An algorithm for discrete optimal power flow

This paper presents a new algorithm to solve an optimal power flow problem which can take into consideration the discrete nature of some facilities in power systems. The optimal power flow problem is formulated as a nonlinear mixed-integer programming problem in which the number of transformer taps and the number of shunt capacitor units and reactor units are treated as discrete variables. This paper attempts to solve such a large-scale nonlinar mixed-integer programming problem by some effective programming techniques. The optimization procedure of the algorithm is that the nonlinear mixed-integer programming problem is linearized iteratively and solved by an approximation method for linear mixed-integer programming. A fundamental feature of the algorithm is that it can guarantee a solution which is discrete, feasible and near-optimal. The validity and efficiency of the algorithm is demonstrated by the numerical results of real-scale optimal power flow problems.     

基于改进遗传算法与原对偶内点法的无功优化混合算法

基于改进遗传算法和原对偶内点法提出一种求解无功优化问题的混合算法。首先通过改进遗传算法求解无功优化问题中的离散变量,然后采用原对偶内点法求解与已获得离散变量最匹配的连续变量。在改进遗传算法中采用交叉、变异算子并基于可行域规则处理离散约束,有效提高了混合优化算法的整体寻优效率。在IEEE 118节点系统中的仿真计算结果验证了本文方法的有效性。该方法已应用于福建电网自动电压控制系统中。     

Capacitor placement of distribution systems using particle swarm optimization approaches

Capacitor placement plays an important role in distribution system planning and operation. In distribution systems of electrical energy, banks of capacitors are widely installed to compensate the reactive power, reduce the energy loss in system, voltage profile improvement, and feeder capacity release. The capacitor placement problem is a combinatorial optimization problem having an objective function composed of power losses and capacitor installation costs subject to bus voltage constraints. Recently, many approaches have been proposed to solve the capacitor placement problem as a mixed integer programming problem. This paper presents a new capacitor placement method which employs particle swarm optimization (PSO) approaches with operators based on Gaussian and Cauchy probability distribution functions and also in chaotic sequences for a given load pattern of distribution systems. The proposed approaches are demonstrated by two examples of application. Simulation results show that the proposed method can achieve an optimal solution as the exhaustive search can but with much less computational time.     

用改进的Tabu搜索方法优化补偿电容器分档投切的研究

对基本的 Tabu搜索方法进行了改进 ,将“改进遗传算法”中的优化编码技术引入 Tabu搜索方法 ,并在此基础上引入动态管理退出迭代判定条件、动态管理 Tabu表深度和动态管理邻域搜索规模等 ,用以处理补偿电容器分档投切的组合优化问题 ,并给出了算例     

基于PSO考虑谐波影响的补偿电容器优化配置

配电网合理的电容器配置不仅可以有效改善电网的电压水平，降低系统的有功网损，而且能够避免谐波谐振或电流放大，该文在建立电容器优化配置问题的非线性整数规划模型时，考虑了电压谐波畸变率约束条件，以保证优化方案下的各节点电压总谐波畸变率控制在规定限值以内。文中应用了一种简单有效，且收敛性很好的演化计算算法－微粒群优化算法（PSO）进行问题的求解，从编码方式，操作过程，目标函数选取，参数调节以及信息共享机制等五个方面分析了该算法的优越性，并给出了用于电容器优化配置问题中算法的具体求解步骤。对2个不同规模的IEEE测试系统的优化计算表明，微粒群算法可以很好地获得电容器优化配置问题的全局最优解。     

求解动态无功优化问题的混合免疫遗传算法

无功优化是电力系统运行中提高经济性和电压安全性的重要措施,为防止静态无功优化可能导致无功控制设备的频繁操作,考虑并联电容器投切组数和有载调压变压器变比档位的调节次数约束,建立了电力系统动态无功优化模型。提出免疫遗传算法与非线性内点法相结合的混合算法进行求解,其中免疫遗传算法处理离散变量,非线性内点法处理连续变量,并在免疫遗传算法中设计独特的编码方式,使抗体能够自动满足动态约束。采用IEEE14系统的24时段无功优化问题进行仿真计算,动态无功优化后离散控制设备的调节次数很少,有功损耗比静态优化结果仅有轻微增加,算例结果验证了混合免疫算法的有效性。     

Optimal capacitor placement in radial distribution networks

The capacitor placement (replacement) problem for radial distribution networks determines capacitor types, sizes, locations and control schemes. Optimal capacitor placement is a hard combinatorial problem that can be formulated as a mixed integer nonlinear program. Since this is a NP complete problem (nonpolynomial time) the solution approach uses a combinatorial search algorithm. The paper proposes a hybrid method drawn upon the Tabu Search approach, extended with features taken from other combinatorial approaches such as genetic algorithms and simulated annealing, and from practical heuristic approaches. The proposed method has been tested in a range of networks available in the literature with superior results regarding both quality and cost of solutions     

A Heuristic Constructive Algorithm for Capacitor Placement on Distribution Systems

This paper presents a heuristic constructive algorithm (HCA) for optimal capacitor placement on distribution systems. This is a nonlinear mixed integer optimization problem. In the proposed approach, the integer variables are represented using sigmoid function, thus interior point optimal power flow formulation can be applied to obtain sensitivity indexes based on Lagrange multipliers, reactive power, and bus voltage. The methodology is applied to two power distribution systems, and the results are compared with those obtained using a genetic algorithm approach.      

求解离散无功优化的非线性原-对偶内点算法

针对无功优化计算中离散变量和连续变量共存问题,提出用直接非线性原一对偶内点法内嵌罚函数的新算法。通过对几个不同规模试验系统计算分析,并与Tabu搜索法求得的结果比较,证明了该方法是有效的,而且在计算速度、收敛性和优化精度上都优于Tabu搜索法。这使内点法在解决非线性混合整数规划无功优化的有效性和实用性方面更进了一步。     

一种适合于解决辐射状配电网电容器最优配置问题的遗传算法

提出了一种可解决辐射状配电网电容器最优配置问题的遗传算法。将电容器看作离散变量 ,对给定的目标函数求最佳的电容器安装位置和容量 ;设计了针对该问题有效的遗传因子 ,并对一个实际的配电网进行了计算 ,得到了较好的结果。对遗传算法用于辐射状配电网的电容器最佳配置问题进行了探讨     

计及控制设备动作次数约束的三阶段动态无功优化算法

为了避免控制设备频繁操作,动态无功优化模型需考虑无功补偿装置投切开关及变压器抽头的允许动作次数约束。但是,动态无功优化属于大规模、多时段、强耦合的混合整数非线性规划问题,对其直接求解是困难的。建立了以有功网损最小为目标函数的动态无功优化模型,并提出一种实用的三阶段动态无功优化算法,该算法的核心是一种具有多项式计算复杂度的前推-回推式动态规划算法。将计及控制设备动作次数约束的动态无功优化问题的求解分解为多个时间断面的连续无功优化计算、理想无功补偿装置无功补偿功率曲线和变压器变比曲线的阶梯化以及在确定各个时段的无功补偿容量和变压器变比情况下的连续无功优化计算3个阶段。对IEEE 30节点系统和某实际区域电网进行测试,结果验证了所提算法的合理性和实用性。     

基于原-对偶内点法和混合整数规划法的机组组合问题研究

电力系统机组组合能带来显著的经济效益,随着电力市场的不断发展,在电力系统优化运行中变得尤为重要。然而电力系统机组组组合问题是一个大规模、非凸、非线性混合整数优化问题,至今仍然没有找到一种理想的优化算法。因此针对其特点,采用了原-对偶内点法和混合整数规划法相结合的算法,首先利用混合整数规划法形成伴随规划来处理离散变量,再通过内点法求解伴随规划子问题和负荷经济分配,充分发挥了两种算法在求解机组组合问题上的优势。文中对标准10机组24时段系统算例进行了仿真测试并与之前的各种优化算法进行了对比,结果表明了本文算法模型解决机组组合问题的有效性和优越性。     

A genetic algorithm approach in optimal capacitor selection with harmonic distortion considerations

This paper reports the research findings of an innovative genetic algorithm approach for optimizing shunt capacitor sizes and their placement in radical distribution systems with the consideration of harmonic distortion limit due to the presence of nonlinear power electronic devices. The algorithm is based on a genetic algorithm solution technique to minimize cost under the additional constraints of maximum limit in harmonic distortion factor. A harmonic distortion calculation is embedded in the genetic algorithm solution routine to enhance the optimal capacitor allocation solution. Results of simulation show that the approach is effective for such a discrete value optimization problem.     

A dynamic model for coordination of generation and transmission expansion planning in power systems

This paper presents a new dynamic approach on the expansion planning problem in power systems. First, the coordination between generation system expansion and transmission system expansion has been formulated as a mixed integer nonlinear programming (MINLP) problem. Then, it has been shown that this MINLP model cannot be efficiently solved by the traditional MINLP solvers. Since the nonlinear term comes from the multiplication of a binary variable by a continuous one, a Benders decomposition approach has been employed to convert the MINLP formulation into a mixed integer linear programming (MILP) master problem, and a linear programming (LP) sub-problem. Besides, different times of construction have been considered for different transmission and generation facilities. In addition, a clustering based algorithm has been proposed to evaluate the reliability of the system at hierarchical level II (HLII). Since this dynamic planning method is an upgraded version of a recent developed static model, the result from both methods have been also compared. A simple 6-bus test system and IEEE 30-bus system have been selected to confirm the effectiveness of the introduced method.     

Optimal capacitor placement for power systems with nonlinear loads

The purpose of this paper is to derive a systematic procedure to decide the optimal location and size of compensation shunt capacitors for distribution systems with harmonic distortion. A set of indices determined by the sensitivity of voltage variation, real power loss and harmonic distortion to the reactive power source is used to decide the optimal location of the shunt capacitors. The problem is formulated as a nonlinear programming of the minimization of real power loss and capacitor cost under the constraints of voltage limits and total harmonic distortion. A practical power system is selected for computer simulation to test the efficiency of the proposed method. It is found that both the system loss and harmonic distortion can be reduced very effectively by this method.     

Capacitor placement, replacement and control in large-scaledistribution systems by a GA-based two-stage algorithm

This paper presents a two-stage algorithm tailored for capacitor placement, replacement and control of general, large-scale, unbalanced distribution systems. The first stage of the proposed algorithm consists of a GA followed by the second stage which consists of a sensitivity-based heuristic method tailored for the capacitor placement, replacement and control problem. The two-stage algorithm is designed to take advantage of the merits of each technique. The GA is employed to find neighborhoods of high quality solutions and to provide a good initial guess for the sensitivity-based heuristic. The heuristic uses the sensitivity of real power loss to reactive power to quickly and locally improve upon the solution provided by the GA with less computation than by allowing the GA to continue. The two-stage algorithm was implemented in the C programming language and tested for a 292 bus unbalanced system with single, two and three-phase branches and grounded and ungrounded portions of the network with promising results     

基于内点法与改进遗传法的无功规划优化混合算法

建立了利用调节发电机端电压、可带载调压变压器分接头与静止电容器组的补偿容量来获得系统年综合费用最小的无功规划优化数学模型。将此问题分成连续优化和离散优化两个子问题,采用非线性内点法和改进遗传算法交替求解的混合算法。在迭代的不同阶段,分别对内点法和改进遗传算法进行收敛条件改进,使两者的优化结果互为基础、相互利用,保证了混合算法的整体寻优效率。118节点系统的无功优化计算表明,所提算法可有效提高单一算法的收敛性能和运算速度。     

计及VSC和DFIG的电网动态无功优化模型

近年来,一系列特高压直流工程的投运和大型风电场等新能源的并网给特高压近区电网无功控制带来了新的挑战。为解决含柔性直流的交直流混联电网的无功优化控制问题,提出了含电压源换流器(Voltage Source Converter, VSC)并考虑双馈感应风机(Doubly-Fed Induction Generator, DFIG)无功支撑的动态无功优化模型。该模型以交直流电网全天网损最小为目标函数,约束包括交直流系统的潮流约束、直流变量的控制约束、离散控制变量动态调节次数约束及节点电压的安全约束。原模型是一个多时段非线性混合整数规划问题,缺乏快速有效的求解方法,通过线性化技术将原模型转化为能有效求解的二阶锥规划(Second Order Cone Programming, SOCP)问题。以IEEE30节点系统为例,通过仿真计算验证了所建模型和算法的有效性。     

A VAR planning method with multiple power-flow states

The goal of reactive power (VAR) planning is to find the minimum cost installation plan of new reactive power sources so that the system voltage is maintained within an acceptable level. The consideration of multiple contingency states, together with the discrete nature of VAR facilities, creates a large-scale nonlinear mixed-integer programming (MIP) problem. To overcome the discrete nature of VAR facilities, an approximate method for the MIP problem is employed since the method is linear-programming based and thus efficient for large-scale problems. To treat the multiple contingencies, a resource directive decomposition approach is used in the proposed algorithm. If the number of installed VAR sources is fixed, the overall problem can be reduced to independent subproblems. Then subproblems are coordinated to give a VAR installation pattern in which installation cost becomes less than before. The algorithm proposed is tested for a 135-node real-size system and the results show the validity and effectiveness of the algorithm.     

Active and reactive dispatch with minimum control movements

This paper proposes a new formulation of the combined Optimal Active and Reactive Dispatch (OARD) problem with Minimum Control Movements (MCM) for the voltage control devices. The main objective of the proposed model is to minimize the total power system operation cost which include fuel cost of generators and switching cost of equipments like tap transformers and shunt capacitors. Practical constraints such as maximum allowable number of switching operation in a day for tap changing transformers and switchable capacitors are taken into consideration. A penalty based approach has been formulated to tackle with the switching costs of adjustable equipments. The problem has been formulated as a nonlinear dynamic optimization problem with the presence of both continuous and discrete control variables and solved using Artificial Bee’s Colony (ABC) algorithm. The approach has been tested on IEEE 30 bus system and the simulation is carried out in MATLAB. In order to verify the effectiveness of the results obtained, both active and reactive power dispatch problems have been solved separately and compared with the proposed approach. Results demonstrate the effectiveness of the proposed approach.