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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. [ABSTRACT FROM AUTHOR]

Phasor Measurement Units (PMUs) are the backbone of smart grids that are able to measure power system observability in real-time. The deployment of synchronized sensors in power networks opens up the advantage of real-time monitoring of the network state. An optimal number of PMUs must be installed to ensure system observability. For that reason, an objective function is minimized, reflecting the cost of PMU installation around the power grid. As a result, a minimization model is declared where the objective function is defined over an adequate number of constraints on a binary decision variable domain. To achieve maximum network observability, there is a need to find the best number of PMUs and put them in appropriate locations around the power grid. Hence, maximization models are declared in a decision-making way to obtain optimality satisfying a guaranteed stopping and optimality criteria. The best performance metrics are achieved using binary integer, semi-definite, and binary polynomial models to encounter the optimal number of PMUs with suitable PMU positioning sites. All optimization models are implemented with powerful optimization solvers in MATLAB to obtain the global solution point. [ABSTRACT FROM AUTHOR]

This study presents an algorithmic approach for optimal placement of phasor measurements units (PMUs) to ensure complete observability in the presence of conventional measurements and zero injection buses. The financial or technical restrictions prohibit the deployment of PMUs at every bus, which in turn motivates their strategic placement around the power system. Topology-based transformations are implemented for observability analysis. Τhe PMU problem allocation is optimized based on measurement observability criteria for achieving solvability of the power state estimation. The Branch-and-Bound algorithm (BB) and Binary-Coded Genetic algorithm (BCGA) are applied to solve the optimization problem. The BCG algorithm incorporates a special truncation procedure to handle integer restrictions on decision variables along with a penalty parameter approach for handling constraints. The proposed algorithms detect the minimum PMU number and their locations required to make the power system numerically observable. The proposed algorithms are applied to IEEE systems as well as a large-scale system with 1011 buses to exhibit the applicability of them to practical power systems. The solution points located using the BCGA are interpreted as nonstrict global minima since they are in complete agreement with those obtained by the BB algorithm in solving the (zero-one) constraint integer linear program. [ABSTRACT FROM AUTHOR]

This article studies deterministic and stochastic algorithms for placing minimum number of phasor measurement units (PMUs) in a power system in order to locate any fault in the power system. The optimization problem is initially formulated in a mixed integer linear programing framework with binary-valued variables as well as in a binary integer linear programing model. Then, the optimization problem is formulated as an equivalent non-linear programing model, minimizing a quadratic objective function subject to equality non-linear constraints defined over a bounded and closed set. The problem is solved by using a Sequential Quadratic Programming algorithm. The non-linear program is illustrated with a 7-bus test system. Also, stochastic algorithms such as binary-coded genetic algorithm and particle swarm optimization have been implemented in solving the optimal PMU placement under fault condition. The accuracy of suggested algorithms is independent from the fault type and its resistance. The optimization models are applied to the IEEE systems. The numerical results indicate that the proposed algorithms locate minimizers at the optimal objective function value in complete agreement with those obtained by branch-and-bound algorithms. [ABSTRACT FROM AUTHOR]

Given an undirected graph representing the network, the optimization problem of finding the minimum number of phasor measurement units to place on the edges such that the graph is fully observed, is studied. The proposal addresses the issue of the optimization using a two-phase branch-and-bound algorithm based on combining both Depth-First Search and Breadth-First Search algorithms to attempt to find guaranteed global solutions for OPP. The problem in question is stated, outlining the underlying mathematical model in use formulated in terms of (pure) mixed-integer-linear-programming (MILP) and the branch-and-bound algorithm adopted to obtain efficient solutions in practice. A topology based on transformations considering pre-existing conventional and zero injection measurements in a power network is implemented. The (zero-one) (MILP) model is applied to IEEE systems. The numerical results indicate that the branch-and-bound ensures solution points at the optimal objective function value from a global-optimization point of view. The synchronized and conventional measurements are included in a (DC) linearized State Estimator (SE). The topological observability analysis is verified numerically based on observability criteria for achieving solvability of state estimation. Large-scale systems is also analyzed to exhibit the applicability of the proposed algorithm to practical power system cases. [ABSTRACT FROM AUTHOR]

The paper proposes a multi-objective based optimization problem to design the optimal placement of phasor measurement units (PMUs), which make the power system network completely observable. The optimization process tries to attain dual objectives: (i) to minimize the total number of PMUs required and (ii) to maximize the measurement redundancy at all buses in a power system. A sequential quadratic programming algorithm is used to determine the number of PMUs and their optimal locations. Existing conventional measurements and the limited PMU channel capacity can also be incorporated in the proposed PMU placement formulation. When a system is made observable with a minimum number of PMUs, lack of communication facilities in substations or a PMU loss will lead to unobservable buses in the power system. Hence, the communication constraints and loss of a PMU have to be considered in the design stage. The proposed method is successfully applied to IEEE test systems in MATLAB, and the simulation results are presented. The simulation results are compared with a binary integer linear programming (BILP) model, also implemented in MATLAB, in order to demonstrate the effectiveness and accuracy of the proposed methodology. The comparative study shows that the proposed model yields the same number of PMUs as the optimal one found by the BILP model for each case study. The advantage of the proposed optimization scheme is that, starting from an initial point, the method is able to yield different PMU placement sets each one having the same minimum number of PMUs, for each case study. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract—This article presents a non-linear programming-based model for the optimal placement of phasor measurement units. The optimal phasor measurement units placement is formulated to minimize the number of phasor measurement units required for full system observability and to maximize the measurement redundancy at all buses in a power system. A sequential quadratic programming algorithm is used for the solution of the proposed model. The existence of power flow and injection measurements, the limited phasor measurement units channel capacity, the lack of communication facilities in substations, and the single phasor measurement units loss are also incorporated into the initial proposed formulation. The non-linear programming model is applied to IEEE 14- and 118-bus test systems in MATLAB. The accuracy and the effectiveness of the proposed method is verified by comparing the simulation results to those obtained by a binary integer programming model also implemented in MATLAB. The comparative study shows that the proposed non-linear programming model yields the same number of phasor measurement units as the binary integer programming model. A remarkable advantage of the non-linear programming against binary integer linear programming is its capability to give more than one optimal solution, each one having the same minimum number of phasor measurement units (same minimum objective value), but at different locations. [ABSTRACT FROM PUBLISHER]

This paper introduces an underdetermined nonlinear programming model where the equality constraints are fewer than the design variables defined on a compact set for the solution of the optimal Phasor Measurement Unit (PMU) placement. The minimization model is efficiently solved by a recursive quadratic programming (RQP) method. The focus of this work is on applying an RQP to attempt to find guaranteed global minima. The proposed minimization model is conducted on IEEE systems. For all simulation runs, the RQP converges superlinearly towards optimality in a finite number of iterations without to be rejected the full step-length. The simulation results indicate that the RQP finds out the minimal number and the optimal locations of PMUs to make the power system wholly observable. [ABSTRACT FROM AUTHOR]

• Interior-Point method is used to solve the optimal phasor measurement unit placement problem. • Placement method can consider any number, type, and position, of pre-existing measurement. • Proposed method delivers the optimal solution in polynomial time, even for large systems. This paper proposes Interior-Point (IP) methods for the solution of the optimal placement of phasor measurement units (PMUs) ensuring complete observability. The optimization problem consists of a quadratic function under a well-determined system of constraints that is, nonlinear equations equal to the number of the design variables defined over the whole search space R n. A hybrid-optimization technique coupling a branch-and-bound and a local search-procedure based on the (IP) methods is used in solving the model. The (IP) methods detect solution points that yield a minimum objective value as the one obtained by branch-and-bound algorithm. The (IP) methods optimizes the required PMU numbers whereas practical constraints as well as contingency issues as single PMU failure, costs of communication infrastructure (CI) from Phasor Data Concentrator to PMUs and prohibitive installations are satisfied. A large-scale system is also analysed to exhibit the applicability of (IP) methods to practical power system cases. [ABSTRACT FROM AUTHOR]