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.     

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.     

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。     

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.     

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。     

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.     

A Novel Topological Genetic Algorithm-Based Phasor Measurement Unit Placement and Scheduling Methodology for Enhanced State Estimation

Phasor measurement units are emerging as a potential tool for on-line power system state estimation. Incorporation of phasor measurement units to the existing power system's monitoring system is impeded by various physical and economic constraints. This article proposes a novel topological genetic algorithm for optimal placement of phasor measurement units along with existing conventional measurement units such that state estimation can be achieved with enhanced accuracy and immunity against power grid contingencies. The proposed algorithm optimally places phasor measurement units so that complete observability of the power system is achieved through them and enhanced redundancy in measurement can be accomplished through conventional measurement units. Since practical phasor measurement unit placements are accomplished in multiple horizons, intelligent sorting and phase optimization methodologies have been presented to attain maximum observability during phasing periods. Placement of phasor measurement units with multiple channel limits has also been studied in this article. The efficacy of the proposed topological genetic algorithm for optimizing the number of phasor measurement units and enhancing state estimation under various operating conditions has been validated through extensive simulation studies conducted in IEEE standard bus systems. Practical case studies have been performed in the western and southern region Indian power grids.     

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。     

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.     

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。     

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 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.     

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 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.     

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.     

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.