Metaheuristic Methods for Optimal Power Flow: A Comparative Analysis of Various Objective Functions

A novel hybrid gravitational search and pattern search algorithm for load frequency control of nonlinear power system

—This article presents a hybrid algorithm based on the particle swarm optimization and gravitational search algorithms for solving optimal power flow in power systems. The proposed optimization technique takes advantages of both particle swarm optimization and gravitational search algorithms by combining the ability for social thinking in particle swarm optimization with the local search capability of the gravitational search algorithm. Performance of this approach for the optimal power flow problem is studied and evaluated on standard IEEE 30-bus and IEEE 118-bus test systems with different objectives that reflect fuel cost minimization, voltage profile improvement, voltage stability enhancement, power loss reduction, and fuel cost minimization with consideration of the valve point effect of generation units. Simulation results show that the hybrid particle swarm optimization–gravitational search algorithm provides an effective and robust high-quality solution of the optimal power flow problem.

Voltage enhancement and loss minimization in a radial network through optimal capacitor sizing and placement based on Crow Search Algorithm

This paper proposes the implementation of various metaheuristic algorithms in solving the optimal power flow (OPF) with the presence of Flexible AC Transmission System (FACTS) devices in the power system. OPF is one of the well-known problems in power system operations and with the inclusion of the FACTS devices allocation problems into OPF will make the solution more complex. Thus, seven metaheuristic algorithms: Barnacles Mating Optimizer (BMO), Marine Predators Algorithm (MPA), Moth–Flame Optimization (MFO), Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Teaching–Learning-Based Optimization (TLBO) and Heap-Based Optimizer (HBO) are used to solve two objective functions: power loss and cost minimizations. These algorithms are selected from the different metaheuristics classification groups, where the implementation of these algorithms into the said problems will be tested on the modified IEEE 14-bus system. From the simulation results, it is suggested that TLBO and HBO perform better compared to the rest of algorithms.

In this study, artificial bee colony, wind driven optimization and gravitational search algorithms are employed in order to solve the optimal power flow problem. The proposed optimization approaches are tested on the standard IEEE 9-bus power system with the objective functions of voltage deviation reduction, active power loss minimization and fuel cost minimization. In addition, the calculation time spent is compared. The simulation results show that, on the one hand, the proposed optimization approaches have the similar potentials in the minimization of active power losses and fuel costs. On the other hand, wind driven optimization algorithm ensures more consistent results than the other ones in the reduction of voltage deviation and in terms of the calculation time spent.

The automatic load frequency control for multi-area power systems has been a challenging task for power system engineers. The complexity of this task further increases with the incorporation of multiple sources of power generation. For multi-source power system, this paper presents a new heuristic-based hybrid optimization technique to achieve the objective of automatic load frequency control. In particular, the proposed optimization technique regulates the frequency deviation and the tie-line power in multi-source power system. The proposed optimization technique uses the main features of three different optimization techniques, namely, the Firefly Algorithm (FA), the Particle Swarm Optimization (PSO), and the Gravitational Search Algorithm (GSA). The proposed algorithm was used to tune the parameters of a Proportional Integral Derivative (PID) controller to achieve the automatic load frequency control of the multi-source power system. The integral time absolute error was used as the objective function. Moreover, the controller was also tuned to ensure that the tie-line power and the frequency of the multi-source power system were within the acceptable limits. A two-area power system was designed using MATLAB-Simulink tool, consisting of three types of power sources, viz., thermal power plant, hydro power plant, and gas-turbine power plant. The overall efficacy of the proposed algorithm was tested for two different case studies. In the first case study, both the areas were subjected to a load increment of 0.01 p.u. In the second case, the two areas were subjected to different load increments of 0.03 p.u and 0.02 p.u, respectively. Furthermore, the settling time and the peak overshoot were considered to measure the effect on the frequency deviation and on the tie-line response. For the first case study, the settling times for the frequency deviation in area-1, the frequency deviation in area-2, and the tie-line power flow were 8.5 s, 5.5 s, and 3.0 s, respectively. In comparison, these values were 8.7 s, 6.1 s, and 5.5 s, using PSO; 8.7 s, 7.2 s, and 6.5 s, using FA; and 9.0 s, 8.0 s, and 11.0 s using GSA. Similarly, for case study II, these values were: 5.5 s, 5.6 s, and 5.1 s, using the proposed algorithm; 6.2 s, 6.3 s, and 5.3 s, using PSO; 7.0 s, 6.5 s, and 10.0 s, using FA; and 8.5 s, 7.5 s, and 12.0 s, using GSA. Thus, the proposed algorithm performed better than the other techniques.

Evolutionary algorithms are among the most powerful algorithms for optimization, Firefly algorithm (FA) is one of them that inspired by nature. It is an easily implementable, robust, simple and flexible technique. On the other hand, Integration of this algorithm with other algorithms, can be improved the performance of FA. Particle Swarm Optimization (PSO) and Gravitational Search Algorithm (GSA) are suitable and effective for integration with FA. Some method and operation in GSA and PSO can help to FA for fast and smart searching. In one version of the Gravitational Search Algorithm (GSA), selecting the K-best particles with bigger mass, and examining its effect on other masses has a great help for achieving the faster and more accurate in optimal answer. As well as, in Particle Swarm Optimization (PSO), the candidate answers for solving optimization problem, are guided by local best position and global best position to achieving optimal answer. These operators and their combination with the firefly algorithm (FA) can improve the performance of the search algorithm. This paper intends to provide models for improvement firefly algorithm using GSA and PSO operation. For this purpose, 5 scenarios are defined and then, their models are simulated using MATLAB software. Finally, by reviewing the results, It is shown that the performance of introduced models are better than the standard firefly algorithm.

In this paper a simple and efficient heuristic search method based on the artificial bee colony (ABC) algorithm is presented and used for the optimal power flow (OPF) problem in power systems with static VAR compensator (SVC) devices. The total generation cost of a power system with SVC devices (which improve the voltage stability at load buses) is optimally minimized with the use of ABC. The ABC, which is based on the foraging behavior of honey bees searching for the best food source, is a recently proposed optimization algorithm. The performance of the presented ABC algorithm was tested and verified on the IEEE 11-bus and IEEE 30-bus power systems by comparing it with several other optimization methods. Furthermore, ABC is used not only for optimizing the total generation cost and active power loss, but also for improving the voltage stability of the 22-bus power system in Turkey. Our results illustrate that ABC can successfully be used to solve nonlinear problems related to power systems.

Optimal power flow (OPF), a mathematical programming problem extending power flow relationships, is one of the essential tools in the operation and control of power grids. To name but a few, the primary goals of OPF are to meet system demand at minimum production cost, minimum emission, and minimum voltage deviation. Being at the heart of power system problems for half a century, the OPF can be split into two significant categories, namely optimal active power flow (OAPF) and optimal reactive power flow (ORPF). The OPF is spontaneously a complicated non-linear and non-convex problem; however, it becomes more complex by considering different constraints and restrictions having to do with real power grids. Furthermore, power system operators in the modern-day power networks implement new limitations to the problem. Consequently, the OPF problem becomes more and more complex which can exacerbate the situation from mathematical and computational standpoints. Thus, it is crucially important to decipher the most appropriate methods to solve different types of OPF problems. Although a copious number of mathematical-based methods have been employed to handle the problem over the years, there exist some counterpoints, which prevent them from being a universal solver for different versions of the OPF problem. To address such issues, innovative alternatives, namely heuristic algorithms, have been introduced by many researchers. Inasmuch as these state-of-the-art algorithms show a significant degree of convenience in dealing with a variety of optimization problems irrespective of their complexities, they have been under the spotlight for more than a decade. This paper provides an extensive review of the latest applications of heuristic-based optimization algorithms so as to solve different versions of the OPF problem. In addition, a comprehensive review of the available methods from various dimensions is presented. Reviewing about 200 works is the most significant characteristic of this paper that adds significant value to its exhaustiveness.

Optimal Power Flow (OPF) is one of most important aspect in power system operation and control. It is a non linear optimization problem based on minimization an objective function such as the active power losses, fuel cost, voltage deviation, voltage stability, reliability evaluation,…etc. Transient stability analysis is an important concept to determine whether the system is stable or not when a heavy disturbance such as the fault or loss of generation or a sudden large increased in the load,…etc occur in the system. In this article the transient stability according to the fault occurrence are used as a constraint in the optimal power flow, where minimization a three objective function of the active power losses, the fuel cost of thermal generation units and the voltage deviation at the load buses separately for each one can improve the transient stability and keep all the generators in the synchronization system. Particle Swarm Optimization PSO of an artificial intelligence optimization techniques has been used for this purpose. Minimization the objective function can be satisfied by choosing an optimal control variables from their constraints keeping the state variables in their limits. The control variables in this article are the generator voltage magnitude, the transformer tap changer and the generator active power except the slack generator while the state variables are the stability system based on increasing the clearing time of the circuit breaker, the slack generator active power, the generator reactive power and the magnitude of the load voltage. Increasing the clearing time of the circuit breaker leads to increase the maximum value of the generator rotor angle and go towards the instability system. The maximum clearing time that keep the system stable is called the Critical Clearing Time TCC. This article used the Optimal Power Flow with Transient Stability as a constraint to increase the Critical Clearing Time TCC with stable system. The proposed algorithm has been tested on the two systems of IEEE 9 bus and IEEE 30 bus and compare the result with other reference. The implementation of this work are programming by the author using matlab software.

Constructal T-shaped porous fins transfer better heat compared to the rectangular counterparts by improving the heat flow through the low resistive links. This type of fins can be used in aerospace engines which demand faster removal of heat without adding extra weight of the overall assembly. Here, in this study, three powerful nature-inspired metaheuristic algorithms such as particle swarm optimization, gravitational search algorithm, and Firefly algorithm have been used to optimize the dominant thermo physical as well as geometric parameters which are responsible for transferring heat at faster rates from the fin body satisfying a volume constraint. The temperature distribution along the stem and the flange has been plotted, and the effect of important parameters on the efficiency has been determined. Three different volumes are selected for the analysis, and the results have shown marked improvement in the optimized heat transfer rate. Particle swarm optimization has reported an increase of 0.81%, while Firefly algorithm reports 0.83% improvement as we increase the fin volume from 500 to 1000 and 0.19% (by PSO) and 0.4% (by FA) as the volume increases from 1000 to 1500. The paper also presents a scheme of reducing the computational effort required by the algorithms to converge around the optimum point. While a reduction of 14.36% computational effort has been achieved in particle swarm optimization’s convergence time, Firefly algorithm took 24.64% less time to converge at the near-optimum point. While particle swarm optimization has converged at better optimal points compared to Firefly algorithm and Gravitational search algorithm, Gravitational search algorithm has outperformed the two algorithms in terms of computational time. Gravitational search algorithm took 61.72 and 29.33% less time to converge as compared to particle swarm optimization and Firefly algorithm, respectively.

In this paper, a hybrid population based meta-heuristic search algorithm named as gravitational search algorithm (GSA) combined with particle swarm optimization (PSO) (GSA–PSO) is proposed for the optimal designs of two commonly used analog circuits, namely, complementary metal oxide semiconductor (CMOS) differential amplifier circuit with current mirror load and CMOS two-stage operational amplifier circuit. PSO and GSA are simple, population based robust evolutionary algorithms but have the problem of suboptimality, individually. The proposed GSA–PSO based approach has overcome this disadvantage faced by both the PSO and the GSA algorithms and is employed in this paper for the optimal designs of two amplifier circuits. The transistors’ sizes are optimized using GSA–PSO in order to minimize the areas occupied by the circuits and to improve the design/performance parameters of the circuits. Various design specifications/performance parameters are optimized to optimize the transistor’s sizes and some other design parameters using GSA–PSO. By using the optimal transistor sizes, Simulation Program with Integrated Circuit Emphasis simulation has been carried out in order to show the performance parameters. The simulation results justify the superiority of GSA–PSO over differential evolution, harmony search, artificial bee colony and PSO in terms of convergence speed, design specifications and performance parameters of the optimal design of the analog CMOS amplifier circuits. It is shown that GSA–PSO based design technique for each amplifier circuit yields the least MOS area, and each designed circuit is shown to have the best performance parameters like gain, power dissipation etc., as compared with those of other recently reported literature. Still the difficulties and challenges faced in this work are proper tuning of control parameters of the algorithms GSA and PSO, some conflicting design/performance parameters and design specifications, which have been partially overcome by repeated manual tuning. Multi-objective optimization may be the proper alternative way to overcome the above difficulties.

In modern power system operation and planning, reactive power is an important part of power system operation to supply electrical load such as an electric motor. However, the reactive current that flows from the generator to load demand can cause voltage drop and active power loss. Hence, it is essential to install a compensating device such as a shunt capacitor close to the load bus to reduce the total power loss of the transmission line and improve the voltage stability of the system. This paper presents the application of a genetic algorithm (GA), particle swarm optimization (PSO), and artificial bee colony (ABC)) to obtain the optimal size of the shunt capacitor where those capacitors are located on the critical bus. To examine the efficacy of the proposed algorithm, Java-Madura-Bali (JAMALI) 500kV power system grid is used as the test system. From the simulation results, the use of PSO and ABC algorithms to obtain the sizing of the capacitor’s capacity can reduce the power loss of around 15.873 MW. Moreover, a different result is showed by the GA approach where the power loss in the JAMALI 500kV power grid can be compressed only up to 15.54 MW or 11.38% from the power system operation without a shunt capacitor. The three soft computing techniques could also maintain the voltage profile within 1.05 p.u and 0.95 p.u.

A novel multi-objective hybrid particle swarm and salp optimization algorithm for technical-economical-environmental operation in power systems

In order to solve the optimal power flow (OPF) problem, a unique algorithm based on a search and rescue method is applied in this study. For the OPF problem under three objective functions, the SAR offers a straightforward and reliable solution. The three objective functions are used to minimize the fuel cost, power loss and voltage deviation as a single objective function. The OPF problem for benchmark test system, including the IEEE-14 bus, IEEE-30 bus, and IEEE-57 bus, are solved by the Search and Rescue algorithm (SAR) under specific objective functions that are determined by the operational and economic performance indices of the power system. To demonstrate the efficacy and possibilities of the SAR algorithm, SAR is contrasted with alternative optimization techniques such as harmony search algorithm, gradient method, adaptive genetic algorithm, biogeography-based optimization, Artificial bee colony, gravitational search algorithm, particle swarm optimization, Jaya algorithm, enhanced genetic algorithm, modified shuffle frog leaping algorithm, practical swarm optimizer, Moth flam optimizer, whale and moth flam optimizer, grey wolf optimizer, cheap optimization algorithm and differential evolution algorithm. The value of minimum power losses based on SAR technique is equal to 0.459733441487247 MW for IEEE-14 bus. The value of minimum total fuel cost based on SAR technique is equal to 8051.12225602148 $/h for IEEE-14 bus. The value of minimum voltage deviation based on SAR technique is equal to 0.0357680148269292 for IEEE-14 bus. The value of minimum power losses based on SAR technique is equal to 2.71286428848434 MW for IEEE-30 bus. The value of minimum total fuel cost based on SAR technique is equal to 798.197578585806 $/h for IEEE-30 bus. The value of minimum voltage deviation based on SAR technique is equal to 0.0978069572088536 for IEEE-30 bus. The value of minimum total fuel cost based on SAR technique is equal to 38017.7691758245 $/h for IEEE-57 bus. The acquired results for the OPF compared to all competitor algorithms in every case of fitness function demonstrate the superiority of the SAR method.