Hybrid Osprey‐Salp Swarm Optimization Algorithm for Single and Multiobjective Optimal Power Flow in Smart Grids With Renewable Energy Integration

A memory-guided Jaya algorithm to solve multi-objective optimal power flow integrating renewable energy sources

Solution of optimal power flow (OPF) problem is very important for power system operation, planning and energy management. OPF analysis aims to find the optimal solution of system nonlinear algebraic equations with satisfying operational constraints. In this paper, a new and efficient technique called Jaya optimizer is comprehensively applied to solve the OPF problem in power systems. Jaya optimization algorithm is characterized with the movement toward the best solution and avoiding the trapping into local optima. Different frameworks are developed for solving the single- and multi-objective (two- to five-objective functions) OPF problems. These frameworks are developed to achieve the following objective functions: fuel cost minimization, voltage deviation minimization, voltage stability enhancement, power loss minimization and emission minimization. In the developed multi-objective OPF framework, Pareto concept is combined with Jaya optimization algorithm to obtain a set of non-dominated solutions, and then the best compromise solution is extracted using fuzzy set theory. The developed OPF frameworks are validate using two standard IEEE test systems with 23 studied cases. The results prove the effectiveness and superiority of the developed OPF frameworks compared with other well-known optimization algorithms.

Multi-objective optimal power flow considering the cost, emission, voltage deviation and power losses using multi-objective modified imperialist competitive algorithm

For the classical multi-objective optimal power flow (MOOPF) problem, only traditional thermal power generators are used in power systems. However, there is an increasing interest in renewable energy sources and the MOOPF problem using wind and solar energy has been raised to replace part of the thermal generators in the system with wind turbines and solar photovoltaics (PV) generators. The optimization objectives of MOOPF with renewable energy sources vary with the study case. They are mainly a combination of 2–4 objectives from fuel cost, emissions, power loss and voltage deviation (VD). In addition, reasonable prediction of renewable power is a major difficulty due to the discontinuous, disordered and unstable nature of renewable energy. In this paper, the Weibull probability distribution function (PDF) and lognormal PDF are applied to evaluate the available wind and available solar power, respectively. In this paper, an enhanced multi-objective mayfly algorithm (NSMA-SF) based on non-dominated sorting and the superiority of feasible solutions is implemented to tackle the MOOPF problem with wind and solar energy. The algorithm NSMA-SF is applied to the modified IEEE-30 and standard IEEE-57 bus test systems. The simulation results are analyzed and compared with the recently reported MOOPF results.

This paper compares the performance of three population-based algorithms including particle swarm optimization (PSO), evolutionary programming (EP), and genetic algorithm (GA) to solve the multi-objective optimal power flow (OPF) problem. The unattractive characteristics of the cost-based OPF including loss, voltage profile, and emission justifies the necessity of multi-objective OPF study. This study presents the programming results of the nine essential single-objective and multi-objective functions of OPF problem. The considered objective functions include cost, active power loss, voltage stability index, and emission. The multi-objective optimizations include cost and active power loss, cost and voltage stability index, active power loss and voltage stability index, cost and emission, and finally cost, active power loss, and voltage stability index. To solve the multi-objective OPF problem, Pareto optimal method is used to form the Pareto optimal set. A fuzzy decision-based mechanism is applied to select the best comprised solution. In this work, to decrease the running time of load flow calculation, a new approach including combined Newton–Raphson and Fast-Decouple is conducted. The proposed methods are tested on IEEE 30-bus test system and the best method for each objective is determined based on the total cost and the convergence values of the considered objectives. The programming results indicate that based on the inter-related nature of the objective functions, a control system cannot be recommended based on individual optimizations and the secondary criteria should also be considered.

In this work, an enhanced slime mould algorithm (ESMA) based on neighborhood dimension learning (NDL) search strategy is proposed for solving the optimal power flow (OPF) problem. Before using the proposed ESMA for solving the OPF problem, its validity is verified by an experiment using 23 benchmark functions and compared with the original SMA, and three other recent optimization algorithms. Consequently, the ESMA is used to solve a modified power flow model including both conventional energy, represented by thermal power generators (TPGs), and renewable energy represented by wind power generators (WPGs) and solar photovoltaic generators (SPGs). Despite the important role of WPGs and SPGs in reducing CO2 emissions, they represent a big challenge for the OPF problem due to their intermittent output powers. To forecast the intermittent output powers from SPGs and WPGs, Lognormal and Weibull probability density functions (PDFs) are used, respectively. The objective function of the OPF has two extra costs, penalty cost and reserve cost. The penalty cost is added to formulate the underestimation of the produced power from the WPGs and SPGs, while the reserve cost is added to formulate the case of overestimation. Moreover, to decrease CO2 emissions from TPGs, a direct carbon tax is added to the objective function in some cases. The uncertainty of load demand represents also another challenge for the OPF that must be taken into consideration while solving it. In this study, the uncertainty of load demand is represented by the normal PDF. Simulation results of ESMA for solving the OPF are compared with the results of the conventional SMA and two further optimization methods. The simulation results obtained in this research show that ESMA is more effective in finding the optimal solution of the OPF problem with regard to minimizing the total power cost and the convergence of solution.

The capabilities of four population based algorithms including multi-objective particle swarm optimization (MOPSO) improved non-dominated sorting genetic algorithm (NSGA-II) improved strength Pareto evolutionary algorithm (SPEA2) and modified Pareto envelop-based selection algorithm (PESA2) to acquire the solution for the multi-objective optimal power flow (Mo-OPF) problem are compared in this paper. For the Mo-OPF problem solution the non-dominated solution sets are created by Pareto optimal method. The best compromise solution among different solutions sets is chosen with the help of a fuzzy based decision mechanism. These operations are carried out on a standard IEEE 30-bus six-generator system subjected to system constraints and power flow balance. The load flow calculation is conducted with the help of iterative method. Total cost minimization of generation and total generation emission minimization are observed as desired function for optimal power flow (OPF) problem. In this paper above algorithms solve Mo-OPF problem on the basis of operational feasibility efficient operation operational speed and best optimal solution for the given objectives.

Optimal power flow (OPF) represents one of the most important issues in the electrical power system for energy management, planning, and operation via finding optimal control variables with satisfying the equality and inequality constraints. Several optimization methods have been proposed to solve OPF problems, but there is still a need to achieve optimum performance. A Slime Mould Algorithm (SMA) is one of the new stochastic optimization methods inspired by the behaviour of the oscillation mode of slime mould in nature. The proposed algorithm is characterized as easy, simple, efficient, avoiding stagnation in the local optima and moving toward the optimal solution. Different frameworks have been applied to achieve single and conflicting multi-objective functions simultaneously (Bi, Tri, Quad, and Quinta objective functions) for solving OPF problems. These objective functions are total fuel cost of generation units, real power loss on transmission lines, total emission issued by fossil-fuelled thermal units, voltage deviation at load bus, and voltage stability index of the whole system. The proposed algorithm SMA has been developed by incorporating it with Pareto concept optimization to generate a new approach, named the Multi-Objective Slime Mould Algorithm (MOSMS), to solve multi-objective optimal power flow (MOOPF) problems. Fuzzy set theory and crowding distance are the proposed strategies to obtain the best compromise solution and rank and reduce a set of non-dominated solutions, respectively. To investigate the performance of the proposed algorithm, two standard IEEE test systems (IEEE 30 bus IEEE 57 bus systems) and a practical system (Iraqi Super Grid High Voltage 400 kV) were tested with 29 case studies based on MATLAB software. The optimal results obtained by the proposed approach (SMA) were compared with other algorithms mentioned in the literature. These results confirm the ability of SMA to provide better solutions to achieve the optimal control variables.

Since the increases in electricity demand, environmental awareness, and power reliability requirements, solutions of single-objective optimal power flow (OPF) and multi-objective OPF (MOOPF) (two or three objectives) problems are inadequate for modern power system management and operation. Solutions to the many-objective OPF (more than three objectives) problems are necessary to meet modern power-system requirements, and an efficient optimization algorithm is needed to solve the problems. This paper presents a many-objective marine predators algorithm (MaMPA) for solving single-objective OPF (SOOPF), multi-objective OPF (MOOPF), and many-objective OPF (MaOPF) problems as this algorithm has been widely used to solve other different problems with many successes, except for MaOPF problems. The marine predators algorithm (MPA) itself cannot solve multi- or many-objective optimization problems, so the non-dominated sorting, crowding mechanism, and leader mechanism are applied to the MPA in this work. The considered objective functions include cost, emission, transmission loss, and voltage stability index (VSI), and the IEEE 30- and 118-bus systems are tested to evaluate the algorithm performance. The results of the SOOPF problem provided by MaMPA are found to be better than various algorithms in the literature where the provided cost of MaMPA is more than that of the compared algorithms for more than 1000 USD/h in the IEEE 118-bus system. The statistical results of MaMPA are investigated and express very high consistency with a very low standard deviation. The Pareto fronts and best-compromised solutions generated by MaMPA for MOOPF and MaOPF problems are compared with various algorithms based on the hypervolume indicator and show superiority over the compared algorithms, especially in the large system. The best-compromised solution of MaMPA for the MaOPF problem is found to be greater than the compared algorithms around 4.30 to 85.23% for the considered objectives in the IEEE 118-bus system.

This paper presents a multi-objective adaptive Clonal selection algorithm (MOACSA) for solving optimal power flow (OPF) problem. OPF problem is formulated as a non-linear constrained multi-objective optimization problem in which different objectives and various constraints have been considered. Fast elitist non-dominated sorting and crowding distance techniques have been used to find and manage the Pareto optimal front. Finally, a fuzzy based mechanism has been used to select a best compromise solution from the Pareto set. The proposed MOACS algorithm has been tested on IEEE 30-bus test system with different objectives such as cost, loss and L-index. Simulation studies are carried out under both normal load and load uncertainty conditions for multi-objective optimal power flow problem with different cases. The results obtained with normal load condition are also compared with fast non-dominated sorting genetic algorithm (NSGA-II), multi-objective harmony search algorithm (MOHS) and multi-objective differential evolutionary algorithm (MODE) methods which are available in the literature.

To overcome the insufficiency of standard bat algorithm in solving the non-convex optimal power flow (OPF) problems, a novel multi-objective modified bat algorithm (MOMBA) is proposed in this paper. The superiority of MOMBA algorithm with constrained Pareto-dominant approach (CPA), which improves the global-exploration ability and population-diversity by nonlinear inertia weight, can be validated by four multi-objective OPF simulation trials. In contrast to the classical penalty function approach (PFA), the effective CPA method can make each obtained power flow solution satisfy all system constraints. The testing cases considering the quadratic fuel cost, emission and active power loss, are implemented on the IEEE 30-bus and IEEE 57-bus systems, including three dual-objective and one triple-objective optimisations. Numerous results demonstrate that the suggested MOMBA algorithm can obtain well distributed Pareto front (PF) and effectively handle the multi-objective OPF problems.

In order to surmount the shortcomings of the standard water cycle algorithm in solving the non-convex optimal power flow (OPF) problem, a multi-objective Gaussian water cycle algorithm (MOGWCA) is proposed. Three multi-objective OPF simulation experiments are used to demonstrate the property of the MOGWCA, which improves the global development capability and population diversity through the Gaussian mutation mechanism. Test cases considering fuel cost, emissions, active power loss and voltage deviation are applied on IEEE 30 and IEEE 57 test systems. A large number of outcomes display that the MOGWCA algorithm can get a well-distributed Pareto front (PF) and effectively solve the multi-objective OPF problem.

This article introduces the Grey Wolf Optimizer (GWO) algorithm, a novel method aimed at tackling the challenges posed by the multi-objective Optimal Power Flow (OPF) problem. Drawing inspiration from the foraging behavior of grey wolves, GWO stands apart from traditional approaches by enhancing initial solutions without relying on gradient data collection from the objective function. In the domain of power system optimization, the OPF problem is widely acknowledged, involving constraints related to generator parameters, valve-point loading, reactive power, and active power. The proposed GWO technique is applied to IEEE 14-bus and 30-bus power systems, targeting four case objectives: minimizing cost with quadratic cost function, minimizing cost with inclusion of valve point, minimizing power loss, and minimizing both cost and losses simultaneously. For the IEEE-14 bus system, which requires meeting a power demand of 259 MW, GWO yields optimal costs of 827.0056 $hr, 833.4691 $hr, 1083.2410 $hr, and 852.2255 $hr across the four cases. Similarly, for the IEEE-30 bus system aiming to satisfy a demand of 283.4 MW, GWO achieves optimal costs of 801.8623 $hr, 825.9321 $hr, 1028.6309 $hr, and 850.4794 $hr for the respective cases. These optimal results are then compared with existing research outcomes, highlighting the efficiency and cost-effectiveness of the GWO algorithm when juxtaposed with alternative methods for solving the OPF problem.

Optimal Power Flow using Glowworm Swarm Optimization

This paper proposes a pseudo-gradient based particle swarm optimization with constriction factor (PG-PSOCF) method for solving multiobjective optimal power flow (MOOPF) problem. The proposed PG-PSOCF is the conventional particle swarm optimization based on constriction factor based on pseudo gradient to enhance its search ability for optimization problems. The proposed method is to deal with the MOOPF problem by minimizing the total cost and emission from generators while satisfying various constraints of real and reactive power balance, real and reactive power limits, bus voltage limits, shunt capacitor limits and transmission limits. Test results on the IEEE 30-bus system have indicated that the proposed method is more efficient than many other methods in the literature. Therefore, the proposed PG-PSOCF can be an effectively alternative method for solving the MOOPF problem.