p.u. Scenario 3: base case with branch 16–17 tripping. 3.1.1 Scenario 1 In this scenario, the base case is adopted. Applying the modal analysis, the eigenvalues of JQV in (15) via the eigenvalue analysis are illustrated in Fig. 3a. In Fig. 3a, the first three minimum eigenvalues, which are 9.5874, 19.3034, and 31.9952, are selected as the critical VSIs to determine the corresponding critical voltage stability buses using participation factor (PF). Figs. 3b and c show the calculated PF of each bus associated with these three minimum eigenvalues. It can be clearly observed from Fig. 3b that, for the 9.5874 pattern, Bus 12 has the largest participation factor (0.1079), which means Bus 12 is the critical voltage stability bus. Similarly, it is also obvious in Figs. 3c and d that Bus 27 and 28 are the critical voltage stability buses of the 19.3034 and 31.9952 patterns, respectively. Therefore, it can be concluded that Bus 12, 27, and 28 are the pilot buses in this scenario. Fig 3Open in figure viewerPowerPoint Scenario 1 (a) Eigenvalues of modal analysis, (b) PF and CRG of Bus 12, (c) PF and CRG of Bus 27, (d) PF and CRG of Bus 28 For these three determined pilot buses, the corresponding CRGs are illustrated in Figs. 3b to c via the proposed approach. In Fig. 3b, it can be obtained that, the CRGs of Bus 12 with respect to Bus 11, 12 and 13 are −0.2343, 1.4830, and −0.2423, respectively, and CRGs with respect to other buses are 0. From these calculated CRGs of Bus 12, it can be deduced that there are strong QV interactions between Bus 12 and Bus 11 and 13 via the characteristics of ℜ. The QV interaction sequence is 12, 13 and 11 sorted by the CRG. Fig. 3b also shows that the new QV interaction sequence of Bus 12 is 12, 13, 11, 7, 8, 4 and 5 according to the PF. Although it is slightly different from the sequence sorted by CRG, the strong QV interaction buses of bus 12 determined by the PF are the same with CRG. This indicates that the proposed method, which uses CRG to evaluate the QV interaction between the buses, is valid. The reason that the orders of QV interaction buses in Fig. 3b are different is that the proposed CRG derived from the power flow Jacobian matrix, is strongly affected by the system topology. Similarly, the QV interaction buses of Bus 27 and 28 are evaluated based on CRG, and the results are compared with the PF in Figs. 3c and d. Comparing results in Figs. 3b–d, it is obvious that the proposed CRG is able to accurately evaluate the QV interactions among the buses. 3.1.2 Scenario 2 In this scenario, with the load of Bus 15 increased 9 p.u., the eigenvalues of JQV in (15) are calculated and shown in Fig. 4a. It can be observed that the first three minimum eigenvalues, which are 8.7405, 18.9880, and 30.8133, correspond to Bus 12, 27 and 28 respectively detected via the PF of each pattern. Hence, it can be inferred that Bus 12, 27, and 28 are still the first three pilot buses in this scenario. Fig 4Open in figure viewerPowerPoint Scenario 2 (a) Eigenvalue of QVA, (b) PF and CRG of Bus 12, (c) PF and CRG of Bus 27, (d) PF and CRG of Bus 28 For these three identified critical buses, the CRGs of these buses are calculated and shown in Figs. 4b–d. From Figs. 4b–d, it is observed that for Bus 12, the strong QV interaction buses are Bus 12, 13, and 11; for Bus 27, the strong QV interaction buses are Bus 27, 26, and 17; for Bus 28, the QV interaction sequence is 28, 29, and 26 sorted by the CRG. Comparing the results of the proposed method with PF in Figs. 4b–d, we can observe that the QV interaction sequence obtained using CRGs are the same with that obtained by the PF. This fact justifies the accuracy of the proposed method in evaluating QV interactions among the buses. Further, comparing the CRGs of the critical buses in Figs. 3 and 4, it is can be found that the ARG of Bus 12 changes from 1.4830 in Scenario 1 to 1.5145 in Scenario 2, the ARGs of Bus 27 in Scenario 1 and Scenario 2 are 2.2726 and 2.3031, respectively, the ARGs of Bus 28 changes from 1.9495 in Scenario 1 to 1.9831 in Scenario 2. Same phenomenon also occurs in the CRGs of the critical buses in Figs. 3 and 4. This change demonstrates that the proposed approach can adaptively evaluate the QV interactions among the buses with the changing of power system operating point, which outperforms the approach in [35]. 3.1.3 Scenario 3 In this scenario, when the branch 16–17 trips, bus 17 is the weakest voltage bus and Bus 17, 27 and 24 are the first three pilot buses, as shown in Fig. 5a. Fig 5Open in figure viewerPowerPoint Scenario 3 (a) Eigenvalue of QVA, (b) PF and CRG of Bus 17, (c) PF and CRG of Bus 24, (d) PF and CRG of Bus 27 The CRGs of Bus 17, 27 and 24 are shown in Figs. 5b–d, and the results of the PF are also shown in the same figures. Fig. 5b indicates that the strong QV interaction buses of Bus 17 are Bus 17, 18, and 27. Fig. 5c illustrates that Bus 27, 26, and 17 has strong QV interactions with Bus 17, 26, and 27, and Fig. 5d shows that the strong QV coupling buses of Bus 24 are Bus 24, 16,and 23. From the results of PF in Figs. 5b–d, it can be observed that Bus 17, 18, and 27 have strong QV interactions with Bus 17, whose strong coupled buses are Bus 27, 17, and 26. The strong QV coupling buses of Bus 24 are Bus 24, 16, and 23, which are the same as the results obtained by the proposed CRG based approach. The above analysis and comparison in the case studies show that the proposed CRG-based QV interaction evaluation method is accurate and effective. Comparing the calculated CRGs of pilot buses among scenarios 1, 2, and 3, it is clear that the proposed QV interaction evaluation method is adaptive to the changing power system operation point. Compared with the approach in [35] which only represents the influence of topology changes, the proposed approach can not only represent the impact of topology changes on QV interactions among the buses, but also assess the QV interactions among the buses with the power flow variations of power systems. 3.1.4 Discussion of VSIs and partitioning VRPCA Although the accuracy and effectiveness of the proposed CRG have been proven by modal analysis, the VSI adopted in the previous section, the minimal eigenvalue of modal analysis cannot directly represent the voltage stability as loading margin or voltage profiles. The minimum eigenvalue of modal analysis reflects the influence of reactive power on voltage stability. However, the system voltage stability is also influenced by active power. Therefore, the bus with the largest participation factor of minimum eigenvalue may not be the voltage stability weakest bus in practical power systems due to the impact of active power demand. For the above scenarios, the voltage profile, loading margin, and continuous power flow (CPF) are employed to identify the weakest bus and make comparison with modal analysis. The results are shown in Fig. 6. It is evident in Fig. 6 that Bus 15 is the weakest bus in the above three scenarios using voltage profile, proposed loading margin (TE in Fig. 6), and CPF. Hence, it indicates that the modal analysis is unable to determine the most voltage stability critical bus accounting for active power demand. Fig 6Open in figure viewerPowerPoint Demonstration of the proposed VSI (a) Voltage profile of Scenario 1, (b) Voltage profile of Scenario 2, (c) Voltage profile of Scenario 3, (d) Loading margin of Scenario 1, (e) Loading margin of Scenario 2, (f) Loading margin of Scenario 3 Further, the results of QV interaction evaluation can be used for partitioning VRPCAs. From Figs. 6d–f, it can be observed that Buses 8, 15, and 27 are the first three most voltage stability critical buses in the above scenarios through the proposed loading margin method. Then, the CRGs of each critical bus in the three scenarios are calculated, and the Volt-VAR coupled buses of the critical buses are summarised in Table 1. According to Table 1, the Volt-VAR control areas are partitioned via Section 2.4 and depicted in Fig. 7. Fig 7Open in figure viewerPowerPoint Pilot VRPCAs in New England 39 (a) Scenario 1, (b) Scenario 2, (c) Scenario 3 Table 1.}, number={3}, journal={IET Science, Measurement and Technology}, author={Jiang, T. and Bai, L. and Yuan, H. and Jia, H. and Li, F. and Cui, H.}, year={2017}, pages={270–278} }
 @article{han_gao_shi_cui_li_2017, title={Security-Based Active Demand Response Strategy Considering Uncertainties in Power Systems}, volume={5}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85028502619&partnerID=MN8TOARS}, DOI={10.1109/ACCESS.2017.2743076}, abstractNote={In modern power systems, the stochastic and interactive characteristics of mixed generations have gained increasing interest, especially when more renewable energy sources are connected to the grid. The uncertainty of renewable energy has notable effects on power system security. In this paper, a set of composite security indices, which are derived from the Hyper-box and Hyper-ellipse Space theory, are extended by a Latin hypercube sampling method to model multiple probabilistic scenarios under uncertainty. Thus, the proposed approach is suitable for power system security assessment with wind power integrated. According to the indices, a security-based active demand response (DR) strategy is proposed. This strategy is able to provide expected active DR capacity based on the forecast wind power fluctuations. Therefore, it can be applied to day-ahead power system dispatches.}, journal={IEEE Access}, author={Han, H. and Gao, S. and Shi, Q. and Cui, H. and Li, F.}, year={2017}, pages={16953–16962} }
 @inproceedings{zhang_li_chen_li_jiang_ning_cui_bai_2016, title={A two-stage MILP formulation for source-load coordinated dispatch with wind power considering peak-valley regulation and ramping requirements}, volume={2016-November}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85002424677&partnerID=MN8TOARS}, DOI={10.1109/PESGM.2016.7741586}, abstractNote={In this paper, a two-stage mixed integer linear programming (MILP) formulation for source-load coordinated dispatch with wind power considering peak-valley regulation and ramping requirements is proposed. First, the peak-load regulation and ramping requirements of the net load curve are analyzed. Second, the first stage optimization model considering incentive-based demand response (IDR) is formulated to optimize the net load curve, in which the objective function is to minimize the compensation costs of IDR. Several constraints are taken into account to reduce the peak-valley regulation needs and meet the ramping requirements. Then, based on the optimized load curve, the second stage day-ahead dispatch optimization model is proposed to optimize the allocation of generation sources, taking the total costs of power generation minimization as the objective function considering thermal unit reserve costs. The proposed model is applied to a 10-unit system with a wind power farm with 600MW installed capacity. Simulation results demonstrate the effectiveness and feasibility of the proposed model.}, booktitle={IEEE Power and Energy Society General Meeting}, author={Zhang, R. and Li, G. and Chen, H. and Li, X. and Jiang, T. and Ning, R. and Cui, H. and Bai, L.}, year={2016} }
 @inproceedings{bai_li_hu_cui_fang_2016, title={Application of battery-supercapacitor energy storage system for smoothing wind power output: An optimal coordinated control strategy}, volume={2016-November}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85001698838&partnerID=MN8TOARS}, DOI={10.1109/PESGM.2016.7741798}, abstractNote={In the application of energy storage for smoothing wind power output, the combination of battery and supercapacitor (SC) is considered as an effective alternative to improve the battery lifetime and enhance the system economy. In this paper, third-order Butterworth low-pass filter and high-pass filter are adopted to smooth the wind power and allocate power between battery and SC. Then, an optimal coordinated control strategy is proposed to determine the cut-off frequencies of the two filters and the power sharing between battery and SC. With this strategy, the total deprecation cost of the system caused by charge/discharge is minimized while satisfying the requirements of wind power integration. Finally, the effectiveness of the proposed method is demonstrated with a simulation study.}, booktitle={IEEE Power and Energy Society General Meeting}, author={Bai, L. and Li, F. and Hu, Q. and Cui, H. and Fang, X.}, year={2016} }
 @article{cui_li_hu_bai_fang_2016, title={Day-ahead coordinated operation of utility-scale electricity and natural gas networks considering demand response based virtual power plants}, volume={176}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84969513657&partnerID=MN8TOARS}, DOI={10.1016/j.apenergy.2016.05.007}, abstractNote={The steady-state coordinated operation of electricity networks and natural gas networks to maximize profits is investigated under market paradigm considering demand response. The components in its gas supply networks are modeled and linearized under steady-state operating conditions where combined cycle gas turbine (CCGT) generators consume natural gas and offer to the electricity market. Interruptible-load based and coupon-based demand response virtual power plants are considered trading in the market like physical generators. A bi-level programming optimization model is formulated with its upper-level representing the coordinated operation to maximize profits and its lower-level simulating the day-ahead market clearing process. This bi-level problem is formulated as a mathematical program with equilibrium constraints, and is linearized as a mixed-integer programming problem. Case studies on a 6-bus power system with a 7-node natural gas system and an IEEE 118-bus power system with a 14-node gas system verify the effectiveness of the coordinated operation model. The impacts of demand response based virtual power plants on the interactions between the two networks are also analyzed.}, journal={Applied Energy}, publisher={Elsevier BV}, author={Cui, Hantao and Li, Fangxing and Hu, Qinran and Bai, Linquan and Fang, Xin}, year={2016}, pages={183–195} }
 @article{bai_li_cui_jiang_sun_zhu_2016, title={Interval optimization based operating strategy for gas-electricity integrated energy systems considering demand response and wind uncertainty}, volume={167}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84949636839&partnerID=MN8TOARS}, DOI={10.1016/j.apenergy.2015.10.119}, abstractNote={In the United States, natural gas-fired generators gained increasing popularity in recent years due to the low fuel cost and emission, as well as the proven large gas reserves. Consequently, the highly interdependency between the gas and electricity networks is needed to be considered in the system operation. To improve the overall system operation and optimize the energy flow, an interval optimization based coordinated operating strategy for the gas-electricity integrated energy system (IES) is proposed in this paper considering demand response and wind power uncertainty. In the proposed model, the gas and electricity infrastructures are modeled in detail and their operation constraints are fully considered, wherein the nonlinear characteristics are modeled including pipeline gas flow and compressors. Then a demand response program is incorporated into the optimization model and its effects on the IES operation are investigated. Based on interval mathematics, wind power uncertainty is represented as interval numbers instead of probability distributions. A case study is performed on a six-bus electricity network with a seven-node gas network to demonstrate the effectiveness of the proposed method; further, the IEEE 118-bus system coupling with a 14-node natural gas system is used to verify its applicability in practical bulk systems.}, journal={Applied Energy}, author={Bai, L. and Li, F. and Cui, H. and Jiang, T. and Sun, H. and Zhu, J.}, year={2016}, pages={270–279} }
 @inproceedings{yuan_li_li_fang_cui_hu_2016, title={Mitigate overestimation of voltage stability margin by coupled single-port circuit models}, volume={2016-November}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85002245062&partnerID=MN8TOARS}, DOI={10.1109/PESGM.2016.7741515}, abstractNote={Wide-area measurement-based voltage stability assessment (VSA) by coupled single-port circuit models has been widely discussed recently. This method models the coupling effects of load buses within a meshed network into extra impedance of a single-port model for each load bus. In simulation studies, overestimations of voltage stability margin using this approach have been observed when critical load bus or buses are decoupled from other load buses. In this paper, the overestimations are reported for the first time through examples and are further analyzed in details. Moreover, to mitigate such overestimations, two methods are proposed: one method uses a mitigation factor based on actual system reactive power response; the other method changes the types of certain weak generation buses when forming the coupled impedance. Both approaches are applied to a sample 4-bus system as well as the IEEE 118-bus system and successfully mitigate the overestimations.}, booktitle={IEEE Power and Energy Society General Meeting}, author={Yuan, H. and Li, X. and Li, F. and Fang, X. and Cui, H. and Hu, Q.}, year={2016} }
 @inproceedings{azim_cui_li_2016, title={Power management strategy combining energy storage and demand response for microgrid emergency autonomous operation}, volume={2016-December}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85009976276&partnerID=MN8TOARS}, DOI={10.1109/APPEEC.2016.7779964}, abstractNote={This paper presents a power management strategy for microgrid emergency autonomous operation subsequent to unplanned islanding events. The proposed approach is composed of two coordinated scheduling stages operating in different time-frames to accommodate the uncertainty and variability associated with renewable generations as well as forecasting errors, and combines distributed generations, energy storage systems and demand side management techniques to ensure secure and stable microgrid autonomous operation. A scenario dependent rule-based approach is adopted for scheduling the microgrid resources which is computationally efficient and particularly suitable for microgrids with limited number of resources. Case study on a grid-connected microgrid test system based on IEEE 13-node distribution feeder demonstrates the effectiveness of the proposed approach in microgrid frequency regulation following an unplanned islanding events.}, booktitle={Asia-Pacific Power and Energy Engineering Conference, APPEEC}, author={Azim, R. and Cui, H. and Li, F.}, year={2016}, pages={2620–2625} }
 @article{liu_gao_cui_yu_2016, title={Probabilistic load flow considering correlations of input variables following arbitrary distributions}, volume={140}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84994667134&partnerID=MN8TOARS}, DOI={10.1016/j.epsr.2016.06.005}, abstractNote={For the purpose of accurately calculating probabilistic load flow (PLF) with correlated input variables following arbitrary distributions, this paper proposes a Latin hypercube sampling (LHS) based PLF method, which combines kernel density estimation with Nataf transformation to improve the calculation performance. First, enhanced kernel density estimation with adaptive-bandwidth is established to precisely depict arbitrary distributions, including the atypical probability density functions (PDF) of power injections from renewable energies such as wind and photovoltaic. Then, considering the correlations of renewable energies and the difficulties of kernel density estimation dealing with correlativity, Gauss–Hermite integral based Nataf transformation is proposed to handle the problem. The proposed method is demonstrated to be feasible and practicable in modified IEEE 14 and IEEE 118 systems with additional wind and photovoltaic power. The results suggest that proposed method is prominent in efficiency and accuracy, and applicable to arbitrary distributions of power injections in PLF calculation.}, journal={Electric Power Systems Research}, author={Liu, Y. and Gao, S. and Cui, H. and Yu, L.}, year={2016}, pages={354–362} }
 @inproceedings{fang_li_cui_bai_yuan_hu_wang_2016, title={Risk Constrained Scheduling of Energy Storage for Load Serving Entities Considering Load and LMP Uncertainties}, volume={49}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84997218156&partnerID=MN8TOARS}, DOI={10.1016/j.ifacol.2016.10.711}, abstractNote={With the substantial technique development, energy storage (ES) is becoming a promising resource to improve the flexibility and reliability of power system operation. Consequently, ES is obtaining increasing attention from both academia and industry. Due to the increasing fluctuation of locational marginal prices (LMP) as a result of the high penetration of variable wind generation, obtaining the deterministic scheduling decision for ES, i.e., charging/discharging, becomes more complex for load serving entities (LSEs). To address this challenge, a risk constrained scheduling model is proposed in which the objective is to maximize the LSE’s profit by optimially scheduling ES charging/discharging profile and considering the possible financial loss risk. Conditional value at risk (CVaR) term has been included in the objective function to negate the risk of associating the uncertainties from forecasting the market price and load. Numerical examples verify the proposed method in ES scheduling considering risk.}, number={27}, booktitle={IFAC-PapersOnLine}, author={Fang, X. and Li, F. and Cui, H. and Bai, L. and Yuan, H. and Hu, Q. and Wang, B.}, year={2016}, pages={318–323} }
 @article{fang_li_wei_cui_2016, title={Strategic scheduling of energy storage for load serving entities in locational marginal pricing market}, volume={10}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84963600736&partnerID=MN8TOARS}, DOI={10.1049/iet-gtd.2015.0144}, abstractNote={IET Generation, Transmission & DistributionVolume 10, Issue 5 p. 1258-1267 Research ArticleFree Access Strategic scheduling of energy storage for load serving entities in locational marginal pricing market Xin Fang, Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, 37996 TN, USASearch for more papers by this authorFangxing Li, Corresponding Author fli6@utk.edu Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, 37996 TN, USASearch for more papers by this authorYanli Wei, Power Supply Department, Southern California Edison, Rosemead, 91770 CA, USASearch for more papers by this authorHantao Cui, Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, 37996 TN, USASearch for more papers by this author Xin Fang, Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, 37996 TN, USASearch for more papers by this authorFangxing Li, Corresponding Author fli6@utk.edu Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, 37996 TN, USASearch for more papers by this authorYanli Wei, Power Supply Department, Southern California Edison, Rosemead, 91770 CA, USASearch for more papers by this authorHantao Cui, Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, 37996 TN, USASearch for more papers by this author First published: 01 April 2016 https://doi.org/10.1049/iet-gtd.2015.0144Citations: 37AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract Cost-effective approaches of storing electrical energy on a large-scale can help the grid operate flexibly and reliably. Public utility commissions view energy storage (ES) as a vital yet complementary part of other clean technologies such as renewable generation. As a coherent framework is being mapped out to increase the penetration of renewables in total electricity generation, load serving entities (LSEs) have been encouraged to procure ES systems to hedge against the intermittence and uncertainty of renewable power such as wind. Owing to the increasing penetration of wind generation, it becomes more complex for LSEs to obtain a deterministic ES scheduling decision, i.e. charging/discharging portfolio. To address this challenge, a bi-level strategic scheduling model is proposed in which the primary objective is to maximise the LSE's profit by optimally scheduling ES charging/discharging profile. The sub-problem is Independent System Operator's (ISO's) economic dispatch for generation cost minimisation, assuming foreseeable impact in market-clearing price from ES. This bi-level model is converted to a stochastic mathematic programme with equilibrium constraints by recasting the lower-level problem as its Karush–Kuhn–Tucker optimality conditions. Numerical examples based on the PJM 5-bus and IEEE 118- bus systems are presented to demonstrate and validate the proposed approach. Nomenclature N number of buses M number of lines t daily hour from 1 to 24 ci,t generation bidding price on bus i ($/MW•h) at time t Gi,t generation dispatch on bus i (MW•h) at time t maximum and minimum generation output at bus i minimum and maximum ramp rate of the generator on bus i Si,t power output of energy storage device on bus i at time t GSFl−i generation shift factor to line l from bus i Limitl transmission limit of line l πi,t locational marginal price on bus i at time t ηi,k electricity retail price for customer k on bus i ($/MW•h) Di,t energy consumption of LSE strategic bidder on bus i at time t energy consumption baseline of bus i at time t A bus set of the LSE strategic bidder SC ES bus set of the LSE strategic bidder S scenario set for considering load uncertainty λt dual variable associated with the power balance equation in economic dispatch at time t dual variables associated with the lower and upper limits of transmission line l at time t dual variables associated with the lower and upper limits of the generator on bus i at time t dual variables associated with the lower and upper limits for the generator's ramp rate on bus i at time t Ei0 initial status of energy storage device at bus i charging/discharging power of energy storage device on bus i at time t ςc, ςd charging/discharging efficiency of energy storage devices binary variables identifying the charging/discharging status of energy storage device on bus i at time t (, the ES is charging and , the ES is discharging). The other variables with a superscript of s identify the variables in scenario s for the consideration of uncertainty. The other variables will be explained in the text. 1 Introduction The energy industry has recently stepped into the era of developing large amounts of renewables and numerous smart grid technologies. Laying out a road map toward a modern and cleaner grid is the task for the independent systems operator's (ISOs) utilities, and regulators. In the United States, wind capacity as a percentage of the total generation capacity increased from 1.1% in 2006 to 3.6% in 2010 [1]. Meanwhile, ISO-managed markets also see significant wind percentage growth in terms of the generation portfolio capacity. Electric Reliability Council of Texas, Midcontinent Independent System Operator and California Independent System Operator (CAISO) are the top three ISO-managed markets with the highest levels of wind penetration [2]. Major challenges arise from the intermittent nature of wind power and the 'non-dispatchability' of wind resources in electric power market operations. The utilisation of energy storage (ES) to increase operational flexibility is commonly regarded as a logical complement for systems with large amounts of wind power. Therefore, regulators and policy makers have started to investigate the impact and benefit of ES integrated into the grid and have initiated some pilot procurement mandates for load serving entities (LSEs) such as utility companies. As LSEs' ES procurement becomes inevitable with increasing scale in the near future, there exists opportunities for LSE to better understand how to optimally schedule ES to get more investment return or to reduce ratepayer's cost. In general, the capability of storing energy electricity and releasing it during the more profitable periods would result in some serious business strategy when more ES devices come into participants' portfolio. In a vertically integrated utility company, ES can be used to coordinate with the company's thermal plants. In a competitive electricity market, an individual ES owner can purchase energy and sell it either on a day-ahead (DA) market or a spot market or through bilateral contracts. It can also participate in multi-markets such as energy and ancillary service (AS) markets [3, 4]. Under current practice, the evaluation of ES from an LSE's perspective would normally include a price-based dispatch and analysis of its cash flow for an extended period of time, i.e. from a few years up to 20 or even 30 years. A pre-defined or forecasted price forward curve is given first. Then, energy and ancillary market co-optimisation is performed to determine the profitability of the ES. Though the lack of interaction between ES operating mode and wholesale electricity clearing prices could stand now, it might not necessarily hold true going forward. California Public Utility Commission has established rules that require all the utilities and other LSEs to procure more than 1300 MW of ES by 2020, i.e. roughly 3–4% of CAISO's summer peak load [5]. Considering the increase in ES penetration will certainly be able to alter the supply/demand curve someday, it is important to investigate the dynamics between ES scheduling mode and market-clearing prices. There are some existing research works in the literatures. For instance, in [6–9] different types of ES devices such as pumped storage units, compressed air, and hydrogen-based ES are utilised by wind generation to mitigate their power output intermittence and gain extra profits from the deregulated electricity market such as the DA market. In [10], the sizing optimisation approach of ES for microgrid is proposed based on discrete Fourier transform. In [11], the impact and benefit of ES in the Netherland's electricity supply integrating for large-scale wind power are investigated from the viewpoint of system and market operators. A robust optimisation method for ES investment in the transmission networks considering the system uncertainties is proposed in [12]. The charging portfolio optimisation for plug-in electric vehicles (PEVs), another form of ES which has an increasing penetration, is proposed in [13–15]. The ES scheduling methods proposed in these research works are from the viewpoints of the wind power generation company, the market operators, or the ES devices such as PEV themselves. In the near future, LSEs such as the utility companies may also play an important role in utilising ES in their power procurement optimisation. Another concern is that ES scheduling is based on the forecast prices in these works and the price dynamics that the impact of ES charging/discharging on the system prices cannot be modelled in these approaches. With the capacity and penetration of ES increasing in the system, this impact should be considered in the market participants' operations including ES. Therefore, this paper proposes a bi-level optimisation model with LSE's main objective being its profit maximisation that also simulates the ISO/ regional system operator's (RTO's) DA market-clearing process, which is modelled as a dc optimal power flow (DCOPF) problem. In this model, the locational marginal price (LMP) is the key variable for the determination of ES revenue, and the impact of ES scheduling decision on LMPs is endogenously modelled. The coupling effect makes the model essentially non-convex and more challenging to solve than normal mathematical programmes. The lower level, ISO's economic dispatch (ED) problem, of the proposed model can be stated as its Karush–Kuhn–Tucker (KKT) optimality conditions and the bi-level optimisation model is an instance of mathematical programme with equilibrium constraints (MPECs) [16–20], which could be further converted to a mixed integer linear programming (MILP) problem and solved by commercial optimisation software. The rest of this paper is organised as follows: Section 2 presents the traditional scheduling model based on forecasted prices and the proposed bi-level model of ES strategic scheduling for LSEs. Section 3 proposes the actual solution to solve the stochastic bi-level model including the procedure of transforming it into MPEC and the conversion from MPEC to MILP problem. Section 4 demonstrates the simulation results and numerical analysis on the PJM 5-bus system and the IEEE 118-bus system to clearly verify the proposed method. Section 5 presents the concluding remarks and points out some future work. 2 Strategic ES scheduling for LSEs The three-layer electricity market framework and the structure of LSEs including ES are shown in Fig. 1. The details of an LSE's strategic scheduling for ES under this market structure will be discussed later. Fig. 1Open in figure viewerPowerPoint Structure of the electricity market and LSEs with ES 2.1 Net revenue of LSEs considering ES The LSE receives a gross revenue from each hour, t, at bus i, given by the product of retail price ηi,t and the electricity consumption . Then, the payment (i.e. the product of spot price πi,t and the electricity bid Di,t) is subtracted since the LSE pays this amount to the ISO/RTO in the wholesale market for purchasing electricity at volatile nodal prices (πi,t). Therefore, the net revenue of an LSE is in (1) (1)If the LSE has no capability to change its load, the electricity bid Di,t should be equal to the electricity consumption to maintain the consumers' reliable electricity consumption. If the LSE installs some ES system at some of its buses, and assumes that the discharging power of ES is positive whereas the charging power is negative, and in this case the demand bids on ES buses can be expressed as (2)where is the forecast demand on the buses of LSE bidder and Di,t is the demand that the LSE bids in ISO's DA market. If the LSE has some ES installed at some buses shown in Fig. 1 (set SC identifies the buses equipped with ES), the total revenue of an LSE with ES can be expressed as follows (3)This model is a general model for an LSE utilising ES in the DA market. 2.2 Traditional scheduling of ES system Traditionally, the daily scheduling of ES system [6–10, 21] is based on the forecasted demand and LMP. and πi,t are forecasted and constant. The model for ES scheduling in this situation is expressed in (4a)–(4g). In the scheduling process, the decision variables are the 24 h ES charging/discharging power output schedules (4a) (4b) (4c) (4d) (4e) (4f) (4g)where and are the minimum and maximum ES capacity status, respectively, at bus i; and are the maximum charging/discharging power of ES devices; (4b) is the actual demand at ES buses; (4c) is the power output of ES (ES's power output is positive for discharging and negative for charging); (4d) is the dynamic capacity limit of ES system; (4e) and (4f) are the charging/discharging power output limit; and (4g) is the charging/discharging status constraint (only one status is active at a specific time). 2.3 Bi-level model for strategic scheduling of ES The objective of the LSE strategic scheduling for ES system is to maximise its net revenue considering the impact of ES on the LMPs. In this process, the decision variables are still the 24 h schedules of ES charging/discharging power output. In this strategic scheduling model, the bus LMP are obtained from ISO's DA ED. Therefore, the strategic scheduling problem is formulated as a bi-level problem in (5a)–(5g), where A is an LSE strategic bidder whose customers may be connected at several buses shown in Fig. 1 (5a) (5b) (5c) (5d) (5e) (5f) (5g) (5h) (5i)where (5b) is the constraint for ES which is the same as traditional scheduling in the previous section; (5c)–(5g) represent the ISO's 24 h ED model which determines the optimal generation dispatch as well as the LMPs; (5h) is the Lagrangian function of ISO's ED model (5c)–(5g) and (5i) is the formulation of LMP. Note, (5c) is the ISO's 24-hour generation cost; (5d) represents the system generation and demand balance at time t; (5e) is the branch flow upper and lower limits; (5f) is the generation output maximum and minimum limits; and (5g) is the generation ramp limits. The variables on the right side of the colons are the dual variables associated with the corresponding equality or inequality constraints on the left side of the colons. The LMP πi,t, which is the partial derivative of the Lagrangian function of ISO's ED model to the nodal demand, can be obtained from the dual variables of the optimal solution of ISO's ED. The Lagrangian function is in (5h) and the LMP formulation is in (5i). The LMP πi,t from the ED depends on demand, Di,t, as well as the bid prices/quantities of generators. 2.4 Baseline demand model In this section, the baseline demand model which corresponds to the D0 in (2) will be presented. On the basis of the forecast of this load level, the LSE optimises the output of ES to participate in the DA market and to obtain maximum profit. The ES schedules are critically dependent on the customers' demand baseline [22] from which the demand bids according to ES charging/discharging can be calculated. Owing to the strong cyclic pattern of customers' electricity consumption over time [23], the demand baseline can be obtained from historical data. For instance, the Southern California Edison utility employs an approach called the '10-Day Average Baseline' [24]. More details concerning the baseline calculation have been introduced in [25]. However, it is out of the research scope of this paper to discuss the pros and cons of various consumer demand baseline methods. 3 Mathematical solution of the proposed model As presented in Section 2, the strategic scheduling of ES in (5a)–(5g) is formulated as a bi-level optimisation problem. The upper level is to maximise the LSE's profit; and the lower level is to minimise the generation cost to model the ISO's DA market-clearing process. Owing to the existence of dependent variables in each level, these two optimisation problems are coupled. For instance, the LMP in the upper-level problem is decided by the lower-level problem of ISO's market-clearing process, while the demands at ES buses in the lower-level market-clearing problem depend on the upper level. In this paper, DCOPF is implemented to clear the ISO's DA market. Owing to the linearity of DCOPF [26–30], its optimal solution should be unique and satisfies the KKT optimality conditions. Consequently, the bi-level optimisation problem is formulated as an MPECs by integrating the lower-level problem into the upper-level problem using its KKT conditions as the extra complementarity constraints [16–18, 20]. According to the strong duality theory, this MPEC model can be converted to an MILP that is solvable by available software. 3.1 Formulation of an MPEC Given that the lower-level problem is an LP problem, the bi-level strategic ES scheduling model can be transformed to a single-level MPEC problem by recasting the lower-level problem as its KKT optimality conditions, then adding them into the upper-level problem as a set of additional complementarity constraints (6a) (6b) (6c) (6d) (6e) (6f) (6g) (6h) (6i) (6j) (6k)where the perpendicular sign ⊥ denotes a zero cross-product of the corresponding variables in vector form. 3.2 Mixed-integer linear programming The model (6a)–(6k) is non-linear due to the product term πi,t × Si,t (both πi,t and Si,t are variables) in the objective function and the complementarity constraints (6f)–(6k). According to the strong duality theory, the objective of the primal problem is equal to the objective of the corresponding dual problem. For the ED problem (5c)–(5g), the relationship between the objectives of the dual and primal problems can be expressed as follows: (7)Substitute (2) into (7), (8)Taking the LMP expression in (5i), the product term πi,t × Si,t in (5a) can be transformed as (9) (9)Substituting (9) into (8) renders (10)Therefore, the objective in (5a) can be expressed as (10) and the MPEC problem is converted as an MILP problem as (11a)and (11b) (11c) (11d) (11e) (11f) (11g) (11h) (11i) (11j) (11k) (11l) (11m) (11n) (11o)where , , , , , and are large enough constants and , , , , , and are the auxiliary binary variables [31]. Note that the retail price ηi,t is fixed in this paper and is a constant in the optimisation model [20, 32]. The objective of the LSE bidder is to maximise its own profit through strategic scheduling of ES under the electricity flat rate, which is the common electricity payment method right now. However, the flexible retail price mechanism can be included in this paper and it will be part of our future work. 3.3 Model extensions to integrate uncertainty In this section, the extensions of the above model, including the uncertainty of wind power and demand, will be discussed. The forecasted wind power production and demand are expressed as a set of probabilistic scenarios (s = 1∼S) with a probability set of {ps}. The scenario below is one example of an ED model that includes wind power and demand uncertainty (12a) (12b) (12c) (12d) (12e) (12f)where is the generation dispatch at time t on bus i [megawatt hour (MW•h)] in the sth scenario. The hourly LMP for each scenario is given by (12f)Therefore, the net revenue of LSE can be formulated as (13a) and then transformed into (13b), while the constraints are modelled in (13c)–(13r) (13a) (13b) (13c) (13d) (13e) (13f) (13g) (13h) (13i) (13j) (13k) (13l) (13m) (13n) (13o) (13p) (13q) (13r) 4 Case studies In this section, the proposed strategic scheduling approach is applied to a modified PJM 5-bus system, which is chosen for its ability to illustrate the concept to the audience, as well as a modified IEEE 118-bus system to demonstrate the algorithm in a larger system. The simulation has been done in the general algebraic modelling system, which has the capability to solve large-scale optimisation problems. 4.1 PJM 5-bus system The test system is modified from the PJM 5-bus system. The system parameters are from [27]. In this paper, the peak load in this system is 780 MW and the total load is equally distributed on buses B, C, and D. The system is depicted in Fig. 2. Two small size generators on bus A are the gas turbines which have the capability to start up quickly. The ramp rate for the other generators is 50% of the maximum power output [33]. Fig. 2Open in figure viewerPowerPoint PJM 5-bus system and generation parameters In the case study, the LSE bidder with ES is located at bus D. The flat electricity rate offered to the customers at bus D by the LSE is set as $21/MW h. The daily load curve is shown in Fig. 3. This load curve is a typical double-peak load curve with the higher peak in the night. The forecast peak load follows the normal distribution. Assume that the standard deviation σ is 5% of mean load u and five scenarios are chosen to represent to load uncertainty [34, 35]. The peak load of five scenarios is [u − 2σ, u − σ, u, u + σ, u + 2σ] and the corresponding probability for each scenario is [0.023, 0.135, 0.684, 0.135, 0.023]. More details concerning the load forecast have been introduced in [23], though it is out of the research scope of this paper to discuss the pros and cons of various demand forecast methods. Fig. 3Open in figure viewerPowerPoint Daily load curve for PJM system on 23 November 2014 4.2 Comparison of traditional scheduling and strategic scheduling In this section, the ES scheduling results from the traditional method in Section 2.2 and the strategic scheduling method proposed in this paper will be compared. The parameters of ES system such as minimum/maximum storage status (Emin/Emax), initial storage capacity (E0), charging/discharging factors (ςc/ςd), and maximum charging/discharging power [Pc(max)/Pd(max)] are listed in Table 1. In this table, the percentage is w.r.t. the total ES capacity. In this paper, the LMP results obtained from ISO's ED under each load scenario without ES are utilised as the forecast LMP for LSE in the traditional scheduling of ES. Table 1. Parameters of ES system Emin 10% Emax 90% E0 20% ςc 0.9 ςd 0.9 Pc(max) 30% Pd(max) 30% The profits of the LSE in the ISO's DA market considering different ES capacities under the traditional method and proposed strategic method is shown in Fig. 4. Fig. 4Open in figure viewerPowerPoint LSE's profit with different ES capacities under different scheduling methods Fig. 4 shows that the profit increases linearly with the ES capacity in the traditional method. Using the strategic method proposed in this paper, the profit has a sharp change with the ES capacity. When the ES capacity is larger than a specified amount (10 MW h in this case), the profit will increase significantly with the ES capacity. This is because, in the traditional method, the impact of ES on the buses' LMPs is not considered. When the capacity of ES increases, the charging and discharging of LSE's ES will have the potential to change the bus load. Consequently, the bus LMPs will change due to the involvement of ES. Therefore, in the strategic method, the LSE can utilise this advantage to gain more profit. The impact of ES on the bus LMP is depicted in Fig. 5, showing that the ES can reduce the LMP on peak hours when its capacity is large. For example, the LMPs during the peak hours in the morning from 9 to 11 AM are reduced significantly when the ES capacity is >20 MW h. Moreover, during the peak hours in the evening from 19 to 22 PM, the duration of high LMPs is shortened with a larger ES capacity. In the real practice, the LSE should consider this impact on the DA scheduling of ES because the profit can change significantly between different scheduling methods of ES. Fig. 5Open in figure viewerPowerPoint Daily LMP at bus D under different ES capacities Fig. 6a is the capacity status of energy system under traditional method and the proposed strategic method. Fig. 6b is the original LMP without ES and with ES under different bidding methods. In these figures, the capacity of ES in the system is 50 MW h. Fig. 6Open in figure viewerPowerPoint Daily ES status and LMP results under different methodsa ES statusb LMP In Fig. 6a, the ES overall pattern of charging/discharging activities is similar between the traditional and strategic methods. The ES will charge during the off-peak hours and discharge during the peak hours. In the traditional method, this pattern is only decided by the daily load curve and the forecast LMP curve. In this method, the ES is prone to deep charging during off-peak hours and deep discharging during peak hours, though it maybe decrease the peak LMP as suggested by the results in the morning peak hours. However, the deep charging at 12 PM after the morning peak hours increases the LMP. Discharging during the evening peak hours just reduces the LMP on 21 PM, and the LMP during the other peak hours does not change from the discharge of ES. Since the demand at the peak hours such as 18–20 PM is so high, the demand reduction through ES does not help reduce the LMP during these hours. On the contrast, in the strategic methods, the impact of ES on the LMP is considered. Therefore, the ES will not deeply charge to increase the off-peak hours LMP, and it plays a more active role in reducing the LMP through discharging on the critical hours such as 17–18 PM, 21–23 PM. During these hours, the LMP can be reduced greatly through the ES discharging. Therefore, the ES discharges at these hours to reduce the LMP during these hours. This is shown in Fig. 6b. During other peak hours (19–20 PM), it cannot reduce the LMP through the ES discharging. Therefore, in the strategic method, the ES will discharge at some critical hours to reduce the LMPs such that the capacity of ES is utilised in its most efficient way to help the LSE obtain more profit. 4.3 IEEE 118-bus system The IEEE 118-bus system [28] is applied here to demonstrate the applicability of the proposed method to larger systems. The system is depicted in Fig. 7. The generation data is listed in Table 2. The maximum ramp rate for each generator is set to 50% of its maximum power output [36]. Seven thermal limits are applied to the transmission system: 100 MW for lines 1–3 and 6–7, 175 MW for lines 3–12 and 46–47, 150 MW for line 15–33, 300 MW for line 71–72, and 250 MW for line 70–75. Table 2. Generation parameters Gen Bus Price, $/MW•h Pmax, MW 1 10 5 550 2 12 7.5 185 3 25 10 320 4 26 12.5 414 5 31 30 107 6 46 35 119 7 49 40 304 8 54 45 148 9 59 50 255 10 61 55 260 11 65 60 491 12 66 65 492 13 69 70 805 14 80 80 577 15 87 90 104 16 89 100 707 17 100 110 352 18 103 120 140 19 111 130 136 Fig. 7Open in figure viewerPowerPoint LSE bidder in IEEE 118-bus system integrated with two wind farms The daily load curve is shown in Fig. 8. This load curve is a typical double-peak load curve with the higher peak at noon. The forecast peak load follows the Gaussian distribution. Similar to the previous case study, we may assume that the standard deviation σ is 5% of mean load u and five scenarios are chosen to represent load uncertainty. The peak load of five scenarios is [u − 2σ, u − σ, u, u + σ, u + 2σ] and the corresponding probability for each scenario is [0.023, 0.135, 0.684, 0.135, 0.023]. Fig. 8Open in figure viewerPowerPoint Daily load curve for IEEE 118-bus system The LSE performing the strategic bidding is located at the northwestern part of the system covering the demands on Bus 1, Bus 2, Bus 3, and Bus 4. LMP on Bus 1–Bus 4 versus the system load level is shown in Fig. 8. The average demand at each bus of this LSE and the corresponding flat electricity rates are shown in Table 3. Table 3. Bus parameters of LSE bidder Bus Base load, MW Flat electricity rate, $/MW•h 1 30.6 17.5 2 12.0 19.5 3 23.4 17.0 4 23.4 13.2 Four ES systems with 30, 10, 20, and 20 MW h are installed on Bus 1–Bus 4, respectively. The parameters of ES are the same as the previous study in Table 1. The results of the LSE bidder in DA market without and with ES are listed in Table 4. Fig. 9 is the ES capacity status under traditional method and strategic method and Fig. 10 is the daily LMP under different methods. Table 4. Profit of LSE under different methods Case ES capacity, bus Profit, $ Traditional Strategic 1 0 221.63 221.63 2 30 (1), 10(2), 20 (3), 20 (4) 575.72 784.76 Fig. 9Open in figure viewerPowerPoint ES status under different}, number={5}, journal={IET Generation, Transmission and Distribution}, author={Fang, X. and Li, F. and Wei, Y. and Cui, H.}, year={2016}, pages={1258–1267} }
 @article{li_cui_wan_2015, title={Distribution network reconfiguration based on second-order conic programming considering EV charging strategy}, volume={35}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84945156897&partnerID=MN8TOARS}, DOI={10.13334/j.0258-8013.pcsee.2015.18.013}, number={18}, journal={Zhongguo Dianji Gongcheng Xuebao/Proceedings of the Chinese Society of Electrical Engineering}, author={Li, H. and Cui, H. and Wan, Q.}, year={2015}, pages={4674–4681} }
 @inproceedings{cui_li_fang_long_2015, title={Distribution network reconfiguration with aggregated electric vehicle charging strategy}, volume={2015-September}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84956852809&partnerID=MN8TOARS}, DOI={10.1109/PESGM.2015.7285650}, abstractNote={With a higher level of electric vehicle load penetrated in the distribution network, reconfiguration could be employed to minimize energy losses. Based on a second-order conic programming formulation, an improved set of network radiality constraints is proposed using power-flow based network connectivity conditions. This proves to be a computationally more efficient method compared to the spanning tree constraints. To incorporate electric vehicle charging in the reconfiguration model, two aggregated charging strategies are proposed: the arbitrary delay and the peak-avoiding delay. The decision of delay hours is formulated as constraints and co-optimized into the reconfiguration model. Case study on the IEEE 33-bus system illustrates the performance of the proposed model and the effectiveness of the proposed charging strategy.}, booktitle={IEEE Power and Energy Society General Meeting}, author={Cui, H. and Li, F. and Fang, X. and Long, R.}, year={2015} }
 @article{li_li_cui_wan_2015, title={Optimal active power dispatch based on slack tie-line power for bi-level power system with wind farm}, volume={35}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84948407804&partnerID=MN8TOARS}, DOI={10.16081/j.issn.1006-6047.2015.11.007}, number={11}, journal={Dianli Zidonghua Shebei/Electric Power Automation Equipment}, author={Li, H. and Li, H. and Cui, H. and Wan, Q.}, year={2015} }
 @article{ding_cui_gu_wan_2012, title={An uncertainty power flow algorithm based on interval and affine arithmetic}, volume={36}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84865306819&partnerID=MN8TOARS}, DOI={10.3969/j.issn.1000-1026.2012.13.009}, number={13}, journal={Dianli Xitong Zidonghua/Automation of Electric Power Systems}, author={Ding, T. and Cui, H. and Gu, W. and Wan, Q.}, year={2012} }