Voltage stability enhancement based on particle swarm optimization and LP technique

Reactive power optimization is a mixed integer nonlinear programming problem where metaheuristics techniques have proven suitable for providing optimal solutions. Optimal reactive power dispatch (ORPD) is a key instrument to achieve secure and economic operation of power systems. Due to complex characteristics of ORPD, heuristic optimization has become an effective solver. In this paper, swarm and evolutionary algorithm have been applied for reactive power optimization. A two-phase hybrid particle swarm optimization (PSO) approach is used to solve optimal reactive power dispatch (ORPD) problem has been presented in this paper. In this hybrid approach, PSO is used to explore the optimal region and direct search is used as local optimization technique for finer convergence. This paper also presents a particle swarm optimization for reactive power and voltage control considering voltage stability. The proposed method determines a control strategy with continuous and discrete control variables such as AVR operating values, OLTC tap positions, and the amount of reactive power compensation equipment. A novel heuristic optimization algorithm namely the Mean-Variance Mapping Optimization (MVMO) is proposed to handle the ORPD problem. The objective of the proposed PSO is to minimize the total support cost from generators and reactive compensators. It is achieved by maintaining the whole system power loss as minimum thereby reducing cost allocation.

The increased integration of renewable energies (REs) raised the uncertainties of power systems and has changed the approach to dealing with power system challenges. Hence, the uncertain nature of all the power system variables needs to be considered while dealing with the optimal planning and operation of modern power systems. This paper presents a probabilistic optimal active and reactive power dispatch (POARPD) based on the point estimate method (PEM), considering the uncertainties associated with load variation and wind power generation. In the POARPD, the deterministic optimal active and reactive power dispatch (OARPD) is performed in two stages, which gives a deterministic two-stage OARPD (TSOARPD). The objectives of TSOARPD are the operating cost (OC) minimization in stage 1 and voltage stability (VS) maximization in stage 2, whereas the VS is improved by maximizing the system’s reactive power reserve (RPR). In this paper, instead of using multiobjective optimal power flow, this TSOARPD is used to give more importance to VS when the system is substantially loaded. The POARPD problem is solved using PEM for modified IEEE-9 bus and standard IEEE-30 bus test systems by considering the correlation between the loads. The results are compared with Monte Carlo simulation (MCS). While solving POARPD, the voltage-dependent load model is used to account for the real-time voltage dependency of power system loads. This paper discusses the detailed procedure of solving POARPD by considering correlation and the increased nonlinearities by giving more importance to VS when the system is heavily loaded.

Voltage stability enhancement is obtained by adjusting the control variables to nearer optimal solutions for the selected objective function. This paper presents the biological swarm behaviour of a bird flocking or fish schooling for solving the optimal reactive power dispatch (ORPD) problem using PSO algorithm. The main idea of this paper is to minimize the sum of the square of voltage deviations at load buses using fast decoupled load flow (FDLF) method and sensitivity parameters relating control and dependent variables. The on-load tap changing transformers (OLTC), Generator exciters, Static VAR Compensators (SVC) are used as control variables for improvement of system parameters like voltage deviation (V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> ), L-index and real power loss. The effectiveness of the proposed method is demonstrated on IEEE New England 39-bus power system for near optimal solutions. The performance of the proposed method is compared with conventional optimization technique and presented for illustration purpose.

The paper presents particle swarm optimization (PSO) with dynamic search strategies based on landscape modality estimation. In order to control search strategies, we introduce landscape modality estimation method using correlation coefficients between rankings of search points to PSO. This estimation method utilizes relationship between fitness and distance to a reference point to classify whether the landscape modality is uni-modal or multi-modal landscape. Our proposal method can switch the strategies properly according to landscape modality of an objective function. To confirm the search ability of the proposal method, we conducted experiments using standard benchmark functions. The experimental results show that the proposal method outperforms other PSO variants.

Reactive power dispatch (RPD) is one of the important tasks in the operation and control of power system. This paper presents a differential evolution (DE)-based approach for solving optimal reactive power dispatch for voltage stability enhancement. The monitoring methodology for voltage stability is based on the L-index of load buses. The objective is to minimize the sum of squares of the L-indices subjected to limits on generator real and reactive power outputs, bus voltages, transformer taps and shunt power control devices such as SVCs. The proposed algorithm has been applied to IEEE 30-bus system to find the optimal settings of reactive power control variables. The optimal reactive power dispatch results are obtained using DE and are compared with and without flexible AC transmission system (FACTS) device such as static synchronous series compensator (SSSC). It is shown that the objective function value is less with the consideration of SSSC device.

Optimal reactive power dispatch (ORPD) is carried out to reduce losses, to improve the voltage profile and voltage stability in a power system. In recent years, several evolutionary computing based optimization techniques to solve optimal reactive power dispatch problem has been proposed. These techniques include genetic algorithm (GA), artificial bee colony (ABC), particle swarm optimization (PSO) and differential evolution (DE) etc. The ORPD problem has been solved as a single objective as well as multi-objective optimization problem using these techniques. This paper presents a brief literature review of the work carried out by the various researchers in this field by using evolutionary computing based techniques.

In this paper, a hybrid algorithm based on Particle Swarm Optimization (PSO) and Cuckoo Search (CS) is detailed with the application of Optimal Reactive Power Dispatch (ORPD). The Levy flight and the elimination mechanism are introduced to the traditional PSO algorithm. Benchmark tests show that the hybrid algorithm has better optimization efficiency than original PSO and CS algorithms. In the application of the ORPD, the fitness function is the total real loss of the distribution network. Inequality constrains are handled by the limitation of searching space. The simulation results on the IEEE-14 bus standard system and a real distribution network illustrate the feasibility and effectiveness of the algorithm. The total real power losses decrease 7.1% and 8% in two applications. The mathematical tests and engineering applications demonstrate that the hybrid algorithm has better searching ability than the standard PSO algorithm, and it is suitable for the solution of ORPD problem.

This paper presents an application of Artificial Neural Network (ANN) algorithm for improving power system voltage stability. The training data is obtained by solving several normal and abnormal conditions using the Linear Programming technique. The selected objective function gives minimum deviation of the reactive power control variables, which leads to the maximization of minimum Eigen value of load flow Jacobian. The considered reactive power control variables are switchable VAR compensators, OLTC transformers and excitation of generators. The method has been implemented on a modified IEEE 30-bus test system. The results obtain from the test clearly show that the trained neural network is capable of improving the voltage stability in power system with a high level of precision and speed.

This paper presents an algorithm to solve the multi-objective Optimal Reactive Power Dispatch (ORPD) problem in an unbalanced bus system. Unlike the traditional ORPD problem, loadability maximization, voltage profile enhancement, loss minimization, and ATC enhancement are achieved under unbalanced conditions. Here, ORPD is effectuated through determining the optimal location and size of the UPFC using a hybrid version of GA and FF. Experimental results on the benchmark IEEE test bus systems demonstrate the ORPD performance of the proposed algorithm over the traditional algorithms, under unbalanced conditions. Moreover, the proposed algorithm is proved for its performance in maintaining a better trade-off among multiple objectives, even under overloading conditions. The analysis also includes an investigation on the sensitivity of the algorithm against the overloading conditions of the bus system. Finally, the experimental results confirm that the proposed algorithm is superior to the conventional algorithms like GA, PSO, a hybrid version of GA-PSO, and the traditional FF algorithm.Abbreviations: ATC: Available Transfer Capability; CMAES: Covariance Matrix-Adapted Evolutionary Strategy; CPF: Continuation Power Flow; DE: Differential Evolution; FACTS: Flexible AC Transmission System; FF: Firefly Algorithm; GA: Genetic Algorithm; GSA: Gravitational Search Algorithm; KHA: Krill Herd Algorithm; LSI: Loss Sensitivity Index; NSGA-II: Non-Dominated Sorting Genetic Algorithm-II; OKHA: Oppositional Krill Herd Algorithms; ORPD: Optimal Reactive Power Dispatch; PSO: Particle Swarm Optimization; UPFC: Unified Power Flow Controller; VDI: Voltage Deviation Index

The stochastic nature of the wind and the highly non linear transform from wind speed to electrical energy makes it more difficult to determine how to dispatch the power in order to guarantee both operational cost reduction and power system security. From a network constraint perspective for the economic dispatch problem one of the factors to be accounted for is voltage security, which impacts both active and/or reactive power dispatch. In this paper, an Optimal Reactive Power Dispatch based on Particle Swarm Optimization (PSO) using Graph Theory has been proposed to overcome the above-mentioned problem. Graph Theory has been used since it becomes very useful in cases of fault detection and isolation or to shed unbalanced nodes in case of excessive or insufficient supply. Simulation studies on the modified IEEE-14 Bus System have been conducted to show the effectiveness of the proposed method.

This paper introduces a self adaptive differential evolution (SADE) and self-tuning Hybrid differential Evolution (HDE) methods for dealing with optimal reactive power dispatch aiming at power loss reduction. The optimum reactive power dispatch of power systems is to allocate reactive power control variables so that the objective function composed of power losses is minimized and the prescribed voltage limits are satisfied. The proposed method determines the optimum settings of reactive power control variables such as, generator excitation, tap changing transformers, and shunt compensation that reduces the power loss, while maintaining the voltage stability. IEEE 14-bus test system from the literature is used to exemplify the performance of the proposed methods. Numerical results show that the proposed methods are better methods than those reported in the literature.

This study addresses a shuffled frog leaping algorithm for solving the multi-objective reactive power dispatch problem in a power system. Optimal Reactive Power Dispatch (ORPD) is formulated as a nonlinear, multi-modal and mixed-variable problem. The intended technique is based on the minimization of the real power loss, minimization of voltage deviation and maximization of the voltage stability margin. Generator voltages, capacitor banks and tap positions of tap changing transformers are used as optimization variables of this problem. A memetic meta-heuristic named as shuffled frog-leaping algorithm is intended to solve multi-objective optimal reactive power dispatch problems considering voltage stability margin and voltage deviation. The Shuffled Frog-Leaping Algorithm (SFLA) is a population-based cooperative search metaphor inspired by natural memetics. The algorithm contains elements of local search and global information exchange. The most important benefit of this algorithm is higher speed of convergence to a better solution. The intended method is applied to ORPD problem on IEEE 57 bus power systems and compared with two versions of differential evolutionary algorithm. The simulation results show the effectiveness of the intended method.

Secure and economical operation of distribution networks needs the management of reactive power resources. Optimal Reactive Power Dispatch (ORPD) optimally manages the reactive power scheduling of generators and distribution generations as well as the Reactive Power Compensation (RPC) devices. This paper investigates the effect of load models on the multi-objective ORPD problem in active distribution networks. Moreover, a modified Grey Wolf Optimizer (GWO), which is called in this paper as Civilized GWO (CGWO), is introduced to solve the ORPD problem. The proposed strategy including multi-objective function, various load models, DG’s reactive power, RPCs and the introduced CGWO, is tested on standard IEEE 33- and 69-bus distribution systems. The obtained results indicate the load models have significant impact on the cost function amount. Moreover, the performance of the proposed algorithm is evaluated using ten standard benchmark functions. The optimization results demonstrate the robustness of the introduced optimization algorithm and its ability in finding the better solutions compared to the Particle Swarm Optimization (PSO), Exchange Market Algorithm (EMA), and original GWO.

Gravitational Search Algorithm (GSA) is a heuristic method based on Newton’s law of gravitational attraction and law of motion. In this paper, to further improve the optimization performance of GSA, the memory characteristic of Particle Swarm Optimization (PSO) is employed in GSAPSO for searching a better solution. Besides, to testify the prominent strength of GSAPSO, GSA, PSO, and GSAPSO are applied for the solution of optimal reactive power dispatch (ORPD) of power system. Conventionally, ORPD is defined as a problem of minimizing the total active power transmission losses by setting control variables while satisfying numerous constraints. Therefore ORPD is a complicated mixed integer nonlinear optimization problem including many constraints. IEEE14-bus, IEEE30-bus, and IEEE57-bus test power systems are used to implement this study, respectively. The obtained results of simulation experiments using GSAPSO method, especially the power loss reduction rates, are compared to those yielded by the other modern artificial intelligence-based techniques including the conventional GSA and PSO methods. The results presented in this paper reveal the potential and effectiveness of the proposed method for solving ORPD problem of power system.

Solution of optimal reactive power dispatch of power systems using hybrid particle swarm optimization and imperialist competitive algorithms