Electricity market equilibrium of nonlinear power systems with reactive power control

The impact of reactive power control on the electricity market equilibrium is investigated. The effects of limitations on the reactive power generation and absorption, and load power factor adjustments, are examined using a novel electricity market equilibrium model that solves large-scale nonlinear power systems with asymmetric strategic firms. The algorithm implemented employs the linear supply function theory for bid-based pool markets. AC power flow analysis is used to represent the electricity network, incorporating variable price-responsive active and reactive load demands. The significance of the reactive power modeling in the electricity market equilibrium is demonstrated using the IEEE 14-bus and IEEE 118-bus systems. It is shown that variations on the reactive power in the system result in different market outcomes, as incentives are given to the strategic generating firms to alter their bidding strategies. The convergence characteristics of the IEEE 118-bus system are graphically presented and discussed to demonstrate the superior computational performance of the proposed algorithm in producing results under strict binding constraints and heavy transmission congestion conditions.     

Optimal VAR control for real power loss minimization using differential evolution algorithm

Differential evolution algorithm (DEA) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been proved to be a promising evolutionary algorithm for solving the ORPD problem and many engineering problems. However, the success of DEA in solving a specific problem crucially depends on appropriately choosing trial vector generation strategies (mutation strategies) and their associated control parameter values. This paper presents a differential evolution technique with various trial vector generation strategies based on optimal reactive power dispatch for real power loss minimization in power system. The proposed methodology determines control variable settings such as generator terminal voltages, tap positions and the number of shunts compensator to be switched, for real power loss minimization in the transmission systems. The DE method has been examined and tested on the IEEE 14-bus, 30-bus and the equivalent Algerian electric 114-bus power system. The obtained results are compared with two other methods, namely, interior point method (IPM), Particle Swarm Optimization (PSO) and other methods in the literature. The comparison study demonstrates the potential of the proposed approach and shows its effectiveness and robustness to solve the ORPD problem.     

Quasi-oppositional differential evolution for optimal reactive power dispatch

This paper presents quasi-oppositional differential evolution to solve reactive power dispatch problem of a power system. Differential evolution (DE) is a population-based stochastic parallel search evolutionary algorithm. Quasi-oppositional differential evolution has been used here to improve the effectiveness and quality of the solution. The proposed quasi-oppositional differential evolution (QODE) employs quasi-oppositional based learning (QOBL) for population initialization and also for generation jumping. Reactive power dispatch is an optimization problem that reduces grid congestion with more than one objective. The proposed method is used to find the settings of control variables such as generator terminal voltages, transformer tap settings and reactive power output of shunt VAR compensators in order to achieve minimum active power loss, improved voltage profile and enhanced voltage stability. In this study, QODE has been tested on IEEE 30-bus, 57-bus and 118-bus test systems. Test results of the proposed QODE approach have been compared with those obtained by other evolutionary methods reported in the literature. It is found that the proposed QODE based approach is able to provide better solution.     

一种含分布式发电系统的三相配电网潮流直接算法

提出一种基于道路矩阵的三相不平衡配电网潮流直接算法,该算法充分利用配电网络的结构特点,建立了节点电压与注入电流的关系矩阵,实现了潮流的直接计算。基于PV节点的特性,推导了PV节点网络的有功电流和无功电流关系,并提出了一种新的处理PV类型分布式发电的方法。将该方法引入到三相系统潮流计算中,保证了PV节点幅值为预设定值（假定无功功率没有越界）。6母线和69母线系统算例验证了该方法简单实用,潮流计算时间短和迭代次数少,具有很好的通用性。     

Multi-objective optimal reactive power dispatch using multi-objective differential evolution

This paper presents multi-objective differential evolution (MODE) to solve multi-objective optimal reactive power dispatch (MORPD) problem by minimizing active power transmission loss and voltage deviation and maximizing voltage stability while varying control variables such as generator terminal voltages, transformer taps and reactive power output of shunt VAR compensators. MODE has been tested on IEEE 30-bus, 57-bus and 118-bus systems. Numerical results for these three test systems have been compared with those acquired from strength pareto evolutionary algorithm 2 (SPEA 2).     

利用发电机调节的稳态潮流控制

在电力系统的稳态运行中,发电机的运行方式对潮流分布起着至关重要的作用。在稳态潮流控制模型中,引入发电机的运行参数作为变量,使模型的变量数不少于方程数以保证模型的可解性;推导了微分灵敏度算法,并将其应用于变量不等式的越限处理,简化了求解过程,加快了模型的求解速度。IEEE 5和30节点系统的算例表明,在考虑电压运行范围和支路定功率传输等约束条件的情况下,模型和算法能在数次迭代运算后成功求解出系统的潮流分布。     

Optimal reactive power control of DGs for voltage regulation of MV distribution systems using sensitivity analysis method and PSO algorithm

This paper addresses the problem of reactive power control of distributed generation (DG) units in the medium voltage (MV) distribution systems to maintain the system voltages within the predefined limits. An efficient approach for the load flow calculation is used here which is based on the topological structure of the network. It has been formulated for the radial distribution systems. A direct voltage sensitivity analysis method is developed in this paper which is also based on the topological structure of the network and independent of the network operating points. Thus, the sensitivity matrix is calculated once with the load flow program and it is used in all the system working conditions. The problem of DGs reactive power control is formulated as an optimization problem which uses the sensitivity analysis for linearizing the system around its operating points. The objective of the optimization problem is to return the system voltages inside the permitted range by using the reactive power of DGs in an optimal way. The optimal solutions are obtained by implementing particle swarm optimization (PSO) algorithm. Then, the results are verified by running a load flow considering new values of DGs reactive power. The procedure is repeated as long as a voltage violation is observed. Simulation results reveal that the proposed algorithm is capable of keeping the system voltages within the permitted limits.     

基于群搜索算法的电力系统无功优化

为了提高电力系统的运行效率和经济性能,用群搜索优化算法(Group Search Optimizer)对电力系统各控制变量进行合理配置,以此减少电力系统无功损耗。群搜索优化算法是一种新兴的群智能优化算法,该算法把群成员分为发现者、追随者和游荡者三种,其中游荡者的位置随机选定,这有效地避免了其他算法容易陷入局部最小值问题。选定电力系统中无功投入量、电压变比、发电机端电压等作为控制变量,通过群搜索优化算法对控制变量进行迭代计算和潮流计算,最终计算出最小的网络损耗及其对应的控制变量值。最后用Matlab7.6对IEEE-14、30节点系统进行仿真,并与其他群智能优化算法进行对比,结果显示,群搜索算法的收敛较快且稳定,最终证明了群搜索算法对无功优化的优越性。     

Optimal reactive power control via loss minimization and voltage control

This paper presents a mathematical formulation of optimal reactive power control problem via loss minimization and voltage control. The model minimizes real power losses, deviation from the optimal active power despatch policy, and the difference between percentage sharing of reactive power by controlling the generator terminal voltage magnitudes, transfer tap setting, and reactive power sources. The constraints set include power flow equations and limits on the variables. A method is developed to solve this problem using reduced gradient and Fletcher's update. Several test problems were solved using the developed technique. Correction to the groups of decision variables are applied simultaneously as well as hierarchically, and the results are compared for 6-bus, 30-bus, and 103-bus sample systems.     

Optimal reactive power dispatch based on harmony search algorithm

This paper presents a harmony search algorithm for optimal reactive power dispatch (ORPD) problem. Optimal reactive power dispatch is a mixed integer, nonlinear optimization problem which includes both continuous and discrete control variables. The proposed algorithm is used to find the settings of control variables such as generator voltages, tap positions of tap changing transformers and the amount of reactive compensation devices to optimize a certain object. The objects are power transmission loss, voltage stability and voltage profile which are optimized separately. In the presented method, the inequality constraints are handled by penalty coefficients. The study is implemented on IEEE 30 and 57-bus systems and the results are compared with other evolutionary programs such as simple genetic algorithm (SGA) and particle swarm optimization (PSO) which have been used in the last decade and also other algorithms that have been developed in the recent years.     

Optimal controllers designs for automatic reactive power control in an isolated wind-diesel hybrid power system

The paper presents the bacterial foraging optimization algorithm (BFOA) and particle swarm optimization (PSO) algorithm based robust controllers for voltage deviations due to the variation of reactive power in an isolated wind-diesel hybrid power system. The isolated wind-diesel system consists of wind energy conversion system (WECS) utilizing a permanent magnet induction generator (PMIG). Further, a synchronous generator (SG) is used with the diesel engine set for power generation. The mismatch between generated and consumed reactive power in the system causes voltage fluctuations, which will occur at generator terminals. These oscillations further causes reduction in the stability and quality of the power supply. The static synchronous compensator (STATCOM) and an automatic voltage regulator (AVR) are used to suppress voltage fluctuations in an isolated wind-diesel hybrid power system. The STATCOM is used as a reactive power compensator and the AVR is used to keep the terminal voltage constant for the synchronous generator. Both STATCOM and AVR are having proportional and integral (PI) controllers with single input. In modeling for the system, a normalized co-prime factorization is applied to show the possible unstructured uncertainties in the power system such as variation of system parameters and generating and loading conditions. The performance and robust stability conditions of the control system are formulated as the optimization problem, which is based on the Hα loop shaping. BFOA and PSO algorithms are implemented to solve this optimization problem and to achieve PI control parameters of STATCOM and AVR simultaneously. In order to show the efficiency of the proposed controllers, the performance of the proposed controllers is compared with the performance of the conventional controller and genetic algorithm (GA) based PI controllers for the same wind-diesel system. The dynamic responses of the system for four different small-disturbance case studies has been carried out in MATLAB environment.     

Optimal reactive power dispatch using ant colony optimization algorithm

This paper proposed a procedure to solve the optimal reactive power dispatch (ORPD) problem using ant colony optimization (ACO) algorithm. The objective of the ORPD problem is to minimize the transmission power losses under control and dependent variable constraints. Proposed sensitivity parameters of reactive power at generation and switchable sources are derived based on a modified model of fast decoupled power flow. The proposed ACO-based algorithm is applied to the IEEE standard 14-bus, 30-bus systems, and a real power system at West Delta Network as a part of the Unified Egyptian Network. The obtained simulation results are compared with those of conventional linear programming, genetic algorithm, and particle swarm optimization technique. Simulation results show the capability of the proposed ACO-based algorithm for solving the ORPD problem, especially with increasing the system size.     

基于一种不可行内点法的电力系统无功优化

在应用内点法进行线性规划时,尚不能保证它的全面收敛性。提出了一种新的算法来求解无功线性优化问题。利用潮流雅可比矩阵直接变换求取灵敏度系数,建立无功优化线性规划模型,同时采用一种不可行内点算法来直接求解该问题。IEEE 14节点、30节点、57节点系统的计算结果表明,该算法能有效求解无功优化线性规划问题,同时在初始点的选择上不要求从内点启动,迭代收敛次数稳定,对计算系统的规模不敏感。     

含风电场的配电网无功优化策略研究

针对传统的配电网无功优化调节手段离散化、难以实现电压的连续调节等问题,研究了含风电场的配电网无功优化模型和算法,分析了双馈感应电机的无功发生能力,将风电场作为连续的无功调节手段参与配电网无功优化。并针对风电出力随机性的特点,用场景功率描述风电的随机出力,使之更具代表性。考虑了配电网的网损、电压偏差以及电压稳定性指标,建立了多目标无功优化模型。提出了基于量子粒子群算法(QPSO)的无功优化方法,该算法通过波函数描述粒子的状态,增加了种群的多样性,有效地避免了种群早熟等问题。用该算法对改进的IEEE33节点进     

基于关联分析的光伏电站无功控制能力评估

在光伏发电蓬勃发展的背景下,光伏电站参与电网无功/电压控制的需求也日趋强烈,有效评估光伏电站的无功控制能力具有重要的理论和现实意义。然而,光伏电站无功控制能力评估研究仍在起步阶段且难度较大,需从评估指标体系构建、指标权重赋值、综合关联评估多个方面进行深入探索。鉴于此,提出了一种基于动态时间弯曲关联分析的光伏电站无功控制能力评估方法,解决综合评估指标体系建立及层次分析赋值问题的同时,将无功控制能力指标评估问题转化为空间上的模式距离关联匹配问题,采用动态时间弯曲法实现不同序列间的关联分析,计算标准、参考及待评估指标序列的关联匹配系数,进而确定无功控制能力等级,实现综合分级评估。并开展典型系统评估应用,验证所提评估方法的适应性及有效性。     

Optimal Planning of Distributed Generators in Distribution Networks Using Modified Firefly Method

Abstract—This article presents a novel algorithm for optimal planning of a dispatchable distributed generator connected to the distribution networks. The proposed algorithm modifies the traditional firefly method to be able to deal with the practically constrained optimization problems by proposing formulas for tuning the algorithm parameters and updating equations. The proposed algorithm rigidly determines the optimal location and size of the distributed generation units in order to minimize the system power loss without violating the system practical constraints. Moreover, the optimal distributed generator location and minimum size for achieving a certain specified power loss are determined using the proposed method and compared to the results of a proposed heuristic technique. The distributed generation units in the proposed algorithms are modeled as voltage controlled nodes with the flexibility to be converted to constant power nodes in the case of reactive power limit violation. The proposed algorithms are implemented in MATLAB and tested on the IEEE 33-bus and the IEEE 37-nodes feeder. The results that are via comparison with published results obtained from other competing methods show the effectiveness, accuracy, and speed of the proposed method.     

An enhanced RCGA for a rapid and reliable load flow solution of electrical power systems

The paper presents a reliable and fast load flow solution by using a real-coded genetic algorithm (RCGA), bus reduction technique and sparsity technique. The proposed load flow solution firstly used reduction technique to eliminate the load buses. Then, the power flow problem is solved for the generator buses only using real-coded GA to calculate the phase angles. Thus, the load flow problem becomes a single objective function, where the voltage magnitudes are specified resulted in reduced computation time for the solution. Once the phase angle has been calculated, the system is restored by calculating the voltages of the load buses in terms of the calculated voltages of the generator buses. A sparsity technique is used to reduce the computation time further as well as the storage requirements. The proposed load flow solution also can efficiently solve the load flow problems for ill-conditioned power systems whereas the conventional RCGA alone fails to solve these systems. The proposed method was demonstrated on 14-bus IEEE, 30-bus IEEE and 300-bus IEEE, and a practical system 362-busbar Iraqi National Grid. The proposed solution has reliable convergence, a highly accurate solution and much less computing time for on-line applications. The method can conveniently be applied for on-line analysis and planning studies of large power systems.     

Optimal reactive power dispatch using quasi-oppositional teaching learning based optimization

This paper presents a newly developed teaching learning based optimization (TLBO) algorithm to solve multi-objective optimal reactive power dispatch (ORPD) problem by minimizing real power loss, voltage deviation and voltage stability index. To accelerate the convergence speed and to improve solution quality quasi-opposition based learning (QOBL) concept is incorporated in original TLBO algorithm. The proposed TLBO and quasi-oppositional TLBO (QOTLBO) approaches are implemented on standard IEEE 30-bus and IEEE 118-bus test systems. Results demonstrate superiority in terms of solution quality of the proposed QOTLBO approach over original TLBO and other optimization techniques and confirm its potential to solve the ORPD problem.     

Modeling and simulation on long-term dynamics of interconnected power system using area COI concept

In order to study long-term frequency and voltage dynamics of interconnected power systems under cascading events, the paper has developed a proper mathematical model and simulation algorithm for it with network structure preserved. Similar to the traditional dynamic power flow, the proposed model assumes that the system has survived in the transient stability and has enough damping torque. Therefore, the relative swings among generator rotors in one area will be neglected in long-term dynamics; and each control area is assumed to have a uniform frequency, represented by its area center of inertia (COI). Fast decoupled method has been extended to solve the structure-preserved multi-area network equations. Computer test results from a modified IEEE30-bus power system demonstrate the validity and effectiveness of the proposed model and algorithm. The work establishes a simulation platform for future study on long-term frequency and voltage stability control strategy and coordination of interconnected power systems.     

利用光伏发电优化功率控制提高电网暂态稳定

随着光伏发电装机容量的逐步提高,光伏高渗透率的区域电网的稳定性面临挑战。因此进行了光伏电站的功率控制研究,在故障暂态过程中,合理减少光伏系统有功输出,保证光伏直流侧稳定,提高光伏逆变器的无功输出能力,以实现电网电压稳定和网内机组功角特性的改善。以美国西部联合电力系统(WSCC)3机9节点系统接入光伏电站为例,验证了所提控制策略能有效提高电网内机组的暂态稳定能力,有利于光伏发电的安全并网,并改善了输出性能。