Optimal Power Flow Problem Research Articles

Optimal Power Flow of Power System with Static VAR Compensator using Moth Flame Optimization with Locational Marginal Price

The determination of a generation unit's locational marginal price (LMP), which depends on our understanding of transmission line capacity and optimal power flow (OPF) based on reality, is crucial to evaluating the performance of the unit and determining its profit. Minimising the total cost of the generators will lower the price of electricity on the market. Since power flow equations are nonlinear, numerical and repetition-based approaches should be used to solve them. The equations in this paper are solved using a Moth Flame Optimization (MFO), and to enhance the performance of the MFO in its structure, for simultaneous calculations of power passing through in transmission lines so that by learning about the capacity of transmission lines, in addition to the optimal power flow becoming a reality, the price of electricity is determined using uniform market pricing, or LMP method. The FACTS device used for the problem is Static Var Compensator (SVC). Finally, values for bus voltages, line losses, power injected to buses, power travelling via lines, total generating costs, and generator profits would be included in the output of the proposed MFO algorithm. Additionally, the results of testing the proposed methodology on the IEEE 30-BUS network reveal improvements on the OPF problem.

Solving optimal power flow problems via a constrained many-objective co-evolutionary algorithm

The optimal power flow problem in power systems is characterized by a number of complex objectives and constraints, which aim to optimize the total fuel cost, emissions, active power loss, voltage magnitude deviation, and other metrics simultaneously. These conflicting objectives and strict constraints challenge existing optimizers in balancing between active power and reactive power, along with good trade-offs among many metrics. To address these difficulties, this paper develops a co-evolutionary algorithm to solve the constrained many-objective optimization problem of optimal power flow, which evolves three populations with different selection strategies. These populations are evolved towards different parts of the huge objective space divided by large infeasible regions, and the cooperation between them renders assistance to the search for feasible and Pareto-optimal solutions. According to the experimental results on benchmark problems and the IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus systems, the proposed algorithm is superior over peer algorithms in solving constrained many-objective optimization problems, especially the optimal power flow problems.

An enhanced arithmetic optimization algorithm for optimal control of reactive power

AbstractIn this article, an enhanced arithmetic optimization algorithm (EAOA) is utilized to resolve the optimal reactive power dispatch problem (ORPD) of power plants, which is a non‐linear, non‐smooth, complex optimization problem. Typically, it is formulated as a constrained optimal power flow problem. This paper utilizes the gamma distribution to generate initial random solutions, which improves the accuracy of the arithmetic optimization algorithm (AOA). The original mode of deviation of math optimizer accelerated (MOA) is replaced with the improved pattern of change in the prey's energy in Harris Hawk Optimization (HHO), which creates a superior balance between the exploration and exploitation of AOA. This paper implements logarithmic and exponential operators in place of division and multiplication operators, which improves the exploration ability of AOA and also utilizes the gamma distribution in the generation of random numbers, which are essential for the selection of operators in both search phase which enlarges the search area and improves the global optimum solution. A parametric analysis is performed on 10 benchmark functions for nine possible values before selecting the algorithm's initial parameters. A comparative statistical analysis along with Friedman's test is carried out on 23 benchmark functions to test the overall performance as compared to Sine‐Cosine Algorithm (SCA), Swarm‐Salp Algorithm, Grey Wolf Optimization (GWO), and basic Arithmetic Optimization Algorithm (AOA). EAOA is applied to the IEEE 57 bus system for optimal reactive power control. EAOA reports a significant reduction in a power loss of 23.2 MW, which is 18.596% smaller than the system's base case power loss of 28.5 MW as compared to Artificial Bee Colony (ABC), Firefly Algorithm (FA), Bat‐inspired Algorithm (BAT), Cuckoo Search Algorithm (CSA), and Modified Ant Lion Algorithm (MALO) which reports a reduction in a power loss of 14.73%, 15.43%, 15.43%, 16.14%, and 16.14% respectively. EAOA reduces the TVD to 0.76 pu, compared to ABC, FA, BAT, CSA, and MALO, which minimizes the TVD to 0.84, 0.82, 0.88, 0.82, and 0.79, respectively. This proves that EAOA performs better in resolving ORCP problems regarding the quality of solutions and convergence. A detailed comparative statistical analysis of EAOA with CSA, BAT, and WOA (Whale Optimization Algorithm) is conducted in terms of Probability Distribution Functions (PDF) and Cumulative Distribution Functions (CDF), along with the Wilcoxson sign rank test, which proves that EAOA gives the solution with a higher degree of precision.

Optimal power flow with distributed energy sources using whale optimization algorithm

<span lang="EN-US">Renewable energy generation is increasingly attractive since it is <br /> non-polluting and viable. Recently, the technical and economic performance of power system networks has been enhanced by integrating renewable energy sources (RES). This work focuses on the size of solar and wind production by replacing the thermal generation to decrease cost and losses on a big electrical power system. The Weibull and Lognormal probability density functions are used to calculate the deliverable power of wind and solar energy, to be integrated into the power system. Due to the uncertain and intermittent conditions of these sources, their integration complicates the optimal power flow problem. This paper proposes an optimal power flow (OPF) using the whale optimization algorithm (WOA), to solve for the stochastic wind and solar power integrated power system. In this paper, the ideal capacity of RES along with thermal generators has been determined by considering total generation cost as an objective function. The proposed methodology is tested on the IEEE-30 system to ensure its usefulness. Obtained results show the effectiveness of WOA when compared with other algorithms like non-dominated sorting genetic algorithm (NSGA-II), grey wolf optimization (GWO) and particle swarm optimization-GWO (PSO-GWO).</span>

A second-order conic approximation to solving the optimal power flow problem in bipolar DC networks while considering a high penetration of distributed energy resources

This article presents an optimal power flow (OPF) formulation based on the branch flow model for bipolar DC grids with asymmetric loading. The proposal considers the power injection formulation of the OPF to obtain the branch flow model equations that allow solving the power flow problem in bipolar DC networks. Furthermore, a nonlinear programming (NLP) optimization model is deduced and transformed into a second-order conic programming one, which involves convex optimization and guarantees a global optimum for the relaxed model, the uniqueness of this solution, and fast convergence. Finally, an approximation based on balanced operation is proposed to simplify the OPF. Several case studies in two test systems composed of 21 and 85 nodes with a bipolar structure demonstrate that the proposal is accurate, fast, and close to the exact solution of the NLP model when compared with competitive literature reports. All optimization models were implemented in the Python language.

Comparative Analysis of the Particle Swarm Optimization and Primal-Dual Interior-Point Algorithms for Transmission System Volt/VAR Optimization in Rectangular Voltage Coordinates

Optimal power flow (OPF) is one of the most widely studied problems in the field of operations research, as it applies to the optimal and efficient operation of the electric power system. Both the problem formulation and solution techniques have attracted significant research interest over the decades. A wide range of OPF problems have been formulated to cater for the various operational objectives of the power system and are mainly expressed either in polar or rectangular voltage coordinates. Many different solution techniques falling into the two main categories of classical/deterministic optimization and heuristic/non-deterministic optimization techniques have been explored in the literature. This study considers the Volt/VAR optimization (VVO) variant of the OPF problem formulated in rectangular voltage coordinates, which is something of a departure from the majority of the studies, which tend to use the polar coordinate formulation. The heuristic particle swarm optimization (PSO) and the classical primal-dual interior-point method (PDIPM) are applied to the solution of the VVO problem and a comparative analysis of the relative performance of the two algorithms for this problem is presented. Four case studies based on the 6-bus, IEEE 14-bus, 30-bus, and 118-bus test systems are presented. The comparative performance analysis reveals that the two algorithms have complementary strengths, when evaluated on the basis of the solution quality and computational efficiency. Particularly, the PSO algorithm achieves greater power loss minimization, whereas the PDIPM exhibits greater speed of convergence (and, thus, better computational efficiency) relative to the PSO algorithm, particularly for higher-dimensional problems. An additional distinguishing characteristic of the proposed solution is that it incorporates the Newton–Raphson load flow computation, also formulated in rectangular voltage coordinates, which adds to the efficiency and effectiveness of the presented solution method.

ALGORITMO DE BUSCA DISPERSA PARA RESOLUÇÃO DE PROBLEMAS DE OTIMIZAÇÃO DISCRETOS E CONTÍNUOS

Optimization problems are very complex to be solved, as they can present multiple optimal solutions and, in certain cases, only a globally optimal solution. The mathematical formulation of these problems is composed of continuous and discrete variables with linear and nonlinear functions. The solution of these problems by mathematical modeling through solvers may not converge to a feasible solution or may demand much computational time, when many variables are considered. Thus, using metaheuristics to solve these problems is desirable according to the literature. The scatter search (SS) metaheuristic algorithm has been highlighted in the literature as an excellent combinatorial optimization algorithm for dealing with quality and diversity solutions. This work aims to present two methods using the SS algorithm to solve problems with continuous and discrete variables. Therefore, the SS algorithm is implemented to solve the traveling salesperson problem (TSP), which is a problem that contains only discrete variables, and also, another version of SS is implemented to solve the optimal power flow (OPF) problem, which has continuous and discrete variables. Two instances of the TSP and three instances of the OPF problem were used. The results show that the SS solves both problems efficiently and presents better results in some cases than the solutions of the same problems using classical mathematical models through solvers. It is concluded that implementing the SS algorithm does not require much effort and that good results can be achieved for solving optimization problems with variables of any nature.

An effective solution to the optimal power flow problem using meta-heuristic algorithms

Financial loss in power systems is an emerging problem that needs to be resolved. To tackle the mentioned problem, energy generated from various generation sources in the power network needs proper scheduling. In order to determine the best settings for the control variables, this study formulates and solves an optimal power flow (OPF) problem. In the proposed work, the bird swarm algorithm (BSA), JAYA, and a hybrid of both algorithms, termed as HJBSA, are used for obtaining the settings of optimum variables. We perform simulations by considering the constraints of voltage stability and line capacity, and generated reactive and active power. In addition, the used algorithms solve the problem of OPF and minimize carbon emission generated from thermal systems, fuel cost, voltage deviations, and losses in generation of active power. The suggested approach is evaluated by putting it into use on two separate IEEE testing systems, one with 30 buses and the other with 57 buses. The simulation results show that for the 30-bus system, the minimization in cost by HJBSA, JAYA, and BSA is 860.54 $/h, 862.31, $/h and 900.01 $/h, respectively, while for the 57-bus system, it is 5506.9 $/h, 6237.4, $/h and 7245.6 $/h for HJBSA, JAYA, and BSA, respectively. Similarly, for the 30-bus system, the power loss by HJBSA, JAYA, and BSA is 9.542 MW, 10.102 MW, and 11.427 MW, respectively, while for the 57-bus system, the value of power loss is 13.473 MW, 20.552, MW and 18.638 MW for HJBSA, JAYA, and BSA, respectively. Moreover, HJBSA, JAYA, and BSA cause reduction in carbon emissions by 4.394 ton/h, 4.524, ton/h and 4.401 ton/h, respectively, with the 30-bus system. With the 57-bus system, HJBSA, JAYA, and BSA cause reduction in carbon emissions by 26.429 ton/h, 27.014, ton/h and 28.568 ton/h, respectively. The results show the outperformance of HJBSA.

An adjustable Predictive&Prescriptive method for the RO-based optimal power flow problem

Traditionally before solving the optimal power flow considering uncertainty (OPF–U) problem, the predicted value of uncertainty parameters, such as wind power, e.g., is derived from data using a statistics approach or machine learning. Based on the predicted uncertainty parameters, the solution to the OPF-U problem can be obtained by the prescriptive analytics technique, such as robust optimization (RO). However, it is unclarified how the prediction error in predictive analytics affects solving the OPF-U problem in prescriptive analytics. We propose an adjustable framework method combining machine learning and RO for the OPF-U problem. The k-nearest neighbor is applied to obtain k samples around the predicted value from sufficient historical data. And the optimization results from a minimum volume ellipsoid set containing the k samples are applied to construct KMV set. Then a robust fluctuation region with an adjustable budget level is gained from the KMV set by a two-term exponential formula, which can be embedded into a two-stage RO model. Computational experiments under test cases of different uncertainty scales show the robustness and adjustability of the proposed fluctuation region are better than the state-of-the-art box and ellipsoidal sets. The solution of the proposed two-stage RO model is more economical than the state-of-the-art RO model. The out-of-sample simulation also demonstrates the proposed adjustable Predictive&Prescriptive method can reduce the computational burden as the scale of the system increases when predictive and prescriptive analytics are separated.

Techno-economic feasibility analysis of grid configuration sizing for hybrid renewable energy system in Turkey using different optimization techniques

Today, with a human population of 7.5 billion, increasing power consumption, and widespread use of high-technology equipment, the need for energy in the world is increasing day by day. The damage to nature caused by non-renewable energy resources and the economic and political disadvantages they cause in countries that must import these resources have led the world to search for alternative energy sources. One of the most important benefits of renewable energy sources is that they can create hybrid energy systems with other energy sources. Hybrid energy systems are structures in that more than one energy generation unit works together to feed the electrical load. In this paper, a hybrid system will be designed by using Homer PRO, to supply the energy consumed in the residential areas of Karaburun and Urla districts of Izmir province in Turkey with hybrid renewable energy systems. Systems of different sizes are designed for 50%, 75%, and 100% penetration rates, and sales to the grid are constrained to 0%, 25%, 50%, and no constraint on sales. Sensitivity analyses have been performed for 10% and 20% more power required by the load. Techno-economic analyses were done for the systems and the optimal system has been identified. The power flow of the optimal system is inspected by defining the network in Python and Fire Hawk Optimizer (FHO), Grey Wolf Optimizer (GWO), and Particle Swarm Optimization (PSO) are used for optimal sizing of the system. The optimal system has a Net Present Cost (NPC) of $52.3 M, 34 wind turbines, and 954 kW PV with conditions of 100% penetration and no restrictions on sales to the grid. FHO proposed 26 wind turbines and 780 kW PVs for Urla and 8 wind turbines, and 174 kW PVs for Karaburun. GWO proposed 25 wind turbines and 747 kW PVs for Urla, 9 wind turbines, and 165 PVs for Karaburun. PSO offered 24 wind turbines and 708 kW PVs for Urla, 10 wind turbines, and 246 kW PVs for Karaburun. When there is no sale to and 25% sales to the grid, it is seen that the optimal scenario is the system with a 50% penetration rate. In fully sale-constrained systems, NPCs are higher than the base system and they can never pay for themselves compared to the base system. It is concluded that smaller-sized systems are more suitable for systems with high constraints. The proposed FHO algorithm and GWO algorithm react to increasing penetration ratios by enlarging the system size in the regions with high load demand. PSO sizes the system like predictions by load demand. FHO reacts quicker to increasing penetrations than PSO and GWO. FHO algorithm is found to be usable to solve optimal power flow problems and optimal system sizing.

Enhanced coati optimization algorithm-based optimal power flow including renewable energy uncertainties and electric vehicles

Power systems now face new issues due to incorporating electric vehicles (EVs) and renewable energy resources (RERs). This paper proposes a novel Enhanced Coati Optimization Algorithm (ECOA) for obtaining the optimal solution of the probabilistic optimal power flow (POPF) problems. The ECOA is a metaheuristic optimization algorithm that is robust and efficient for solving complex problems. It is used to tackle the OPF problem, which considers the stochastic characteristics of RERs. Moreover, EVs are included in the presented power systems in this paper. The novel approach is tested and verified on the IEEE-57 and IEEE-118 networks. The effectiveness of the proposed method is demonstrated by making a comparison with other metaheuristic-based methods. To obtain a practical study, real data of wind speed, solar irradiance, and electric vehicles profile are incorporated in the dynamic analyses. The simulation results show that the ECOA is robust and efficient for solving the OPF problem. It can also improve the performance of power systems with RESs and EVs. The findings of this research demonstrate that the suggested approach is promising for power system optimization problems, including RERs and EVs.

An accelerated primal‐dual method for semi‐definite programming relaxation of optimal power flow

AbstractThe application of a semi‐definite programming (SDP) approach to the Alternating Current Optimal Power Flow problem has attracted significant attention in recent years. However, the SDP relaxation of optimal power flow (OPF) can be computationally intensive and lead to memory issues when dealing with large‐scale power systems. To overcome these challenges, we have developed APD–SDP, an optimisation solver based on a first‐order primal–dual algorithm. This framework incorporates various acceleration techniques, such as rescaling, step size decay and reset, adaptive line search, and restart, to improve efficiency. To further speed up computations, we have developed a customised eigenvalue decomposition component by exploiting the 3 × 3 block structure in the dual SDP formulation. Experimental results demonstrate that APD–SDP outperforms other commercial and open‐source SDP solvers on large‐scale and high‐dimensional PGLib‐OPF datasets.

An enhanced turbulent flow of water-based optimization for optimal power flow of power system integrated wind turbine and solar photovoltaic generators

This paper uses enhanced turbulent flow in water-based optimization (TFWO), specifically ETFWO, to achieve optimal power flow (OPF) in electrical networks that use both solar photovoltaic (PV) units and wind turbines (WTs). ETFWO is an enhanced TFWO that alters the TFWO structure through the promotion of communication and collaboration. Individuals in the population now interact with each other more often, which makes it possible to search more accurately in the search area while ignoring local optimal solutions. Probabilistic models and real-time data on wind speed and solar irradiance are used to predict the power output of WT and PV producers. The OPF and solution methods are evaluated using the IEEE 30-bus network. By comparing ETFWO to analogical other optimization techniques applied to the same groups of constraints, control variables, and system data, we can gauge the algorithm’s robustness and efficiency in solving OPF. It is shown in this paper that the proposed ETFWO algorithm can provide suitable solutions to OPF problems in electrical networks with integrated PV units and WTs in terms of energy generation costs, improved voltage profiles, emissions, and losses, compared to the traditional TFWO and other proposed algorithms in recent studies.

A leader supply-demand-based optimization for large scale optimal power flow problem considering renewable energy generations

The supply-demand-based optimization (SDO) is among the recent stochastic approaches that have proven its capability in solving challenging engineering tasks. Owing to the non-linearity and complexity of the real-world IEEE optimal power flow (OPF) in modern power system issues and like the existing algorithms, the SDO optimizer necessitates some enhancement to satisfy the required OPF characteristics integrating hybrid wind and solar powers. Thus, a SDO variant namely leader supply-demand-based optimization (LSDO) is proposed in this research. The LSDO is suggested to improve the exploration based on the simultaneous crossover and mutation mechanisms and thereby reduce the probability of trapping in local optima. The LSDO effectiveness has been first tested on 23 benchmark functions and has been assessed through a comparison with well-regarded state-of-the-art competitors. Afterward, Three well-known constrained IEEE 30, 57, and 118-bus test systems incorporating both wind and solar power sources were investigated in order to authenticate the performance of the LSDO considering a constraint handling technique called superiority of feasible solutions (SF). The statistical outcomes reveal that the LSDO offers promising competitive results not only for its first version but also for the other competitors.

A Methodology to Evaluate Reactive Power Reserves Scarcity During the Energy Transition

The lack of reserves for reactive power production and absorption is an envisioned, still basically unexplored, threat to the voltage profile adequacy and thereby secure operation of transmission grids during the energy transition toward renewable-dominated power production. This paper proposes a novel, generic, comprehensive, and realistic methodology to identify when this issue of reactive power reserves (RPRs) scarcity during plausible scenarios of the energy transition would become severe. The computational core of the proposed methodology comprises four different AC security-constrained optimal power flow (SCOPF) problems: one conventional, two tailored ones that assess the RPRs scarcity in production and absorption modes, respectively, and an optimal reactive power dispatch. The methodology is versatile, offering the possibility to assess RPRs in different timescales, ranging from day-ahead short-term operation to years-ahead long-term operation, and considering appropriate renewable energy production forecasts and day-dependent load profiles. The proposed methodology can serve as a decision support tool for the transmission system operator (TSO), allowing to plug and play different plausible energy transition scenarios (e.g., differing in terms of sequence and timing of: phased out power plants as well as location, type, and size of renewable energy sources deployed) and ultimately informing the TSO about the timing where RPRs become insufficient to maintain security. Without loss of generality, the value of the proposed methodology is extensively demonstrated in a 60-bus Nordic32 system, considering 52 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N-1$</tex-math></inline-formula> line and generator contingencies, while the tractability of AC SCOPF problems is assessed in a 1,203-bus system.

Distributed Optimal Power Flow in Unbalanced Distribution Grids With Non-Ideal Communication

The use of distributed optimization for solving optimal power flow (OPF) problems in distribution networks is increasing as the number of controllable devices and the span of service areas increase. However, the performance of the distributed optimization algorithm largely depends on the availability and quality of communication links between the computing entities. In this paper, we evaluate the performance of the alternating direction method of multipliers (ADMM) for solving the OPF problem for volt-VAr optimization (VVO) under non-ideal communication. The overall problem is formulated by considering the unbalanced operation of multi-phase distribution networks. The algorithm's performance is first analyzed, assuming there is an ideal communication between computing entities, which serves as a benchmark for further analysis. Then, two non-ideal communication models, namely (1) sporadic communication failure and (2) communication under a noisy transmission, are applied to the information exchange architecture of the ADMM. Extensive numerical experiments are conducted with two test systems, the IEEE 123-bus feeder and a 2522-bus network scaled down from the IEEE 8500-bus system; these are used to evaluate the performance of the algorithm. The results indicate that the ADMM-based distributed VVO algorithm has deteriorated performance under high levels of communication failure and high levels of noise injection. Additionally, although the centralized-VVO counterpart has some computational superiority when the overall problem is convex and no communication impairments exist, the distributed-VVO has superior immunized solution performance under realistic communication constraints.

Fast Optimal Power Flow With Guarantees via an Unsupervised Generative Model

Climate change concerns are driving the widespread integration of renewable generation sources, storage systems, electric vehicles and diverse consumer loads. Inherent variabilities of these power entities introduce uncertainties that affect the economical operations and integrity of the electrical grid. Thus, optimal power flow (OPF) studies must be conducted at high granularity in order to account for these fluctuations. However, due to the non-convex nature of the OPF problem, solving it in real-time still remains an open challenge. In this paper, a novel data-driven approach that combines generative learning, information theory and domain knowledge is proposed to enable real-time OPF studies. In order to train this model, only <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feasible</i> datapoints are necessary - not optimal values. Once trained, the time required to compute the solution is extremely fast and falls within the sub-second range. No information pertaining to the topology or power flow equations is required once the model is trained. Theoretical guarantees on optimality and feasibility of the solutions generated by the proposed ML model are established. Comprehensive practical and comparative studies conducted demonstrate the efficacy of the proposed data-driven approach for solving OPF in real-time.

Evaluating Power Transfer of Transmission Lines and Proposing Power Transfer Reduction Actions to Enhance Small-Signal Stability

Small-signal stability (SSS) is one of the limiting factors for determining the power transfer capability (PTC) of transmission lines. Control centers try to optimally operate the system with the lowest probability of instability after a line outage contingency. Hence, this article proposes a novel framework to evaluate the PTC from the viewpoint of SSS, and for the violated cases, proper actions for power transfer reduction (PTR) are applied. The proposed methodology is based on a SSS optimal power flow problem. First, the proposed method identifies the stressful line by developing a novel index. Then, different dynamic parameters, which can be calculated quickly and reliably are introduced to evaluate the PTC of stressful line from the SSS viewpoint. Afterward, appropriate actions are enabled for the violated scenarios. These actions include generator redispatching and load shedding, which are exploited based on sensitivity analysis. The proposed framework not only can modify the power transfer of the understudy line, but also considers PTC constraints of other lines. The suggested scheme is evaluated on both IEEE 39 bus and 118 bus test systems. The obtained results confirm that the proposed scheme superiorly evaluates PTC and enhances SSS by applying the PTR action to preserve system security.

A Novel Ameliorated Moth Swarm Algorithm for Optimization of Hybrid Power System Incorporating FACTS Controllers

In power system engineering, a recent trend is to integrate conventional thermal units (CTUs) and alternative energy sources (AESs) for cost-effective and environmentally friendly operation. In the current work, the optimal power flow (OPF) problem that integrates CTUs with three highly intermittent energy sources wind energy (WE), photovoltaic energy (PVE), and electric vehicle (EV) as a vehicle to grid (V2G) source is being developed. Using various probability distribution functions (PDFs), an interpretable probabilistic strategy is devised to deal with the uncertainties of the aforementioned energy sources. To ensure stable operational conditions, a single static series compensator (SSSC) is optimally configured and placed in the combined power system. Further, to address the instability and generation uncertainty of an overloaded AESs-based power system, a single SSSC and a single unified power flow controller (UPFC) is optimally placed and configured simultaneously. The ameliorated moth swarm algorithm (AMSA) is proposed for the solution of the developed complex OPF model by combining a) chaotic mapping technique (CMT) and b) a novel mutation tactic with conventional MSA. The performance of the proposed AMSA is verified by utilizing ten standard benchmark functions. Furthermore, the proposed technique's performance is assessed using nine different power-related, uncertainty-induced, and single SSSC-included test setups, taking into account both IEEE 30 and 118-bus-based test power networks. For a more in-depth analysis of the ability of the proposed technique, it is further applied to optimise AESs-based IEEE 118-bus test network under enhanced load level and in the presence of optimally placed single SSSC and single UPFC. The efficacy of our proposed AMSA technique is compared against seven powerful metaheuristic techniques, both analytically and statistically. The results of the tests reveal that the proposed AMSA outperforms the other methods investigated in terms of quality and accuracy.

Probabilistic optimal power flow in wind energy integrated power system based on the K‐medoids data clustering method considering correlated uncertain variables

AbstractRenewable energy sources have increasingly been integrated into power systems because of their superior environmental, technical, and economic advantages. However, the uncertainty of these sources besides load fluctuations and equipment outages brings new challenges to power system operating and planning studies. Also, the correlation between uncertain variables makes operational decisions more and more complicated. Probabilistic assessment of power systems is essential to evaluate uncertainties’ effects and make reasonable decisions. Methods with high accuracy and low computational burden are efficient for online and fast requirements such as optimal power flow (OPF) problems. A clustering method based on the K‐medoids technique is used for the probabilistic assessment of the power system in the OPF problem. Unlike other clustering techniques the K‐medoids method can manage discrete variables such as equipment outages besides other continuous variables such as load and wind generation. This paper presents an OPF problem considering the uncertainty of renewable energy sources, load fluctuations, and transmission lines outage as well as the correlation among them. The probabilistic assessment is conducted by the K‐medoids method and the optimization problem is solved by the cooperation search algorithm (CSA) as an efficient evolutionary algorithm. Numerical results using the IEEE standard 30 and 118 bus test systems show the efficiency of the proposed method in terms of accuracy and computational burden.