Solving Optimal Power Flow Problem Research Articles

Optimal power flow calculation in hybrid power system involving solar, wind, and hydropower plant using weighted mean of vectors algorithm

One of the most complex and motivating issues in power system is optimal power flow (OPF), which is a constrained optimization problem characterized by non-linearity and non-convexity. From these specifications, researchers competed in the past decades to find optimal solutions to OPF problem while keeping system stability. This paper presents an efficient optimization approach to deal with OPF problem in the hybrid renewable energy systems involving wind turbines, solar photovoltaic and small hydropower plant using optimization method depends on weighted mean of vectors INFO. Total generation cost, active power losses, and combined cost and emission are the principle goal, taking into account both reserve and penalty cost appropriate to over and under estimation respectively in the generation cost model. To evaluate the performance of INFO in solving OPF problem, modified IEEE 30-bus and IEEE 57-bus test systems will be utilized. The obtained results are compared with several algorithms such as Gorilla troop optimizer GTO, artificial ecosystem-based optimization AEO, Barnacles Mating Optimizer BMO for the same test systems keeping the same conditions. Simulation results have indicated the superiority of INFO while respecting all constraints. INFO can minimize total generation cost to 788.9417 $/h for IEEE 30-bus and 5259.2040 $/h for IEEE 57-bus. The results demonstrate clearly that the INFO is a highly efficient algorithm that is an encouraging tool for solving OPF problem. The promising findings highlight the potential of the INFO algorithm to smoothest the integration of RES, and its role in promoting sustainable energy solutions. Furthermore, the one-way analysis of variance (ANOVA) test, a statistical approach, was employed to evaluate the superiority of the proposed algorithm and to highlight a certain level of confidence to our study.

Model-Informed Generative Adversarial Network (MI-GAN) for Learning Optimal Power Flow

The optimal power flow (OPF) problem, as a critical component of power system operations, becomes increasingly difficult to solve due to the variability, intermittency, and unpredictability of renewable energy brought to the power system. Although traditional optimization techniques, such as stochastic and robust optimization approaches, could be leveraged to address the OPF problem, in the face of renewable energy uncertainty, i.e., the dynamic coefficients in the optimization model, their effectiveness in dealing with large-scale problems remains limited. As a result, deep learning techniques, such as neural networks, have recently been developed to improve computational efficiency in solving OPF problems with the utilization of data. However, the feasibility and optimality of the solution may not be guaranteed, and the system dynamics cannot be properly addressed as well. In this paper, we propose an optimization model-informed generative adversarial network (MI-GAN) framework to solve OPF under uncertainty. The main contributions are summarized into three aspects: (1) to ensure feasibility and improve optimality of generated solutions, three important layers are proposed: feasibility filter layer, comparison layer, and gradient-guided layer; (2) in the GAN-based framework, an efficient model-informed selector incorporating these three new layers is established; and (3) a new recursive iteration algorithm is also proposed to improve solution optimality and handle the system dynamics. The numerical results on IEEE test systems show that the proposed method is very effective and promising.

Gaussian bare-bones Levy circulatory system-based optimization for power flow in the presence of renewable units

The Optimal Power Flow (OPF) is a vital issue in electrical networks to ensure the economical and safe operation to transfer electrical energy that is very complex, non-linear, and limited. In the electrical networks with Renewable Energy Sources (RES), the OPF problem is a much more complex and constrained optimization problem because incorporating the intermittent nature of RESs, including Wind Turbine (WT) and Photovoltaic (PV), which have been used in this article, and OPF is often used to optimize various problems. In this research, an effort has been made to modify and improve the performance of a new algorithm named Circulatory System-Based Optimization (CSBO) to a more powerful algorithm for complex OPF problems, and the result of this research was to present a more effective and powerful algorithm named Gaussian Bare-bones Levy CSBO (GBLCSBO). CSBO mimics the mating behavior of the circulatory system in the body. The IEEE 30-bus and 118-bus test networks are adopted to validate the capability of the suggested approach in minimizing four objectives, which include the total generation cost, voltage deviation, power loss, and pollution emission.Finally, to know the performance and strength of GBLCSBO for solving various OPF problems, several new powerful algorithms include Seagull Optimization Algorithm (SOA), Teaching-Learning-Based Optimization (TLBO), Gray Wolf Optimizer (GWO), Multi-Verse Optimizer (MVO) have been used to compare with GBLCSBO. Also, the CEC 2017 test functions were used to measure the performance of GBLCSBO in a broader range of optimization problems.The optimization results in both topics of OPF problems and various test functions compared with various algorithms showed that GBLCSBO is both strong and robust and has a suitable and comparative performance in a wide range of different optimization problems such as OPF. According to the obtained results, the GBLCSBO demonstrates high potential in solving OPF problems.

Optimal power flow using a hybridization algorithm of arithmetic optimization and aquila optimizer

In this paper, a hybridization method based on Arithmetic optimization algorithm (AOA) and Aquila optimizer (AO) solver namely, the AO-AOA is applied to solve the Optimal Power Flow (OPF) problem to independently optimize generation fuel cost, power loss, emission, voltage deviation, and L index. The proposed AO-AOA algorithm follows two strategies to find a better optimal solution. The first strategy is to introduce an energy parameter (E) to balance the transition between the individuals’ procedure of exploration and exploitation in AO-AOA swarms. Next, a piecewise linear map is employed to reduce the energy parameter’s (E) randomness. To evaluate the performance of the proposed AO-AOA algorithm, it is tested on two well-known power systems i.e., IEEE 30-bus test network, and IEEE 118-bus test system. Moreover, to validate the effectiveness of the proposed (AO-AOA), it is compared with a famous optimization technique as a competitor i.e., Teaching-learning-based optimization (TLBO), and recently published works on solving OPF problems. Furthermore, a robustness analysis was executed to determine the reliability of the AO-AOA solver. The obtained result confirms that not only the AO-AOA is efficient in optimization with significant convergence speed, but also denotes the dominance and potential of the AO-AOA in comparison with other works.

Optimal Power Flow of Hybrid Wind/Solar/Thermal Energy Integrated Power Systems Considering Costs and Emissions via a Novel and Efficient Search Optimization Algorithm

The OPF problem has significant importance in a power system’s operation, planning, economic scheduling, and security. Today’s electricity grid is rapidly evolving, with increased penetration of renewable power sources (RPSs). Conventional optimal power flow (OPF) has non-linear constraints that make it a highly non-linear, non-convex optimization problem. This complex problem escalates further with the integration of renewable energy resource (RES), which are generally intermittent in nature. This study suggests a new and effective improved optimizer via a TFWO algorithm (turbulent flow of water-based optimization), namely the ITFWO algorithm, to solve non-linear and non-convex OPF problems in energy networks with integrated solar photovoltaic (PV) and wind turbine (WT) units (being environmentally friendly and clean in nature). OPF in the energy networks is an optimization problem proposed to discover the optimal settings of an energy network. The OPF modeling contains the forecasted electric energy of WT and PV by considering the voltage value at PV and WT buses as decision parameters. Forecasting the active energy of PV and WT units has been founded on the real-time measurements of solar irradiance and wind speed. Eight scenarios are analyzed on the IEEE 30-bus test system in order to determine a cost-effective schedule for thermal power plants with different objectives that reflect fuel cost minimization, voltage profile improvement, emission gases, power loss reduction, and fuel cost minimization with consideration of the valve point effect of generation units. In addition, a carbon tax is considered in the goal function in the examined cases in order to investigate its effect on generator scheduling. A comparison of the simulation results with other recently published algorithms for solving OPF problems is made to illustrate the effectiveness and validity of the proposed ITFWO algorithm. Simulation results show that the improved turbulent flow of water-based optimization algorithm provides an effective and robust high-quality solution of the various optimal power-flow problems. Moreover, results obtained using the proposed ITFWO algorithm are either better than, or comparable to, those obtained using other techniques reported in the literature. The utility of solar and wind energy in scheduling problems has been proposed in this work.

Developing a strategy based on weighted mean of vectors (INFO) optimizer for optimal power flow considering uncertainty of renewable energy generation.

In recent years, more efforts have been exerted to increase the level of renewable energy sources (RESs) in the energy mix in many countries to mitigate the dangerous effects of greenhouse gases emissions. However, because of their stochastic nature, most RESs pose some operational and planning challenges to power systems. One of these challenges is the complexity of solving the optimal power flow (OPF) problem in existing RESs. This study proposes an OPF model that has three different sources of renewable energy: wind, solar, and combined solar and small-hydro sources in addition to the conventional thermal power. Three probability density functions (PDF), namely lognormal, Weibull, and Gumbel, are employed to determine available solar, wind, and small-hydro output powers, respectively. Many meta-heuristic optimization algorithms have been applied for solving OPF problem in the presence of RESs. In this work, a new meta-heuristic algorithm, weighted mean of vectors (INFO), is employed for solving the OPF problem in two adjusted standard IEEE power systems (30 and 57 buses). It is simulated by MATLAB software in different theoretical and practical cases to test its validity in solving the OPF problem of the adjusted power systems. The results of the applied simulation cases in this work show that INFO has better performance results in minimizing total generation cost and reducing convergence time among other algorithms.

Cross-entropy boosted CRO-SL for optimal power flow in smart grids

Optimal power flow (OPF) is a complex, highly nonlinear, NP-hard optimization problem, in which the goal is to determine the optimal operational parameters of a power-related system (in many cases a type of smart or micro grid) which guarantee an economic and effective power dispatch. In recent years, a number of approaches based on metaheuristics algorithms have been proposed to solve OPF problems. In this paper, we propose the use of the Cross-Entropy (CE) method as a first step depth search operator to assist population-based evolutionary methods in the framework of an OPF problem. Specifically, a new variant of the Coral Reefs Optimization with Substrate Layers algorithm boosted with CE method (CE+CRO-SL) is presented in this work. We have adopted the IEEE 57-Bus System as a test scenario which, by default, has seven thermal generators for power production for the grid. We have modified this system by replacing three thermal generators with renewable source generators, in order to consider a smart grid approach with renewable energy production. The performance of CE+CRO-SL in this particular case study scenario has been compared with that of well-known techniques such as population’s methods CMA-ES and EPSO (both boosted with CE). The results obtained indicate that CE+CRO-SL showed a superior performance than the alternative techniques in terms of efficiency and accuracy. This is justified by its greater exploration capacity, since it has internally operations coming from different heuristics, thus surpassing the performance of classic methods. Moreover, in a projection analysis, the CE+CRO-SL provides a profit of millions of dollars per month in all cases tested considering the modified version of the IEEE 57-Bus smart grid system.

Learning to solve DCOPF: A duality approach

The optimal power flow (OPF) problem is a fundamental tool in power system operation and control. Because of the increase in uncertain renewable resources, solving OPF problems fast and accurately provides significant values because of a large number of load and generation scenarios need to be accounted for. Recent works have focused on using neural networks to replace iterative solvers to speed up the computation of OPF problems. A critical challenge is to ensure solutions satisfy the hard constraints in the OPF problem, which is difficult to do in end-to-end machine learning. In this work, by leveraging the rich theory of duality and physical interpretations of OPF, we design a learning-based approach that has theoretical characterizations of constraint satisfaction. This approach is an order of magnitude faster than standard solvers, and performs much better than other learning methods in terms of feasibility and optimality.

Solution of constrained mixed‐integer multi‐objective optimal power flow problem considering the hybrid multi‐objective evolutionary algorithm

An Optimal power flow (OPF) is non-linear and constrained multi-objective problem. OPF problems are expensive and evolutionary algorithms (EAs) are computationally complex to obtain uniformly distributed and global Pareto front (PF). Therefore, here, hybrid two-phase algorithm integrated with parameter less constraint technique is applied to solve OPF problem. Proposed technique combines single and multi-objective EAs to find better convergence and evenly distributed PF. For the validation and effectiveness of proposed algorithm, various conflicting objective functions are formulated and implemented on IEEE 30 and 300-bus network. Each case is independently run twenty times. Hyper volume indicator technique is employed to find the best PF, and the best-compromised solution is obtained by using fuzzy decision-making technique. Recently, maximum integration of wind and solar power is highly encouraged. Complexity of OPF is increased with the integration of uncertain renewable energy resources. Hence, 30-bus test system is modified by replacing some conventional generators with the wind and solar generation. Uncertainties in wind, solar and load demand are modelled by appropriate probability distribution functions. Simulation results show that the proposed method can find the near global PF of highly complex problems subject to satisfying all the operational constraints.

A Slime Mould Algorithm Programming for Solving Single and Multi-Objective Optimal Power Flow Problems with Pareto Front Approach: A Case Study of the Iraqi Super Grid High Voltage

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.

An Improved Equilibrium Optimizer Algorithm for Solving Optimal Power Flow Problem with Penetration of Wind and Solar Energy

The paper is proposed an improved equilibrium optimizer (IEO) algorithm to solve the optimal power flow (OPF) problem with the participation of a renewable energy source (RES). In the proposed IEO method, the “exponential term” is replaced by a function that does not dependent on the number of iterations. This modification of the IEO algorithm increases exploration ability compared to EO algorithm. In addition, the exploration of the proposed IEO algorithm will not decrease according to the number of iterations which avoids to get stuck at the local optimal solution. The IEO algorithm is tested on two IEEE 30-bus and IEEE 118-bus systems with three different objective functions. The performance of the proposed IEO method is compared with equilibrium optimizer (EO), artificial ecosystem optimization (AEO), cuckoo search algorithm (CSA), teaching-learning-based optimization (TLBO), artificial bee colony (ABC), and many other existing methods. Besides, a simple probabilistic formula for calculating RES output power based on the Monte-Carlo simulation model is proposed in this paper to reduce the computation time for the OPF problem with RES. The simulation results obtained show that the proposed IEO algorithm has better quality of the solution as well as stability level compared to the original EO algorithm and other algorithm. Thus, the proposed IEO algorithm is also one of effective and reliable algorithms for handling OPF problem with RES.

Fully Decentralized, Cost-Effective Energy Demand Response Management System with a Smart Contracts-Based Optimal Power Flow Solution for Smart Grids

Recent advances in control, communication, and management systems, as well as the widespread use of renewable energy sources in homes, have led to the evolution of traditional power grids into smart grids, where passive consumers have become so-called prosumers that feed energy into the grid. On the other hand, the integration of blockchain into the smart grid has enabled the emergence of decentralized peer-to-peer (P2P) energy trading, where prosumers trade their energy as tokenized assets. Even though this new paradigm benefits both distribution grid operators and end users in many ways. Nevertheless, there is a conflict of interest between the two parties, as on the one hand, prosumers want to maximize their profit, while on the other hand, distribution system operators (DSOs) seek an optimal power flow (OPF) operating point. Due to the complexity of formulating and solving OPF problems in the presence of renewable energy sources, researchers have focused on mathematical modeling and effective solution algorithms for such optimization problems. However, the control of power generation according to a defined OPF solution is still based on centralized control and management units owned by the DSO. In this paper, we propose a novel, fully decentralized architecture for an OPF-based demand response management system that uses smart contracts to force generators to comply without the need for a central authority or hardware.

An Improved Multi Objective Mayfly Algorithm for Solving Optimal Power Flow Problem Considering Different Loading Conditions

This paper presents an improved multi-objective mayfly algorithm (IMOMA) to resolve the optimal power flow (OPF) problem in a regulated power system network with different loading conditions. The OPF problem, considered a multi-objective optimization problem, comprises multiple objective functions related to economic, technical, operational and security aspects. The IMOMA algorithm has been developed by implementing the simulated binary crossover (SBX), polynomial mutation and dynamic crowding distance (DCD) operators in the original multi-objective mayfly algorithm (MOMA).The OPF problem is analyzed by considering multiple objective functions in the IEEE30-bus test system, the IEEE118-bus test system and the 62-bus Indian utility system. The hypervolume performance metric is used to compare the performance of the MOMA and IMOMA with respect to different operating scenarios. Further, loading conditions ranging between 150% and 50% of the base load are considered for the evaluation. The effectiveness of the IMOMA over the MOMA is observed from the results of the different loads. The best compromise solution is obtained from a set of pareto optimal solutions by implementing the TOPSIS method.

Adaptive Range Composite Differential Evolution for Fast Optimal Reactive Power Dispatch

This paper proposes a novel adaptive range composite differential evolution (ARCoDE) algorithm to efficiently and accurately solve optimal reactive power dispatch (ORPD) problem. Because of a novel adaptive range strategy for control parameters, the proposed ARCoDE possesses superior exploration and exploitation capabilities that can efficiently handle the ORPD problem involving complicated constraints and discrete and continuous variables. This has been demonstrated in case studies using the IEEE optimal power flow testbeds considering complex wind and demand scenarios. The superior performance of ARCoDE has been further validated through comparisons with several award-winning algorithms in 2014 IEEE Competition on “Application of Modern Heuristic Optimization Algorithms for Solving Optimal Power Flow Problems”, given limited iterations of in evolutionary optimization process.

Kriging Assisted Surrogate Evolutionary Computation to Solve Optimal Power Flow Problems

This paper proposes a Kriging assisted strategy to expedite evolutionary computation for solving Optimal Power Flow (OPF) problems. First, two algorithms were developed–a Kriging Assisted Genetic Algorithm (KAGA) and a Kriging Assisted Particle Swarm Optimization (KAPSO) - and tested using unconstrained benchmark functions; it was found that both algorithms provided reliable and robust solutions. Accordingly, KAGA and KAPSO were selected and tested on the IEEE 30 and 118 bus systems for minimizing generation costs and active power losses. It is shown that the proposed KAPSO outperforms other algorithms, especially in terms of the computation time. In reference to the solution quality yielded by KAGA and KAPSO, the proposed Kriging assisted strategy offers a promising method to improve the performance of evolutionary based computation when solving OPF problems.

Optimal power flow with stochastic wind power and FACTS devices: a modified hybrid PSOGSA with chaotic maps approach

Nowadays, the increasing usage of renewable energy sources (RES) in modern power systems introduces new challenges in power system planning and operation. Specifically, a high penetration of RESs introduces additional complexity into the optimal power flow (OPF) problem, which has a highly nonlinear complex structure. Under this environment, this paper discusses a modified hybrid particle swarm optimization and gravitational search algorithm (PSOGSA) integrated with chaotic maps (CPSOGSA) to apply the composite benchmark test functions and to solve the OPF problem with stochastic wind power and flexible alternating current transmission system (FACTS) devices. Numerical studies are used to illustrate effectiveness of the proposed CPSOGSA approach against other approaches such as moth swarm algorithm, grey wolf optimizer, and whale optimization algorithm. Additionally, to demonstrate the superiority and robustness of CPSOGSA algorithm, Wilcoxon signed-rank test is applied for all case studies. Case studies indicate the potential of CPSOGSA method in effectively solving OPF problem with stochastic wind power and FACTS devices.

Review on population-based metaheuristic search techniques for optimal power flow

<span>Optimal power flow (OPF) is a non-linear solution which is significantly important in order to analyze the power system operation. The use of optimization algorithm is essential in order to solve OPF problems. <br /> The emergence of machine learning presents further techniques which capable to solve the non-linear problem. The performance and the key aspects which enhances the effectiveness of these optimization techniques are compared within several metaheuristic search techniques. This includes the operation of particle swarm optimization (PSO) algorithm, firefly algorithm (FA), artificial bee colony (ABC) algorithm, ant colony optimization (ACO) algorithm and differential evolution (DE) algorithm. This paper reviews on the key elements that need to be considered when selecting metaheuristic techniques to solve OPF problem in power <br /> system operation.</span>

An Efficient Adaptive Moth Flame Optimization Algorithm for Solving Large-Scale Optimal Power Flow Problem with POZ, Multifuel and Valve-Point Loading Effect

This paper offers an enhanced adaptive moth flame optimization (AMFO) algorithm to solve the optimal power flow (OPF) problems efficiently. The idea of moth flame optimization (MFO) is motivated by the movement of moth headed about the moon direction. AMFO is primarily centered on the notion of MFO with adjusting the direction of moths in an adaptive manner around the flame. AMFO is compared with standard MFO for 14 different benchmark test suites. Standard IEEE 118-bus test system is used to substantiate the effectiveness and robustness of AMFO algorithm. The authentication of the suggested algorithm is established on 12 case studies for various single-objective functions like fuel cost minimization, emission minimization, active power loss minimization, voltage stability enhancement and voltage profile improvement. The simulation findings of the suggested algorithm are compared with those found by other well-known optimization methods. The achieved results demonstrate the ability and strength of AMFO approach to solving OPF problems. The outcomes divulge that AMFO algorithm can obtain accurate and improved OPF solutions compared with the other methods. A comparison among the convergence qualities of AMFO and the different techniques demonstrates the predominance of AMFO to achieve the optimal power flow solution with rapid convergence.

Optimal Power Flow on DC Microgrids: A Quadratic Convex Approximation

This express brief shows a convex quadratic approximation for the optimal power flow (OPF) in direct-current microgrids (dc- ${\mu }$ Grid) via Taylor’s series expansion. This approach can be used for solving OPF problems on radial and meshed dc- ${\mu }$ Grids with multiple constant power terminals, allowing to cover a wide range of configurations. Two test dc- ${\mu }$ Grids with 10 and 21 nodes were used to validate the proposed model. Nonlinear large-scale solvers were employed to compare the proposed linearization with the conventional nonlinear nonconvex model.

Optimal Power Flow in Direct-Current Power Grids via Black Hole Optimization

This paper addresses the Optimal Power Flow (OPF) problem in DC power microgrids via a combinatorial optimization technique known as Black Hole Optimization (BHO). Such optimization method allows to solve OPF problems via algorithmic strategies trough a master-slave formulation. In the master stage, the total power generated by each Distributed Generator (DG) is determined by the BHO, while the slave strategy is entrusted with solving the resulting conventional power flow problem via a classical Gauss-Seidel (GS) numerical method. For comparison purposes, this work uses nonlinear optimization methods available in General Algebraic Modeling System (GAMS) as well as continuous metaheuristic optimization techniques. Two test feeders with 21 and 69 nodes were considered for validating the proposed hybrid BHO-GS optimization method, which enables to demonstrate its applicability, robustness and efficiency compared to conventional approaches. The results of all the simulations were obtained via MATLAB 2017a.