Modified Newton method for reactive dispatching

This paper describes a new approach to the optimal reactive dispatch problem, based on an augmented Lagrangian function of the original problem. The Karush–Kuhn–Tucker (KKT) optimality conditions are solved by the modified Newton method. The second-order information in the original system of equations is approximated and the first-order information is kept intact The proposed method requires less computer memory than those algorithms currently available. The effectiveness of the proposed approach has been examined by solving the IEEE 30-bus and the BRAZILIAN 810-bus systems.     

Optimal siting and sizing of UPFC using evolutionary algorithms

This paper addresses an application of evolutionary algorithms to optimal siting and sizing of UPFC which are formulated as single and multiobjective optimization problems. The decision variables such as optimal location, both line and distance of UPFC from the sending end, control parameters of UPFC and system reactive power reserves are considered in the optimization process. Minimization of total costs including installation cost of UPFC and enhancement of the loadability limit are considered as objectives. To reduce the complexity in modeling and the number of variables and constraints, transformer model of UPFC is used for simulation purposes. CMAES and NSGA-II algorithms are used for optimal siting and sizing of UPFC on IEEE 14 and 30 bus test systems. NSGA-II algorithm is tested on IEEE 118 bus system to prove the versatility of the algorithm when applied to large systems. To validate the results of transformer model of UPFC for optimal siting and sizing, results using other models are considered. In single objective optimization problem, CMAES algorithm with transformer model yields better results when compared to other UPFC models. The statistical results conducted on 20 independent trials of CMAES algorithm authenticate the results obtained. For validating the results of NSGA-II with transformer model for optimal siting and sizing of UPFC, the reference Pareto front generated using multiple run CMAES algorithm by minimizing weighted objective is considered. In multiobjective optimization problem, the similarity between the generated Pareto front and the reference Pareto front validates the results obtained.     

Solving multiobjective optimal reactive power dispatch using modified NSGA-II

This paper addresses an application of modified NSGA-II (MNSGA-II) by incorporating controlled elitism and dynamic crowding distance (DCD) strategies in NSGA-II to multiobjective optimal reactive power dispatch (ORPD) problem by minimizing real power loss and maximizing the system voltage stability. To validate the Pareto-front obtained using MNSGA-II, reference Pareto-front is generated using multiple runs of single objective optimization with weighted sum of objectives. For simulation purposes, IEEE 30 and IEEE 118 bus test systems are considered. The performance of MNSGA-II, NSGA-II and multiobjective particle swarm optimization (MOPSO) approaches are compared with respect to multiobjective performance measures. TOPSIS technique is applied on obtained non-dominated solutions to determine best compromise solution (BCS). Karush-Kuhn-Tucker (KKT) conditions are also applied on the obtained non-dominated solutions to substantiate a claim on optimality. Simulation results are quite promising and the MNSGA-II performs better than NSGA-II in maintaining diversity and authenticates its potential to solve multiobjective ORPD effectively.     

An extended probabilistic model building genetic network programming using both of good and bad individuals

Classical estimation of distribution algorithms (EDAs) generally use truncation selection to estimate the distribution of the good individuals while ignoring the bad ones. However, various researches in evolutionary algorithms (EAs) have reported that the bad individuals may affect and help solving the problem. This paper proposes a new method to use the bad individuals by studying the substructures rather than the entire individual structures to solve reinforcement learning (RL) problems, which generally factorize their entire solutions to the sequences of state–action pairs. This work was studied in a recent graph‐based EDA named probabilistic model building genetic network programming (PMBGNP), which could solve RL problems successfully, to propose an extended PMBGNP. The effectiveness of this work is verified in an RL problem, namely robot control. Compared to other related work, results show that the proposed method can significantly speed up the evolution efficiency. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Optimal reactive power planning using evolutionary algorithms: acomparative study for evolutionary programming, evolutionary strategy,genetic algorithm, and linear programming

This paper presents a comparative study for three evolutionary algorithms (EAs) to the optimal reactive power planning (ORPP) problem: evolutionary programming, evolutionary strategy, and genetic algorithm. The ORPP problem is decomposed into P- and Q-optimization modules, and each module is optimized by the EAs in an iterative manner to obtain the global solution. The EA methods for the ORPP problem are evaluated against the IEEE 30-bus system as a common testbed, and the results are compared against each other and with those of linear programming     

Teaching Advanced Features of Evolutionary Algorithms Using Japanese Puzzles

In this paper, a method to teach advanced features of evolutionary algorithms (EAs), using a famous game known as Japanese puzzles is presented. The authors show that Japanese puzzles are constrained combinatorial optimization problems, that can be solved using EAs with different encodings, and are challenging problems for EAs. Other features, such as special operators and local search heuristics and its hybridization with genetic algorithms, can also be taught using these puzzles. The authors report an experience using this method in a course taught at the Universidad de Alcalaacute, Madrid, Spain     

WLAV state estimation for power system containing multitype FACTS devices

This paper presents the state estimation of power system in which not only the bus voltages but also the states of the flexible AC transmission system (FACTS) are considered as the state variables. By using the rectangular form of state variables and equivalent measurement techniques, a linear measurement model with constraints of FACTS device is obtained. The predictor–corrector interior point method based on the weighted least absolute value criterion is developed for solving the optimization problem. Simulation results on the modified IEEE 14‐bus and 118‐bus test systems are provided. The numerical results indicate the effectiveness of the proposed approach. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Application of Multi-Objective Evolutionary Optimization Algorithms to Reactive Power Planning Problem

This paper presents a new approach to treat reactive power (VAr) planning problem using multi-objective evolutionary algorithms (EAs). Specifically, strength Pareto EA (SPEA) and multi-objective particle swarm optimization (MOPSO) approaches have been developed and successfully applied. The overall problem is formulated as a nonlinear constrained multi-objective optimization problem. Minimizing the total incurred cost of the VAr planning problem and maximizing the amount of available transfer capability (ATC) are defined as the main objective functions. The aim is to find the optimal allocation of VAr devices in such a way that investment and operating costs are minimized and at the same time the amount of ATC is maximized. The proposed approaches have been successfully tested on IEEE 14 buses system. As a result a wide set of optimal solutions known as Pareto set is obtained and encouraging results show the superiority of the proposed approaches and confirm their potential to solve such a large-scale multi-objective optimization problem. Copyright © 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Application of pattern search method to power system valve-point economic load dispatch

Direct search (DS) methods are evolutionary algorithms used to solve constrained optimization problems. DS methods do not require any information about the gradient of the objective function at hand, while searching for an optimum solution. One of such methods is pattern search (PS) algorithm. This study presents a new approach based on a constrained pattern search algorithm to solve well-known power system economic load dispatch problem (ELD) with valve-point effect. For illustrative purposes, the proposed PS technique has been applied to various test systems to validate its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method has been assessed and investigated through comparison with results reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving power system economic load dispatch problem.     

Development of a novel algorithm for optimal capacitor placement in distribution systems

Optimal capacitor placement in distribution systems solved by the hybrid method of CODEQ (called HCODEQ method) is proposed in this work. The concepts of chaotic search, opposition-based learning, and quantum mechanics are used in the CODEQ method to overcome the drawback of parameters selection in the differential evolution (DE). However, a larger population size must be used in the CODEQ method. That is a drawback for all evolutionary algorithms (EAs). To overcome this drawback, acceleration operation and migrating operation are embedded into the CODEQ method, i.e. HCODEQ method. The use of these two operations can increase the convergence speed without decreasing the diversity among individuals. One benchmark function and various-scale capacitor placement systems are used to compare the performance of the proposed method, CODEQ method, DE, simulated annealing (SA), and ant system (AS). Numerical results show that the performance of the HCODEQ method is better than the other methods.     

Forecasting of solar irradiance with just‐in‐time modeling

PV power output mainly depends on solar irradiance, which is affected by various meteorological factors. Thus, it is required to predict solar irradiance in the future for the efficient operation of PV systems. In this paper we develop a novel approach for solar irradiance forecasting, in which we combine the black–box model (JIT modeling) with the physical model (GPV data). We investigate the predictive accuracy of solar irradiance over a wide controlled area of each electric power company by utilizing measured data from 44 observation points throughout Japan provided by JMA and 64 points around Kanto provided by NEDO. Finally, we propose an applied forecasting method of solar irradiance to deal with difficulties in compiling databases. We also consider the influence of different GPV default times on solar irradiance prediction. © 2012 Wiley Periodicals, Inc. Electr Eng Jpn, 182(4): 19–28, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.22338     

Small signal stability enhancement of a large scale power system using a bio-inspired whale optimization algorithm

A whale optimization algorithm (WOA)-based power system stabilizer (PSS) design methodology on modified single machine infinite bus (MSMIB) and multi-machine systems to enhance the small-signal stability (SSS) of the power system is presented. The PSS design methodology is implemented using an eigenvalue (EV)-based objective function. The performance of the WOA is tested with several CEC14 and CEC17 test functions to investigate its potential in optimizing the complex mathematical equations. The New England 10-generator 39-bus system and the MSMIB system operating at various loading conditions are considered as the test systems to examine the proposed method. Extensive simulation results are obtained which validate the effectiveness of the proposed WOA method when compared with other algorithms.     

Combined heat and power economic dispatch using exchange market algorithm

Combined heat and power economic dispatch (CHPED) is one of the critical issues in power systems, playing key role in economic performance of the system. CHPED is a challenging optimization problem of non-linear and non-convex type. Thus, evolutionary and heuristic algorithms are employed as effective tools in solving this problem. This paper applies newly proposed exchange market algorithm (EMA) on CHPED problem. EMA is a powerful and robust algorithm. With two powerful absorbing operators pulling solutions toward optimality and two smart searching operators, EMA is able to extract optimum point in optimization problem. In order to examine the proposed algorithm’s capabilities and find optimum solution for CHPED problem, several test systems considering valve-point effect, system power loss and system constraints are optimized. The obtained results prove high capability of EMA in extracting optimum points. The results also show that this algorithm can be utilized as an efficient and reliable tool in solving CHPED problem.     

Inverse optimal adaptive control for non‐linear uncertain systems with exogenous disturbances

A Lyapunov‐based inverse optimal adaptive control‐system design problem for non‐linear uncertain systems with exogenous ℒ︁₂ disturbances is considered. Specifically, an inverse optimal adaptive non‐linear control framework is developed to explicitly characterize globally stabilizing disturbance rejection adaptive controllers that minimize a nonlinear‐nonquadratic performance functional for non‐linear cascade and block cascade systems with parametric uncertainty. It is shown that the adaptive Lyapunov function guaranteeing closed‐loop stability is a solution to the Hamilton–Jacobi–Isaacs equation for the controlled system and thus guarantees both optimality and robust stability. Additionally, the adaptive Lyapunov function is dissipative with respect to a weighted input–output energy supply rate guaranteeing closed‐loop disturbance rejection. For special integrand structures of the performance functionals considered, the proposed adaptive controllers additionally guarantee robustness to multiplicative input uncertainty. In the case of linear‐quadratic control it is shown that the operations of parameter estimation and controller design are coupled illustrating the breakdown of the certainty equivalence principle for the optimal adaptive control problem. Finally, the proposed framework is used to design adaptive controllers for jet engine compression systems with uncertain system dynamics. Copyright © 2000 John Wiley & Sons, Ltd.     

求解大规模水火最优潮流问题的近似牛顿方向解耦算法

分解后计算效率低和解的最优性差一直是困扰大规模水火最优潮流(HTOPF)研究与应用的两个关键问题。针对这些问题,提出了一种求解HTOPF的精确高效的解耦算法。基于近似牛顿方向直接对原问题KKT(Karush-Kuhn-Tucker)条件解耦的思想,将含梯级电厂的HTOPF问题分解为火电问题和水电问题。火电问题分解为单时段最优潮流问题,并进一步划分为多区域子问题;根据水电厂类型的不同将水电问题分解为单个固定水头、单个变化水头水电厂子问题以及梯级水电厂群优化子问题。求解过程中,每个子问题只迭代一次而不用求其最优解,极大地提高了计算效率。仿真计算结果表明:所提算法具有良好的适应性和稳定性,不仅显著减少了内存占用,而且在串行求解时CPU计算时间缩短了3~4倍,在并行计算条件下可获得10~20倍甚至1 000倍以上的加速比,并保证所得最优目标值与准确值之间的误差在10-8以下,确保了分解协调结果的最优性。     

Efficient reconfiguration of distribution networks using extended pruning‐grafting operators

Network reconfiguration is a complicated, combinatorial, constrained optimization problem with many candidate switching options as well as structural and operational constraints. Introduction of evolutionary algorithms (EAs) to distribution network operation has opened many new opportunities. However, many applications of these methods suffer from high computational burden. In addition, conventional crossover/mutation operators cannot generally produce radial configurations. Performance of EAs is significantly affected by modeling of the problem and the employed operators. This paper employs a branch‐based modeling of a distribution network and proposes two new EA operators that are an extension and redefinition of the preserve ancestor operator (PAO) and change ancestor operator (CAO). They are fast, exclusively produce radial configurations, and remove PAO/CAO operators' limitation. Hence, they can be utilized for a more efficient application of EAs to the network reconfiguration problem. Performance of the new operators is compared to the original PAO/CAO operators, two sets of operators in a binary representation (conventional crossover/mutation operators and an enhanced version of them), and a set of operators in an integer representation (conventional crossover and directed mutation operators). Simulations show the efficiency of the proposed method in terms of convergence speed, response time, and the quality of results. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

基于CES型效用函数的热—电市场消费者最优决策

随着电锅炉、热泵等清洁加热设备的普及,电网和供热网的耦合日益密切。在多种能源参与交易的市场环境下,多市场主体间存在复杂的博弈关系,分析消费者的决策行为及其对能源价格的影响是重要的研究课题。设计了热—电综合市场交易机制,提出了基于常数替代弹性(CES)效用函数的消费者决策模型,该模型亦可为研究其他能源市场问题提供重要借鉴。进一步通过KarushKuhn-Tucker最优性条件和线性规划对偶定理得到市场均衡的混合整数线性规划条件,通过模式搜索算法求解消费者的最优策略。在IEEE 33节点配电网和32节点供热网构成的测试系统上验证了所述方法的有效性,并分析了各因素对市场均衡的影响。     

Economic load dispatch with nonsmooth cost functions using evolutionary particle swarm optimization

This paper presents an evolutionary particle swarm optimization (EPSO) method for solving the nonconvex economic load dispatch (ELD) problem. In practice, the nonconvex and the discontinuous cost function should be considered when optimizing ELD problem with constraints such as valve point effects, prohibited operating zones, ramp‐rate limits, and transmission loss of the system. In view of these constraints, the ELD problem is difficult to solve by any mathematical method. In EPSO, the evolutionary programming concept (combination, tournament competition, sorting, and selection) is employed in the classical PSO method in order to find the best individual and best group position based on the survival particle. The effectiveness of the EPSO is tested on 3‐, 6‐, 15‐, and 38‐unit systems. The results obtained by EPSO are also compared with classical PSO and other results reported in the literature. It is concluded that the EPSO method can produce lower generation cost compared to the existing methods. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

综合负荷聚合商参与的配电—气能源系统供需互动均衡模型

在综合能源系统背景下,提出一种基于主从博弈机制的配电—气能源系统与多个综合负荷聚合商的互动均衡模型。考虑次日能源价格的制定,配电—气系统以总利润最大化为目标求解日前最优能流。在价格机制作用下,综合负荷聚合商通过优化能源配置降低自身能源购置成本,从而实现配电—气系统与综合负荷聚合商的互利共赢。为求取主从博弈均衡解,采用二阶锥松弛(SOCP)和罚凸凹过程(PCCP)消除配电—气系统优化模型中的非凸源,并应用KKT条件和强对偶理论将原模型转化为单层凸优化模型。由此通过迭代求解混合整数二阶锥规划问题逐渐缩紧配气网管道气流松弛域,最终获得博弈均衡解。最后,以IEEE 33节点配电网和20节点配气网构成的系统为例进行仿真说明,所得结果验证了文中模型及方法的有效性。     

State estimation of discrete‐time systems with arbitrarily correlated noises

In this paper, the state estimation problem for discrete‐time systems is considered where the noises affecting such systems do not require any constraint condition for the correlation and distribution, that is, the noises can be arbitrarily correlated and arbitrarily distributed random vector. For this, two filtering algorithms based on the criterion of linear minimum mean‐square error are proposed. The first algorithm is an optimal algorithm that can exactly compute the linear minimum mean‐square error estimate of system states. The second algorithm is a suboptimal algorithm that is proposed to reduce the computation and storage load of the proposed optimal algorithm. Computer simulations are carried out to evaluate the performance of the proposed algorithms. Copyright © 2013 John Wiley & Sons, Ltd.