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This paper presents conservative probabilistic bounds for the spectrum of the admittance matrix and classical linear power flow models under uncertain network parameters; for example, probabilistic line contingencies. Our proposed approach…
Renewable energy sources such as wind and solar have received much attention in recent years and large amount of renewable generation is being integrated to the electricity networks. A fundamental challenge in power system operation is to…
The optimal power flow (OPF) problem is one of the most fundamental problems in power system operations. The non-linear alternating current (AC) power flow equations that model different physical laws (together with operational constraints)…
Optimization is widely used to determine the physical and financial exchange of wholesale electricity in organized markets. Guarantees of solution optimality and feasibility rest largely on convexity, which is not in general a…
This paper investigates the impact of the changes in the demand of power systems on the quality of the solution procured by the convex relaxation methods for the AC optimal power flow (ACOPF) problem. This investigation needs various…
Power systems modeling and planning has long leveraged mathematical programming for its ability to provide optimality and feasibility guarantees. One feature that has been recognized in the optimization literature since the 1970s is the…
Stepwise controllable devices, such as switched capacitors or stepwise controllable loads and generators, transform the nonconvex AC optimal power flow (AC-OPF) problem into a nonconvex mixed-integer (MI) programming problem which is…
The Optimal Power Flow (OPF) problem is central to the reliable and efficient operation of power systems, yet its non-convex nature poses significant challenges for finding globally optimal solutions. While convex relaxation techniques such…
We investigate the distributed DC-Optimal Power Flow (DC-OPF) problem for a dynamic and uncertain environment. The unpredictable supply of renewable resources and varying prices of the electricity market are a few factors responsible for…
As the penetration of wind generation increases, the uncertainty it brings has imposed great challenges to power system operation. To cope with the challenges, tremendous research work has been conducted, among which two aspects are of most…
The increasing renewable penetration introduces significant uncertainty in power system operations. At the same time, the existing transmission grid is often already congested, and urgently needed reinforcements are frequently delayed due…
The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial,…
The increasing deployment of end use power resources in distribution systems created active distribution systems. Uncontrolled active distribution systems exhibit wide variations of voltage and loading throughout the day as some of these…
The power flow equations, which relate power injections and voltage phasors, are at the heart of many electric power system computations. While Newton-based methods typically find the "high-voltage" solution to the power flow equations,…
In the present paper, several types of efficiency conditions are established for vector optimization problems with cone constraints affected by uncertainty, but with no information of stochastic nature about the uncertain data. Following a…
In this paper, we discuss our approach and algorithmic framework for solving large-scale security constrained optimal power flow (SCOPF) problems. SCOPF is a mixed integer non-convex optimization problem that aims to obtain the minimum…
The conventionally independent power, water, and heating networks are becoming more tightly connected, which motivates their joint optimal energy scheduling to improve the overall efficiency of an integrated energy system. However, such a…
The convex restriction of the power flow feasible sets identifies the convex subset of power injections where the solution for power flow is guaranteed to exist and satisfy the operational constraints. In contrast to convex relaxations, the…
Linear approximations of the AC power flow equations are of great significance for the computational efficiency of large-scale optimal power flow (OPF) problems. Put differently, the feasibility of the obtained solution is essential for…
This paper addresses the distributed optimal frequency control of multi-area power system with operational constraints, including the regulation capacity of individual control area and the power limits on tie-lines. Both generators and…