Minimum Number Of Phasor Measurement Units Research Articles

Observable placement of phasor measurement units for defense against data integrity attacks in real time power markets

Integrity data (DI) attacks are considered malicious cyber threats to the economic performance of power markets in current power systems. A cyber attacker could mislead the system operator by implementing a DI attack, through the deviation of measured information, and causes non-optimal power distribution and erroneous participation in the electricity market (EM). This paper proposes a placement scheme of phasor measurement units (PMUs) to defend against these attacks, so that network observability is guaranteed; the possibility of detecting DI attacks by the operator is increased; and the effect of electricity price fluctuations caused by these attacks is prevented. For this purpose, we introduce two possible indices to determine the degree of attack detectability and the magnitude of system congestion variation. Accordingly, the two-objective placement model of PMUs is upgraded, in which the minimum number of PMUs and their placement must be specified to improve the proposed indices so as to minimize the possibility of financial misconduct taking place in the real time market. Using IEEE standard systems, the effectiveness of this PMU placement-based defense scheme has been confirmed.

Resiliency Estimation of Synchrophasor Communication Networks in a Wide Area Measurement System

The power grid is evolving into a smart grid due to the diverse energy generation and distribution. This complex grid has to be continuously monitored in real-time for its safe operation. Sensors known as phasor measurement units (PMUs) are used for obtaining health information pertaining to the grid in terms of time-synchronized voltage and current phasors. Measurements from several PMUs are sent through a synchrophasor communication network (SCN) to the phasor data concentrator (PDC). The PMUs, the PDC and the SCN together constitute the wide area measurement system (WAMS). Being an important constituent of the WAMS, the resiliency estimation of SCNs is paramount for their proper design. Resilience is a measure of the systems resistance to the disturbances or a measure of its ability to bounce back to a functional state in the event of failure. This paper presents a quantitative metric for estimating the resiliency of SCNs. Monte Carlo simulation (MCS) models are used to simulate random component failures, and the data is used for measuring the resiliency of the SCNs. A multi-objective genetic algorithm (GA) is used for optimizing the placement of PMUs and the PDC, to observe the power system with the minimum number of PMUs, and to simultaneously maximize the resilience. The practical power grid of West Bengal, India, is analyzed as a case study. This work can be a significant contribution to the power sector as it assists in the proper planning and placement of the communication infrastructure in a WAMS.

Wide area monitoring and measurements using mixed integer linear programming in deregulated power system for smart grid

This paper deals with different methods involved in the determination of complete observability of power system under wide area monitoring using Phasor Measurement Unit (PMU). There are numerous methods available in literature for the determination of optimal locations of PMU for complete system observability, but out of all those methods, fast selection of best suitable with minimum number of PMUs at optimal location for complete observability, is still a challenge to power engineers for applying online in Smart Grid under deregulation environment. After detail analysis with various methods, this paper proposes an algorithm for selecting best possible method for determining optimal locations of PMUs. The analysis compares performance of the available methods, e.g., Binary Integer Linear Programming, Admittance Bus Matrix Method and Mixed Integer Linear Programing using General Algebraic Modelling System. To investigate the effectiveness of the proposed method for complete observability using system observability redundancy index (SORI), Indian Northern Regional Power Grid (NRPG-246 bus system) has also been considered here.

Connectivity Matrix Algorithm: A New Optimal Phasor Measurement Unit Placement Algorithm

The maximum benefits of the phasor measurement unit (PMU) in state estimation and other applications in the power system can be achieved if the system is completely observed by PMUs only. The minimum number of PMUs needed to obtain full observability is very important in order to reduce the overall cost. This paper presents a new algorithm for optimal PMU placement (OPP) in transmission and distribution systems. A new concept and vision of the optimization problem is presented. A new approach to implement zero-injection buses is proposed which may be also used in other algorithms. The simulation result of IEEE 14, 24, 30, 57 and 118 bus systems as transmission systems, IEEE 33, 34 and 123 bus systems as distribution systems, and Jordanian power system as an actual system are presented and compared with the existing techniques. The proposed technique is simple to implement and accurate compared to other existing methods. The results confirm the efficiency of the proposed algorithm. The computational time is less than 0.2 seconds for all cases. MATLAB 2016a is used to validate the algorithm.

PMU Placement for Measurement Redundancy Distribution Considering Zero Injection Bus and Contingencies

This article proposes a method for optimal placement of phasor measurement units (PMUs) to improve measurement redundancy distribution in a system under normal operating condition or in presence of contingency. The minimum number of PMUs is determined using integer linear programming method, after which the measurement redundancy is optimized using a novel model to represent the redundancy level of each bus. Weight parameters are assigned to auxiliary variables, which enables control of priority of different redundancy level. The impact of zero injection bus is integrated into the model, as well as the channel limitation of PMUs and existing measurements. Besides, contingency is modeled in a generalized form, which enables N-1 or N-2 contingency analysis. The proposed method is tested on various IEEE systems, and the results show that the number of PMUs obtained by the proposed method is further reduced comparing with other methods, while with a highly improved measurement redundancy.

Multi Objective for PMU Placement in Compressed Distribution Network Considering Cost and Accuracy of State Estimation

A phasor measurement unit (PMU) can provide phasor measurements to the distribution network to improve observability. Based on pre-configuration and existing measurements, a network compression method is proposed to reduce PMU candidate locations. Taking the minimum number of PMUs and the lowest state estimation error as the objective functions and taking full observability of distribution network as the constraint, a multi objective model of optimal PMU placement (OPP) is proposed. A hybrid state estimator based on supervisory control and data acquisition (SCADA) and PMU measurements is proposed. To reduce the number of PMUs required for full observability, SCADA measurement data are also considered into the constraint by update and equivalent. In addition, a non-dominated sorting genetic algorithm-II (NSGA-II) is applied to solve the model to get the Pareto set. Finally, the optimal solution is selected from the Pareto set by the technique for order preference by similarity to ideal solution (TOPSIS). The effectiveness of the proposed method is verified by IEEE standard bus systems.

A novel linear framework for Phasor Measurement Unit placement considering the effect of adjacent zero-injection buses

A novel linear approach for Phasor Measurement Units (PMUs) placement is proposed in this paper to ensure the topological observability taking into consideration the impacts caused by the adjacent zero-injection buses (ZIBs). The observability analysis in the paper is performed utilizing merely the main topological observability rules. Furthermore, the model is developed to include all possible single contingencies both on the lines and PMUs even where adjacent ZIBs are highly interconnected. To this end, the common approach for handling contingencies is enhanced. Moreover, the presented framework incorporates a subsidiary objective, i.e. maximizing the measurement redundancy among the set of solutions with the minimum number of PMUs beside the main objective, i.e. minimizing the number of the required PMUs. In this regard, a unified Integer Linear Programming (ILP) is used to solve the proposed optimisation problem. It is worth noting that the suggested approach is applied to different test systems like IEEE 14-bus, 30-bus, 39-bus, 57-bus as well as 118-bus system to validate the effectiveness and efficiency of the proposed framework and the obtained results are compared to those reported by the prior researches.

Application of domination integrity of graphs in PMU placement in electric power networks

In this paper, we propose the application of the concept of power domination integrity to an electric power network. A phasor measurement unit (PMU) is used to analyze and control the power system by measuring voltage phase in electrical nodes and transmission lines. Due to the high cost of PMUs, it is necessary to minimize the number of PMUs such that the depth of observability is ensured. Placing PMUs in a network can be formulated as a graph theoretic problem of finding the minimum number of nodes (PMUs) in a graph that has a maximum number of links with other nodes. To achieve this, the concept of domination in graph theory is applied to power networks by redefining ``adjacency'' of a vertex as an ``observed'' vertex. The power domination number identifies the number of PMUs to be placed. The proposed concept of power domination integrity gives not only the minimum number of PMUs but also identifies the optimal locations for PMU placement in an electric power network.

Optimal PMU placement for pessimistic dynamic vulnerability assessment

This study proposes a novel optimal phasor measurement unit (PMU) placement method for dynamic vulnerability assessment with minimum number of PMUs. PMU measurements should reflect the change of power system status as earlier as possible when a contingency occurs. Therefore, those buses which are sensitive to the change of power system status have to be equipped with PMUs to monitor the fragile areas of power systems. First, a large power system is partitioned into several coherent clusters. Next, a probabilistic vulnerability index defined as the objective function and a binary quadratic programming model are proposed for this purpose. Finally, the proposed method is tested on IEEE 9-, 39-, and 145-bus systems. Results show that this method results in a PMU configuration with minimum number of devices and high vulnerability index. Such a PMU placement is able to estimate the vulnerability of power systems.

Optimal Location of Phasor Measurement Unit Using Ant Colony Optimization Under Contingency

Accurate and fast monitoring is achieved by using the real time synchronized phasor data obtained from Phasor Measurement Unit (PMU). As the cost of PMU is more expensive, it is not economical to install PMU at all the nodes of a power system. Therefore, it is very much essential to implement an optimal method for PMU location. In this research work, implementation of Ant Colony Optimization (ACO) for optimal PMU placement under normal and single PMU loss conditions is discussed. The PMUs are placed in such a manner that all voltage phasors and current phasors are measurable with a minimum number of PMUs. The proposed ACO is able to locate the PMUs optimally enabling the complete measurement of all voltage and current phasors with a minimum number of PMUs. The ACO is an efficient optimization algorithm to optimize the placement of the PMU for measuring the voltage and current phasors with minimum no of PMU. The proposed method is demonstrated in IEEE 14 bus, IEEE 30 bus, and IEEE 57 bus to find the optimal location of PMU under normal and for single PMU loss conditions.

Fault localization for transmission lines with optimal Phasor Measurement Units

This paper discusses a novel fault localization algorithm for multi-terminal transmission lines. The technique is tested for different fault types and fault locations. The exact fault location is determined along with the latitude and longitude by involving geo-referenced data of the power system. In addition, Phasor Measurement Units (PMUs) are effectively used for complete system observability. The number of PMUs is optimised using Genetic Algorithm. Thus, the objective is to find the distance of the fault occurrence and to locate the fault point along with the latitude and longitude, using optimal PMUs. For evaluation purpose, Indian Utility (TamilNadu Electricity Board) 49 bus system is used and validated, using software such as MATLAB, Power World Simulator and Google Earth View. The results show the effectiveness of the proposed technique to spot the exact fault point in the transmission lines with a minimum number of PMUs, to make the concept economical.

Multistage hybrid evolutionary computing-based optimal PMU placement for large scale power grid network

Phasor measurement unit (PMU) is one of the most significant grid components that plays vital role in ensuring reliable power transmission and distribution. The optimal PMU placement (OPP) in power system can not only ensure grid cost reduction, real-time monitoring and control, but can reduce the operational complexities and overheads significantly. This paper proposes a novel multistage hybrid evolutionary computing scheme for OPP solution. Our proposed model applied adaptive genetic algorithm (AGA) for initial state point retrieval for OPP, which was then fed as input to the pattern search (PS)-based PMU placement optimisation. Our proposed AGA-PS scheme ensures OPP solution by retrieving minimum number of PMUs and its optimal location across grid network to make power system completely observable under varied cases. The simulation results with IEEE 14, IEEE 39, IEEE 118 and KPTCL 155 bus networks has exhibited that the proposed AGA-PS outperforms major existing approaches in terms of optimal OPP solutions.

Integrated Mutation Strategy With Modified Binary PSO Algorithm for Optimal PMUs Placement

Optimal phasor measurement units (PMUs) placement refers to the strategic placement of PMUs to achieve the full observability of power systems with a minimum number of PMUs. A strategic placement is needed because of the economic or technical restriction that hinders the deployment of PMUs on every bus. A modified version of the binary particle swarm optimization method is proposed in this paper by integrating a mutation strategy and the V-shaped sigmoid function for placing the PMUs that maintains the full power system observability in the presence of zero-injection bus, single PMU loss, and PMU's channel limits while maximizing the measurement redundancy. The solution that has the highest measurement redundancy was selected as the best placement of PMUs. The use of mutation strategy and V-shaped sigmoid function in this paper improves the population diversity, thereby minimizing the chance of the particles being trapped in the local optima, consequently leading to a quality solution. In order to validate its effectiveness, the results obtained by the proposed method are compared with other published techniques to demonstrate the accuracy and validity of the proposed technique. The results of the IEEE 300-bus system show that the proposed method effectively managed to reduce the number of PMUs needed.

On-line Assessment of Voltage Stability using Synchrophasor Technology

Series of blackouts encountered in recent years in power system have been occurred because either of voltage or angle instability or both together was not detected within time and progressive voltage or angle instability further degraded the system condition, because of increase in loading. This paper presents the real-time assessment methodology of voltage stability using Phasor Measurement Unit (PMU) with observability of load buses only in power network. PMUs are placed at strategically obtained location such that minimum number of PMU’s can make all load buses observable. Data obtained by PMU’s are used for voltage stability assessment with the help of successive change in the angle of bus voltage with respect to incremental load, which is used as on-line voltage stability predictor (VSP). The real-time voltage phasors obtained by PMU’s are used as real time voltage stability indicator. The case study has been carried out on IEEE-14 bus system and IEEE-30 bus systems to demonstrate the results.

Optimal PMU location in power systems using MICA

This study presented a modified imperialist competitive algorithm (MICA) for optimal placement of phasor measurement units (PMUs) in normal and contingency conditions of power systems. The optimal PMU placement problem is used for full network observability with the minimum number of PMUs. For this purpose, PMUs are installed in strategic buses. Efficiency of the proposed method is shown by the simulation results of IEEE 14, 30, 57, and 118-bus test systems. Results of the numerical simulation on IEEE-test systems indicated that the proposed technique provided maximum redundancy measurement and minimum request of PMUs so that the whole system could be topologically observable by installing PMUs on the minimum system buses. To verify the proposed method, the results are compared with those of some recently reported methods. When MICA is used for solving optimal PMU placement (OPP), the number of PMUs would be usually equal to or less than those of the other existing methods. Results indicated that MICA is a very fast and accurate algorithm for OPP solution.

Optimal Phasor Measurement Unit Placement for Monitoring of PEA Bowin Power

This paper presents an optimal method of Phasor Measurement Unit (PMU) placement in Bowin area distribution grid of the Provincial Electricity Authority (PEA) using the Improved Greedy Method (IGM) in order to achieve a minimum number of PMUs for complete observability of all bus voltages. The proposed method introduces the criteria of bus selection for PMU placement, regarding a number of branches connected to the selected bus as well as the length of those branches. Subsequently, the mismatches of the observed voltages resulted from the proposed method are compared with those resulted from the Depth First Search (DFS) using the Power System Analysis Toolbox (PSAT) and the original Greedy method (GDY) to reveal the effectiveness of the proposed placement methods. For the DFS and GDY methods, a bus with the highest number of connected branches is initially selected as the first PMU bus. However, if there is more than one bus, the first PMU bus will be randomly selected from those qualified. On the other hand, the PMU bus firstly selected by the IGM must have the highest number of connected branches as well as the minimum total distance or total impedance of all observable buses. The findings resulted from the IGM are the optimal PMU placement with the total distance of the connected branches less than the other methods, especially for, large-scale networks. According to the comparison results among the DFS, GDY and IGM, the mean absolute error (MAE) of the angle and the magnitude voltage of all buses resulted from the IGM is the lowest for a wide range of load conditions, while the MAE resulted from the DFS is the highest.

Intelligent-search technique based strategic placement of synchronized measurements for power system observability

Synchronized phasor measurements placement problem is commonly solved by formulating it as a mathematical optimization problem, which is limited by huge computational burden especially for larger systems. This paper proposes a novel intelligent search based approach for placement of phasor measurement units (PMUs) in the power system while maintaining complete observability. The proposed approach works in two stages. Stage I utilizes best first search to identify the possible locations of PMUs in order to obtain system observability and these locations are used as inputs to stage II. Stage II determines the optimal locations of PMUs by applying pruning to the inputs received from stage I, such that the system observability is achieved with the minimum number of PMUs. The proposed approach has been further extended to incorporate the presence of conventional flow measurements. An important feature of the proposed placement method is its capability to handle both single as well as multiple flow measurements connected to a bus. The proposed method has been tested on IEEE 14-bus, IEEE 30-bus and a practical 246-bus Indian networks for system intact condition as well as during single transmission line and single PMU loss. The effectiveness of the proposed method has been demonstrated by comparing the numerical results obtained using the proposed method with the existing methods.

Optimal Configuration of PMU in Power System

In order to use the least number of phasor measurement unit (PMU) to guarantee the power system completely observable, an optimal PMU configuration method in power system was put forward. The pre-configuration of PMU was done considering the actual situation of power grid. The genetic algorithm (GA) was used for PMU configuration. Modify the formulae of crossover probability and mutation probability in traditional genetic algorithm to overcome the evolutionary stagnation when the maximum fitness value and the average fitness value in group were equal. The improved adaptive genetic algorithm (IAGA) was obtained. In order to eliminate the premature convergence of GA resulted from the chance and randomness of the crossover operation and mutation operation, the preventing premature operation was introduced. This method combined the IAGA and the preventing premature operation. It has good global astringency, and it can ensure the network complete observability with the minimum number of PMU.

English

Phasor Measurement Unit (PMU) is a relatively new technology that, when employed in power networks, offers real-time synchronised measurements of the voltages at buses and currents along the lines that connect them. This is accomplished by using a GPS based monitoring system which facilitates time synchronisation of measurements and unlike SCADA, makes the measured data available in Real-Time format. SCADA is not able to provide Real-time data due to the low speeds at which RTUs (Remote Terminal Units) provide data. Availability of time-stamped phasor measurements makes PMUs preferable for power system monitoring and control applications such as State Estimation, Instability Prediction Analysis, Real time monitoring of the system conditions, Islanding Detection, System Restoration and Bad Data Detection. Since PMUs are expensive, their procurement and installation needs to be planned both in terms of economy and utility. Usually utilities like to see that the power network becomes fully observable with minimum number of PMUs placed at strategic buses. Where full observability refers to all the buses in the network are actively monitored. Thus the problem of optimal placement of PMUs is formulated as an optimization problem where the number of PMUs is minimized subject to complete system observability. This paper solves the optimal placement of PMUs for power system observability using Integer Linear Programming (ILP) methodology. The method is tested on IEEE 14 Bus System.

Reliability-Based Incremental PMU Placement

This paper presents a new reliability-based incremental phasor measurement unit (PMU) placement method via an enumeration-based integer linear programming optimization approach. By evaluating the proposed reliability indices for node and system observability, incremental PMUs are sequentially placed on the locations where the reliability of entire system's observability can be best improved at each step. As a result, a pre-set desired reliability of the system's observability can be achieved while using the minimal number of PMUs. The proposed method is generic and flexible in a way that different kinds of failures that impact the reliability of system observability can be easily included in the method. The 1st-order and 2nd-order failures of PMUs and lines are considered in this paper. The proposed method is validated using a 4-node system, the IEEE 14-node system and the IEEE RTS 96 test system. Simulation results show that the proposed method is effective and efficient in enhancing the reliability of observability for any system regardless of what the initial PMU placement of the system may be.