Artificial bee colony algorithm for solving multi-objective optimal power flow problem

This paper presents a new and efficient method for solving optimal power flow (OPF) problem in electric power systems. In the proposed approach, artificial bee colony (ABC) algorithm is employed as the main optimizer for optimal adjustments of the power system control variables of the OPF problem. The control variables involve both continuous and discrete variables. Different objective functions such as convex and non-convex fuel costs, total active power loss, voltage profile improvement, voltage stability enhancement and total emission cost are chosen for this highly constrained nonlinear non-convex optimization problem. The validity and effectiveness of the proposed method is tested with the IEEE 9-bus system, IEEE 30-bus system and IEEE 57-bus system, and the test results are compared with the results found by other heuristic methods reported in the literature recently. The simulation results obtained show that the proposed ABC algorithm provides accurate solutions for any type of the objective functions.     

Optimal reactive power dispatch based on harmony search algorithm

This paper presents a harmony search algorithm for optimal reactive power dispatch (ORPD) problem. Optimal reactive power dispatch is a mixed integer, nonlinear optimization problem which includes both continuous and discrete control variables. The proposed algorithm is used to find the settings of control variables such as generator voltages, tap positions of tap changing transformers and the amount of reactive compensation devices to optimize a certain object. The objects are power transmission loss, voltage stability and voltage profile which are optimized separately. In the presented method, the inequality constraints are handled by penalty coefficients. The study is implemented on IEEE 30 and 57-bus systems and the results are compared with other evolutionary programs such as simple genetic algorithm (SGA) and particle swarm optimization (PSO) which have been used in the last decade and also other algorithms that have been developed in the recent years.     

Optimal power flow using differential evolution algorithm

This paper presents an efficient and reliable evolutionary-based approach to solve the optimal power flow (OPF) problem. The proposed approach employs differential evolution algorithm for optimal settings of OPF problem control variables. The proposed approach is examined and tested on the standard IEEE 30-bus test system with different objectives that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. The proposed approach results are compared with the results reported in the literature. The results show the effectiveness and robustness of the proposed approach.     

Optimal power flow using differential evolution algorithm

This paper presents an evolutionary-based approach to solve the optimal power flow (OPF) problem. The proposed approach employs differential evolution (DE) algorithm for optimal settings of OPF control variables. The proposed approach is examined and tested on the standard IEEE 30-bus test system with different objective functions that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. In addition, non-smooth piecewise quadratic cost function has been considered. The simulation results of the proposed approach are compared to those reported in the literature. The results demonstrate the potential of the proposed approach and show its effectiveness and robustness to solve the OPF problem for the systems considered.     

Differential search algorithm for solving multi-objective optimal power flow problem

In this paper, a simple and efficient nature inspired search method based on differential search algorithm (DSA) has been presented and used for optimal power flow (OPF) problem in power systems. By using the proposed DSA method, the power system parameters such as real power generations, bus voltages, load tap changer ratios and shunt capacitance values are optimized for the certain objective functions. Different types of single-objective and multi-objective functions on IEEE 9-bus, IEEE 30-bus and IEEE 57-bus power systems are used to test and verify the efficiency of the proposed DSA method. By comparing with several optimization methods, the results obtained by using the proposed DSA method are presented in detail. The results achieved in this work illustrate that the DSA method can successfully be used to solve the non-linear and non-convex problems related to power systems.     

Optimal power flow for a deregulated power system using adaptive real coded biogeography-based optimization

The optimization is an important role in the wide geographical distribution of electrical power market, finding the optimum solution for the operation and design of power systems has become a necessity with the increasing cost of raw materials, depleting energy resources and the ever growing demand for electrical energy. Using adaptive real coded biogeography-based optimization (ARCBBO), we present the optimization of various objective functions of an optimal power flow (OPF) problem in a power system. We aimed to determine the optimal settings of control variables for an OPF problem. The proposed approach was tested on a standard IEEE 30-bus system and an IEEE 57-bus system with different objective functions. Simulation results reveal that the proposed ARCBBO approach is effective, robust and more accurate than current methods of power flow optimization in literature.     

Combined heat and power economic dispatch by harmony search algorithm

The optimal utilization of multiple combined heat and power (CHP) systems is a complicated problem that needs powerful methods to solve. This paper presents a harmony search (HS) algorithm to solve the combined heat and power economic dispatch (CHPED) problem. The HS algorithm is a recently developed meta-heuristic algorithm, and has been very successful in a wide variety of optimization problems. The method is illustrated using a test case taken from the literature as well as a new one proposed by authors. Numerical results reveal that the proposed algorithm can find better solutions when compared to conventional methods and is an efficient search algorithm for CHPED problem.     

Multi-objective optimal reactive power dispatch using multi-objective differential evolution

This paper presents multi-objective differential evolution (MODE) to solve multi-objective optimal reactive power dispatch (MORPD) problem by minimizing active power transmission loss and voltage deviation and maximizing voltage stability while varying control variables such as generator terminal voltages, transformer taps and reactive power output of shunt VAR compensators. MODE has been tested on IEEE 30-bus, 57-bus and 118-bus systems. Numerical results for these three test systems have been compared with those acquired from strength pareto evolutionary algorithm 2 (SPEA 2).     

Transient stability constrained optimal power flow using oppositional krill herd algorithm

Transient stability constrained optimal power flow (TSCOPF) is becoming an effective tool for many problems in power systems since it simultaneously considers economy and dynamic stability of system operations. It is increasingly important because modern power systems tend to operate closer to the stability boundaries due to the rapid increase of electricity demand and the deregulation in power sector. TSCOPF is, however, a nonlinear optimization problem with both algebraic and differential equations which is difficult to solve even for small power network. In order to solve the TSCOPF problem efficiently, a relatively new optimization technique, named as krill herd algorithm (KHA), is employed in this paper. KHA simulates the herding behavior of krill swarms in response to specific biological and environmental processes to solve multi-dimensional, linear and nonlinear problems with appreciable efficiency. To accelerate the convergence speed and to improve the simulation results, opposition based learning (OBL) is also incorporated in the basic KHA method. The simulation results, obtained by the basic KHA method and the proposed oppositional KHA (OKHA) algorithm, are compared to those obtained by using some other recently developed methods available in the literature. In this paper, case studies conducted on 10 generator New England 39-bus system and 17 generator 162-bus system indicate that the proposed OKHA approach is much more, computationally, efficient than the other reported popular state-of-the-art algorithms including the basic KHA and the proposed method is found to be a promising tool to solve the TSCOPF problem of power systems.     

无功优化遗传算法中的潮流算法改进研究

分析了潮流计算的数学模型 ,介绍了快速解耦法求解潮流 ,提出了一些改进措施 ,借以避免每次潮流计算都要反复形成第一因子表的缺点 ,采取收敛精度可变的手段 ,可使无功优化计算时间下降 65 %左右     

Optimal power flow by BAT search algorithm for generation reallocation with unified power flow controller

Optimal power flow with generation reallocation is a suitable method for better utilization of the existing system. In recent years, Flexible AC Transmission System (FACTS) devices, have led to the development of controllers that provide controllability and flexibility for power transmission. Out of the FACTS devices unified power flow controller (UPFC) is a versatile device, capable of controlling the power system parameters like voltage magnitude, phase angle and line impedance individually or simultaneously. The main aim of this paper is to minimize real power losses in a power system using BAT search algorithm without and with the presence of UPFC. Minimization of real power losses is done by considering the power generated by generator buses, voltage magnitudes at generator buses and reactive power injection from reactive power compensators. The proposed BAT algorithm based Optimal Power Flow (OPF) has been tested on a 5 bus test system and modified IEEE 30 bus system without and with UPFC. The results of the system with and without UPFC are compared in terms of active power losses in the transmission line using BAT algorithm. The obtained results are also compared with Genetic algorithm (GA).     

Differential evolution algorithm for emission constrained economic power dispatch problem

In this paper, a differential evolution (DE) algorithm is developed to solve emission constrained economic power dispatch (ECEPD) problem. Traditionally electric power systems are operated in such a way that the total fuel cost is minimized regardless of emissions produced. With increased requirements for environmental protection, alternative strategies are required. The proposed algorithm attempts to reduce the production of atmospheric emissions such as sulfur oxides and nitrogen oxides, caused by the operation of fossil-fueled thermal generation. Such reduction is achieved by including emissions as a constraint in the objective of the overall dispatching problem. A simple constraint approach to handle the system constraints is proposed. The performance of the proposed algorithm is tested on standard IEEE 30-bus system and is compared with conventional methods. The results obtained demonstrate the effectiveness of the proposed algorithm for solving the emission constrained economic power dispatch problem.     

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

Computational intelligence tools are attracting added attention in different research areas and research in power systems is not different. This paper provides an overview of major computational issues with regard to the optimal power flow (OPF). Then, it offers a brief summary of major computational intelligence tools. A detailed coverage of most OPF related research work that make use of modern computational intelligence techniques is presented next.     

Optimal power flow with emission and non-smooth cost functions using backtracking search optimization algorithm

Economic operation of electric energy generating systems is one of the prevailing problems in energy systems. In this paper, a new method called the Backtracking Search Optimization Algorithm (BSA) is proposed for solving the optimal power flow problem. This method is tested for 16 different cases on the IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus test systems. In addition to the traditional generating fuel cost, multi-fuels options, valve-point effect and other complexities have been considered. Furthermore, different objectives such as voltage profile improvement, voltage stability enhancement and emission reduction are considered. The obtained results are compared with those obtained using some well-known optimization algorithms. This comparison highlights the effectiveness of the BSA method for solving different OPF problems with complicated and non-smooth objective functions.     

Quasi oppositional harmony search algorithm based controller tuning for load frequency control of multi-source multi-area power system

This paper deals with the load frequency control (LFC) study of single-area and interconnected two-area power system having diversified power sources. The two areas considered in the present study are identical. Each area is having thermal, hydro and gas based power plants. Split-shaft model of gas turbine is used in the present work as one of the diversified generating unit for the purpose of LFC study. Optimal gains of the classical controllers (like integral controller, proportional–integral controller and proportional–integral–derivative (PID) controller, one installed at a time in the studied models) are obtained by using a novel music-inspired metaheuristic harmony search algorithm (HSA) which incorporates quasi opposition based learning technique for memory initialization and also for generation jumping. Single-area power system with diverse power sources is considered and its optimal transient performances are obtained and compared for step load perturbation. The same approach is further extended to two-area interconnected power system consisting of diverse power sources with nominal values of area input parameters. The performance of PID controller is found to be the best one for the studied power system models. It is also revealed that the performance of the interconnected two-area power system with AC–DC tie line is better in comparison to AC tie line.     

Multi-objective optimal reactive power flow including voltage security and demand profile classification

This paper proposes a method to optimize reactive power flow (ORPF) with regard to multiple objectives while maintaining system voltage security across a time-domain. Compromise programming is employed in the ORPF formulation, which is designed to minimize both losses and payment for the reactive power service in the framework of the UK daily balancing market. In coordination with ORPF, continuation power flow (CPF) is applied to evaluate and maintain the voltage security margin of the system. Prior to the optimisation procedure, the related control parameters can be grouped with the aid of a load classification method in order to simplify the control actions. During the optimisation, through the application of both ORPF and CPF, multi-objective optimisation can be achieved with voltage security at an acceptable level. The Ward and Hale 6-bus system and a 60-bus UK test system are presented to illustrate the application of the proposed modeling framework.     

Efficiency improvements in meta-heuristic algorithms to solve the optimal power flow problem

This paper presents three efficient approaches for solving the Optimal Power Flow (OPF) problem using the meta-heuristic algorithms. Mathematically, OPF is formulated as non-linear equality and inequality constrained optimization problem. The main drawback of meta-heuristic algorithm based OPF is the excessive execution time required due to the large number of load flows/power flows needed in the solution process. The proposed efficient approaches uses the concept of incremental power flow model based on sensitivities, and lower, upper bounds of objective function values. By using these approaches, the number of load flows/power flows to be performed are substantially, resulting in the solution speed up. The original advantages of meta-heuristic algorithms, such as ability to handle complex non-linearities, discontinuities in the objective function, discrete variables handling, and multi-objective optimization, are still available in the proposed efficient approaches. The proposed OPF formulation includes the active and reactive power generation limits, Valve Point Loading (VPL) effects and Prohibited Operating Zones (POZs) of generating units. The effectiveness of proposed approaches are examined on the IEEE 30, 118 and 300 bus test systems, and the simulation results confirm the efficiency and superiority of the proposed approaches over the other meta-heuristic algorithms. The proposed efficient approaches are generic enough to use with any type of meta-heuristic algorithm based OPF.     

A Multi-objective Shuffled Bat algorithm for optimal placement and sizing of multi distributed generations with different load models

In this paper a new and efficient hybrid multi-objective optimization algorithm is proposed for optimal placement and sizing of the Distributed generations (DGs) in radial distribution systems. A Multi-objective Shuffled Bat algorithm is proposed to evaluate the impact of DG placement and sizing for an optimal improvement of the distribution system with different load models. In this study, the ideal sizes and locations of DG units are found by considering the power losses, cost and voltage deviation as objective functions to minimize. Furthermore, the study is verified with voltage dependent load models like industrial, residential, commercial and mixed load models. The feasibility of the proposed technique is verified with the 33 bus distribution network and also the qualitative comparisons against a well-known technique, known as Non-dominated Sorting Genetic Algorithm II (NSGA-II) is done and results are presented.     

Chaotic artificial bee colony algorithm based solution of security and transient stability constrained optimal power flow

Due to the increase rapidly of electricity demand and the deregulation of electricity markets, the energy networks are usually run close to their maximum capacity to transmit the needed power. Furthermore, the operators have to run the system to ensure its security and transient stability constraints under credible contingencies. Security and transient stability constrained optimal power flow (STSCOPF) problem can be illustrated as an extended OPF problem with additional line loading and rotor angle inequality constraints. This paper presents a new approach for STSCOPF solution by a chaotic artificial bee colony (CABC) algorithm based on chaos theory. The proposed algorithm is tested on IEEE 30-bus test system and New England 39-bus test system. The obtained results are compared to those obtained from previous studies in literature and the comparative results are given to show validity and effectiveness of proposed method.