Optimal Placement Of Phasor Measurement Units Research Articles

Intrusion Detection, Measurement Correction, and Attack Localization of PMU Networks

Accurate state estimation is essential for correct supervision of power grids. With the existence of cyber-attacks, state estimation may become inaccurate, which can eventually lead to wrong supervisory decision making. To detect cyber-attacks in power grids equipped with phasor measurement units (PMUs), a new intrusion detection system based on clustering approach, called PMU Intrusion Detection System (PMUIDS), is proposed in this article. After solving the optimal PMU placement in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -1 contingency, several static state estimations are obtained by removing the measurements of one PMU in each time. The resulting state vectors are clustered in two steps: First, subtractive clustering is employed to obtain the number of clusters, which determines the number of integrity attacks; and second, fuzzy C-means clustering assigns the state vectors to the corresponding clusters, which determines the attacked PMUs. In addition, two theorems are proved, which indicate that the attacker cannot coordinate successful stealth attacks in cases that by removing attacked PMUs from state estimation, the power system still remains full observable. Furthermore, in the case of possible stealth attacks, the attacker cannot falsify the estimation of any arbitrary state variable. The hardware-in-the-loop results on a sample power system show that the proposed approach can detect integrity attacks, determine the number of attacks, obtain the correct state vector, and localize the attacks, even in case of multiple simultaneous attacks.

Optimal PMU Placement Considering Depth of Unobservability

Optimal PMU Placement Considering Depth of Unobservability

Minimizing the Total Cost of WAMS Using Artificial Electric Field Algorithm

Wide area monitoring system (WAMS) is one of the most important technologies in modern power systems, it gathers the synchronized time stamped measurements from wide area across power system through a high reporting measuring device such as synchronized phasor measurement units (PMUs).Due to the high cost of PMU itself and its installation cost, it is often difficult to install PMU at each bus in the power system. However, there are several approaches to solve the optimal PMU placement (OPP) with various optimization algorithms. In this paper, a realistic cost model has been proposed to provide optimal PMUs placement (OPP). The proposed model has been solved using artificial electric field algorithm (AEFA), which is a novel optimization algorithm, it was proposed by 2019. In this paper, a binary form of AEFA has been proposed to solve the proposed cost model. AEFA has been implemented in MATALB programming environment, and the results demonstrate that the proposed cost model provides a realistic view of WAMS cost. Additionally, the results have been compared with other optimization algorithm, and it demonstrates that the AEFA is efficient to solve the OPP problem.

Modified branch‐and‐bound algorithm for unravelling optimal PMU placement problem for power grid observability: A comparative analysis

Modified branch‐and‐bound algorithm for unravelling optimal PMU placement problem for power grid observability: A comparative analysis

Cyber attacks on PMU placement in a smart grid: Characterization and optimization

Phasor measurement units (PMUs) have been integrated into the smart grid for monitoring the operational state of system and improving the reliability. Due to the high cost of PMU installment, the optimal placement strategies have attracted considerable attention in the literature. However, the impacts of cyber threats on the placement have been largely ignored owing to the cyber complexities. This paper initializes the study on the optimal PMU placement in a smart grid under the cyber threats. A probabilistic model is developed for assessing the unobservable risk of the power grid. We characterize the impacts of several cyber factors on the PMU placements including the number of directly attacked PMUs, the dependence among attack outcomes, and risk propagation. We further study the impacts of cyber attacks on the allocation strategies under a bi-level placement model. In particular, a novel ‘greedy’ algorithm for PMU placement is introduced with the presence of cyber risks. Our studies show that the cyber risk can significantly increase the unobservability risk of a power system which in turn requires additional PMU allocations, and the dependence among cyber attacks can lead to more unobservable risk.

Communication infrastructure for situational awareness enhancement in WAMS with optimal PMU placement

Real time monitoring and control of a modern power system has achieved significant development since the incorporation of the phasor measurement unit (PMU). Due to the time-synchronized capabilities, PMU has increased the situational awareness (SA) in a wide area measurement system (WAMS). Operator SA depends on the data pertaining to the real-time health of the grid. This is measured by PMUs and is accessible for data analytics at the data monitoring station referred to as the phasor data concentrator (PDC). Availability of the communication system and communication delay are two of the decisive factors governing the operator SA. This paper presents a pragmatic metric to assess the operator SA and ensure optimal locations for the placement of PMUs, PDC, and the underlying communication infrastructure to increase the efficacy of operator SA. The uses of digital elevation model (DEM) data of the surface topography to determine the optimal locations for the placement of the PMU, and the microwave technology for communicating synchrophasor data is another important contribution carried out in this paper. The practical power grid system of Bihar in India is considered as a case study, and extensive simulation results and analysis are presented for validating the proposed methodology.

Globally optimal phasor measurement unit placement using branch and bound algorithm

Abstract This paper presents a new global optimal Phasor Measurement Unit (PMU) placement approach based on branch and bound algorithm. The proposed technique provides the global minimum number and locations of PMUs for any power system. Different objective functions are investigated including (i) minimum number and optimum location of PMUs for full observability, and (ii) maximum system observability with specific number of PMUs (PMU Investment phasing). Moreover, the loss of a power system element or a PMU is also considered. The effects of modeling zero-injection buses and using power flow measurements on the quality of the outputs and real-time studies are presented. The proposed technique is applied to the IEEE 14-, 30-, 57- and 118-bus systems using the MATLAB platform. A comparison between the proposed technique and recently published work is held. The proposed method improves the integer linear programming accuracy, shows superiority over other techniques, and reduces the overall cost.

An optimal placement of phasor measurement unit using new sensitivity indices

This paper presents an alternative approach to solve an optimal phasor measurement unit (PMU) placement by introducing two new sensitivity indices. The indices are constructed from the information measured from PMUs such as voltage magnitude and angle. These two parameters are essential for power system stability assessment and control. Therefore, fault analysis is carried out to obtain the voltage magnitude and angle deviations at all buses in order to construct the indices. An exhaustive search method is used to solve the linear integer programming problem where all possible combinations of PMU placement are evaluated to obtain the optimal solution. Unfortunately, the traditional objective function to minimize the total number of PMU placement leads to multiple solutions. The indices can be used to assess multiple solutions of PMU placement from the exhaustive method. In this work, an optimal solution is selected based on the performance of PMU placement in according to the indices. The proposed method is tested on the IEEE 14 bus test system. Only four PMUs are required to monitor the whole test system. However, the number of PMUs can be reduced to three PMUs after applying zero injection bus elimination.

Probabilistic Optimal PMU Placements Under Limited Observability Propagations

The problem of phasor measurement units (PMUs) placement for state estimation in modern power grids has emerged with renewed interest in recent years. Conventional optimal PMU placement (OPP) formulations without limitations on observability propagations pose the power grid at the higher risk of losing its observability under unexpected contingencies or malicious cyberattacks. In order to mitigate these impacts in PMU deployments, by extending our proposed enhanced OPP formulation under the concept of the observability propagation depth (OPD), a probabilistic variation of this enhanced OPP is presented. To further explore the robustness of OPP problems under severe contingencies, a linearized probabilistic observability model is proposed and incorporated with the previous enhanced OPP model into a bilevel optimization framework. Thus, in addition to derive the minimum number of PMUs by solving the enhanced OPP model in the upper level, the optimal PMU configuration with the maximal probabilistic observability can also be depicted in the lower level. By solving the dual problem of the lower-level problem under Karush–Kuhn–Tucker conditions, this bilevel optimization formulation can be reformulated into a single-level mixed-integer linear programming problem, which can be easily solved by commercial optimization tools. Extensive simulations are conducted on several IEEE test-bed systems as well as the Polish-2383 system to demonstrate the feasibility and the effectiveness of the proposed formulation. Simulation results indicate that there is strong evidence that the probability of losing the observability of a bus is positively related to its OPD.

Multiple Solutions for Optimal PMU Placement Using a Topology-Based Method

This paper presents a novel topology-based optimal PMU placement strategy. The proposed strategy provides the entire feasible solution space which gives the observability of the power system by working on binary connectivity matrix of the system. From the feasible solution space, multiple optimal solutions are obtained. Providing multiple optimal solutions gives flexibility to the system operator to choose one optimal solution which best fits sub-ordinate objectives rather than providing single optimal solution which gives no choice to the operator. This novel strategy has been tested on IEEE 14-bus and IEEE 30-bus system. Multiple optimal solutions are obtained while maintaining observability and maximizing redundancy. For demonstrating the advantage of multiple optimal solutions, minor objectives, such as direct monitoring of generator and weak buses are illustrated. One of the multiple solution which best fits to the minor objectives is chosen as a final optimal solution. The proposed method ensures global optimal solution for various objectives under consideration. In addition, normalized Bus observability index and normalized System observability redundancy index are presented to overcome the drawback of SORI and BOI.

Tri-Objective Optimal PMU Placement Including Accurate State Estimation: The Case of Distribution Systems

This paper presents a tri-objective Optimal Phasor Measurement Units (PMUs) Placement (OPP) strategy that is focused on the minimization of i) the total number of PMU channels, ii) the maximum state estimation uncertainty based only on high-rate PMU data and iii) the sensitivity of state estimation to line parameter tolerances. The proposed formulation keeps into account system observability with and without contingencies due to single-line and PMU faults. Also, it includes the effect of possible zero-injection buses and a-priori constraints on both the number of PMU channels and the type of PMU measurements performed at each bus. Due to the nonlinear combinatorial nature of the proposed OPP problem, this is solved through a custom implementation of the nondominated sorting genetic algorithm II (NSGA-II). The analysis of the proposed OPP strategy is focused on distribution systems. The placement results obtained using four test systems of different size show that increasing the number of buses instrumented with PMUs and/or the number of PMU channels beyond given thresholds just leads to larger costs with negligible further reductions in both state estimation uncertainty and sensitivity to line parameters tolerances. Moreover, if PMUs with just two three-phase channels are used, we can avoid instrumenting between 30% and 40% of buses with a minor impact on state estimation performance even in the case of contingencies. This percentage can be slightly increased if multi-channel PMUs are used. However, this choice generally is not profitable.

A Novel Algorithm for Optimal Phasor Measurement Unit Placement for Full Power System Topological Observability

A Novel Algorithm for Optimal Phasor Measurement Unit Placement for Full Power System Topological Observability

Optimal Phasor Measurement Unit Placement Using a Honey Bee Mating Optimization (HBMO) Technique Considering Measurement Loss and Line Outages

Phasor measurement units (PMUs) are important devices for protection, monitoring, and control of modern power systems. Unlike the supervisory control and data acquisition (SCADA) system which only measure the magnitude, PMUs can provide a set of synchronized phasor measurements with high sampling rate with the accuracy of less than one second, for better system monitoring especially during the outages. Since the PMUs are costly devices, system operator is not able to install a PMU at each bus to maximize the observability of system. To this end, determination of the number of PMUs in the system for having a 100% observability is pivotal. In this paper, honey bee mating optimization (HBMO) approach is utilized to allocate PMUs in modern power systems. Moreover, the impact of line outages, as well as measurement loses, are considered. The simulation results show the effectiveness of the proposed method on solving the PMU placement problem. http://www.crpase.com/xml/20210701211.xml

Optimal PMU Placement Using Genetic Algorithm for 330kV 52-Bus Nigerian Network

The phasor Measurement Unit is a modern tracking tool mounted on a network to track and manage power systems. PMU is accurate and time-synchronized device that gives voltage phasor measurements in nodes and current phasor measurements connected to those nodes where the PMU is installed. This study introduces the Genetic Algorithm for optimization of allocation of PMUs to enable maximum observation of the power network. The optimal PMU placement (OPP) problem is developed to minimize the quantity of PMU to be placed. The set and optimized model can efficiently position PMU in any network, considering the regular operation and zero injection (ZIN). Thus, the allocation algorithm implemented on IEEE 14-bus systems, the result was compared to that of existing works which achieved the same system of redundancy index. As a further study, the proposed approach is applied to the Nigerian 330kV new 52-bus systems, under operational arrangements for maximum observability of the network system. The technique formulated to handle normal operation and zero injection node succeeded in producing comparable results with other available techniques.

Development of wide area monitoring system for smart grid application

PMU can directly measure positive sequence voltage, phase and system frequency. In this paper, the design and implementation for optimum placement of PMU in power system network (PSN) has been performed using 5 different intelligent approaches at an emulation platform. Different case studies based on IEEE 7, 14 and 30 bus system have been performed and analyzed. In the studies, PMU device is used for the measurement of voltage and current magnitude as well as its phase and its performance has been compared with measured real signals of PSN. PMU measurement gives the accurate results and reliability to PSN. But PMUs are not economical, so PSN operator needs to install a minimum number of PMU in PSN so that system should be fully observable in a real-time scenario. In this paper for optimal placement of PMU, five different intelligent methods have been analyzed for three different bus systems and obtained results are compared. For the further validation of selected PMUs for the PSN, a state estimation using WLS algorithm has been performed using conventional data and PMU data on IEEE14 and IEEE30 bus systems. The obtained results for voltage estimation error and phase estimation error with and without PMU data are compared.

Optimal Allocation of Synchrophasor Units in the Distribution Network Considering Maximum Redundancy

Phasor Measurement Unit (PMU) is a smart measuring device commonly used in wide-area monitoring systems. It provides the synchronized phasor values and the magnitudes of voltages and currents in real-time for the proper state calculation of the electrical network in a common time reference frame. But in order to avoid unnecessary placements, minimize installation cost, and due to the lack of communication facilities at the substations, the placing of PMUs at every location is not possible. Therefore several optimization techniques have been developed to solve the Optimal PMU Placement (OPP) problem. The OPP problem aims to reduce the number of PMUs by achieving a completely observable network. Many solutions to the OPP problem have been proposed for the transmission networks with the use of conventional and heuristic-based approaches, but very few for distribution networks. In this paper, the Binary Grey Wolf Optimization (BGWO) algorithm is proposed to solve the OPP problem considering the measurement redundancy (MR) to achieve complete observability of the distribution network. Finally, case studies have been done by implementing the proposed algorithm on different IEEE test feeders such as the IEEE -13, -33, -37, and -123 node feeder systems. The obtained results are compared with previous studies to verify the feasibility and efficiency of the proposed technique.

A Bounded Exhaustive Search Technique for Optimal Phasor Measurement Unit Placement in Power Grids

This paper proposes a technique to determine the possible optimal placement of the phasor measurement unit (PMU) in power grids for normal operating conditions. All possible combinations of PMU placement, including infeasible combinations, are typically considered in finding the optimal solution, which could be a massive search space. An integer search algorithm called the bounded search technique is introduced to reduce the search space in solving a minimum number of PMU allocations whilst maintaining full system observability. The proposed technique is based on connectivity and symmetry constraints that can be derived from the observability matrix. As the technique is coupled with the exhaustive technique, the technique is called the bounded exhaustive search (BES) technique. Several IEEE test systems, namely, IEEE 9-bus, IEEE 14-bus, IEEE 24-bus and IEEE 30-bus, are considered to showcase the performance of the proposed technique. An initial Monte Carlo simulation was carried out to evaluate the capability of the bounded search technique in providing a smaller feasible search space. The effectiveness of the BES technique in terms of computational time is compared with the existing exhaustive technique. Results demonstrate that the search space can be reduced tremendously, and the computational burden can be eased, when finding the optimal PMU placement in power grids.

Optimal PMU arrangement considering limited channel capacity and transformer tap settings

The transition from the conventional power systems to smart grids has led to the modernisation of the measuring infrastructure used for their monitoring and control. Among the devices used to accomplish these tasks, phasor measurement units (PMUs) play a key role since they can provide extremely accurate synchronised voltage and current phasor measurements. The optimal PMU placement (OPP) problem, which focuses on minimising the number of PMUs for full system observability, has long been a popular research topic. The vast majority of the available OPP techniques have treated each transformer tap setting (voltage turns ratio and phase-shifting angle) as a fixed network parameter. Such an assumption can lead to misdirecting residuals in adjacent valid measurements when the modelled tap setting is incorrect. The aim of this study is to propose a substation-oriented OPP method based on a binary semidefinite programming algorithm, considering the observability of the transformer tap settings and the limited PMU channel capacity. The method is illustrated using an 8-bus test system. Numerical results using different size IEEE systems are presented and discussed. The proposed approach is further applied to the Polish 3120-bus system to show its efficacy in solving the OPP problem for large-scale power systems.

Optimal PMU placement approach for power systems considering non-Gaussian measurement noise statistics

This paper investigates how to add a limited number of Phasor Measurement Units (PMUs) to the existing monitoring system so as to improve the estimation accuracy further. The existing methods are usually based on Gaussian noise assumption and the weighted least squares (WLS) estimator is taken into account. However, the Gaussian noise assumption is not always true in reality and the WLS is non-robust in this case. This paper proposes a new optimal PMU placement approach where the distribution of measurement noise can be non-Gaussian or Gaussian and many robust estimators such as the maximum likelihood estimator, Multiple-Segment, Quadratic-Linear, Square-Root and Schweppe-Huber Generalized-M estimator are considered. Based on the new Gain matrix obtained from the influence function approximation, the D-optimal and E-optimal experiment criterions are exploited in the optimal PMU placement problem. A convex relaxation in conjunction with an optimization improvement method based on the Fedorov exchange algorithm is utilized to solve the optimizing problem. Simulations on the IEEE 57-bus system and the Polish 2383-bus system are carried out to evaluate the effective performance of the proposed approach.

WITHDRAWN: Taxonomy of evolutionary techniques application in power systems

Application of optimization techniques in power systems has begun over last 50 years. In recent times, evolutionary techniques and in general nature-inspired techniques have gained lots of attention and found to be useful for solving various engineering optimization applications. This is due to increase in robustness, reliability, growing demand for artificial intelligence methods, parallel computing, and availability of open source software. Therefore, in the present paper an attempt to briefly review and explore the application of these techniques in power systems in four main areas, namely, economic load dispatch (ELD), load frequency control (LFC), optimal power flow (OPF), and optimal PMU placement (OPP) problems is made. A number of papers are listed in this taxonomy which illustrations the contribution in each paper.