Power System Optimization Problems Research Articles

Identification study of solar cell/module using recent optimization techniques

This paper proposes the application of a novel metaphor-free population optimization based on the mathematics of the Runge Kutta method (RUN) for parameter extraction of a double-diode model of the unknown solar cell and photovoltaic (PV) module parameters. The RUN optimizer is employed to determine the seven unknown parameters of the two-diode model. Fitting the experimental data is the main objective of the extracted unknown parameters to develop a generic PV model. Consequently, the root means squared error (RMSE) between the measured and estimated data is considered as the primary objective function. The suggested objective function achieves the closeness degree between the estimated and experimental data. For getting the generic model, applications of the proposed RUN are carried out on two different commercial PV cells. To assess the proposed algorithm, a comprehensive comparison study is employed and compared with several well-matured optimization algorithms reported in the literature. Numerical simulations prove the high precision and fast response of the proposed RUN algorithm for solving multiple PV models. Added to that, the RUN can be considered as a good alternative optimization method for solving power systems optimization problems.

Optimal Intelligence Planning of Wind Power Plants and Power System Storage Devices in Power Station Unit Commitment Based

Renewable energy sources (RES) such as wind turbines (WT) and solar cells have attracted the attention of power system operators and users alike, thanks to their lack of environmental pollution, independence of fossil fuels, and meager marginal costs. With the introduction of RES, challenges have faced the unit commitment (UC) problem as a traditional power system optimization problem aiming to minimize total costs by optimally determining units’ inputs and outputs, and specifying the optimal generation of each unit. The output power of RES such as WT and solar cells depends on natural factors such as wind speed and solar irradiation that are riddled with uncertainty. As a result, the UC problem in the presence of RES faces uncertainties. The grid consumed load is not always equal to and is randomly different from the predicted values, which also contributes to uncertainty in solving the aforementioned problem. The current study proposes a novel two-stage optimization model with load and wind farm power generation uncertainties for the security-constrained UC to overcome this problem. The new model is adopted to solve the wind-generated power uncertainty, and energy storage systems (ESSs) are included in the problem for further management. The problem is written as an uncertain optimization model which are the stochastic nature with security-constrains which included undispatchable power resources and storage units. To solve the UC programming model, a hybrid honey bee mating and bacterial foraging algorithm is employed to reduce problem complexity and achieve optimal results.

Global Sensitivity Analysis Applied to Train Traffic Rescheduling: A Comparative Study

The adjustment of rail traffic in the event of an electrical infrastructure disruption presents an important decision-making process for the smooth operation of the network. Railway systems are complex, and their analysis relies on expensive simulations, which makes incident management difficult. This paper proposes the use of sensitivity analysis in order to evaluate the influence of different traffic adjustment actions (e.g., spacing between trains and speed reduction) on the train supply voltage, which must never drop below the critical value prescribed by technical standards. Three global sensitivity analysis methods dedicated to black box, multivariate, nonlinear models are considered: generalized Sobol indices, energy distance-based indices, and regional sensitivity analysis. The three methods are applied to a simple traffic rescheduling test case and give similar results, but at different costs. Regional sensitivity analysis appears to be the most suitable method for the present application: it is easy to implement, rather fast, and accounts for constraints on the system output (a key feature for electrical incident management). The application of this method to a test case representative of a real rescheduling problem shows that it provides the information needed by the traffic manager to reschedule traffic in an efficient way. The same type of approach can be used for any power system optimization problem with the same characteristics.

HGWO-SA: A Novel Hybrid Grey Wolf Optimizer-Simulated Annealing Algorithm for Engineering and Power System Optimization Problems

: The improved variants of a Grey wolf optimizer have good exploration capability for the global optimum solution. However, the exploitation competence of the existing variants of grey wolf optimizer is unfortunate. Researchers are continuously trying to improve the exploitation phase of the existing grey wolf optimizer, but still, the improved variants of grey wolf optimizer lack in local search capability. In the proposed research, the exploitation phase of the existing grey wolf optimizer has been further improved using a simulated annealing algorithm and the proposed hybrid optimizer has been named as hGWO-SA algorithm. The effectiveness of the proposed hybrid variant has been tested for various benchmark problems, including multi-disciplinary optimization and design engineering problems and unit commitment problems of the electric power system and it has been experimentally found that the proposed optimizer performs much better than existing variants of grey wolf optimizer. The feasibility of hGWO-SA algorithm has been tested for small & medium scale power systems unit commitment problems, in which, the results for 4 unit, 5 unit, 6 unit, 7 unit, 10 units, 19 unit, 20 unit, 40 unit and 60 units are evaluated. The 10-generating units are evaluated with 5% and 10% spinning reserve. The results obviously show that the suggested method gives the superior type of solutions as compared to other algorithms.

OPTIMAL REGULATION OF LOCAL ENERGY SYSTEM WITH RENEWABLE ENERGY SOURCES

The paper is devoted to solving the balancing problem in local power systems with renewable energy sources. For a power system optimization problem, whose operation depends on random weather factors, a convex parameter optimization or optimal control problem was solved using controlled generation, for each individual realization of a random process as a deterministic function, and then statistical processing of results over a set of random realizations was performed and distribution density functions of the desired target function were constructed, followed by estimation of expected values and their confidence intervals. The process describing current deviations of generated power from mean value is modelled as discrete stray model and has properties of Ornstein-Uhlenbeck process, which allowed varying the duration of unit interval, in particular to select data bases of operating objects with inherent temporal discreteness of their monitoring systems. Random components are investigated and modelled, while the average values are considered to be deterministic and are provided within a predictable schedule using also traditional energy sources (centralised power grid). A mathematical model of the combined operation of renewable energy sources in a system with variable load, electric storage device and auxiliary regulating generator is implemented as a scheme of sequential generation and consumption models and random processes describing the current state of the power system. The operation of the electricity accumulators is dependent on the processes mentioned, but in the full balance, it appears together with generation or load losses, which are cumulative sums of unbalanced power and may have a different distribution from the normal one. However, these processes are internal, relating to the redistribution of energy within a generation system whose capacity is generally described satisfactorily, given the relevant criteria, by a normal law. Under this condition, it is possible to estimate the probability of different circumstances - over- or under-generation, that is, to give a numerical estimate of the reliability of energy supply.

Multi-Mean Scout Particle Swarm Optimization (MMSCPSO) based Reactive Power Optimization in Large-Scale Power Systems

The particle swarm optimization (PSO) is a population-based algorithm belonging into metaheuristic algorithms and it has been used since many decades for handling and solving various optimization problems. However, it suffers from premature convergence and it can easily be trapped into local optimum. Therefore, this study presents a new algorithm called multi-mean scout particle swarm optimization (MMSCPSO) which solves reactive power optimization problem in a practical power system. The main objective is to minimize the active power losses in transmission line while satisfying various constraints. Control variables to be adjusted are voltage at all generator buses, transformer tap position and shunt capacitor. The standard PSO has a better exploitation ability but it has a very poor exploration ability. Consequently, to maintain the balance between these two abilities during the search process by helping particles to escape from the local optimum trap, modifications were made where initial population was produced by tent and logistic maps and it was subdividing it into sub-swarms to ensure good distribution of particles within the search space. Beside this, the idle particles (particles unable to improve their personal best) were replaced by insertion of a scout phase inspired from the artificial bee colony in the standard PSO. This algorithm has been applied and tested on IEEE 118-bus system and it has shown a strong performance in terms of active power loss minimization and voltage profile improvement compared to the original PSO Algorithm, whereby the MMSCPSO algorithm reduced the active power losses at 18.681% then the PSO algorithm reduced the active power losses at 15.457%. Hence, the MMSCPSO could be a better solution for reactive power optimization in large-scale power systems.

Vulnerability Assessment of Deep Reinforcement Learning Models for Power System Topology Optimization

This paper studies the vulnerability of deep reinforcement learning (DRL) models for power systems topology optimization under data perturbations and cyber-attack. DRL has recently solved many complex power system optimization problems. However, it has been practically proven that small perturbations of input data can lead to drastically different control decisions and induce danger. To evaluate and mitigate the security risks of DRL models in power systems, we propose a vulnerability assessment method for such DRL models under noisy data and cyber-attack. In specific, we assess the vulnerability of a DRL model in a way that perturbations are constructed to minimize the model’s performance. Besides, several vulnerability indices are proposed to identify the characteristics of perturbations that may cause malfunction of DRL. Simulations on the 14-bus system and the IEEE 118-bus system for topology optimization are carried out to validate the effectiveness of the proposed vulnerability assessment method. The results show that the performance of DRL models for power systems can be significantly degraded under cyber-attack and data perturbations, especially when a proposed vulnerability index has abnormal values.

Optimal Allocation and Sizing of Multi DG Units Including Different Load Model Using Evolutionary Programming

This paper presents the optimal allocation and sizing of multi distributed generation (DG) units including different load models using evolutionary programming (EP) in solving power system optimization problem. This paper also studies on the effect of multi DG placement in different load model. To optimize the power distribution system, multi DG units were used to reduce losses power distribution system. By using EP, the optimal allocation and sizing of multi-DG was determined in order to obtain maximum benefits from its installation. The propose technique was tested into IEEE 69-bus distribution system. The result shows the placement of DG can reduce power loss 89% to 98%. The placement of multi-DG unit has better performance compare to single DG.

Decentralized Dual Proximal Gradient Algorithms for Non-Smooth Constrained Composite Optimization Problems

Decentralized dual methods play significant roles in large-scale optimization, which effectively resolve many constrained optimization problems in machine learning and power systems. In this article, we focus on studying a class of totally non-smooth constrained composite optimization problems over multi-agent systems, where the mutual goal of agents in the system is to optimize a sum of two separable non-smooth functions consisting of a strongly-convex function and another convex (not necessarily strongly-convex) function. Agents in the system conduct parallel local computation and communication in the overall process without leaking their private information. In order to resolve the totally non-smooth constrained composite optimization problem in a fully decentralized manner, we devise a synchronous decentralized dual proximal (SynDe-DuPro) gradient algorithm and its asynchronous version (AsynDe-DuPro) based on the randomized block-coordinate method. Both SynDe-DuPro and AsynDe-DuPro algorithms are theoretically proved to achieve the globally optimal solution to the totally non-smooth constrained composite optimization problem relied on the quasi-Fejér monotone theorem. As a main result, AsynDe-DuPro algorithm attains the globally optimal solution without requiring all agents to be activated at each iteration and thus is more robust than most existing synchronous algorithms. The practicability of the proposed algorithms and correctness of the theoretical findings are demonstrated by the experiments on a constrained Decentralized Sparse Logistic Regression (DSLR) problem in machine learning and a Decentralized Energy Resources Coordination (DERC) problem in power systems.

Linear power flow formulations and optimal operation of three-phase autonomous droop-controlled Microgrids

Linear power flow formulations enable the integration of power flow constraints to linearly constrained power system optimization problems in transmission and distribution systems. Typical examples include the application of DC power flow and DistFlow to distribution system reconfiguration and restoration. While non-linear power flow equations and its associated optimal power flow have been developed in the literature, there is no existing linear power flow formulation for islanded droop-controlled microgrids to the best of the authors' knowledge. To address this need, this paper presents two linear power flow approximations for three-phase islanded droop-controlled microgrids. The first approximation was derived based on the current injection method and the second approximation was derived from the three-phase DistFlow formulation. The two approximations were verified using detailed time-domain simulations at steady-state in PSCAD with resulting mean errors of the nodal voltages being under 1%. To demonstrate the application of the proposed power flow formulations, the two approximations were expanded for integration in optimal power flow formulations for islanded droop-controlled microgrids to minimize cost. Unlike the existing non-linear models, the linear power flow formulations presented in this paper can be solved easily using non-iterative linear matrix operation and its optimal power flow extensions are linearly constrained.

Hybrid Flower Pollination Algorithm with Sequential Quadratic Programming Technique for Solving Dynamic Combined Economic Emission Dispatch Problem

This paper presents the solution of highly complex, non-linear, multi-objective Dynamic Combined Economic Emission Dispatch (DCEED) problem. DCEED is a power system optimization problem with conflicting objectives of fuel cost and emission. DCEED includes constraints like valve point loading effect, Transmission Losses and Ramp Rate limits. Solution of DCEED problem is given by a novel Hybridized Flower Pollination Algorithm (FPA) with Sequential Quadratic Programming (SQP). FPA is a nature inspired population based meta-heuristic optimization technique that models its search on the flower pollination process. The non-convex nature of generation because of numerous operational, physical and dynamic constraints, makes search space highly multi model and complex. This makes DCEED a challenging as well as an attractive problem for research. The effectiveness of FPA-SQP is tested and validated by applying it on IEEE Standard 5-unit and 10-unit non-convex test system in MATLAB environment for the time interval of 24 hours. The results achieved by this algorithm show significant reduction in cost and emission as compared to other available techniques in the literature.

Development of a Lévy flight and FDB-based coyote optimization algorithm for global optimization and real-world ACOPF problems

This article presents an improved version of the coyote optimization algorithm (COA) that is more compatible with nature. In the proposed algorithm, fitness-distance balance (FDB) and Levy flight were used to determine the social tendency of coyote packs and to develop a more effective model imitating the birth of new coyotes. The balanced search performance, global exploration capability, and local exploitation ability of the COA algorithm were enhanced, and the premature convergence problem resolved using these two methods. The performance of the proposed Levy roulette FDB-COA (LRFDBCOA) was compared with 28 other meta-heuristic search (MHS) algorithms to verify its effectiveness on 90 benchmark test functions in different dimensions. The proposed LRFDBCOA and the COA ranked, respectively, the first and the ninth, according to nonparametric statistical results. The proposed algorithm was applied to solve the AC optimal power flow (ACOPF) problem incorporating thermal, wind, and combined solar-small hydro powered energy systems. This problem is described as a constrained, nonconvex, and complex power system optimization problem. The simulation results showed that the proposed algorithm exhibited a definite superiority over both the constrained and highly complex real-world engineering ACOPF problem and the unconstrained convex/nonconvex benchmark problems.

Solving power systems optimization problems in the presence of renewable energy sources using modified exchange market algorithm

This paper introduces a novel evolutionary algorithm namely modified exchange market algorithm (MEMA) to solve the various problems in the power system operation topics such as combined heat and power economic emission dispatch (CHPEED), and multi-area economic dispatch (MAED) in the presence of renewable energy sources (RESs). The MEMA is a new version of the EMA that has been modified to improve its performance and to find a better solution with high robustness. To scrutiny the applicability of the MEMA, it is employed to solve the different problems with considering RESs. Also, to prove the scalability and evaluate the performance of the proposed method, several large and small scale test systems are used in each case. Also, three different approaches are considered to investigate the impacts of RESs. In the first approach, RESs are assumed to be a negative load, while in the latter case, their cost impacts on the problem are also considered. Finally, in the last approach, the uncertainty of RES and its stochastic nature are considered. In all test systems, the results obtained by the proposed method are compared with the results of other suggested techniques in this era. Also, the robustness of the proposed method is investigated using parametric and non-parametric statistical tests. The comparative and statistical analysis confirm the superiority and robustness of the proposed method over the other methods in all test systems.

Solution of Combined Economic Emission Dispatch Problem Using Improved and Chaotic Population-Based Polar Bear Optimization Algorithm

This paper proposes a novel improved polar bear optimization (IPBO) algorithm and employs it along with polar bear optimization (PBO) and chaotic population-based variants of polar bear optimization algorithm to solve combined economic emission dispatch (CEED) problem. PBO is a meta-heuristic technique inspired by the hunting mechanisms of polar bears in harsh arctic regions based only on their sense of sight. Polar bears in nature exhibits hunting of prey not only on their sight but also on their keen sense of smell. Hence, a novel improved variant of PBO which enhances its operation by equipping it with tracking capabilities utilizing polar bears sense of smell has been proposed in this study. The validity of novel IPBO is tested through 5 benchmark functions and 140 units Korean ED problem. Furthermore, the impact of different population initialization methods is also observed on the capabilities of conventional PBO. The proposed chaotic population based PBO, improved PBO (IPBO) and PBO are employed to solve IEEE 3 unit and 6-unit CEED problem. CEED is a multi-objective power system optimization problem with conflicting objectives of cost and emission. The simulations performed undertake each objective individually as well as collectively. The results achieved by each technique are analyzed statistically through Wilcoxon rank sum test (WRST), probability density function and cumulative density function. Both the statistical and numerical analysis of results showcase the strength of each solution technique as well as their ability to improve cost and emissions in the solution of CEED problem.

Optimization of Electrical Power Systems Using Hybrid PSO-GA Computational Algorithm: a Review

Since the intelligent optimization algorithms has been successful in solving tested functions, the electrical power system researchers have done many studies and applications using optimal strategies. Any topic of power system has been optimized using those algorithms such as the quality, the stability, the voltage profile, the reliability, the smart grid, and the economic generations. With the increasing demand for electricity, the traditional methods to solve the optimization problems cannot meet the demand, and with the deepening of research, many emerging technologies are applied to the solution of power system optimization problems. However, when solving practical engineering problems, there are still many challenges. Genetic Algorithm and Particle Swarm Optimization are two of the most famous strategies that are applied to solve the power system problems. This paper focuses on the advantages of advance hybrid computational algorithm in order to optimize the performance of electrical power system. The detail of the hybrid of classical intelligent algorithm Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), which have been used to solve the power system problems, has been briefly summarized. In addition, the hybrid algorithm is classified into several types depending on the method of the computation between them. The parallel, the Serial, and the impeded hybrid are the main types of this classification. Finally, future suggestions of the important power system applications using the hybrid GA-PSO are introduced according to the corresponding methods, which have given good results for engineering systems.

A Genetic Based Algorithm for Short-Term Thermal Generating Unit Commitment.(Dept.E)

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.

Optimal power flow solution with stochastic wind power using the Lévy coyote optimization algorithm

Optimal power flow (OPF) is one of the most fundamental single/multi-objective, nonlinear, and non-convex optimization problems in modern power systems. Renewable energy sources are integrated into power systems to provide environmental sustainability and to reduce emissions and fuel costs. Therefore, some conventional thermal generators are being replaced with wind power sources. Although wind power is a widely used renewable energy source, it is intermittent in nature and wind speed is uncertain at any given time. For this reason, the Weibull probability density function is one of the important methods used in calculating available wind power. This paper presents an improved method based on the Levy Coyote optimization algorithm (LCOA) for solving the OPF problem with stochastic wind power. In the proposed LCOA, Levy Flights were added to the Coyote optimization algorithm to avoid local optima and to improve the ability to focus on optimal solutions. To show the effect of the novel contribution to the algorithm, the LCOA method was tested using the Congress on Evolutionary Computation-2005 benchmark test functions. Subsequently, the solution to the OPF problem with stochastic wind power was tested via the LCOA and other heuristic optimization algorithms in IEEE 30-bus, 57-bus, and 118-bus test systems. Eighteen different cases were executed including fuel cost, emissions, active power loss, voltage profile, and voltage stability, in single- and multi-objective optimization. The results showed that the LCOA was more effective than the other optimization methods at reaching an optimal solution to the OPF problem with stochastic wind power.

Distributed economic MPC for LFC of multi-area power system with wind power plants in power market environment

The rising penetration of renewable energy and the diverse power transaction mechanisms in power market environment (PME) make the control problem of the power system more difficult. Considering environmental pressure and market competition pressure, it is more important to ensure the economic operation of power system in the control process. This paper presents a novel distributed economic model predictive control (DEMPC) strategy for the load frequency control (LFC) problem of a practical multi-area power system incorporating wind power plants (WPPs) in PME. Meanwhile, the real time economic optimization is achieved by integrating the economic factors into the objective function. A distribution company (DISCO) participation matrix (DPM) is applied to visualize the liberalization of power transactions between the DISCOs and dispatchable generation companies (DGENCOs). Area participation factors (apfs) are introduced to present the allocation of uncontracted load demands. The DEMPC controllers solve the optimization problem of power system with external disturbances and constraints including frequency fluctuation constraint, control input constraints, output power of WPP constraint and pitch angle constraint of the wind turbine. Response results for a three-area power system including WPPs and thermal power plants demonstrate the certain improvement of the system performance with the participation of wind turbines and the high-efficiency of the proposed DEMPC strategy.

Minimize Linearization Error of Power Flow Model Based on Optimal Selection of Variable Space

Linear power flow models are widely used in power system analysis because it brings huge computational benefits, especially for power system optimization problems. The improvement of the linearization accuracy is greatly beneficial to the power system operation considering the large amount of power scheduled based on linear power flow models. We find that the linearization error substantially changes with different selections of the variable space. In this paper, we formulate a model to find the linear power flow model with the minimized linearization error based on the optimal selection of the variable space. The expression of the variable space is generalized as a polynomial function. A simplified model of power losses is proposed. The difference between the selection of the variable space and the common hot-start approaches is illustrated. The effectiveness of the proposed linear power flow model is verified by power flow calculation and optimal power flow (OPF) calculation in the IEEE and Polish test systems.

Large-scale economic load dispatch using squirrel search algorithm

PurposeEconomic load dispatch (ELD) is one of the crucial optimization problems in power system planning and operation. The ELD problem with valve point loading (VPL) and multi-fuel options (MFO) is defined as a non-smooth and non-convex optimization problem with equality and inequality constraints, which obliges an efficient heuristic strategy to be addressed. The purpose of this study is to present a new and powerful heuristic optimization technique (HOT) named as squirrel search algorithm (SSA) to solve non-convex ELD problems of large-scale power plants.Design/methodology/approachThe suggested SSA approach is aimed to minimize the total fuel cost consumption of power plant considering their generation values as decision variables while satisfying the problem constraints. It confers a solution to the ELD issue by anchoring with foraging behavior of squirrels based on the dynamic jumping and gliding strategies. Furthermore, a heuristic approach and selection rules are used in SSA to handle the constraints appropriately.FindingsEmpirical results authenticate the superior performance of SSA technique by validating on four different large-scale systems. Comparing SSA with other HOTs, numerical results depict its proficiencies with high-qualitative solution and by its excellent computational efficiency to solve the ELD problems with non-smooth fuel cost function addressing the VPL and MFO. Moreover, the non-parametric tests prove the robustness and efficacy of the suggested SSA and demonstrate that it can be used as a competent optimizer for solving the real-world large-scale non-convex ELD problems.Practical implicationsThis study has compared various HOTs to determine optimal generation scheduling for large-scale ELD problems. Consequently, its comparative analysis will be beneficial to power engineers for accurate generation planning.Originality/valueTo the best of the authors’ knowledge, this manuscript is the first research work of using SSA approach for solving ELD problems. Consequently, the solution to this problem configures the key contribution of this paper.