Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.

Optimal power flow: a bibliographic survey I

Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey (this article) examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.

Optimal power flow: A bibliographic survey II non-deterministic and hybrid methods

This paper presents a hybrid particle swarm optimization algorithm (HPSO) as a modern optimization tool to solve the discrete optimal power flow (OPF) problem that has both discrete and continuous optimization variables. The problem is classified as constrained mixed integer nonlinear programming with multimodal characteristics. The objective functions considered are the system real power losses, fuel cost, and the gaseous emissions of the generating units. Two different types of fuel cost functions are considered in this study, namely the conventional quadratic function and the augmented quadratic function to introduce more accurate modeling that incorporates the valve loading effects. The latter model presents nondifferentiable and nonconvex regions that challenge most gradient-based optimization algorithms. The proposed algorithm makes use of the PSO, known for its global searching capabilities, to allocate the optimal control settings while Newton-Raphson algorithm minimizes the mismatch of the power flow equations. A hybrid inequality constraint handling mechanism that preserves only feasible solutions without the need to augment the original objective function is incorporated in the proposed approach. To demonstrate its robustness, the proposed algorithm was tested on the IEEE 30-bus system with six generating units. Several cases were investigated to test and validate the consistency of detecting optimal or near optimal solution for each objective. Results are compared to solutions obtained of MATPOWER software outcomes that employs sequential quadratic programming algorithm to solve the OPF. The impact of the proposed inequality constraint handling method in improving the HPSO performance is illustrated. Furthermore, a study of HPSO parameters tuning with regard to the OPF problem is presented and analyzed.

Hybrid Particle Swarm Optimization Approach for Solving the Discrete OPF Problem Considering the Valve Loading Effects

Applications of computational intelligence techniques for solving the revived optimal power flow problem

Optimal power flow (OPF) is one of the most important optimization problems in the energy industry. In its simplest form, OPF attempts to find the optimal power that the generators within the grid have to produce to satisfy a given demand. Optimality is measured with respect to the cost that each generator incurs in producing this power. The OPF problem is non-convex due to the sinusoidal nature of electrical generation and thus is difficult to solve. Using small angle approximations leads to a convex problem known as DC OPF, but this approximation is no longer valid when power grids are heavily loaded. Many approximate solutions have been since put forward, but these do not scale to large power networks. In this paper, we propose using graph neural networks (which are localized, scalable parametrizations of network data) trained under the imitation learning framework to approximate a given optimal solution. While the optimal solution is costly, it is only required to be computed for network states in the training set. During test time, the GNN adequately learns how to compute the OPF solution. Numerical experiments are run on the IEEE-30 and IEEE-118 test cases.

Optimal Power Flow Using Graph Neural Networks

A modified particle swarm optimization (MPSO) algorithm is presented. In the new algorithm, particles not only studies from itself and the best one but also from other individuals. By this enhanced study behavior, the opportunity to find the global optimum is increased and the influence of the initial position of the particles is decreased At last, the method adopting MPSO algorithm to solve the optimal power flow problem is given. The numeric simulation for a 5-bus system shows that this algorithm is feasible to solve optimal power flow problem.

Cui-Ru Wang

Papers

A modified particle swarm optimization algorithm and its application in optimal power flow problem

Solving traveling salesman problem based on improved particle swarm optimization algorithm