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。     

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.     

Placement of Synchronized Measurements for Power System Observability

This paper presents a method for the use of synchronized measurements for complete observability of a power system. The placement of phasor measurement units (PMUs), utilizing time-synchronized measurements of voltage and current phasors, is studied in this paper. An integer quadratic programming approach is used to minimize the total number of PMUs required, and to maximize the measurement redundancy at the power system buses. Existing conventional measurements can also be accommodated in the proposed PMU placement method. Complete observability of the system is ensured under normal operating conditions as well as under the outage of a single transmission line or a single PMU. Simulation results on the IEEE 14-bus, 30-bus, 57-bus, and 118-bus test systems as well as on a 298-bus test system are presented in this paper.      

电力系统相量测量装置最优配置混合算法的研究

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最优配置问题。将遗传算法和禁忌算法有效结合形成禁忌遗传算法,该算法在改进交叉和变异算子的基础上,继承和发展了遗传算法基于多点搜索、鲁棒性强等诸多优点,每当群体有出现早熟而陷入局部最优解的趋势时,利用禁忌搜索增强算法的爬山能力,避免算法早熟而陷入局部最优解,增强算法的全局收敛能力和收敛速度。与遗传算法和禁忌搜索方法相比,禁忌遗传算法具有更好的全局收敛能力和收敛速度。最后采用IEEE14,IEEE30和IEEE57节点系统对算法的有效性进行了验证。     

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.     

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.     

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.     

基于改进自适应遗传算法的系统可观测PMU最优配置

以电力系统配置同步相量测量单元（PMU）个数最少、系统有最大测量冗余度为目标,全网可观测为约束,提出PMU最优配置模型,同时针对实际电网中存在某些重要节点已经初步安装PMU或者必须安装PMU的情况,提出了特殊约束条件,并给出了相应的求解算法。在此基础上,用改进自适应遗传算法求解此模型,保证全局最优。对某省49节点电网进行的计算表明,改进的自适应遗传算法收敛到全局最优解的概率优于传统的遗传算法和自适应遗传算法,更适用于工程实际。     

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.     

Robust Measurement Design by Placing Synchronized Phasor Measurements on Network Branches

This paper is concerned about optimal placement of synchronized phasor measurements that can monitor voltage and current phasors along network branches. Earlier investigations on placement of phasor measurement units (PMUs) have assumed that a PMU could be placed at a bus and would provide bus voltage phasor as well as current phasors along all branches incident to the bus. This study considers those PMUs which are designed to monitor a single branch by measuring the voltage and current phasors at one end of the monitored branch. It then determines the optimal location of such PMUs in order to make the entire network observable. The paper also addresses the reliability of the resulting measurement design by considering loss or failure of PMUs as well as contingencies involving line or transformer outages. Developed placement strategies are illustrated using IEEE test systems.      

Phasor measurement unit placement techniques for complete and incomplete observability

This paper presents techniques for identifying placement sites for phasor measurement units (PMUs) in a power system based on incomplete observability. The novel concept of depth of unobservability is introduced and its impact on the number of PMU placements is explained. Initially, we make use of spanning trees of the power system graph and a tree search technique to find the optimal location of PMUs. We then extend the modeling to recognize limitations in the availability of communication facilities around the network and pose the constrained placement problem within the framework of Simulated Annealing (SA). The SA formulation was further extended to solve the pragmatic phased installation of PMUs. The performance of these methods is tested on two electric utility systems and IEEE test systems. Results show that these techniques provide utilities with systematic approaches for incrementally placing PMUs thereby cushioning their cost impact.     

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。     

A PMUs placement methodology based on inverse of connectivity and critical measurements

This paper presents a methodology to determine the optimal location of phasor measurement units (PMUs) in any network to make it observable. This proposed methodology is based on network connectivity information and unreachability index (URI), where URI is the difficulty to observe any node in the network and it is computed using the inverse of connectivity. In order to choose the optimal bus, it is basically considered to observe a low connectivity bus from an adjacent bus selected by weighting factors that are based on logical analysis of the observability theory combined with the URI; this process stops until the network is observable. The purpose is minimize the number of PMUs in a network with the optimal location and the aim to get a low number of critical measurements (CM) with a high total redundancy (TR), in order to obtain an optimal distribution of PMUs on the network. The proposal is considered as an easy solver for PMU’s placing on the network due to important reduction in complexity and computational cost, besides comparable results are as good as those papers using recent optimization methods such as metaheuristics and stochastics, without taking into account that the proposal can handle huge networks. The algorithm is applied to the IEEE 14, 30, 57, 118 and 300-bus systems, and also to medium and large power systems of 1006, 3305, 15,000, 20,000 and 30,000 buses with success.     

基于改进的整数规划法结合零注入节点的PMU优化配置方法

为了提高同步相量测量装置的优化速度并利用最少数量的相量量测单元(PMU),结合零注入节点的特性,提出了基于整数规划算法的PMU优化配置算法。根据电力系统全网的可观测性建立其数学模型,并考虑了零注入节点的相关特点,求解系统模型获得PMU的优化位置。对IEEE-14节点、IEEE-18节点、IEEE-30节点以及IEEE-118节点系统分别进行了实验仿真,并利用Matlab以及Lingo工具对所提改进的整数规划法进行了验证,对约束方程进行优化,获得了PMU的数量和位置。将该算法与整数规划算法、模拟退火法以及改进过的遗传算法相比较,该算法可以用更少数量的PMU设备使全网可观,验证了该方法的有效性和优越性。     

Transmission system wide-area back-up protection using current phasor measurements

Zone-3 of distance relays might maloperate during stresses frequently encountered in power systems, such as power swing, load encroachment, and voltage instability. This paper proposes a new protection algorithm for discrimination between short-circuit faults and other stresses in the transmission networks. The proposed method compares the sum of currents at the predetermined buses before and after the disturbance occurrence using synchronized current phasor measurements. The faulted area and line are identified as well. The optimal placement of phasor measurement units (PMUs) is tackled using a mathematical model. One of the main advantages of the proposed algorithm is decreasing the number of required PMUs in comparison with those of existing wide-area back-up protection schemes. In virtue of its computational speed, the proposed method can be exploited as a practical back-up protection cooperating with conventional protection schemes. The extensive simulation studies carried out on the IEEE 57-bus test system verify applicability of the proposed algorithm as a reliable back-up protection scheme for lines.     

Optimal PMU placement for power system state estimation with random component outages

Phasor measurement units (PMUs) provide globally synchronized measurements of voltage and current phasors in real-time and at a high sampling rate. Hence, they permit improving the state estimation performance in power systems. In this paper we propose a novel method for optimal PMU placement in a power system suffering from random component outages (RCOs). In the proposed method, for a given RCO model, the optimal PMU locations are chosen to minimize the state estimation error covariance. We consider both static and dynamic state estimation. To reduce the complexity, the search for the optimal PMU locations is constrained to the set of locations guaranteeing topological observability. We present numerical results showing the application and scalability of our method using the IEEE 9-bus, 14-bus, 39-bus and 118-bus systems.     

Optimal Placement of Phasor Measurement Units with Linear and Non-linear Models

Abstract—This article presents a non-linear programming-based model for the optimal placement of phasor measurement units. The optimal phasor measurement units placement is formulated to minimize the number of phasor measurement units required for full system observability and to maximize the measurement redundancy at all buses in a power system. A sequential quadratic programming algorithm is used for the solution of the proposed model. The existence of power flow and injection measurements, the limited phasor measurement units channel capacity, the lack of communication facilities in substations, and the single phasor measurement units loss are also incorporated into the initial proposed formulation. The non-linear programming model is applied to IEEE 14- and 118-bus test systems in MATLAB. The accuracy and the effectiveness of the proposed method is verified by comparing the simulation results to those obtained by a binary integer programming model also implemented in MATLAB. The comparative study shows that the proposed non-linear programming model yields the same number of phasor measurement units as the binary integer programming model. A remarkable advantage of the non-linear programming against binary integer linear programming is its capability to give more than one optimal solution, each one having the same minimum number of phasor measurement units (same minimum objective value), but at different locations.     

基于01整数规划的多目标最优PMU配置算法

针对目前缺乏多目标PMU配置方法,提出了一种基于线性01规划的多目标优化配置算法。并在此基础上导出了三种特殊模型,分别处理系统在正常运行方式下完全可观测的PMU布点问题,在线路N-1故障时系统仍可观测的PMU布点问题及在PMU N-1故障时系统仍可观测的PMU布点问题。该方法的突出特点在于能够同时将以上三种布点需求使用统一的形式同时处理,并且最终的布点方案在保证PMU数目最少或保证配置PMU所需费用最少的基础上获得了最高的测量冗余度。通过IEEE30、IEEE 57、IEEE118节点系统布点验证了该方法的有效性和灵活性。