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).     

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.     

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.     

Steady-state load shedding schemes: a performance comparison

This paper presents a formulation of the optimal steady-state load shedding problem that uses the sum of the squares of the difference between the connected active and reactive load and the supplied active and reactive power. The latter are treated as dependent variables modelled as functions of bus voltages only. The equality constraints associated with the power system load curtailment problem are the power flow equations in polar form utilizing the nodal admittance matrix approach. The inequality constraints are characterized by limits on line flows, voltage magnitudes and angles, and active and reactive power generations. The MINOS nonlinear optimization package is used to implement the optimization process. Testing is done using IEEE 14- and 30-bus power systems, and results obtained. The optimal results are compared with results obtained using two earlier approaches. The results obtained using the proposed approach appear to give a better optimal state of the power system.     

Artificial bee colony algorithm for solving multi-objective optimal power flow problem

This paper presents a new and efficient method for solving optimal power flow (OPF) problem in electric power systems. In the proposed approach, artificial bee colony (ABC) algorithm is employed as the main optimizer for optimal adjustments of the power system control variables of the OPF problem. The control variables involve both continuous and discrete variables. Different objective functions such as convex and non-convex fuel costs, total active power loss, voltage profile improvement, voltage stability enhancement and total emission cost are chosen for this highly constrained nonlinear non-convex optimization problem. The validity and effectiveness of the proposed method is tested with the IEEE 9-bus system, IEEE 30-bus system and IEEE 57-bus system, and the test results are compared with the results found by other heuristic methods reported in the literature recently. The simulation results obtained show that the proposed ABC algorithm provides accurate solutions for any type of the objective functions.     

计及静态电压稳定约束的无功优化规划

选择无功补偿设备投资和系统有功网损的综合费用作为目标函数,同时考虑满足电压水平和电压稳定性两个约束条件来探讨无功规划问题。选取用电压稳定裕度不低于某一个允许的最小稳定裕度来表示电压稳定约束。分别对正常运行工作点和电压崩溃点引入2组变量和潮流方程,从而使得电压稳定裕度可以用临界运行状态下负荷的总视在功率与正常运行状态下负荷的总视在功率之差来显式表达。该模型相对于传统无功规划模型的优势表现在能够根据稳定裕度的目标值直接求得在合理电压水平下的最佳无功补偿配置方案,但其优化模型的等式和不等式约束及变量的数目却大幅增加,使得计算量远大于传统的无功规划问题。在IEEE 14节点和118节点2个试验系统的计算表明,采用非线性原对偶内点法求解该模型时,其计算精度及收敛性都比较好。     

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.     

A two-point estimate method for uncertainty modeling in multi-objective optimal reactive power dispatch problem

Due to nonlinear and discrete variables and constraints, optimal reactive power dispatch (ORPD) is a complex optimization problem in power systems. In this paper, the purpose is to solve multi objective ORPD (MO-ORPD) problem considering bus voltage limits, the limits of branches power flow, generators voltages, transformers tap changers and the amount of compensation on weak buses. The objectives of this paper are real power losses and voltage deviations from their corresponding nominal values, which are conflicting objectives. Because of the stochastic behavior of loads, the MO-ORPD problem requires a probabilistic approach. Hence, in this paper, a two-point estimate method (TPEM) is proposed to model the load uncertainty in MO-ORPD problem. Moreover, the proposed method is compared with some other methods such as deterministic approaches and Monte Carlo simulations (MCS). The obtained results approve the efficiency of the proposed methodology. The proposed models are implemented and solved using GAMS optimization package and verified using IEEE 14-bus and IEEE 30-bus standard test systems.     

考虑过渡过程的多目标无功/电压优化控制模型

基于时间断面的无功/电压优化控制模型忽略了控制设备动作时间及2次优化控制期间的系统变化,因此不能准确反映优化控制效果。提出考虑过渡过程影响的多目标无功/电压优化控制模型,通过对过渡过程的智能分段和负荷变化方向的动态评估,并应用智能ε-支配域并行算法,能更精确地对电网有功损耗、控制设备动作引起的电压波动以及由于负荷变化所导致的的系统电压稳定负荷裕度变化量进行优化控制。通过IEEE30节点模型和一实际系统模型的仿真,验证了所提模型较传统无功/电压优化控制模型具有更好的优化控制能力。     

基于轨迹灵敏度的交直流受端系统暂态电压两阶段控制

针对交直流受端系统暂态电压调控能力不足的现状,提出一种基于轨迹灵敏度的交直流受端系统暂态电压两阶段控制方法。构建以最优无功补偿容量和紧急控制成本最小为目标函数的两阶段暂态电压控制模型。借助摄动法求取暂态电压稳定裕度对控制量的轨迹灵敏度,将非线性暂态电压控制模型转化为二次规划模型来提高暂态电压控制效率。为避免故障期间交直流受端系统暂态电压的大幅跌落,实施静止同步补偿器和新一代调相机协同的预防控制,充分发挥无功补偿装置在暂态电压不同跌落程度下的动态无功支撑优势。针对实施暂态电压预防控制后恢复阶段的低电压延时恢复问题,实施包含基于电压源换流器的高压直流和传统调压措施的紧急控制来加快暂态电压恢复速度。修改后的IEEE 39节点系统和实际系统算例结果验证了所提暂态电压控制方法的准确性和有效性。     

An expert system for voltage and reactive power control of a powersystem

A methodology called the sensitivity tree, which can be easily used to form an expert system for real-time control, is proposed. Based on this methodology, an expert system for the control of voltage and reactive power of a power system is developed. The main objective of this expert system is to help the operator detect buses experiencing abnormal conditions, select the most effective control measures, and calculate the control actions required to overcome the voltage violation. The control measures used to alleviate the voltage problem are capacitor compensation, transformer tap changes, and generator terminal voltage changes. By keeping the bus voltage in the entire system within limits, system security is increased. The expert system is written in the PROLOG language. Simulation studies with this expert system applied to a 30-bus power system show satisfactory results     

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.     

Cost-based reactive power pricing with voltage security consideration in restructured power systems

In the restructuring power industry, voltage security has become a challenging problem since power systems tend to operate closer to security boundaries and as a consequence, the voltage instability, which is caused by insufficient reactive power supply, poses a serious threat to system security and reliability. Establishing an equitable and effective reactive power market with consideration of the voltage security problem is very important to provide a reliable restructured power system. Therefore, this paper proposes a cost-based reactive power pricing, which can integrate the reactive power cost minimization and the voltage security problem into the optimal power flow (OPF) problem, and the sequential quadratic programming (SQP) is employed to solve the optimization problem. The effectiveness of the proposed method is verified using a modified IEEE 14-bus system. A study on the effects of the voltage stability margin (VSM) requirement under normal condition and contingencies on the reactive power cost is also presented.     

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。     

多目标无功优化的向量评价自适应免疫粒子群算法

为了克服粒子群算法在高维复杂问题寻优时容易陷入局部搜索的现象,提出了一种自适应免疫粒子群算法。该算法利用引入免疫系统的免疫信息处理机制和自动调整动量系数的自适应因子,从整体上达到系统的最佳控制方案。并将基于目标向量的个体评价方法与自适应免疫粒子群算法相结合,提出了基于向量评价的自适应免疫粒子群算法(vector evaluated adaptive immune particle swarm optimization,VEAIPSO)来解决多目标无功优化问题。通过引入静态电压稳定指标,建立了以系统有功损耗最小、节点电压偏移量最小及静态电压稳定裕度最大为目标的多目标无功优化模型。IEEE30和IEEE118节点系统算例仿真结果表明,该算法能有效地解决多目标无功优化问题,并具有良好的收敛稳定性和较高的寻优精度。     

基于混沌免疫混合算法的多目标无功优化

针对目前评价多目标函数解的不足,提出了将多目标函数各个解映射成多维空间中不同的点,利用这些点与理想点之间的欧氏距离来衡量各个解的优劣;同时针对无功优化、混沌优化算法和免疫算法的特点,提出了在采用免疫算法进行无功优化的记忆抗体群中,运用混沌优化方法和免疫算法的交叉和变异等操作对无功优化的连续变量和离散变量进行交替优化求解,并将它们运用于以降低有功损耗,提高电压稳定裕度及减小电压偏移为目标的无功优化中;通过 IEEE-30和IEEE-118节点算例系统验证了混合算法及最优解评价方法的正确性和可行性。     

基于广义主从分裂的输配电网一体化分布式无功优化方法

大量分布式电源接入配电网后,输、配电网间无功电压关系更加密切,传统输、配电网无功优化孤立进行已不再合适。根据输、配电网运行管理的独立性,提出了一种基于广义主从分裂思想的输配电网一体化分布式无功优化方法。输配全局无功优化问题分解为输电网优化主子问题、各配电网优化从子问题及边界一致性判别问题。各子网无功优化子问题采用对偶规划类算法求解,离散变量采用罚函数法处理以保持增广拉格朗日函数的可微性。通过由对偶乘子构造的边界灵敏度实现输、配电网子问题间的解耦,输配电网控制中心间通过传递边界变量及其灵敏度信息实现分布式协调。对IEEE 30节点系统(输电网)和含多种分布式电源的IEEE 33节点系统(配电网)进行仿真,验证了所提方法的有效性。     

A fuzzy-based optimal reactive power control

A mathematical formulation of the optimal reactive power control problem using fuzzy set theory is presented. The objectives are to minimize real power losses and improve the voltage profile of a given system. Transmission losses are expressed in terms of voltage increments by relating the control variables to the voltage increments in a modified Jacobian matrix. This formulation does not require Jacobian matrix inversion, and hence it will save computation time and memory space. The objective function and the constraints are modeled by fuzzy sets. Linear membership functions of the fuzzy sets are defined and the fuzzy linear optimization problem is formulated. The solution space is defined as the intersection of the fuzzy sets describing the constraints and the objective functions. Each solution is characterized by a parameter that determines the degree of satisfaction with the solution. The optimal solution is the one with the maximum value for the satisfaction parameter. Results for test systems reveal the advantages of the approach     

基于模拟植物生长算法的电力系统无功优化

将模拟植物生长算法应用于电力系统无功优化。提出了将无功补偿容量、变压器主变抽头和发电机节点电压3种类型的控制变量采用统一模式转化成整型变量的方法。对Ward-Hale 6节点、IEEE 30节点系统的计算分析及连续型发电机节点电压的离散点个数对计算结果影响的探讨表明:兼具随机性和方向性搜索机制的模拟植物生长算法具有较强的全局搜索能力,且使用方便,为解决电力系统无功优化问题提供了一种新途径。     

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.