arXiv subjects

Amin Gholami

Publications and source records attributed to Amin Gholami.

7 recordsLinked to original sources

arXiv2023

An ADMM-based Distributed Optimization Method for Solving Security-Constrained AC Optimal Power Flow

In this paper, we study efficient and robust computational methods for solving the security-constrained alternating current optimal power flow (SC-ACOPF) problem, a two-stage nonlinear optimization problem with disjunctive constraints, that is central to the operation of electric power grids. The first-stage problem in SC-ACOPF determines the operation of the power grid in normal condition, while the second-stage problem responds to various contingencies of losing generators, transmission lines, and transformers. The two stages are coupled through disjunctive constraints, which model generators' active and reactive power output changes responding to system-wide active power imbalance and voltage deviations after contingencies. Real-world SC-ACOPF problems may involve power grids with more than 30k buses and 22k contingencies and need to be solved within 10-45 minutes to get a base case solution with high feasibility and reasonably good generation cost. We develop a comprehensive algorithmic framework to solve SC-ACOPF that meets the challenge of speed, solution quality, and computation robustness. In particular, we develop a smoothing technique to approximate disjunctive constraints into a smooth structure which can be handled by interior-point solvers; we design a distributed optimization algorithm to efficiently generate first-stage solutions; we propose a screening procedure to prioritize contingencies; and finally, we develop a reliable and parallel architecture that integrates all algorithmic components. Extensive tests on industry-scale systems demonstrate the superior performance of the proposed algorithms.

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arXiv2022

Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition

The optimal power flow problem is central to many tasks in the design and operation of electric power grids. This problem seeks the minimum cost operating point for an electric power grid while satisfying both engineering requirements and physical laws describing how power flows through the electric network. By additionally considering the possibility of component failures and using an accurate AC power flow model of the electric network, the security-constrained AC optimal power flow (SC-AC-OPF) problem is of paramount practical relevance. To assess recent progress in solution algorithms for SC-AC-OPF problems and spur new innovations, the U.S. Department of Energy's Advanced Research Projects Agency--Energy (ARPA-E) organized Challenge 1 of the Grid Optimization (GO) competition. This paper describes the SC-AC-OPF problem formulation used in the competition, overviews historical developments and the state of the art in SC-AC-OPF algorithms, discusses the competition, and summarizes the algorithms used by the top three teams in Challenge 1 of the GO Competition (Teams gollnlp, GO-SNIP, and GMI-GO).

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arXiv2021

The Impact of Damping in Second-Order Dynamical Systems with Applications to Power Grid Stability

We consider a broad class of second-order dynamical systems and study the impact of damping as a system parameter on the stability, hyperbolicity, and bifurcation in such systems. We prove a monotonic effect of damping on the hyperbolicity of the equilibrium points of the corresponding first-order system. This provides a rigorous formulation and theoretical justification for the intuitive notion that damping increases stability. To establish this result, we prove a matrix perturbation result for complex symmetric matrices with positive semidefinite perturbations to their imaginary parts, which may be of independent interest. Furthermore, we establish necessary and sufficient conditions for the breakdown of hyperbolicity of the first-order system under damping variations in terms of observability of a pair of matrices relating damping, inertia, and Jacobian matrices, and propose sufficient conditions for Hopf bifurcation resulting from such hyperbolicity breakdown. The developed theory has significant applications in the stability of electric power systems, which are one of the most complex and important engineering systems. In particular, we characterize the impact of damping on the hyperbolicity of the swing equation model which is the fundamental dynamical model of power systems, and demonstrate Hopf bifurcations resulting from damping variations.

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arXiv2021

Stability of Multi-Microgrids: New Certificates, Distributed Control, and Braess's Paradox

This paper investigates the theory of resilience and stability in multi-microgrid networks. We derive new sufficient conditions to guarantee small-signal stability of multi-microgrids in both lossless and lossy networks. The new stability certificate for lossy networks only requires local information, thus leads to a fully distributed control scheme. Moreover, we study the impact of network topology, interface parameters (virtual inertia and damping), and local measurements (voltage magnitude and reactive power) on the stability of the system. The proposed stability certificate suggests the existence of Braess's Paradox in the stability of multi-microgrids, i.e. adding more connections between microgrids could worsen the multi-microgrid system stability as a whole. We also extend the presented analysis to structure-preserving network models, and provide a stability certificate as a function of original network parameters, instead of the Kron reduced network parameters. We provide a detailed numerical study of the proposed certificate, the distributed control scheme, and a coordinated control approach with line switching. The simulation shows the effectiveness of the proposed stability conditions and control schemes in a four-microgrid network, IEEE 33-bus system, and several large-scale synthetic grids.

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arXiv2021

A Distributed Scheme for Stability Assessment in Large-Scale Structure-Preserving Models via Singular Perturbation

Assessing small-signal stability of power systems composed of thousands of interacting generators is a computationally challenging task. To reduce the computational burden, this paper introduces a novel condition to assess and certify small-signal stability. Using this certificate, we can see the impact of network topology and system parameters (generators' damping and inertia) on the eigenvalues of the system. The proposed certificate is derived from rigorous analysis of the classical structure-preserving swing equation model and has a physically insightful interpretation related to the generators' parameters and reactive power. To develop the certificate, we use singular perturbation techniques, and in the process, we establish the relationship between the structure-preserving model and its singular perturbation counterpart. As the proposed method is fully distributed and uses only local measurements, its computational cost does not increase with the size of the system. The effectiveness of the scheme is numerically illustrated on the WSCC system.

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arXiv2020

A Fast Certificate for Power System Small-Signal Stability

Swing equations are an integral part of a large class of power system dynamical models used in rotor angle stability assessment. Despite intensive studies, some fundamental properties of lossy swing equations are still not fully understood. In this paper, we develop a sufficient condition for certifying the stability of equilibrium points (EPs) of these equations, and illustrate the effects of damping, inertia, and network topology on the stability properties of such EPs. The proposed certificate is suitable for real-time monitoring and fast stability assessment, as it is purely algebraic and can be evaluated in a parallel manner. Moreover, we provide a novel approach to quantitatively measure the degree of stability in power grids using the proposed certificate. Extensive computational experiments are conducted, demonstrating the practicality and effectiveness of the proposal.

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arXiv2018

Towards Resilient Operation of Multi-Microgrids: An MISOCP-Based Frequency-Constrained Approach

High penetration of distributed energy resources (DERs) is transforming the paradigm in power system operation. The ability to provide electricity to customers while the main grid is disrupted has introduced the concept of microgrids with many challenges and opportunities. Emergency control of dangerous transients caused by the transition between the grid-connected and island modes in microgrids is one of the main challenges in this context. To address this challenge, this paper proposes a comprehensive optimization and real-time control framework for maintaining frequency stability of multi-microgrid networks under an islanding event and for achieving optimal load shedding and network topology control with AC power flow constraints. The paper also develops a strong mixed-integer second-order cone programming (MISOCP)-based reformulation and a cutting plane algorithm for scalable computation. We believe this is the first time in the literature that such a framework for multi-microgrid network control is proposed, and its effectiveness is demonstrated with extensive numerical experiments.

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