@inproceedings{chandra_mehta_chakrabortty_2015, title={Equilibria analysis of power systems using a numerical homotopy method}, DOI={10.1109/pesgm.2015.7285823}, abstractNote={In this paper, we present a homotopy based numerical continuation algorithm to efficiently compute all feasible equilibria of a complex power system model. The dynamic characteristics of conventional power systems are undergoing a sea change due to the impact of large-scale integration of renewables, storage elements, new type of loads etc. Several parameters of these components affect the power system operation leading to multiple feasible equilibria which may be intractable by the traditional load flow techniques. In contrast, our algorithm finds all the feasible solutions over a certain parameter space. We illustrate the results through the simulation of a 5-machine power system model with wind, storage elements, and dynamic loads. We observed that the wind velocity and the reference to the wind bus voltage strongly affect the number and the stability of the system equilibria. Knowledge of these equilibria can benefit small-signal stability assessment and system level planning.}, booktitle={2015 ieee power & energy society general meeting}, author={Chandra, S. and Mehta, D. and Chakrabortty, Aranya}, year={2015} }
 @inproceedings{chandra_mehta_chakrabortty_2015, title={Exploring the impact of wind penetration on power system equilibrium using a numerical continuation approach}, DOI={10.1109/acc.2015.7172011}, abstractNote={In this paper we investigate how the equilibrium characteristics of conventional power systems may change with an increase in wind penetration. We first derive a differentialalgebraic model of a power system network consisting of synchronous generators, loads and a wind power plant modeled by wind turbines and doubly-fed induction generators (DFIG). The models of these three components are coupled via nonlinear power flow equations. In contrast to the traditional approach for solving the power flows via iterative methods that often lead to a local solution, we apply a recently developed parameterhomotopy based numerical continuation algorithm to compute all possible solutions. The method obtains all the solutions of the power flow equations over multiple values of the wind penetration. We observe that depending on the penetration limit and the setpoint value for the magnitude of the wind bus voltage, the system may exhibit several undesired or even unstable equilibria. We illustrate these results through a detailed simulation of a 5-machine power system model with wind injection, and highlight how the solutions may be helpful for small-signal stability assessment.}, booktitle={2015 american control conference (acc)}, author={Chandra, S. and Mehta, D. and Chakrabortty, Aranya}, year={2015}, pages={4339–4344} }
 @article{chandra_gayme_chakrabortty_2014, title={Coordinating Wind Farms and Battery Management Systems for Inter-Area Oscillation Damping: A Frequency-Domain Approach}, volume={29}, ISSN={["1558-0679"]}, DOI={10.1109/tpwrs.2013.2282367}, abstractNote={This paper presents a set of linear control designs for shaping the inter-area oscillation spectrum of a large radial power system through coordinated control of a wind farm and a battery energy system (BES). We consider a continuum representation of the power system with the wind and battery power modeled as point-source forcings. A spectral analysis of the system demonstrates that its oscillation spectrum strongly depends on the locations of these power injections, implying that there are siting locations that produce more favorable spectral responses. However, the ability to site a wind farm or BES at a specific location may be limited by geographic, environmental, economic or other considerations. Our work provides a means to circumvent this problem by designing co-ordinated controllers for the power outputs of the wind farm and the BES by which one can shape the spectral response of the system to a desired response. The design is posed as a parametric optimization problem that minimizes the error between the two spectral responses over a finite range of frequencies. The approach is independent of the locations of the wind farm and the BES, and can be implemented in a decentralized fashion.}, number={3}, journal={IEEE TRANSACTIONS ON POWER SYSTEMS}, author={Chandra, Souvik and Gayme, Dennice F. and Chakrabortty, Aranya}, year={2014}, month={May}, pages={1454–1462} }
 @inproceedings{chandra_weiss_chakrabortty_gayme_2014, title={Impact analysis of wind power injection on time-scale separation of power system oscillations}, DOI={10.1109/pesgm.2014.6938975}, abstractNote={In this work, we present an analytical relationship between the two time-scale behavior of coherent power system networks with increasing levels of wind penetration. We first derive a mathematical model coupling the electro-mechanical swing dynamics of the grid integrated with the dynamics of a doubly-fed induction machine via power flow. We then consider the system to be comprised of r coherent areas and apply a similarity transformation to explicitly show that the integrated system may exhibit a three time-scale behavior depending on the amount of wind power injection. This effect is illustrated using simulations of a model of the US Western Interconnection.}, booktitle={2014 ieee pes general meeting - conference & exposition}, author={Chandra, S. and Weiss, M. D. and Chakrabortty, Aranya and Gayme, D. F.}, year={2014} }
 @inproceedings{chandra_gayme_chakrabortty_2013, title={Using battery management systems to augment inter-area oscillation control in wind-integrated power systems}, DOI={10.1109/acc.2013.6580748}, abstractNote={This paper presents a control design for shaping the inter-area oscillations of a wind-integrated power system through coordination between a wind power controller and a controlled battery energy system (BES). We consider a continuum representation of the power system dynamics subject to two point source forcings from wind and battery power, each injected at specified electrical distances along the transfer path. The inter-area oscillation modes of a wind-integrated power system have previously been shown to be highly dependent on the location where wind power is injected, as a result of which a particular injection site may produce a desired spectral response. A wind power controller may be used to achieve the response in an arbitrary location but the effect is limited to small frequency ranges. In the present work, we design co-dependent linear controllers for the wind power and the BES in charging mode, and show that the addition of this controlled BES greatly improves the spectral matching within the inter-area oscillation range. We illustrate the performance of our controllers using power system models inspired by US west coast transfer paths such as the Pacific AC Inter-tie.}, booktitle={2013 american control conference (acc)}, author={Chandra, S. and Gayme, D. F. and Chakrabortty, Aranya}, year={2013}, pages={5809–5814} }