Modern Techniques for the Optimal Power Flow Problem: State of the Art

Abstract

Due to its significance in the operation of power systems, the optimal power flow (OPF) problem has attracted increasing interest with the introduction of smart grids. Optimal power flow developed as a crucial instrument for resource planning effectiveness as well as for enhancing the performance of electrical power networks. Transmission line losses, total generation costs, FACTS (flexible alternating current transmission system) costs, voltage deviations, total power transfer capability, voltage stability, emission of generation units, system security, etc., are just a few examples of objective functions related to the electric power system that can be optimized. Due to the nonlinear nature of optimal power flow problems, the classical approaches may become locked in local optimums, hence, metaheuristic optimization techniques are frequently used to solve these issues. The most recent optimization strategies used to solve optimal power flow problems are discussed in this paper as the state of the art (according to the authors, the most pertinent studies). The presented optimization techniques are grouped according to their sources of inspiration, including human-inspired algorithms (harmony search, teaching learning-based optimization, tabu search, etc.), evolutionary-inspired algorithms (differential evolution, genetic algorithms, etc.), and physics-inspired methods (particle swarm optimization, cuckoo search algorithm, firefly algorithm, ant colony optimization algorithm, etc.).

Three on Three Optimizer: A New Metaheuristic with Three Guided Searches and Three Random Searches

“…Equation (5) states that an agent is randomly selected among the population. Equation (6) states that the candidate of the third guided search is generated based on the movement of the corresponding agent relative to a randomly selected agent. Equation (7) states that the candidate of the first random search is generated based on the neighborhood search around the corresponding agent.…”

“…In the minimization, the optimal global solution is the solution with the lowest value. Some experimental parameters in the minimization, such as delay [1], total order completion time [2], idle time [2], tardiness cost and maintenance [3], project duration [4], energy consumption [5], transmission losses [6], and so on. On the other hand, in maximization, the optimal global solution is the solution with the highest value.…”

“…On the other hand, in maximization, the optimal global solution is the solution with the highest value. Some parameters in the maximization are profit [7], voltage stability [6], revenue [8], service level [9], and so on.…”

A Review of State-of-the-Art Techniques for Power Flow Analysis

“…The method is about substituting the curve y = f(x) for the tangent to the curve itself, starting from any point. After a number of iterations, the recurrence relation of the method is given by the following expression [6]. 𝑥 𝑛+1 = 𝑥 𝑛 -𝑓(𝑥 𝑛 )/ 𝑓′(𝑥 𝑛 ) However, when looking for a solution that is too far away from the considered interval, sometimes, Newton-Raphson may fail to converge [6].…”

“…Another limitation associated with these methods is that they may converge to a root different from the expected one or even diverge if the starting value is not close enough to the root. Therefore, the new state of the art methods of PF analysis is discovered to generally give better results than the classical methods and give the power the room to flow perfectly, fitting the new grid changes like Decentralized Generation (DG) [6]. These State-of-the-Art methods include Direct Matrix-Current Application (DM-CA) and Direct Matrix-Impedance Approximation (DM-IA) [5], Particle Swamp Optimization (PSO) Algorithm for Optimal PF Incorporating Wind Farm [6], Hybrid Firefly and Particle Swarm Optimization (HFPSO) [7], Artificial Neural Networks (ANNs) [8], Quasi-Oppositional Heap-Based Optimization (QOHBO) Technique [9], Three Stage Semi-Implicit Approach (3S-SIA) [10], Mann Iteration Process (MIP) For Ill-Conditioned System [11], Hybrid of Currentbalance and Power-balance formulation using Rectangular Coordinates (HCPB) [12], Modified Gauss-Seidel (MGS) [13], Batched Fast Decoupled Method [14], Newton-Raphson Load Flow Analysis in Power System Networks with STATCOM in New Approach [14] and so on.…”