Minimizing the number of PMUs and their optimal placement in power systems

This paper presents a new method for minimizing the number of PMUs and their optimal placement in power systems. The proposed method provides suitable constraints for power systems with two adjacent injection measurements (IMs). In addition, suitable constraints for considering the connection of two buses to each other and to an injection bus are proposed. The proposed constraints result in a reduction in the number of PMUs even though the system topological observability is complete. Existing conventional measurements are also considered. First, the number of PMUs is minimized in such a way that the system topological observability is complete. Then the optimal placement is done to maximize the measurements redundancy. The resulting phased to be installed in multiple stages. The optimal number of PMUs that ensure system topological observability under failure of a PMU or a line is also simulated. Simulations are performed on IEEE 30, 57 and 118 bus test systems by binary integer programming. The results show that the number of PMUs is equal to or less than the corresponding results of recently published papers, while the system topological observability is complete, and measurement redundancy is increased.     

ILP-based multistage placement of PMUs with dynamic monitoring constraints

This paper addresses two aspects of the optimal Phasor Measurement Unit (PMU) placement problem. Firstly, an ILP (Integer Linear Programing) model for the optimal multistage placement of PMUs is proposed. The approach finds the number of PMUs and its placement in separate stages, while maximizing the system observability at each period of time. The model takes into account: the available budget per stage, the power system expansion along with the multistage PMU placement, redundancy in the PMU placement against the failure of a PMU or its communication links, user defined time constraints for PMU allocation, and the zero-injection effect. Secondly, it is proposed a methodology to identify buses to be observed for dynamic stability monitoring. Two criteria, which are inter-area observability and intra-area observability, have been considered. The methodology identifies coherent groups in large power systems by using a new technique based on graph theory. The technique requires neither full stability studies nor a predefined number of groups. Also, a centrality criterion is used to select a bus for monitoring each coherent area and supervise inter-area oscillations. Then, PMUs are located to ensure complete observability inside each area (intra-area monitoring). Methodology is applied on the 14-bus test system, the 57-bus test system with expansion plans, and the 16-machine 68 bus test system. Results indicate that the optimization model finds the optimal number of PMUs when the PMU placement by stages is required, while the observability at each stage is maximized. Additionally, it is shown that expansion plans and particular requirements of observability can be considered in the model without increasing the number of required PMUs, and the zero-injection effect, which reduces the number of PMUs, can be considered in the model.     

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。     

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。     

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.      

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.      

A Multi-objective PMU Placement Method in Power System via Binary Gravitational Search Algorithm

This paper presents a Binary Gravitational Search Algorithm (BGSA) methodology for the optimal placement of Phasor Measurement Units (PMUs) to achieve full and maximum observability of the power system. The gravitational search technique has been extended in this investigation to incorporate binary variables for this purpose. The objective of proposed methodology is to minimize the total number of PMUs installed at various buses, which in turn minimize installation cost of the PMUs and improves observability redundancy by including an additional objective. Thus, the PMU placement problem has been expressed as a multi-objective problem. Besides, single PMU outage or single line outage cases in the presence of zero injection buses have been investigated. In this algorithm, the searcher agents are the collection of masses, which interact with each other using Newton's laws of gravity and motion. The proposed BGSA has been applied to the IEEE 14-bus, -30-bus, -118-bus, Northern Regional Power Grid 246-bus Indian system, and Polish 2383-bus system. Case studies reveal that the lower number of PMUs or equal number of PMUs has been produced by the proposed method compared to methods reported in the literature. In cases of equal number of PMUs, the observability produced by proposed method is higher or at least equal.     

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。     

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。     

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.     

Novel Clustering-based Hidden Markov Model (CHMM) optimization approach for optimal PMU placement

A Phasor Measurement Unit (PMU) is an important device for monitoring the wide-area power distribution network. Placement of the PMUs across the network enables reliable monitoring of the network to identify the faults in the bus system. Due to the increase in the installation cost of the PMUs, optimal placement of the PMU is a significant task. But the existing techniques do not provide the optimal solution for the PMU placement. To overcome this issue, this paper proposes a novel Clustering-based Hidden Markov Model (CHMM) optimization approach to achieve optimal placement of PMUs in the power distribution network. Optimal PMU placement is achieved by applying cluster formation in the bus system to extract the data with neighboring buses. Best optimal position for placing the PMU is estimated by using Fuzzy logic-based rale formation to update the binary table of the bus system. The HMM approach is used for updating weight in the cluster formation. Our system is implemented in various bus systems like IEEE 28-bus system, 69-bus system and also in Karnataka 155-bus system. The proposed approach is implemented in the IEEE bus system and Karnataka Power Transmission Corporation Limited (KPTCL) bus system and compared with the existing approaches, based on the total number of PMU placement. The proposed approach achieves better performance in the optimal placement of PMU than the existing optimization algorithms.     

Weak bus-constrained PMU placement for complete observability of a connected power network considering voltage stability indices

Phasor measurement units (PMUs) are preferred for installation at weak buses in a power network. Therefore, the weak buses need to be located and the strategic locations of PMUs identified to ensure network observability. Thus, the primary aim of this work is to identify the placements of the maximum number of PMUs installed at the weak buses in the electrical network. The voltage collapse proximity indicator, line stability index, fast voltage stability index, and a new voltage stability indicator utilizing load flow measurement are used to determine the weak buses. A novel deterministic methodology based on a binary-integer linear programming model is then proposed to determine the optimal locations of PMUs. The effect of a single PMU outage considering the weak buses is also demonstrated. The effectiveness of the developed approach is tested and validated on the standard IEEE 14-, 118-, 300-, and New England 39-bus systems. The obtained results are also compared to those using different weak bus methodologies.     

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.     

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     

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.     

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SCADA/PMU混合量测的广域动态实时状态估计方法

根据来自监视控制与数据采集(supervisory control and data acquisition，SCADA)系统和相量测量单元(phasor measurement unit，PMU)的数据特点，提出了一种基于SCADA/PMU混合量测的广域动态实时状态估计方法，该方法充分利用了各节点间电压变化的相互联系，通过SCADA系统提供的初始值和安装PMU的节点的电压量测可简单地获得其他未安装PMU节点的电压相量。该方法有效地解决了在PMU配置不足的情况下如何观测电网状态以及如何在动态过程下实时观测电网。最后，通过对新英格兰10机39节点系统的多种故障进行仿真，验证了该方法的有效性和准确性。     

Optimal allocation of phasor measurement unit for full observability of the connected power network

This paper presents binary particle swarm optimization (BPSO) technique for the optimal allocation of phasor measurement units (PMUs) for the entire observability of connected power network. Phasor measurement units are considered as one of the most important measuring devices in the prospect of connected power network. PMUs function may be incorporated to the wide-area connected power networks for monitoring and controlling purposes. The optimal PMU placement (OPP) problem provides reference to the assurance of the minimal number of PMUs and their analogous locations for observability of the entire connected power networks. Binary particle swarm optimization (BPSO) algorithm is developed for the solution of OPP problem. The efficacy and robustness of the proposed method has been tested on the IEEE 14-bus, IEEE 30-bus, New England 39-bus, IEEE 57-bus, IEEE 118-bus and Northern Regional Power Grid (NRPG) 246-bus test system. The results obtained by proposed approach are compared with other standard methods and it is observed that this BPSO based placement of phasor measurement units is found to be the best among all other techniques discussed.     

基于改进自适应遗传算法的PMU优化配置

为了利用最少数目的相量测量单元(PMU)保证电力系统在正常运行时和线路N?-1故障时都能完全可观,提出一种基于改进自适应遗传算法(IAGA)的PMU优化配置方法。将PMU配置分为两个阶段:第一阶段以PMU安装数目最少和正常运行时系统完全可观为目标配置PMU;第二阶段在已有配置结果的基础上继续安装PMU,以保证线路N-1故障时系统仍完全可观。修改IAGA中交叉概率和变异概率的计算公式,克服了当群体最大适应度值与平均适应度值相等时进化停滞的缺点,优化了进化过程,同时方便了数学计算;对每一代个体进行防早熟操作,消除了由交叉运算和变异运算的偶然性及随机性导致的进化早熟。算例分析结果表明,该方法在PMU配置数目、配置方案种类、收敛性及实用性上有显著优势,证明了该方法的正确性和优越性。