—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.

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.

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.

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.

The impact of the generalized pattern search algorithm (GPSA) on power system complete observability utilizing synchrophasors is proposed in this work. This algorithmic technique is an inherent extension of phasor measurement unit (PMU) minimization in a derivative-free framework by evaluating a linear objective function under a set of equality constraints that is smaller than the decision variables in number. A comprehensive study about the utility of such a system of equality constraints under a quadratic objective has been given in our previous paper. The one issue studied in this paper is the impact of a linear cost function to detect optimality in a shorter number of iterations, whereas the cost is minimized. The GPSA evaluates a linear cost function through the iterations needed to satisfy feasibility and optimality criteria. The other issue is how to improve the performance of convergence towards optimality using a gradient-free mathematical algorithm. The GPSA detects an optimal solution in a fewer number of iterations than those spent by a recursive quadratic programming (RQP) algorithm. Numerical studies on standard benchmark power networks show significant improvement in the maximum observability over the existing measurement redundancy generated by the RQP optimization scheme already published in our former paper.