Solution of optimal reactive power dispatch of power systems using hybrid particle swarm optimization and imperialist competitive algorithms

Management of reactive power resources is essential for secure and stable operation of power systems in the standpoint of voltage stability. In power systems, the purpose of optimal reactive power dispatch (ORPD) problem is to identify optimal values of control variables to minimize the objective function considering the constraints. The most popular objective functions in ORPD problem are the total transmission line loss and total voltage deviation (TVD). This paper proposes a hybrid approach based on imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) to find the solution of optimal reactive power dispatch (ORPD) of power systems. The proposed hybrid method is implemented on standard IEEE 57-bus and IEEE 118-bus test systems. The obtained results show that the proposed hybrid approach is more effective and has higher capability in finding better solutions in comparison to ICA and PSO methods.     

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).     

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.     

A novel fuzzy index for steady state voltage stability analysis and identification of critical busbars

In this paper, a novel fuzzy index is proposed for the prediction of steady state voltage stability conditions in transmission networks. The uncertainties in the input parameters are efficiently modeled in terms of fuzzy sets by assigning trapezoidal and triangular membership functions. The results include fuzzy load flow solutions for the base case and critical conditions with and without contingencies. The proposed fuzzy voltage stability index clearly indicates the location and status of critical busbars. Case studies have been conducted on standard test systems (IEEE 14-bus, 30-bus, and 57-bus) with proper validation of the results.     

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.     

An approach for real power scheduling to improve system stability margins under normal and network contingencies

In the present day power system planning and operation, considerable interest is being shown in system security and stability analysis. Pattern of load sharing/generation scheduling that results in heavy flows tend to incur greater losses, threaten stability, security and ultimately making certain generation patterns undesirable. Generation schedules mainly based on economic criteria may lead to lower reserve margins and therefore diminished reliability is a serious concern for the systems. With increased loading of existing power transmission systems, the problem of voltage stability and voltage collapse has also become a major concern in power system planning and operation. While the voltage stability is more dependent on the reactive power sources/voltage profile in the system, it is also a function of real power flows. In this paper, network sensitivity between load voltages and source voltages to compute voltage stability index (L), is used as the basis to evaluate desirable load sharing for improving stability margins. The proposed method has been tested on typical sample systems and also on a practical 24-bus equivalent power system, and results are presented to illustrate the proposed approach.     

计及无功潮流影响的传输介数概念及其电网关键线路辨识研究

在潮流介数的基础上,考虑了线路在传输无功潮流方面的作用,提出线路传输介数并将其用于辨识电网关键线路。由于充足的无功支持是电压稳定性的基础,将无功传输的作用纳入到关键线路辨识方法中后,传输介数能准确地辨识出影响系统电压稳定性的重要线路。关键线路的连续故障会导致有功和无功传输通道的破坏,需要切除部分负荷以维持系统频率和电压稳定,故采用基于最优潮流的失负荷量作为故障线路重要性的评价指标,以验证具有高传输介数的线路在电网运行中承担关键作用。IEEE39和IEEE118节点系统算例表明,传输介数能够辨识出系统中影响节点电压稳定水平的重要线路,其辨识效果优于潮流介数,基于传输介数的电网关键线路辨识方法具有合理性和有效性。     

基于同步相量测量的电压稳定指标

针对输电网提出了一种基于同步相量测量信息的电压稳定指标。电力系统可以分解成许多电能传输路径,以传输路径首节点电压与末节点电压在首节点电压上的投影之差与首节点电压的比值作为计算电压稳定与否的指标。该指标根据最弱电能传输路径利用局部电压相量测量信息直接计算得出,避免了复杂的潮流计算。局部电压相量测量数据由相量测量单元PMU提供。基于一种快速有效的PMU配置方法,利用直接测量或间接计算的数据作为此稳定指标计算所需要的电压相量信息。运用图论的基本思想寻找电能最弱传输路径。通过计算电能最弱传输路径的电压稳定指标和系统无功储备情况判断系统电压稳定度,当系统接近不稳定状态时,最弱传输路径的电压稳定指标值趋向于临界值0.5。在IEEE5节点和IEEE30节点系统上的仿真表明了该指标预测系统电压崩溃的有效性和正确性。     

Distributed control algorithm for optimal reactive power control in power grids

Reactive power generation has been commonly used for power loss minimization and voltage profile improvement in power systems. However, the opportunity cost of reactive power generation should be considered since it affects the frequency control capability of the generator to some degree. This paper proposed a distributed nonlinear control based algorithm to achieve the optimal reactive power generation for multiple generators in a power grid. The reactive power control setting update for each generator only requires local measurement and information exchange with its neighboring buses. It is demonstrated that the proposed algorithm can reduce the non-convex objective function monotonically till convergence and achieve comparable solutions to the centralized technique: particle swarm optimization with faster convergence speed. The proposed algorithm has been tested on the IEEE 9-bus, 39-bus and 162-bus systems to validate its effectiveness and scalability.     

Optimal placement of DG in radial distribution systems based on new voltage stability index under load growth

This paper presents a comparison of Novel Power Loss Sensitivity, Power Stability Index (PSI), and proposed voltage stability index (VSI) methods for optimal location and sizing of distributed generation (DG) in radial distribution network. The main contribution of the paper is: (i) optimal placement of DGs based on Novel Power Loss Sensitivity and PSI methods, (ii) proposed voltage stability index method for optimal DG placement, (iii) comparison of sensitivity methods for DG location and their size calculations, (iv) optimal placement of DG in the presence of load growth, (v) impact of DG placement at combined load power factor, (vii) impact of DG on voltage stability margin improvement. Voltage profile, the real and reactive powers intake by the grid, real and reactive power flow patterns, cost of energy losses, savings in cost of energy loss and cost of power obtained from DGs are determined. The results show the importance of installing the suitable size of DG at the suitable location. The results are obtained with all sensitivity based methods on the IEEE 12-bus, modified 12-bus, 69-bus and 85-bus test systems.     

基于随机优化的割集空间电压稳定域可视化

电压稳定域可视化能够方便调度人员监视电力系统的电压安全裕度,为其决策提供依据。为克服现有算法不能给出概率意义可信度的不足,分别提出了基于理想模型（独立正态分布）的随机优化算法和基于一般模型（非独立正态分布）的数据拟合Monte Carlo算法,以实现割集空间电压稳定域的可视化。其中,基于理想模型的随机优化算法不需要产生大量的随机数,计算过程简洁、高效,且可得到割集空间电压稳定域边界超平面近似的方程。进一步,为了评价利用该超平面方程判断电压稳定的可信度,提出用随机优化的目标函数—正确率作为置信度指标。基于该指标选择割集功率,可显著提高电压稳定评估的正确率。此外,文中将割集空间概念推广到拟割集空间,使电压稳定域的可视化更准确,更易于工程实现。IEEE39节点系统的仿真分析验证了所述算法的有效性。     

Power system voltage instability riskmitigation via emergency demandresponse-based whale optimizationalgorithm

In recent years, due to the economic and environmental issues, modern power systems often operate proximately to the technical restraints enlarging the probable level of instability risks. Hence, efficient methods for voltage instability prevention are of great importance to power system companies to avoid the risk of large blackouts. In this paper, an event-driven emergency demand response (EEDR) strategy based on whale optimization algorithm (WOA) is proposed to effectively improve system voltage stability. The main objective of the proposed EEDR approach is to maintain voltage stability margin (VSM) in an acceptable range during emergency situations by driving the operating condition of the power system away from the insecure points. The optimal locations and amounts of load reductions have been determined using WOA algorithm. To test the feasibility and the efficiency of the proposed method, simulation studies are carried out on the IEEE 14-bus and real Algerian 114-bus power systems.     

一种新的节点静态电压稳定指标及切负荷算法

提出了一种可以考虑负荷波动的节点静态电压稳定指标,该指标可以表示节点静态电压崩溃的概率,进而识别出系统的薄弱节点。基于这一指标提出了一种保证节点静态电压稳定的切负荷算法。IEEE 30节点系统的仿真结果表明所提出的节点静态电压稳定指标计算简单快速,可用于电力系统运行状态的实时监视。     

Power injection modeling and optimal multiplier power flow algorithm for steady-state studies of unified power flow controllers

This paper presents an optimal multiplier based Newton-Raphson power flow algorithm for reliably and efficiently handling power systems with embedded flexible AC transmission systems (FACTS) devices such as unified power flow controllers (UPFCs). A power injection transformation of a two voltage source UPFC model is derived in rectangular form. After detailed analyses of issues in implementation of UPFCs in power flow programmes by various power flow algorithms, the optimal multiplier power flow method for ill-conditioned systems is adopted. The proposed UPFC model and power flow algorithm have been programmed and vigorously tested in a number of systems. The results on the IEEE 30-bus test system and a 306-bus practical system are reported and compared with conventional user defined model type programmes, which clearly illustrate the effectiveness of the proposed algorithm.     

电力系统电压稳定分区和关键断面的确定

电网的关键断面能够体现电力系统运行的薄弱环节,是电网稳定性分析和监视的重点对象。文中针对电压稳定研究的需要,提出了电力系统节点间的连接关系和联系紧密程度的评价方法,建立与电网网架结构相对应的图模型,然后引入了谱聚类算法,进行输电网分区分析,可层次递推地给出系统的合理分区,继而可确定各分区间的关键断面。通过IEEE 14节点算例和河南电网的应用分析结果表明,该算法能够准确有效地确定系统的电压稳定关键断面。     

Quasi-Oppositional Swine Influenza Model Based Optimization with Quarantine for optimal allocation of DG in radial distribution network

Optimal allocation of Distributed Generations (DGs) is one of the major problems of distribution utilities. Optimum locations and sizes of DG sources have profoundly created impact on system losses, voltage profile, and voltage stability of a distribution network. In this paper Quasi-Oppositional Swine Influenza Model Based Optimization with Quarantine (QOSIMBO-Q) has been applied to solve a multi-objective function for optimal allocation and sizing of DGs in distribution systems. The objective is to minimize network power losses, achieve better voltage regulation and improve the voltage stability within the frame-work of the system operation and security constraints in radial distribution systems. The limitation of SIMBO-Q algorithm is that it takes large number of iterations to obtain optimum solution in large scale real systems. To overcome this limitation and to improve computational efficiency, quasi-opposition based learning (QOBL) concept is introduced in basic SIMBO-Q algorithm. The proposed QOSIMBO-Q algorithm has been applied to 33-bus and 69-bus radial distribution systems and results are compared with other evolutionary techniques like Genetic Algorithm (GA), Particle Swarm Optimization (PSO), combined GA/PSO, Teaching Learning Based Optimization (TLBO) and Quasi-Oppositional Teaching Learning Based Optimization (QOTLBO). Numerical studies represent the effectiveness and out-performance of the proposed QOSIMBO-Q algorithm.     

计及无功/电压特性的停电模型及自组织临界性分析

在总结已有停电模型的基础上,根据电压稳定理论,建立了电力系统停电模型。该模型包含电压静态稳定分析模块,可以从无功／电压角度研究和揭示电网演化的自组织临界特征;所构造的电压稳定分析模块采用3种电压稳定分析方法：临界电压分析法、基于常规潮流和最优潮流的无功／电压模态分析法,其中第3种方法是第2种方法的扩展,具有较大的可信度。IEEE 30节点系统的仿真表明：所建立的停电模型能够较实际地体现电力系统运行和建设的动态过程,进而全面反映负荷损失和电压稳定水平的演化趋势,并从无功／电压角度评估电力系统的安全运行水平。     

基于电压稳定及FACTS配置的输电能力的研究

输电能力是电网技术的重要指标,也是反映电网输电容量的市场信号。介绍了考虑电压稳定性后,采用线路电压稳定指标快速筛选出严重预想事故集,并用连续潮流法计算输电能力;同时叙述了采用临界状态下线路电压稳定指标来评估FACTS配置安装地点对输电能力的影响,以快速捕获最佳安装位置。通过IEEE5节点和IEEE30节点标准系统验证了此方法的有效性。     

A new multi-objective fuzzy-GA formulation for optimal placement and sizing of shunt FACTS controller

The location and sizing of FACTS controllers for voltage stability enhancement is an important consideration for practical power systems. In this paper, a strategy for placement and sizing of shunt FACTS controller using Fuzzy logic and Real Coded Genetic Algorithm is proposed. A fuzzy performance index based on distance to saddle node bifurcation, voltage profile and capacity of shunt FACTS controller is proposed. The proposed technique can be used to find the most effective location and optimal size of the shunt FACTS devices. The proposed approach has been applied on IEEE 14-bus and IEEE 57-bus test systems. The application results are promising.     

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.