Allocation Of Phasor Measurement Units Research Articles

Mathematical Models for the Single-Channel and Multi-Channel PMU Allocation Problem and Their Solution Algorithms

Phasor measurement units (PMUs) are deployed at power grid nodes around the transmission grid, determining precise power system monitoring conditions. In real life, it is not realistic to place a PMU at every power grid node; thus, the lowest PMU number is optimally selected for the full observation of the entire network. In this study, the PMU placement model is reconsidered, taking into account single- and multi-capacity placement models rather than the well-studied PMU placement model with an unrestricted number of channels. A restricted number of channels per monitoring device is used, instead of supposing that a PMU is able to observe all incident buses through the transmission connectivity lines. The optimization models are declared closely to the power dominating set and minimum edge cover problem in graph theory. These discrete optimization problems are directly related with the minimum set covering problem. Initially, the allocation model is declared as a constrained mixed-integer linear program implemented by mathematical and stochastic algorithms. Then, the 0/1 integer linear problem is reformulated into a non-convex constraint program to find optimality. The mathematical models are solved either in binary form or in the continuous domain using specialized optimization libraries, and are all implemented in YALMIP software in conjunction with MATLAB. Mixed-integer linear solvers, nonlinear programming solvers, and heuristic algorithms are utilized in the aforementioned software packages to locate the global solution for each instance solved in this application, which considers the transformation of the existing power grids to smart grids.

A co-optimized approach for state estimation based micro phasor measurement unit allocation in power distribution infrastructure

Due to the highly complex and dynamic electrical characteristics of the 3-phase unbalanced power delivery networks (PDNs), it is challenging for utilities to observe the network entirely. This impediment necessitates the PDNs to become intelligent nowadays in the presence of various smart devices. Micro-phasor measurement units (µPMUs) are expected to play a crucial role in observing the smart power distribution system due to their micro-seconds resolution and millidegree precision accuracy. The placement of µPMUs in PDNs is also very challenging due to their associated costs. So, allocating a minimal number of µPMUs in PDN with fulfilling the topological observability can elucidate the issue of real-time visibility of the entire system. This paper presents a novel co-optimized placement strategy of µPMUs (CPMP) in PDNs that minimizes the µPMU numbers and the estimation error in the buses other than the µPMU assigned nodes. This work also displays a novel dynamic heuristic distribution system state estimation (DDSSE) to estimate the system's unknown states by using only the information of bus voltage phasors at the µPMU specified buses. The DDSSE is used to estimate the root mean square error (RMSE) in estimated voltage magnitudes and angles. Besides this, the efficacy of the grey-wolf optimizer (GWO) is presented in this work to solve the newly formulated placement problem. The results are validated on an Indian 19-bus and 34-bus unbalanced radial distribution system (URDS), and a detailed comparative study of different heuristic algorithms is also analyzed in this work.

WAMS-Based Fuzzy Logic PID Secondary Voltage Control of the Egyptian Grid

This paper presents the application of fuzzy logic PID secondary voltage control to the Egyptian power system model. The study included tertiary voltage control, Wide Area Measurement System (WAMS) configuration, a selection of pilot buses, and fuzzy logic PID secondary voltage control to improve the system performance. The secondary voltage control was applied using a fuzzy PID coordinated controller, a reactive power integral controller, Automatic Voltage Regulators (AVRs), and regional generators. The tertiary voltage control was implemented based on the optimal power flow to maximize the reactive power reserve. A novel optimization technique is presented to select pilot buses based on different operating conditions and compared to other techniques. The optimal WAMS configuration included the best allocation of Phasor Measurement Units (PMUs), Phasor Data Concentrators (PDCs), and the required communication infrastructure considering geographical regions with minimum cost. The Egyptian power grid considering 500/220 kV level is simulated by using DIgSILENT software to perform static and dynamic analyses, while the WAMS optimization problems and fuzzy logic PID controller design are performed by employing MATLAB software.

Optimal PMU Allocation Strategy for Completely Observable Networks With Enhanced Transient Stability Characteristics

The installation of phasor measurement units (PMUs) in contemporary electrical networks provides enhanced monitoring and control capabilities of the entire system. However, the placement of additional PMU devices is constrained by the relatively high cost and complicated communication infrastructure. Consequently, optimizing the allocation of PMU units is required to achieve complete visibility of the power system operation while minimizing the associated cost. This paper presents a coherent approach for solving the optimal PMU placement (OPP) in order to reduce the total number of PMUs that is required to completely observe the network. Furthermore, the proposed formulation of the OPP allocation problem considers several objectives such as cost minimization, redundancy and efficiency maximization in addition to various constraints like incorporation of zero-injection buses, single PMU failure, single line outage and consideration of flow measurements. Moreover, a two-stage approach is proposed to ensure the numerical observability of the obtained PMU placement. The proposed framework relies on solving a mixed integer linear programming problem for the OPP placement problem based on conventional measurements. The rank of the gain matrix is thereafter computed to check if the solution is numerically observable. In contrast to reported studies in the literature, transient stability enhancement is augmented in the formulation of the optimization problem such that the redundancy of predetermined buses is guaranteed without increasing the total number of installed PMU units. A novel spectral cluster-based online coherency grouping is employed to identify buses which possess the ideal characteristics in terms of transient stability support.

Allocation of Optimal PMUs for Power System Observability Using PROMETHEE Approach

Phasor measurement units (PMUs) are becoming a vital measurement device in wide-area monitoring, operation, and control. The allocation of PMU at each bus will make that bus directly observable. However, considering the high installation costs, it is not feasible to place PMU at each bus. Thus, placing the PMUs at optimal locations is extremely important. In this study, the Preference Ranking Organization Method for Enrichment of Evaluation (PROMETHEE)-based multi-criteria decision-making (MCDM) technique has been applied for the optimal allocation of phasor measurement units (PMUs) with the aim of achieving full system observability. Along with the entire network observability, the proposed approach provides maximum measurement redundancy (MR) too. Unlike some previous popular MCDM techniques, the proposed approach obtains optimal PMU placement (OPP) solution without performing pruning operations. Different criterion has been formulated to construct a decision matrix (DM). This DM helps in calculating the net outranking flow (NOF) of all the buses during the PROMETHEE approach. Based on the maximum NOF value, the PMUs are placed at those buses. The proposed approach also considers the inclusion of zero injection buses (ZIBs). Further, cases such as single PMU outage and existence of conventional measurements have been considered while determining optimal locations of PMUs. The proposed algorithm is demonstrated on IEEE 14-bus, 30-bus, 57-bus, and 118-bus systems, one Indian practical utility, i.e., Northern Regional Power Grid (NRPG) 246-bus system, and larger Polish 2383-bus system. To prove the effectiveness of the proposed algorithm, it has been compared with some of the popular existing techniques.

Optimal allocation of phasor measurement units in distribution power systems

Phasor measurement unit (PMU) is deemed a pivotal tool in wide-area monitoring, protection, and control of power systems. The optimal allocation of PMUs has recently received more attention. In this paper, Binary Integer Programming (BIP) technique is proposed to optimally allocate PMUs in the power network keeping complete observability of the network and reducing the total numbers of PMUs. The proposed technique is tested and examined through different systems to investigate the effectiveness of BIP. Additionally, the BIP is compared with different techniques to verify its superiority and reveal the main contributions of BIP-based algorithms using different IEEE test systems. The proposed method shows an efficient technique while placing PMUs through direct, simple, and linear formulas regardless of the network scale or configuration; transmission, or distribution systems. Moreover, the whole process consumes the least time slots to hit the intended goal because of the problem formulating criteria.

Allocation of phasor measurement unit using an admissible searching‐based algorithm A‐star and binary search tree for full interconnected power network observability

AbstractIn this research work, an admissible searching‐based algorithm A‐star and binary search tree is proposed to unravel the optimal phasor measurement unit (PMU) placement problem (OPPP) for achieving full interconnected power network observability considering contingencies. The proposed method is an advanced version of the best‐first search method that finds minuscule paths to the best solution. Moreover, it is an optimal and complete search method. Optimal signifies that the proposed method is guaranteed to unravel the minimum cost from origin to the terminus point and Complete denotes that it is going to determine all the possible paths that are available to us from the origin to the destination. The binary tree is used for this purpose as its structural design is well‐matched with the proposed method. Integrating an A‐star algorithm and binary search tree enhances the optimization and performance toward unraveling the OPPP. Also, for more than one solution of OPPP, redundancy measurement is taken into consideration. The proposed method is applied on standard IEEE‐14, ‐30, ‐118, New England‐39, and northern regional power grid (NRPG) 246‐bus test systems. Furthermore, to check the scalability of the proposed method, the Polish 2383‐bus system is considered. The obtained experimental results were compared to established procedures published in peer‐reviewed journals, and the proposed methodology outperformed the other comparison approaches. Thus, the proposed method successfully accomplishes complete observability of the power networks.

Modified emperor penguin optimizer for optimal allocation of energy storage system and phasor measurement units

In this paper a novel method, Modified Emperor Penguin Optimizer Algorithm (MEPOA) is developed for optimal allocation of Energy Storage System (ESS) and Phasor Measurement Units (PMU) in the power distribution system. The main objective of this research is to enhance voltage stability considering power balance and voltage limit constraints. The MEPOA are to produce the group limit, calculate hotness around the group, find the distance, and compute the efficient mover. The proposed MEPOA is performed in MATLAB platform and the implementation is tested with standard IEEE 33-bus networks. The simulation results show that the proposed MEPOA give better ESS and PMU allocation.

Optimal PMU allocation for high-sensitivity wide-area backup protection scheme of transmission lines

In spite of the outstanding benefits provided via phasor measurement units (PMUs) to smart grids in the field of wide area protection, they increase the cost of the infrastructure. Based on PMU location and system topology, subsets of buses and lines are formed representing backup protection zones (BPZs). This paper introduces a proposed criterion to overcome the shortage in formulating the BPZs. Also, this paper presents a proposed framework to define the optimal PMU locations regarding wide area BPZs. The framework is expressed as a multi-objective function, which aims to enhance the system observability, increase the number of transmission lines belonging to BPZs and increase the BPZ threshold sensitivity. The genetic algorithm technique (GA) is used to obtain the optimal locations of PMUs for different cases. The effectiveness of the proposed framework is evaluated by investigating the 14-bus IEEE standard system for different cases of fault location, type and resistance. Furthermore, the 39-bus system is considered for some cases as a larger system. The results show the possibility of enhancing the sensitivity of the BPZs of the system regarding optimal PMU locations.

Optimized Allocation of Phasor Measurement Units in Transmission Systems Using Particle Swarm Optimization

Optimized Allocation of Phasor Measurement Units in Transmission Systems Using Particle Swarm Optimization

Multi-objective MILP model for PMU allocation considering enhanced gross error detection: A weighted goal programming framework

This paper proposes a multi-objective mixed-integer linear programming (MILP) model for the optimal phasor measurement unit (PMU) placement (OPP) problem. A majority of the solutions presented for the OPP problem focus on minimizing cost while guaranteeing system observability. While this is a good approach to the OPP problem, the effect of PMU allocation on various energy management system applications should also be considered. This paper addresses the OPP problem considering PMU installation costs, system observability, and gross error detection. In order to allocate PMUs considering gross error detection, the Vulnerability Index (VI) is used to quantify the vulnerability of each element in the system. A weighted goal programming (WGP) framework, which allows for the optimization of contradictory goals, which is a characteristic of the goals considered in this paper, is presented. The goals and weights of the framework are user inputs to the program besides a hard budget restriction. The results of this paper show how the WGP framework allows the priorities of the decision maker to influence the final PMU allocation presented by the MILP, making this model a valuable framework for utilities planning to install PMUs on their network.

Optimal PMU Placement using Binary Particle Swarm and Artificial Bee Colony with Channel Limitations and Redundancy.

Phasor Measurement Unit (PMU) being expensive and to be placed optimally, a meta-heuristic approach of Binary particle swarm optimization (BPSO) and Binary artificial bee colony optimization (BABC) is made for the optimal allocation of PMU in a power system. The PMU locations resulted are served by basic system conditions like network configuration, critical generators, and loads. The pattern of locations on including Zero-Injection Buess (ZIB) is also discussed. The redundancy in case of PMU loss is coined so as to obtain a complete observability of the power system. the channel limitations of device is also taken into consideration for better results in real-time systems. Optimal PMU locations for IEEE 30-bus and 14-bus systems with channel limits are compared with all above considerations. The number of PMU locations is reduced as channel limits increases. The simulated PMU locations are decreased with improved observability by Binary Artificial Bee Colony Optimization as compared to Binary Particle Swarm Optimization.

Optimal Allocation of Phasor Measurement Units Considering Various Contingencies and Measurement Redundancy

This article presents an efficient and comprehensive method to find out the minimum number of and the corresponding locations of phasor measurement units (PMUs) guaranteeing full numerical observability of a power system as well as maximize the measurement redundancy in conjunction with preexisting conventional measurements. Furthermore, the effect of number of available channels of PMUs on their optimal placement can be taken into account. The proposed optimal PMU placement (OPP) formulation is extended to consider the case of two types of contingencies, single PMU loss and single branch outage. The objective of the OPP method is the numerical observability, unlike the majority of earlier works which are based on topological observability and do not always ensure numerical observability required for the successful execution of state estimation (SE). The problem is formulated as a binary semidefinite programming (BSDP) model with binary decision variables, minimizing a linear objective function subject to linear matrix inequality (LMI) observability constraints. The BSDP problem is solved using an outer approximation scheme based on binary integer linear programming. The effectiveness of the proposed method is verified on different IEEE test systems.

Multi-Level Reliability Allocation of Phasor Measurement Unit Using Bayesian Networks

The phasor measurement unit (PMU) provides synchrophasors at different locations in power grids. Therefore, its breakdown adversely affects grid monitoring and operation. In existing literature, PMU reliability has been performed using methods like Markov model, event trees, and reliability graphs. Although these methods have explored different aspects of component reliability and their combinations for overall PMU reliability evaluation, this paper puts forth additional information related to contribution of sub-modules and components toward overall PMU reliability through Bayesian networks (BNs). Moreover, the proposed methodology has ability to assess PMU status based on state of its components. Akin to a multi-level system, PMU consists of sub-modules and components. Hence, reliability improvement of PMU through reliability allocation to its sub-modules and components has been adopted. A framework has been developed to merge the information from different levels for modeling components, sub-modules, and PMU as a whole. This method also enables us to compute individual component sensitivity to failures. The efficacy of improved PMU reliability is validated based on significant improvement of observability reliability (OR), loss of data expectation (LODE), and loss of situational awareness (LOSA) has also been reported. Also, additionally a pragmatic and cost-effective design has been investigated so as to improve overall PMU reliability.

A Stage-wise Optimal PMU Allocation using BCSA for Improving the Sensitive Bus Observability

Despite of substantial development in measurement technology of phasor measurement units (PMUs), the utilization of PMU is still barely appreciated by the power industries due to its high installation cost. It motivated the researchers to find an optimal set of locations to obtain full observability of a network with least number of PMUs. A stage-wise optimal PMU allocation (SWOPA) approach is proposed in this paper using binary crow search algorithm (BCSA) based on the measurement reliability assessment of some sensitive buses. The effectiveness of the multiple outcomes (MOCs) obtained while solving the OPA problem is analyzed and a sensitive bus observability (SBO) assessment, associated with generator, weaker, and transformer-connected buses is mathematically modeled in this regards to determine the best outcome from those MOCs. The observability criteria of such sensitive buses are also incorporated in order to provide ranking in PMU bus nomination at each stage. The proposed method is demonstrated on IEEE 57-bus test system and its performance is verified with other methods.

Sensitive Constrained Optimal PMU Allocation with Complete Observability for State Estimation Solution

In this paper, a sensitive constrained integer linear programming approach is formulated for the optimal allocation of Phasor Measurement Units (PMUs) in a power system network to obtain state estimation. In this approach, sensitive buses along with zero injection buses (ZIB) are considered for optimal allocation of PMUs in the network to generate state estimation solutions. Sensitive buses are evolved from the mean of bus voltages subjected to increase of load consistently up to 50%. Sensitive buses are ranked in order to place PMUs. Sensitive constrained optimal PMU allocation in case of single line and no line contingency are considered in observability analysis to ensure protection and control of power system from abnormal conditions. Modeling of ZIB constraints is included to minimize the number of PMU network allocations. This paper presents optimal allocation of PMU at sensitive buses with zero injection modeling, considering cost criteria and redundancy to increase the accuracy of state estimation solution without losing observability of the whole system. Simulations are carried out on IEEE 14, 30 and 57 bus systems and results obtained are compared with traditional and other state estimation methods available in the literature, to demonstrate the effectiveness of the proposed method.

Critical Bus Constrained Optimal PMU Allocation with Zero Injection Modeling for Complete Observability

Objectives: This paper presents a critical bus constrained optimal allocation of Phasor Measurement Units (PMUs) considering Zero Injection Bus (ZIB) modeling for complete observability of the system. Identification of critical or weak buses with more branches incident on it are considered to determine accurate states of the system. Methods/Statistical Analysis: Allocation of PMUs at every bus in a network is infeasible, which leads to excessive cost. So to minimize number of PMUs and to locate them at critical buses in priority, a new critical bus constrained binary integer programming (BIP) method is proposed.ZIB constraints are modeled to further minimize the PMUs. Findings: Optimal allocation of PMUs in case of single line outage is considered with ZIB modeling. Critical buses with ZIB modeling and without ZIB modeling are compared to show the importance of ZIB modeling. Application/Improvements: MATLAB simulations carried out on IEEE 14-, 24-, 30- and 57-bus test systems and results are compared and presented.

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.

Optimal phasor measurement unit placement for numerical observability in the presence of conventional measurements using semi‐definite programming

This study presents a new approach for optimal placement of synchronised phasor measurement units (PMUs) to ensure complete power system observability in the presence of non-synchronous conventional measurements and zero injections. Currently, financial or technical restrictions prohibit the deployment of PMUs on every bus, which in turn motivates their strategic placement across the power system. PMU allocation is optimised here based on measurement observability criteria for achieving solvability of the power system state estimation. Most of the previous work has proposed topological observability based methods for optimal PMU placement (OPP), which may not always ensure numerical observability required for successful execution of state estimation. The proposed OPP method finds out the minimum number and the optimal locations of PMUs required to make the power system numerically observable. The problem is formulated as a binary semi-definite programming (BSDP) model, with binary decision variables, minimising a linear objective function subject to linear matrix inequality observability constraints. The BSDP problem is solved using an outer approximation scheme based on binary integer linear programming. The developed method is conducted on IEEE standard test systems. A large-scale system with 3120 buses is also analysed to exhibit the applicability of proposed model to practical power system cases.

A two-phase investment model for optimal allocation of phasor measurement units considering transmission switching

Ensuring the reliability of an electrical power system requires a wide-area monitoring and full observability of the state variables. Phasor measurement units (PMUs) collect in real time synchronized phasors of voltages and currents which are used for the observability of the power grid. Due to the considerable cost of installing PMUs, it is not possible to equip all buses with PMUs. In this paper, we propose an integer linear programming model to determine the optimal PMU placement plan in two investment phases. In the first phase, PMUs are installed to achieve full observability of the power grid whereas additional PMUs are installed in the second phase to guarantee the N−1 observability of the power grid. The proposed model also accounts for transmission switching and single contingencies such as failure of a PMU or a transmission line. Results are provided on several IEEE test systems which show that our proposed approach is a promising enhancement to the methods available for the optimal placement of PMUs.