基于多目标进化算法的PMU的优化配置

研究了配置相量测量单元(PMU)后电力系统可观测性的判断方法,以保证电力系统完全可观测为约束条件,以配置PMU数目最小和保证测量量具有最大量测冗余度为目标,建立了PMU最优配置问题的数学模型。这是一个多目标优化问题,需要寻求一组Pareto最优解,应用多目标进化算法求解该问题可以得到多种满足条件的PMU配置可行方案。最后,以IEEE39节点系统为例验证了该方法的合理性。     

Multi‐objective PMU placement optimization considering the placement cost including the current channel allocation and state estimation accuracy

The optimal phasor measurement unit (PMU) placement problem in power systems has been considered and investigated by many researchers for accurate and fast state estimation by PMUs. However, the current channel cost of the PMU affects the total placement cost. This paper proposes a novel formulation in the multi‐objective optimal PMU placement, which minimizes the PMU placement cost with the current channel selection and the state estimation error. The current channel selection is represented as a decision variable in the optimization. For trade‐off objective functions, the Pareto approach by nondominated sorting genetic algorithm II (NSGA‐II) is applied in the optimization. The result of the numerical experiment in this paper demonstrates the advantage of considering the appropriate PMU current channel allocation, compared with the conventional method that ignores it, in the modified IEEE New England 39‐bus test system. As a result, the proposed method obtained a better Pareto solution compared with the conventional one because of the consideration for the current channel selection. An advantage of the proposed PMU placement is that it is able to reduce the total PMU placement cost while maintaining the state estimation accuracy.     

基于改进粒子群算法的PMU装置数量增加过程中的最优配置方法

针对现有电力系统相量测量装置(PMU)在系统中的最优配置问题,进一步考虑了系统发展过程中PMU数量增加的最优配置问题。以电力系统线性量测模型为基础,通过拓扑分析方法,以全系统可观为约束,以系统最大冗余度为目标,并使用改进的粒子群算法进行计算,实现PMU数量增加过程中的最优配置。通过算例证明了算法的有效可靠。     

基于图论的电力系统PMU布点优化算法

基于最小支配集理论和电力系统线性量测模型,提出了可观测节点集合、WAMS可观测矩阵两个概念以及一种新的节点可观测性计算规则。以保证系统的完全可观测性和以系统图的最小支配集为搜索范围构成约束条件, 以电力系统状态完全可观测和相量测量装置（PMU）配置数目最小为目标,形成了PMU配置优化问题。并应用禁忌搜索(TS)方法求解该问题,保证了全局寻优。最后采用 IEEE 14、30、57 、118节点系统和新英格兰 39 节点系统对该方法进行了验证,仿真结果表明该方法的有效性和可行性。     

用免疫BPSO算法和N-1原则多目标优化配置PMU

为了在满足全网的完全可观测的前提下实现PMU安装投入的性价比最高,通过理论分析得出判断电网节点拓扑可观测的依据,并提出以N-1可靠性检验原则对PMU配置方案进行冗余性检验,由此以全网完全可观测、PMU数目最少和N-1量测冗余度最高为目标建立了PMU多目标优化配置数学模型,并设计了一种结合免疫系统信息处理机制的二进制粒子群优化算法对模型进行求解。该算法综合了粒子群优化算法简单快速和免疫系统种群多样性的优点,明显改善了进化后期算法的收敛性能和全局寻优能力。对新英格兰39母线系统进行PMU多目标优化配置仿真及量测冗余性分析的结果表明,该法对PMU配置方案的量测可靠性及其所需PMU数量进行综合评价可方便快捷地得到性价比最优的方案,较之普通的PMU单目标优化配置方法更为合理和灵活。     

电力系统PMU最优配置数字规划算法

随着相量量测装置(PMU)硬件技术的逐渐成熟和高速通信网络的发展,PMU在电力系统中的状态估计、动态监测和稳定控制等方面得到了广泛应用.为达到系统完全可观,在所有的节点上均装设PMU既不可能也没有必要.文中提出一种基于系统拓扑可观性理论的数字规划算法,利用PMU和系统提供的状态信息,最大限度地对网络拓扑约束方程式进行了简化,以配置PMU数目最小为目标,形成了PMU最优配置问题,并采用禁忌搜索算法求解该问题.其突出优点是利用了系统混合测量集数据,即不仅考虑了PMU实测数据,同时计及了可用的潮流数据.在IEEE14节点和IEEE 118节点系统的仿真结果表明,与常规的PMU最优配置算法相比,所提出的数字规划算法可以实现安装较少数量的PMU而整个系统可观的目标.     

基于免疫BPSO算法与拓扑可观性的PMU最优配置

以电力系统状态完全可观测和相量测量单元PMU配置数目最小为优化目标,基于PMU的功能特点和电力网络的拓扑结构信息,形成快速且通用的电网拓扑可观测性判别方法,并设计了一种结合免疫系统信息处理机制的二进制粒子群优化算法对目标函数进行求解,该算法综合了粒子群优化算法简单快速和免疫系统种群多样性的优点,明显改善了进化后期算法的收敛性能和全局寻优能力.最后通过对IEEE14和新英格兰39母线系统进行PMU优化配置仿真及量测冗余性分析,验证了本文方法的有效性和优越性.     

Optimal placement of PMUs with limited number of channels for complete topological observability of power systems under various contingencies

In optimal PMU placement problem, a common assumption is that each PMU installed at a bus can measure the voltage phasor of the installed bus and the current phasors of all lines incident to the bus. However, available PMUs have limited number of channels and cannot measure the current phasors of all their incident lines. The aim of this paper is to recognize the effect of channel capacity of PMUs on their optimal placement for complete power system observability. Initially, the conventional full observability of power networks is formulated. Next, a modified algorithm based on integer linear programming model for the optimal placement of these types of PMUs is presented. The proposed formulation is also extended for assuring complete observability under different contingencies such as single PMU loss and single line outage. Moreover, the problem of combination of PMUs with different number of channels and varying costs in optimal PMU placement is investigated. Since the proposed optimization formulation is regarded to be a multiple-solution one, total measurement redundancy index is evaluated and the solution with the highest redundancy index is selected as the optimal solution. The proposed formulation is applied to several IEEE standard test systems and compared with the existing techniques.     

PMU最优配置问题的混合优化算法

为使得电力系统在完全可观测的条件下,PMU安装数目最少,提出了一种混合优化算法以解决相量测量单元PMU的最优配置问题.混合优化算法以粒子群优化算法为主体,引入交叉、变异操作,并结合模拟退火机制控制粒子的更新.在处理解的约束问题时,采用了一种基于概率的启发式修补策略,避免修复后的解特征单一.将混合算法与其他算法在多个IEEE标准系统上进行了比较分析,结果表明在较大规模系统上,混合优化算法收敛率比标准粒子群算法提高数倍,计算量比模拟退火算法减少了数十倍,表明了较好的可行性和较高的效率.     

Optimal Multistage Scheduling of PMU Placement: An ILP Approach

This paper addresses various aspects of optimal phasor measurement unit (PMU) placement problem. We propose a procedure for multistaging of PMU placement in a given time horizon using an integer linear programming (ILP) framework. Hitherto, modeling of zero injection constraints had been a challenge due to the intrinsic nonlinearity associated with it. We show that zero injection constraints can also be modeled as linear constraints in an ILP framework. Minimum PMU placement problem has multiple solutions. We propose two indices, viz, BOI and SORI, to further rank these multiple solutions, where BOI is bus observability index giving a measure of number of PMUs observing a given bus and SORI is system observability redundancy index giving sum of all BOI for a system. Results on IEEE 118 bus system have been presented. Results indicate that: (1) optimal phasing of PMUs can be computed efficiently; (2) proposed method of modeling zero injection constraints improve computational performance; and (3) BOI and SORI help in improving the quality of PMU placement.     

一种改进的相量测量装置最优配置方法

以电力系统状态完全可观测和相量测量装置(PMU)配置数目最小为目标,提出了一种改进的PMU最优配置方法.将启发式方法和模拟退火方法有效结合以确保得到最优解,提高了基于启发式方法的初始PMU配置方案的质量,通过改进配置模型缩小了模拟退火方法的寻优范围,从而提高了求解速度.还提出了一种基于节点邻接矩阵的快速可观测性分析方法.最后采用IEEE 14、IEEE 30、IEEE 118节点系统和新英格兰39节点系统对该方法进行了验证.     

船舶电力系统相量测量单元多目标优化配置问题

为实现船舶电力系统潮流方程直接可解,同时保证相量测量单元(PMU)配置数目最少和N-1电压相量可解冗余度最高,提出了船舶电力系统PMU多目标优化配置方法。首先根据船舶电力系统不同工况下潮流方程的特点,分析得到PMU配置方案是否满足不同工况下潮流方程直接可解的判断方法;在此基础上,着重考虑最大运行工况下PMU配置数目最少和N-1电压相量可解冗余度最高的要求,建立了PMU多目标优化配置模型,并采用量子遗传优化算法对模型进行求解。以24节点典型船舶电力系统为例对所提方法进行了说明和验证,结果表明,该方法可实现全局多目标寻优,从而找到准确而完整的Pareto最优前沿。得到的PMU优化配置方案可为船舶电力系统配置PMU提供参考。     

Power system observability with minimal phasor measurementplacement

The placement of a minimal set of phasor measurement units (PMUs) so as to make the system measurement model observable, and thereby linear, is investigated. A PMU placed at a bus measures the voltage as well as all the current phasors at that bus, requiring the extension of the topological observability theory. In particular, the concept of spanning tree is extended to that of spanning measurement subgraph with an actual or a pseudomeasurement assigned to each of its branches. The minimal PMU set is found through a dual search algorithm which uses both a modified bisecting search and a simulated-annealing-based method. The former fixes the number of PMUs while the latter looks for a placement set that leads to an observable network for a fixed number of PMUs. In order to accelerate the procedure, an initial PMU placement is provided by a graph-theoretic procedure which builds a spanning measurement subgraph according to a depth-first search. From computer simulation results for various test systems it appears that only one fourth to one third of the system buses need to be provided with PMUs in order to make the system observable     

基于记忆的改进克隆算法及其PMU配置多目标优化应用

以PMU安装数、量测系统可观测性和基于混合量测的状态估计精度三者为优化目标的PMU优化配置(OPP)是二层规划问题。该文证明了用单次状态估计精度评价量测系统性能的可行性，提出精度加权估算公式。将二层规划目标简化为分段函数，提出基于记忆的改进克隆算法。除模仿生物免疫系统的克隆选择和受体编辑机制外，该算法引入记忆加速算子以强化邻域搜索，并分段调整循环补充规模、高频变异与重组操作概率，从而显著加快和稳定进化进程，避免搜索陷入局部最优解。基于IEEE 14/57节点系统的算例表明，该算法能快速稳定地求出全局最优解及近似解，比原克隆算法等更适用。     

Optimal PMU placement method for complete topological and numerical observability of power system

This paper presents a new method of optimal PMU placement (OPP) for complete power system observability. A two-stage PMU placement method is proposed, where stage-1 finds out the minimum number of PMUs required to make the power system topologically observable and stage-2 is proposed to check if the resulted PMU placement (from stage-1) leads to a full ranked measurement Jacobian. In case the PMUs placed, ensuring topological observability in stage-1, do not lead to the Jacobian of full rank, a sequential elimination algorithm (SEA) is proposed in stage-2 to find the optimal locations of additional PMUs, required to be placed to make the system numerically observable as well. The proposed method is tested on three systems and the results are compared with three other topological observability based PMU placement methods. The simulation results ensure the complete system observability and also demonstrate the need of using stage-2 analysis along with the topological observability based PMU placement methods.     

基于改进自适应遗传算法的电力系统相量测量装置安装地点选择优化

将进化参数衰减因子与基于适应度变化的自适应遗传算法相结合,提出了一种新的自适应遗传算法,使遗传算法在进化过程中能够同时根据个体适应度和进化时间的变化自动调整交叉与变异概率,克服了原有自适应遗传算法易早熟的缺点,提高了最优解的多样性和寻优速度.精英个体保留策略保证了整个算法的全局收敛性.在约束条件处理时,采用了不可行解启发性修复方法,提高了算法的优化效果.基于图论的深度优先方法用于系统可观性分析.将新的自适应遗传算法应用于优化相量测量装置安装地点选择,实现了安装地点最少,而整个系统可观的目标.该算法已在某省46节点系统的优化计算中得到了验证.     

Optimal Placement of Phasor Measurement Units Using Immunity Genetic Algorithm

This paper investigates the application of immunity genetic algorithm (IGA) for the problem of optimal placement of phasor measurement units (PMUs) in an electric power network. The problem is to determine the placement sites of the minimal set of PMUs which makes the system observable. Incorporating immune operator in the canonical genetic algorithm (GA), on the condition of preserving GA's advantages, utilizes some characteristics and knowledge of the problems for restraining the degenerative phenomena during evolution, so as to improve the algorithm efficiency. This type of prior knowledge about some parts of optimal solution exists in the PMU placement problem. So, the IGA is adopted in this paper to solve the problem. Also, a new effect which is preventing from familial reproduction is studied which shows an increase in converging speed. The effectiveness of the proposed method is verified via IEEE standard systems and a realistic large-scale power system.      

考虑系统完全可观测性的PMU最优配置方法

基于电力系统线性量测模型，研究了引入相量测量单元（PMU）相关量测集后的增广关联矩阵的电力系统可观测性拓扑分析方法，以保证系统结构完全可观测性和最大量测数据冗余度为约束，以配置PMU数目最小为目标，形成了PMU最优配置问题，并应用禁忌搜索（TS）方法求解该问题，保证了全局寻优。算例表明，该方法准确可靠、有效可行。     

Optimal placement of PMUs to maintain network observability using a modified BPSO algorithm

This paper presents a novel approach to optimal placement of Phasor Measurement Units (PMUs) for state estimation. At first, an optimal measurement set is determined to achieve full network observability during normal conditions, i.e. no PMU failure or transmission line outage. Then, in order to consider contingency conditions, the derived scheme in normal conditions is modified to maintain network observability after any PMU loss or a single transmission line outage. Observability analysis is carried out using topological observability rules. A new rule is added that can decrease the number of required PMUs for complete system observability. A modified Binary Particle Swarm Optimization (BPSO) algorithm is used as an optimization tool to obtain the minimal number of PMUs and their corresponding locations while satisfying associated constraint. Numerical results on different IEEE test systems are presented to demonstrate the effectiveness of the proposed approach.     

Fault Location Observability Using Phasor Measurement Units in a Power Network Through Deterministic and Stochastic Algorithms

This article studies deterministic and stochastic algorithms for placing minimum number of phasor measurement units (PMUs) in a power system in order to locate any fault in the power system. The optimization problem is initially formulated in a mixed integer linear programing framework with binary-valued variables as well as in a binary integer linear programing model. Then, the optimization problem is formulated as an equivalent non-linear programing model, minimizing a quadratic objective function subject to equality non-linear constraints defined over a bounded and closed set. The problem is solved by using a Sequential Quadratic Programming algorithm. The non-linear program is illustrated with a 7-bus test system. Also, stochastic algorithms such as binary-coded genetic algorithm and particle swarm optimization have been implemented in solving the optimal PMU placement under fault condition. The accuracy of suggested algorithms is independent from the fault type and its resistance. The optimization models are applied to the IEEE systems. The numerical results indicate that the proposed algorithms locate minimizers at the optimal objective function value in complete agreement with those obtained by branch-and-bound algorithms.