Optimal power dispatch in hybrid power system for medium- and large-scale practical power systems using self-adaptive bonobo optimizer algorithm

The modern electrical system consists of traditional thermal generating units and renewable energy sources (RESs). However, the incorporation of RESs into the grid is a very challenging problem due to their intermittent nature. This study involves implementing the optimal power flow (OPF) problem in a system that includes wind and solar energy and thermal power generators (ThPGs). Moreover, to deal with the intermittent nature of RES, the power output from the solar and wind power outputs are estimated using lognormal and Weibull probability distribution functions (PDF) respectively. The main goal to be optimized is to reduce the total generation cost of the network, which includes the cost of thermal generators as well as the direct, overestimation, and underestimating costs of RESs. To tackle the proposed OPF problem of a hybrid power system, this paper employs improved particle swarm optimization (IPSO). The effectiveness of the proposed method is demonstrated using a modified IEEE 30 bus with RESs integration.

International audience

In recent decades, the energy market around the world has been reshaped to accommodate the high penetration of renewable energy resources. Although renewable energy sources have brought various benefits, including low operation cost of wind and solar PV power plants, and reducing the environmental risks associated with the conventional power resources, they have imposed a wide range of difficulties in power system planning and operation. Naturally, classical optimal power flow (OPF) is a nonlinear problem. Integrating renewable energy resources with conventional thermal power generators escalates the difficulty of the OPF problem due to the uncertain and intermittent nature of these resources. To address the complexity associated with the process of the integration of renewable energy resources into the classical electric power systems, two probability distribution functions (Weibull and lognormal) are used to forecast the voltaic power output of wind and solar photovoltaic, respectively. Optimal power flow, including renewable energy, is formulated as a single-objective and multi-objective problem in which many objective functions are considered, such as minimizing the fuel cost, emission, real power loss, and voltage deviation. Real power generation, bus voltage, load tap changers ratios, and shunt compensators values are optimized under various power systems’ constraints. This paper aims to solve the OPF problem and examines the effect of renewable energy resources on the above-mentioned objective functions. A combined model of wind integrated IEEE 30-bus system, solar PV integrated IEEE 30-bus system, and hybrid wind and solar PV integrated IEEE 30-bus system is performed using the equilibrium optimizer technique (EO) and other five heuristic search methods. A comparison of simulation and statistical results of EO with other optimization techniques showed that EO is more effective and superior and provides the lowest optimization value in term of electric power generation, real power loss, emission index and voltage deviation.

Unit Commitment is one of the most complex and difficult optimization problem in power systems. The objective of the optimal commitment is to determine the on/off states of the units in the system to meet the load demand and spinning reserve requirements at each time period, such that the overall cost of generation is minimized, while satisfying the various operational constraints. This paper presents the application of an improved genetic algorithm (GA) with crossover, mutation, and advanced operators such as repair and swap mutation to determine the commitment order of the thermal units in power generation. The proposed GA has been successfully applied to 10 and 26 generating-unit systems. Robustness of the proposed GA is demonstrated by comparison to the dynamic programming algorithm. The comparison results show the effectiveness of the proposed GA in solving the unit commitment problem with sufficient accuracy and low computational time.

The optimal power flow (OPF) problem was introduced by Carpentier in 1962 as a network constrained economic dispatch problem. Since then, it has been intensively studied and widely used in power system operation and planning. In the past few decades, many stochastic optimization methods such as Genetic Algorithm (GA), Evolutionary Programming (EP), and Particle Swarm Optimization (PSO) have been applied to solve the OPF problem. In particular, PSO is a newly proposed population based stochastic optimization algorithm. The main idea behind it is based on the food-searching behavior of birds and fish. Compared with other stochastic optimization methods, PSO has comparable or even superior search performance for some hard optimization problems in real power systems. Nowadays, some modifications such as breeding and selection operators are considered to make the PSO superior and robust. In this paper, we propose the Modified PSO (MPSO), in which the mutation operator of GA is incorporated into the conventional PSO to improve the search performance. To verify the optimal solution searching ability, the proposed approach has been evaluated on an IEEE 30-bus test system. The results showed that performance of the proposed approach is better than that of the standard PSO.

This paper investigates potential of modified differential evolution (MDE) algorithm, to find solution for optimal power flow (OPF) problem of power system. The performance of the proposed MDE algorithm is experienced on the modified IEEE-30 bus test systems integrating flexible ac transmission systems (FACTS) devices, that is, thyristor controlled phase shifter (TCPS) and thyristor controlled series capacitor (TCSC) at preset locations. The OPF problem of the present work is formulated with five different objective functions viz. (a) fuel cost (with valve point effect) minimization, (b) power transmission losses minimization, (c) emission reduction (d) fuel cost (without valve point effect) minimization and (e) minimization of combined economic and environmental cost. The proposed implementation exploits MDE, resulting in a much shorter execution time while retaining the best possible solution of OPF problem.

The incorporation of renewable energy sources (RES) such as wind and solar power plants into traditional power systems offers numerous technical and environmental benefits. However, improper operation of power grids with RES may lead to high operating costs and higher system losses, as well as voltage fluctuations. To solve these problems, in this paper a formulation of the dynamic optimal power flow (DOPF) problem has been proposed with the integration of RES in the grid. The maximum allowable number of switching operations in a day for on-load tap-changer (OLTC) of transformers is taken into consideration as practical constraint. For 24 hours, the objective functions were to minimize the total operating cost (including fuel cost and cost of power loss), minimize power loss and the daily number of tap operations for transformer's OLTC. The minimization of the daily number of operations for transformers was taken as the goal to preserve the service life of transformers, reduce maintenance and depreciation. The objectives were minimized by coordination between control variables such as the output power of generators, the voltage of generators, transformer tap changer, and shunt capacitor. The improved practical swarm optimization (PSO) algorithm has been employed successfully to solve DOPF with discrete and continuous decision variables in the electric power system.

Modern power systems which integrate renewable energy sources (RESs), such as wind or solar energy sources and plug-in electric vehicles (PEVs), need to carry out the uncertainty due to the access of demanded or injected power. Therefore, it is necessary to consider uncertainty costs in optimal power flow problems. To develop the uncertainty cost functions, log-normal probability distribution function (PDF) for solar irradiance, normal PDF for unloading and loading behavior of PEVs, and Rayleigh PDF for wind speed are considered. In this work, a dynamic optimal power flow (DOPF) model is formulated by considering the uncertainties of RESs and PEVs. A newly hybrid metaheuristic algorithm named cross entropy (CE) covariance matrix adaption evolutionary strategy (CMAES) is proposed to evaluate the DOPF problem in a modified IEEE 118-bus system. The application of adaptive step length in the CMAES method improves the local exploitation capability, while the CE method is used in the initial stage for global exploration due to its fast convergence. Simulation results indicate that the proposed technique can solve the DOPF problems with RESs and PEVs effectively and can provide high-quality solutions compared to different techniques. The conventional statistical method called ANOVA test is performed for comparative analysis of different techniques. The results of this test show the validation of CE-CMAES compared to different optimization techniques. Therefore, the proposed method could be easily and efficiently applied by power system operators in real-time optimal power flow operations.

This paper proposed the Lagrangian optimization model for Optimal Power Flow (OPF) problem. It is designed by relaxing the constraints from the Quadratic Programming (QP) problem. The objective of this model is to minimize the total cost of active power generation. The solution of QP is obtained by different optimization techniques like Particle Swarm Optimization (PSO) method, Genetic Algorithm (GA), Differential Evolution (DE) algorithm. In this paper, the optimum value of QP is obtained by the proposed model and it is compared with other methods PSO, GA, DE. The results of the methods have been tested through the standard IEEE 30 bus system. Based on numerical calculations and graphical representation, the optimal generation cost for OPF can be achieved.

This study presents an improved chaotic flower pollination algorithm (CFPA) with a view to handle the optimal power flow (OPF) problem integrating a hybrid wind and solar power and generate the optimal settings of generator power, bus voltages, shunt reactive power, and tap setting transformers. In spite of the benefits of FPA, it encounters two problems like other evolutionary algorithms: entrapment in local optima and slow convergence speed. Thus, to deal with these drawbacks and enhance the FPA searching accuracy, a hybrid optimization approach CFPA which combines the stochastic algorithm FPA that simulates the flowering plants process with the chaos methodology is applied in this manuscript. Therefore, owing to the various nonlinear constraints in OPF issue, a constraint handling technique named superiority of feasible solutions (SF) is embedded into CFPA. To confirm the performance of the chaotic FPA, a set of different well-known benchmark functions were employed for ten diverse chaotic maps, and then the best map is tested on IEEE 30-bus and IEEE 57-bus test systems incorporating the renewable energy sources (RESs). The obtained results are analyzed statistically using non-parametric Wilcoxon rank-sum test in view of evaluating their significance compared to the outcomes of the state-of-the-art meta-heuristic algorithms such as ant bee colony (ABC), grasshopper optimization algorithm (GOA), and dragonfly algorithm (DA). From this study, it may be established that the suggested CFPA algorithm outperforms its meta-heuristic competitors in most benchmark test cases. Additionally, the experimental results regarding the OPF problem demonstrate that the integration of RESs decreases the total cost by 12.77% and 33.11% for the two systems, respectively. Thus, combining FPA with chaotic sequences is able to accelerate the convergence and provide better accuracy to find optimal solutions. Furthermore, CFPA (especially with the Sinusoidal map) is challenging in solving complex real-world problems.

The growing penetration of renewable energy sources (RES) has boosted the necessity of cost-effective and flexible power system operations. Battery Energy Storage Systems (BESS) provide a real-world solution by improving grid reliability, facilitating flexible dispatch, and renewable integration. This paper models the Economic Dispatch (ED) problem with BESS integration, with an objective to minimize overall generation cost subject to operation constraints of thermal units and BESS. Two optimization methods are compared: (i) fmincon, a gradient-based constrained nonlinear solver, and (ii) the JAYA algorithm, a parameter-free metaheuristic that repeatedly pushes solutions towards best and away from worst. Simulation studies on a 6-bus system with six thermal units show that integration with BESS highly enhances operation flexibility and lowers costs. The total generation cost was reduced from Rs.23.74 million to Rs.21.21 million, corresponding to a saving of Rs.2.53 million (10.66%) using FMINCON whereas using JAYA algorithm the tota generation cost was reduced from Rs.23.68 million to Rs.20.83 million, corresponding to a saving of Rs.2.85 million (12.06%). The Jaya algorithm performs better consistently compared to fmincon in both cost minimization and the speed of convergence, showing its suitability for solving large-scale nonlinear power system optimization problems.

In the paper, a modified coyote optimization algorithm (MCOA) is proposed for finding highly effective solutions for the optimal power flow (OPF) problem. In the OPF problem, total active power losses in all transmission lines and total electric generation cost of all available thermal units are considered to be reduced as much as possible meanwhile all constraints of transmission power systems such as generation and voltage limits of generators, generation limits of capacitors, secondary voltage limits of transformers, and limit of transmission lines are required to be exactly satisfied. MCOA is an improved version of the original coyote optimization algorithm (OCOA) with two modifications in two new solution generation techniques and one modification in the solution exchange technique. As compared to OCOA, the proposed MCOA has high contributions as follows: (i) finding more promising optimal solutions with a faster manner, (ii) shortening computation steps, and (iii) reaching higher success rate. Three IEEE transmission power networks are used for comparing MCOA with OCOA and other existing conventional methods, improved versions of these conventional methods, and hybrid methods. About the constraint handling ability, the success rate of MCOA is, respectively, 100%, 96%, and 52% meanwhile those of OCOA is, respectively, 88%, 74%, and 16%. About the obtained solutions, the improvement level of MCOA over OCOA can be up to 30.21% whereas the improvement level over other existing methods is up to 43.88%. Furthermore, these two methods are also executed for determining the best location of a photovoltaic system (PVS) with rated power of 2.0 MW in an IEEE 30-bus system. As a result, MCOA can reduce fuel cost and power loss by 0.5% and 24.36%. Therefore, MCOA can be recommended to be a powerful method for optimal power flow study on transmission power networks with considering the presence of renewable energies.

A new hybrid evolutionary algorithm for multi-objective optimal power flow in an integrated WE, PV, and PEV power system

The performance of a power system can be measured and evaluated by its power flow analysis. Along with the penetration of renewable energies such as wind and solar, the power flow problem has become a complex optimization problem. In addition to this, constraint handling is another challenging task of this problem. The main critical problem of this dynamic power system having such variable energy sources is the intermittency of these VESs and complexity of constraint handling for a real-time optimal power flow (RT-OPF) problem. Therefore, optimal scheduling of generation sources with constraint satisfaction is the main goal of this study. Hence, a renewable energy forecasting–based, day-ahead dynamic optimal power flow (DA-DOPF) is presented in this paper with the forecasting of solar and wind patterns by using artificial neural networks. Moreover, contribution factors are calculated using triangular fuzzy membership function (T-FMF) in the sub-interval time slots. Furthermore, the superiority of feasible (SF) solution constraint handling approach is used to avoid the constraint violation of inequality constraints of optimal power flow. The IEEE 30-bus transmission network has been amended to integrate a solar photovoltaic and wind farm in different buses. In this approach, the computing program is based on MATPOWER which is a tool of MATLAB for load flow analysis which uses the Newton–Raphson technique because of its rapid convergence. Meteorological information has been gathered during the time frame January 1, 2015, to December 31, 2017, from Danyore Weather Station (DWS) at Hunza, Pakistan. A Levenberg–Marquardt calculation–based artificial neural network model is utilized to foresee the breeze speed and sunlight-based irradiance in light of its versatile nature. Finally, the results are discussed analytically to select the best generation schedule and control variable values.

In this paper, we consider the Optimal Power Flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the OPF problem. It consists in a spatial branch-and-bound algorithm based on a compact quadratically-constrained convex relaxation. It is computed by solving the semidefinite rank relaxation of OPF once at the root node of the algorithm. An important result is that the optimal value of our compact relaxation is equal to the rank relaxation value. Then, at every sub-nodes of our branch-and-bound, the lower bound is obtained by solving a quadratic convex problem instead of an SDP. Another contribution is that we add only O(n+m) variables that model the squares of the initial variables, where n is the number of buses in the power system and m the number of transmission lines, to construct our relaxation. Then, since the relations between the initial and auxiliary variables are non-convex, we relax them to get a quadratic convex relaxation. Finally, in our branch-and-bound algorithm, we only have to force a reduced number of equalities to prove global optimality. This quadratic convex relaxation approach is here tailored to the OPF problem, but it can address any application whose formulation is a quadratic optimization problem subject to quadratic equalities and ring constraints. Our first experiments on instances of the OPF problem show that our new algorithm Compact OPF (COPF) is more efficient than the standard solvers and other quadratic convex relaxation based methods we compare it with.