Review of Optimal PMU Placement Methods

Review of Optimal PMU location MethodsAbstract-The Phasor Measurement Unit (PMU) is very important implement for monitor and control of the power corpse. PMUs give real time, synchronized meters of voltages at the b practices and also current variant values which ar incident to those buses where these PMUs atomic number 18 situated. It is unnecessary and impractical to place PMU at to each one bus to estimate the states because the PMUs and communication facilities are very costly. It is necessary to determine the minimum result of PMUs for entire observability of the power ne devilrk. The optimum stance of PMUs (OPP) difficulty solved by various proficiencys such(prenominal) as mathematical program, meta heuristic rule program techniques. A literature review on these technologies to solve OPP bother is proposed in this make-up.I. INTRODUCTIONAt present due to increased power demand, fast growth of generation, transmission, and development in power ashess congested t he existing earningss and therefore stableness margin of these networks are decreased. In this situation to make sure proper and stable operation of the power spot, an accurate measurement and administration states monitoring is take. This was usu wholey d bingle by Supervisory Control and Data Acquisition (SCADA) system, where system states musical theme depends on unsynchronized measurement1. These measurements have errors such as measurement and telemetry bias. To smite these limitations in the SCADA, Wide Area come after Protection and Control (WAMPAC) system is utilize2. This system consist Phasor Measurement Units (PMUs) as fundamental components which give synchronized and real time voltages and currents phasor measurement3. Global Positioning System Satellite (GPS) provides reference timing signals to achieve synchronization of sampling voltage and current waveform with respect to this reference time. A PMU directly measures the voltage Phase of the bus where thes e PMUs are placed and also measure the current phases of a few or all the kickoffes connected to that bus. In recent years to improve monitoring use of PMUs are rapidly increases, so it needs to place these PMUs on all of the buses for estimable observability of the network. It is also inconceivable to place these units on entire system buses because PMUs and communication services are very costly4. Thus determination of the best number of PMUs and its location for overall observability of the system is very important.A proper regularityology is required to find the optimum number of the PMUs which will in fully observe the power network. To solve the Optimal PMUs Placement (OPP) line of work a number of orders have been employed5. These modes usually classified into schematic methods and advanced heuristic and modern metaheuristic methods6 Linear computer programing, Non bianalogue Programming, Dynamic Programming are the common optimization methodologies are proposed to solve this problem. Problems such as difficulties of retrieveing local minima and handling constraints in naturalized techniques are overcome by advanced heuristic and modern metaheuristic optimization methodology. These methodologies are Depth First Search, Minimum Spanning Tree, Simulated Annealing, Tabu Search, Genetic algorithmic programs, Differential Evaluation, Immune Algorithms, Partical Swarm Optimization or pismire Colony Optimization 7. This stem reviews the research work and studies that have been done in the area of best attitude of phasor measurement units (PMUs). Mainly the conventional and recent advanced heuristic and metaheuristic optimization techniques are presented in this paper to solve the typical best placement of PMUs problem. The formulation of this problem is described in dent II.The newfound methods to solve the OPP problem are discussed in Sections III and IV. Section V concludes this paper.II. OPTIMAL PMU PLACEMENT (OPP) PROBLEM FORMULATI ONPMU is an intelligent device which measures the phase value of voltage and current of bus which are connected to it.Figure 1 reads PMUs which purely isolated form a Wide Area Monitoring System (WAMS).GPS time stamped measurement signals are fed to a Phasor Data Concentrator (PDC) by using PMUs. The PDC collects and sorts the phasor measurements and signal processor converts data of PMUs into useful information which is discernible on Human Machine Interface (HMI).The operator can easily access the critical information of the power system state. Some rules can be use for the placement of PMUs which are given in 8 like, assigning one voltage measurement at the bus where PMU is hardened, one branch current measurement, one voltage and current pseudo measurement.Figure 1.Layout of PMU on with GPS time stamped signalsThe PMUs can be placed at planned buses to completely observe the total network. These located PMUs are measuring the voltage phase value of that bus and current phase values of the lines which are connected to the same bus. The aim is to completely observe the network with an optimum number of PMUs. The problem for n-bus system is formulated and solved by Integer Programming method 6as given belowMin athletic field to f(x)Where x = binary decision variable vector,.The nonlinear constraint expressions are created considering the placement and types of available measurements. Assume the phasor value of voltage at the bus where PMU located and values of current phasors along the branches which connected to that bus will be easily accessible. The other adjacent bus voltages will also be accessible. curb the solution vector which is a set of minimum and satisfy above equation. The constraint function can be defined with the help of Binary Connectivity hyaloplasm A which gives the information about bus connectivity of power network. The elements of matrix A is defined as,= 0 otherwise.The constraint equations are considered for the three cases (1) PMU measurements only, (2) PMU measurements and guessings (i.e. zero barbs) and (3) PMU measurements, injections, and flows.Different formulations of the PMU placement problem with special constraints have been presented in the literature, Effects of Zero Injection Buses9, Effect of conventional measurements10, single or multiple PMU loss contingency11, single branch outage12, contingency of single line outage or single PMU loss13, effect of PMU channel limit14.III. MATHEMATICAL PROGRAMMING METHODSInteger Programming (IP) is a numerical programming method it also known as mathematical programing. It solves an optimization problem which has whole number design variables. According to reference 15, whether they are linear, nonlinear or quadratic, an integer programming is divided into Integer Linear Programming (ILP), Integer Nonlinear Programming (INLP) and Integer Quadratic Programming (IQP) respectively.This paper gives the implementation of Integer Linear Programming (ILP) for optimal PMU placement for full power system observability. Modeling of zero injection constraints in ILP frame work has given. A method has been proposed to the systems having zero injection busses in which we use binary connectivity matrix passing and the modified matrix can be employ in Integer Linear programming (ILP) for optimal PMU placement. ILP approach has also been given for the systems considering single PMU outage. The results specify that 1) optimal PMU placement for full power system observability can be computed effectively 2) connectivity matrix modification based approach for systems having zero injection buses is computationally efficient and easy to execute 3) number of PMUs has to increase for systems considering single PMU outage. The proposed algorithms have been well-tried for IEEE 9 bus, IEEE 14 bus, IEEE 24 bus strain systems on MATLAB environment 16.This paper presents a unified binary semidefinite programming (BSDP) model with binary decision vari ables, for optimal placement of phasor measurement units, considering the impact of pre-existing conventional and synchronized phasor measurements as well as the limited channel capacity of phasor measurement units. A linear quarry function is minimized subject to linear matrix inequality observability constraints. The developed method is solved with an outer approximation scheme based on binary integer linear programming. The proposed method is illustrated using the IEEE 14-bus test system. Simulations are conducted on the IEEE 57-bus and 118-bus test systems to prove the validity of the proposed method 17.For the observability of system, an Integer Linear Programming (ILP) method is used. It also reduces the number of PMUs and maximizes the measurement redundancy in the power system buses. This paper utilizes two approaches, Newton Raphson method and Weight Least Squares (WLS) state estimation method for estimating voltage magnitude and phase angles at each bus. The true value ob tained from NR method is compared with the estimated values obtained from WLS with and without the inclusion of PMU measurements. The employed techniques are time- tried on IEEE- 14 and 30 bus system for determining the optimal points of placement of PMUs to measure the accurate voltage magnitude and phase angle at each bus 18.We define the desired solution as the PMU placement that also achieves best overall state estimation instruction execution. Accordingly, we derive the state estimator of all buses in a three-phase network and propose a) greedy algorithm and b) integer programming optimization method to determine the optimal solution. The comparative performance of these two methods is presented via evaluation of transmission and distribution test networks 19.This paper aims to optimize the PMU (Phasor Measurement Unit) placement for a full observation of the power network and the minimum number of PMUs. In this paper competition of Mixed Integer Non-Linear Programming and he uristically algorithms such as Bacterial Foraging Algorithm was presented. The results are demonstrated with PMU placement optimization simulation and a redundancy measurement analysis by using IEEE14-bus and Tehran Regional electric comp either 41-bus networks 20.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 21.B. everlasting(a) SearchExhaustive search is a general optimization technique that systematically enumerates all possible candidates for the solution and selects the candidate that satises the constraints at the optimum value of the objective function. Its main advantage is that it guarantees the nding of the global optimum. However, it is not suitable for monstrous-scale systems with huge search space.Observability of bulk power transmission network by means of a minimum number of phasor measurement units (PMUs), with the aid of the network topology, is a great challenge. This paper presents a novel equivalent integer linear programming method (EILPM) for the exhaustive search-based PMU placement. The state estimation implemented based on such a placement is completely linear, thereby eliminating drawbacks of the conventional SCADA-based state estimation. Additional constraints f or observability preservation following single PMU or line outages can easily be implemented in the proposed EILPM. Furthermore, the limitation of communication take is dealt with by translation of nonlinear terms into linear ones. Optimal PMU placement is carried out on the IEEE 118-bus test system in unalike scenarios. The comparison mingled with obtained results of EILPM and those of other methods reveals optimality of the solutions. Moreover, the proposed method is successfully applied on the Iranian National Grid, which demonstrates it can effectively be employed for practical power networks 22.This paper gives Exhaustive Search (ES) algorithms for optimal PMU placement for full power system observability. The results specify that 1) optimal PMU placement for full power system observability can be computed effectively 2) connectivity matrix modification based approach for systems having zero injection buses is computationally efficient and easy to execute 3) number of PMUs h as to increase for systems considering single PMU outage. The proposed algorithms have been tested for IEEE 9 bus, IEEE 14 bus, IEEE 24 bus test systems onMATLAB environment 16.This paper presents a unified binary semidefinite programming (BSDP) model with binary decision variables, for optimal placement of phasor measurement units, considering the impact of pre-existing conventional and synchronized phasor measurements as well as the limited channel capacity of phasor measurement units. A linear objective function is minimized subject to linear matrix inequality observability constraints. The developed method is solved with an outer approximation scheme based on binary integer linear programming. The proposed method is illustrated using the IEEE 14-bus test system. Simulations are conducted on the IEEE 57-bus and 118-bus test systems to prove the validity of the proposed method 17.IV. HEURISTIC ALGORITHMSA. Genetic Algorithm (GA)Genetic algorithm (GA) is adaptive heuristic searc h algorithm that repeats the process of natural evolution. This process is used to generate solutions to optimization and also search problem, The exercise of Genetic Algorithms (GA) in tackling engineering problems has been a major issue arousing the curiosity of researchers and practitioners in the area of systems and engineering research, operations research and management sciences in the former(prenominal) decades are described in 23.This paper models genetic algorithm into the Map Reduce model, so the MapReduce genetic algorithm (MRGA) possesses some parallel computing performance, such as scalability, better fitness convergence and so on. MRGA is implemented on computing clusters of Hadoop to search the optimal configuration of PMU. Meanwhile, this feasibility and the computing performance of MRGA is sustain by the IEEE14-node system, IEEE118-node system, and Wp2383-node system. This method has significant advantages in the installed PMU number, the diversity of solution, t he astringency and the practicability 24.B. Tabu Search (TS)This paper introduces a recursive Tabu search (RTS) method to solve the OPP problem. More specifically, the traditional Tabu search (TS) metaheuristic algorithm is executed multiple times, while in the initialisation of each TS the best solution build from all previous executions is used. The proposed RTS is found to be the best among three alternative TS initialisation schemes, in regard to the impact on the success rate of the algorithm. A numerical method is proposed for checking network observability, distant most existing metaheuristic OPP methods, which are based on topological observability methods. The proposed RTS method is tested on the IEEE 14, 30, 57 and 118-bus test systems, on the New England 39-bus test system and on the 2383-bus power system. The obtained results are compared with other reported PMU placement methods. The simulation results show that the proposed RTS method finds the minimum number of PMUs , unlike earlier methods which may find either the same or even higher number of PMUs 25.The contribution of this paper is as follows at first, analyze the measurement placement design of the electric power system using the software PSAT. Second, the heuristic approach, Tabu search (TS), based on topological analysis is proposed to solve the problem. The heuristic algorithm uses augmented incidence matrix to focus on the power system state estimator model then an Optimal PMU Placement (OPP) problem is formulated for the configuration with the minimum number of measurements that satisfies the observability constraints. Tests on the IEEE 14-Bus system and the TN are used to demonstrate the validity, flexibility, and efficiency of the proposed approach 26.C. Simulated Annealing (SA)This paper proposes a two-step optimization approach for optimal placement of phasor measurement unit (PMU) to obtain complete observability of power system in the case of preinstalled PMUs. The complete obs ervability of the system in the case of normal operation and pre-installed PMUs is formulated and then, different contingency conditions in the system are considered, i.e. single line outage and single bus outage. At the first step of the proposed two-step optimization approach, a minimization model is applied to convex programing (cvx) to achieve the minimum number of PMUs which guarantees the complete observability of the system. At the second step, simulated annealing (SA) is applied to maximize the measurement redundancy. Additionally, to further reduce the number of required PMUs the zero-injection bus effect is considered. At last, the proposed approach is tested on several IEEE standard systems, i.e. IEEE 14-bus, 30-bus, 39-bus, IEEE 16-machine 68-bus and 118-bus, to demonstrate the effectiveness of the proposed approach 13.This paper presents a novel Multi-Stage Simulated Annealing algorithm for the joint placement of PMUs along with the existing conventional measurement uni ts in the power grid network. The proposed multi-stage optimization method enables Simulated Annealing to reach the optimal point faster than conventional Simulated Annealing methods. The controlled uphill movements during various stages facilitate to obtain best possible solution 27.D. Differential Evolution (DE)In this paper, differential evolution (DE) algorithm has been proposed to solve an optimal joint placement problem of phasor measurement units (PMUs) and conventional measurements which enable to determine the state variables of the power system. The problem is to minimize the number of PMUs required for network observability and to maximize the PMU measurements redundancy. This is achieved by selecting a solution with maximum System Observability Redundancy Index (SORI) if multiple optimal solutions exist. The resulting nonlinear integer programming (NLIP) problem is solved by the proposed DE method for the optimal solution by considering different power system problems vi z. a 7-bus test and IEEE 14-bus systems with and without the consideration of zero injection buses. Results thus obtained have also been validated with existing solution techniques 28.E. Particle Swarm Optimization (PSO)An exponential binary molecule swarm optimization (EBPSO) algorithm is proposed to solve the OPP problem for a completely observable network. Various practical contingencies such as zero injection, single PMU outage are considered in the proposed algorithm along with the normal operating condition. Multiple solutions for OPP problem can improve the feasibility of the placement methodology in a practical environment. Even though any bus is selected as candidate location but it may not be possible to install a PMU on that bus due to the overleap of necessary infrastructure. On the contrary, few buses in practical systems which require close and precise monitoring should be directly observed by PMU. Placing some supererogatory PMUs can solve this problem but economic ally it is not preferable. Hence, having alternative solutions can be very effective. To ensure multiple solutions and improve the performances, an adaptive exponentially decaying inertia weight coefficient is developed. A sigmoid function is introduced to update the position of the particles in binary form. Both inter connected (IEEE 14-bus and 30-bus) and radial (IEEE 39-bus) system are tested to check the feasibility and effectiveness of the algorithm 29.This paper proposes a Particle Swarm Optimization based method to find the optimal PMU locations in a given grid topology. This method was tested successfully with the IEEE 14-bus, 30-bus, and 68-bus systems as well as with a large portion of the Brazilian power system 30.This paper presents an Improved PSO Algorithm (IPSO) to solve the problem of optimal Phasor Measurement Unit (PMU) placement. The aim of Optimal PMU Placement problem is to guarantee both full observabilities of the power grid and minimal number of PMU. In the I mproved PSO Algorithm, the point of genetic algorithm and the simulated annealing process is involved into basic particle swarm optimization. To deal with the constraints, an change Algorithm is developed and it can avoid costing much time and trapping local optimal solution. IEEE systems are tested to show the feasibility and effectiveness of the algorithm 31.F. Immune Algorithm (IA)G. Iterated Local Search (ILS)The objective of the paper is to minimise the size of the PMU configuration while allowing full observability of the network. The method proposed initially suggests a PMU distribution which makes the network observable. The Iterated Local Search (ILS) metaheuristic is then used to minimise the size of the PMU configuration needed to observe the network. The algorithm is tested on IEEE test networks with 14, 57 and 118 nodes and compared to the results obtained in previous publications 32.H. Spanning Tree SearchThe objective is to use the spanning tree approach and tree sea rch technique for optimal placement of multichannel and minimum channel synchronized phasor measurement units (PMUs) in order to have full observability of Power System. The novel concept of depth of observability is used and its impact on the number of PMU placements is explained. The spanning tree approach is used for the power system graphs and a tree search technique is used for finding the optimal location of PMUs. This is tested on IEEE-14 and IEEE-30 bus system. The same technique is modified to optimally place minimum channel PMUs on the same IEEE-14 and IEEE-30 bus systems. Matlab tool has been used for fulfilling the objective 33.I. Greedy AlgorithmPaper 34 propose a greedy PMU placement algorithm and show that it achieves an approximation ratio of (1-1/e) for any PMU placement budget. We further show that the performance is the best that one can achieve, in the sense that it is NP-hard to achieve any approximation ratio beyond (1-1/e). Such performance guarantee makes the greedy algorithm very attractive in the practical scenario of multi-stage installations for utilities with limited budgets. Finally, simulation results demonstrate the near-optimal performance of the proposed PMU placement algorithm.This paper studies the placement problem of PMUs in distribution system considering the system reconfiguration. System reconfiguration is achieved using the ant colony optimization method to solve the minimum power losses problem. A Greedy algorithm is used as an optimization tool to determine the minimal number of PMUs and their locations. The 33-bus distribution system is studied for optimal installation of PMUs with different distribution network topologies 35.J. Recursive Security AlgorithmThe recursive security algorithm is a spanning tree search of multiple solutions, with a different scratch point.Recursive spanning tree algorithm of PSAT is applied to find out the minimal placement locations for observability of all buses. The Thevenins equival ent parameters have been obtained from the measured and estimated voltages at the load buses and electrical resistance matrix Zbus. The parameters obtained are used to find the voltage stability boundary. Results on the IEEE-14 bus system and IEEE-30 bus system are presented to illustrate the proposed approach 36.K. Teaching-Learning-Based optimization AlgorithmIn this paper, Teaching-Learning-Based optimization Algorithm (TLBO) is presented for solving the problem of placement of PMU optimally in a power system network for complete observability. The TLBO algorithm enables optimal PMU placement by zero injection measurements and also by not including zero injection measurements. The algorithm has been tested on standard test systems such as IEEE 14-bus, IEEE 30-bus, IEEE 57-bus and the results are contrasted with other optimization algorithms like Genetic Algorithm and Binary PSO 37.L. Improved binary particle swarmThis paper presents the improved binary particle swarm (IBPSO) meth od that converges faster and also manage to maximize the measurement redundancy compared to the existing BPSO method. This method is applied to IEEE-30 bus system for the case of considering zero-injection bus and its effectiveness is verified by the simulation results done by using MATLAB software 38.M. Best first search (BFS) algorithmThis paper utilizes best first search (BFS) algorithm to determine the optimal placement of PMUs for complete observability of a power system under normal operating conditions. The additional redundancy offered by this method has been removed by applying a pruning technique to further minimize the number of PMUs determined by BFS algorithm. The proposed method has been used to determine the optimal PMU placement solutions for the standard IEEE 14-bus system, IEEE 30-bus system and a practical 246-bus Indian system. The results obtained with the proposed method have been compared with the existing methods such as integer linear programming. It has bee n found that the proposed method is able to achieve the complete system observability with the minimum number of PMUs required 39.N. Mixed heuristic/matheuristic methodThis paper presents a new method for the optimal allocation of PMUs in substations with a focus on the two-level state estimation process that was recently proposed in the specialized literature. A confused heuristic/matheuristic method is proposed to determine the number and location of those units in such a way to provide robust observability characteristics. Its reliable, robust, and precise results are shown for small and large substation layouts 40.O. Measurement esthesia analysisThis article presents a novel algorithm to find optimal sets of Phasor Measurement Units (PMUs) in power systems using measurement sensitivity analysis aiming for spot detection without multi-estimation. The algorithm generalizes the impedance method in switching detection through optimizing PMU utilization in order to detect a fault with desired precision in interconnected power systems. By deriving bus voltage and currents sensitivity indices to the fault location and impedance, possible deviations of the estimated fault location and/or impedance due to measurement noise, accuracy, precision limits, or simply the inability of a measurement point to sense a fault is evaluated. Therefore, the algorithm can solve Optimal PMU Placement (OPP) for desired fault detection precision based on these indices for various points of measurement observing faults in the system. Finally, avoiding multi-estimation guarantees the unique mapping between measurements of the selected PMU sets and faults throughout the system. The proposed algorithm is performed on the IEEE 7-bus and 14-bus benchmark systems and the fault location capability is evaluated through neural networks 41.P. Modified binary merry andrew optimization algorithmIn this study, a new evolutionary algorithm named as modified binary cuckoo optimization algorithm (MBCOA) is presented to solve optimal PMU placement (OPP) problem. The proposed method is classified as topological approaches. The basis of the method is in the lifestyle of the brood parasite bird named cuckoo that immigrates to the best habitat to obtain sufficient food and suitable nests for egg laying. The proposed binary structure is not introduced and applied to OPP problem up to now. OPP is tested on different networks consist of IEEE 14, 30, 57 and 118 bus test systems during normal operation and single event contingencies, i.e. single PMU failure and single line outage. The proposed MBCOA is also applied to 2383 and 2746 bus test systems to show its ability to handle large scale power networks. It is shown that MBCOA can obtain the best result from the search region with a minimum number of iterations 42.References1M. A. Rahman, A. H. M. Jakaria, and E. Al-shaer, form-only(prenominal) Analysis for reliable Supervisory Control and Data Acquisition in Smart Grids, in 2016 46th Annual IEEE/IFIP internationalist Conference on Dependable Systems and Networks (DSN), 2016, pp. 263-274.2Jiaping Liao and Cheng He, Wide-area monitoring protection and control of future power system networks, in 2014 IEEE Workshop on Advanced Research and Technology in Industry uses (WARTIA), 2014, pp. 903-905.3M. 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