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

An Adaptive Optimization-Based Load Shedding Scheme in Microgrids

This paper proposes an adaptive optimization-based approach for under frequency load shedding (UFLS) in microgrids following an unintentional islanding. In the first step, the total amount of load curtailments is determined based on the system frequency response (SFR) model. Then, the proposed mixed-integer linear programming (MILP) model is executed to find the best location of load drops. The novel approach specifies the least cost load shedding scenario while satisfying network operational limitations. A look-up table is arranged according to the specified load shedding scenario to be implemented in the network if the islanding event occurs in the microgrid. To be adapted with system real-time conditions, the look-up table is updated periodically. The efficiency of the proposed framework is thoroughly evaluated in a test microgrid with a set of illustrative case studies

Stability, control, and optimization of nonlinear dynamical systems with applications in electric power networks

Electric power systems in recent years have witnessed an increasing adoption of renewable energy sources as well as restructuring of distribution systems into multiple microgrids. These trends, together with an ever-growing electricity demand, are making power networks operate closer to their stability margins, thereby raising numerous challenges for power system operators. In this thesis, we focus on two major challenges: How to efficiently assess and certify the stability of power systems; and how to optimize the operation of multiple microgrids while maintaining their stability. In the first part of the thesis, we focus on the first question, and study one of the most fundamental models of power systems, namely the swing equation model. We develop sufficient conditions under which the equilibrium points of swing equations are asymptotically stable. We also discuss the connection between the stability of equilibrium points and the network structure. This for example reveals an analog of Braess’s Paradox in power system stability, showing that adding power lines to the system may decrease the stability margin. Based on the developed theories, we also introduce several distributed control schemes for maintaining the stability of the system. Since swing equations belong to a more general class of second-order ordinary differential equations (ODEs) which are the cornerstone of studying many other physical and engineering systems, a considerable part of this thesis is devoted to the study of this general class of ODEs, where we investigate the impact of damping as a system parameter on the stability, hyperbolicity, and bifurcation in such systems. In the second part of the thesis, we address the second question and provide a computationally efficient method for optimizing multi-microgrid operation while ensuring its stability. Our goal is to maintain the frequency stability of multi-microgrid networks under an islanding event and to achieve optimal load shedding and network topology control with AC power flow constraints. Attaining this goal requires solving a challenging optimization problem with stability constraints. To cope with this challenge, we develop a strong mixed-integer second-order cone programming (MISOCP)-based reformulation and a cutting plane algorithm for scalable computation of the problem. The optimization frameworks and stability certificates developed in this thesis can be used as powerful decision support tools for power system operators.Ph.D

Investigating the effectiveness of tax penalties in Ardebil, Iran

Correctly implementing the provisions of direct tax law is of the most important objectives of Tax Affairs Organization; accordingly, tax penalty system is among the most crucial guarantees for enforcement of this law. On the other hand, since tax is of long standing in Iran, compared to the majority of developing countries and some developed ones, the performance of tax system is an indicative of weaknesses with respect to law efficiency. Reluctant acceptance, and inefficiency of the previous tax law as well as the penalty system belonging to it, has caused to be revised and reformed. Reformation of the pervious law and creation of the existing one were aimed at accomplishing the objectives of development program in tax sector. However, with regard to what should have been materialized according to the anticipations, the country's tax law suffers from significant drawbacks with some existing articles and paragraphs. The present paper investigates two domains of jobs and companies in Ardabil province, and reveals the ineffectiveness of penalty system in these two tax sources

Investigating the effectiveness of tax penalties in Ardebil, Iran

Correctly implementing the provisions of direct tax law is of the most important objectives of Tax Affairs Organization; accordingly, tax penalty system is among the most crucial guarantees for enforcement of this law. On the other hand, since tax is of long standing in Iran, compared to the majority of developing countries and some developed ones, the performance of tax system is an indicative of weaknesses with respect to law efficiency. Reluctant acceptance, and inefficiency of the previous tax law as well as the penalty system belonging to it, has caused to be revised and reformed. Reformation of the pervious law and creation of the existing one were aimed at accomplishing the objectives of development program in tax sector. However, with regard to what should have been materialized according to the anticipations, the country's tax law suffers from significant drawbacks with some existing articles and paragraphs. The present paper investigates two domains of jobs and companies in Ardabil province, and reveals the ineffectiveness of penalty system in these two tax sources

Investigating the effectiveness of tax penalties in Ardebil, Iran

Correctly implementing the provisions of direct tax law is of the most important objectives of Tax Affairs Organization; accordingly, tax penalty system is among the most crucial guarantees for enforcement of this law. On the other hand, since tax is of long standing in Iran, compared to the majority of developing countries and some developed ones, the performance of tax system is an indicative of weaknesses with respect to law efficiency. Reluctant acceptance, and inefficiency of the previous tax law as well as the penalty system belonging to it, has caused to be revised and reformed. Reformation of the pervious law and creation of the existing one were aimed at accomplishing the objectives of development program in tax sector. However, with regard to what should have been materialized according to the anticipations, the country's tax law suffers from significant drawbacks with some existing articles and paragraphs. The present paper investigates two domains of jobs and companies in Ardabil province, and reveals the ineffectiveness of penalty system in these two tax sources

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