Publications

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With increasing penetration of variable renewable generation, battery energy storage systems (BESS) are becoming important for power system stability due to their operational flexibility. In this paper, we propose a method for determining the minimum BESS rated power that guarantees security constraints in a grid subject to disturbances induced by variable renewable generation. The proposed framework leverages sensitivity-based inverse uncertainty propagation where the dynamical responses of the states are parameterized with respect to random variables. Using this approach, the original nonlinear optimization problem for finding the security-constrained uncertainty interval may be formulated as a quadratically-constrained linear program. The resulting estimated uncertainty interval is utilized to find the BESS rated power required to satisfy grid stability constraints.

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Transient stability control of power systems is based on actions that are taken automatically following a disturbance to ensure that the system remains in synchronism. Examples of such measures include generator rejection and the insertion of dynamic braking resistors. Methods like these are designed to rapidly absorb excess energy or otherwise alter the generation-demand balance at key points in the system. While these methods are often effective, they lack the ability to inject real power to compensate for a deficit. Utility-scale inverter-based resources, particularly energy storage systems, enable bidirectional modulation of real power with the bandwidth necessary to provide synchronizing torque. These resources, and the control strategies they enable, have garnered substantial research interest. This paper provides a critical review of research on real power modulation strategies for transient stability control. The design of these control strategies is heavily informed by the methods used to assess changes in the transient stability margins. Rigorously assessing these changes is difficult because the dynamics of large-scale power systems are inherently nonlinear. The well-known equal-area criterion is physically intuitive, but conceptual extensions are necessary for multi-machine systems. So-called direct methods of transient stability analysis offer a more general alternative; however, these methods require many simplifying assumptions and have difficulty incorporating detailed system dynamics. In this paper, we discuss data-driven methods for offline stability assessment based on Koopman operator theory.

Dynamic injection shift factor (DISF) is the linear sensitivity factor that estimates the incremental line flows in a transmission network subject to load disturbances. The DISF provides fast computation of post-disturbance line flows without solving nonlinear equations of power-system dynamics for a given pre-disturbance operating condition. Furthermore, DISF can be utilized to derive other critical sensitivity factors used for fast contingency screening and generation dispatch in real-time markets. However, deriving the DISF analytically is difficult due to nonlinearity of power-system models. In this paper, we propose an approach based on a linear Koopman operator and a data-driven algorithm to construct a representative linear model for generator and network dynamics. The linear model constructed by the proposed approach is utilized to find an analytic expression of the DISF. Then, the DISF provides numerical tools to estimate line flows accurately subject to power injection changes in the network at any instant in time without solving nonlinear power-system equations.

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We consider a class of nonlinear control synthesis problems where the underlying mathe-matical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

This document describes the Power and Energy Storage Systems Toolbox for MATLAB, abbreviated as PSTess. This computing package is a fork of the Power Systems Toolbox (PST). PST was originally developed at Rensselaer Polytechnic Institute (RPI) and later upgraded by Dr. Graham Rogers at Cherry Tree Scientific Software. While PSTess shares a common lineage with PST Version 3.0, it is a substantially different application. This document supplements the main PST manual by describing the features and models that are unique to PSTess. As the name implies, the main distinguishing characteristic of PSTess is its ability to model inverter-based energy storage systems (ESS). The model that enables this is called ess.m , and it serves the dual role of representing ESS operational constraints and the generator/converter interface. As in the WECC REGC_A model, the generator/converter interface is modeled as a controllable current source with the ability to modulate both real and reactive current. The model ess.m permits four-quadrant modulation, which allows it to represent a wide variety of inverter-based resources beyond energy storage when paired with an appropriate supplemental control model. Examples include utility-scale photovoltaic (PV) power plants, Type 4 wind plants, and static synchronous compensators (STATCOM). This capability is especially useful for modeling hybrid plants that combine energy storage with renewable resources or FACTS devices.

We consider an optimal control synthesis problem for a class of control-affine nonlinear systems. We propose Sum-of-Square based computational framework for optimal control synthesis. The proposed computation framework relies on the convex formulation of the optimal control problem in the dual space of densities. The convex formulation to the optimal control problem is based on the duality results in dynamical systems' stability theory. We used the Sum-of-Square based computational framework for the finite-dimensional approximation of the convex optimization problem. The efficacy of the developed framework is demonstrated using simulation results.

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