Towards Smart Energy Grids: A Box-Constrained Nonlinear Underdetermined Model for Power System Observability Using Recursive Quadratic Programming

Abstract

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.Energies 2020, 13, 1724 2 of 17 OPP problem is unraveled using the mixed-integer semi-definite programming approach subjected to linear matrix inequality. This technique is based on numerical observability, whereas most of the other techniques are based on topological observability, which may or may not ensure numerical observability to be executed successfully for state estimation. In [16,17], mixed-integer linear programming and nonlinear programming techniques are compared to check their suitability for networks of different sizes.Stochastic algorithms have also been used for the OPP problem. A recursive tabu search is suggested in [18], which has been claimed superior to multiple Tabu search and higher observability. Binary particle swarm optimization (BPSO) algorithm is developed for the solution of the OPP problem in [19]. In [20], the authors proposed a BPSO algorithm to minimize the number of substations in which installations must be performed for making all voltage levels observable while being subject to various practical constraints. Authors of [21] proposed the binary gravitational search algorithm to solve the OPP problem. Authors in [22], presented a modified binary Cuckoo optimization algorithm for the solution of the OPP problem with maximum redundancy. Genetic algorithms (GA) have been applied to determine the optimal allocation of PMUs in [23,24].Accurate knowledge of transmission system parameters, such as series impedance, optimizes distance relay settings and impedance-based fault location. A new method is developed to measure transmission line impedances and admittances from synchronized phasor measurements in [25].A new on-line method for estimating transmission line constants of a power system is proposed in [26]. In [27], a new State Estimation (SE) framework is proposed for processing Remote Terminal Unit (RTU) and PMU measurements separately in order to leave the traditional weighted least square (WLS)-based SE software unchanged. Phasor measurement unit based fault location techniques are proposed in [28][29][30]. Other methods, such as an optimized extreme learning machine-based approach, use synchrophasors to ensure real-time power transient stability prediction [31].Up to now, a BILP model is written to its st...

Multiple μPMU placement solutions in active distribution networks using nonlinear programming approach

“…The step size parameter is identified by the line search procedure, based upon the Armijo rule. 21 This step size parameter is calculated to produce a sufficient decrease in a penalty function, which determines optimality progress. The SQP is said to be converged when the difference between the current objective value and the previous objective value is less than the optimality tolerance.…”

“…However, eliminating redundant constraints expands the search space, due to which more feasible solutions are identified. 21 Further, the MATLAB codes of the NLP SQP algorithm are included with the gradients of the objective and constraints functions. It is done because, in NLP fmincon routine, finite difference approximation determines the gradients of objective function and constraints for solving the QP subproblems.…”

“…The optimization approaches, broadly classified into heuristic [13][14] and deterministic, [15][16][17][18][19][20][21][22] implemented in transmission system cannot be used directly in ADNs due to many distinct differences between ADNs and transmission network [23][24][25] :…”

An approach for economic design of wide area monitoring system by co‐optimizing phasor measurement unit placement and associated communication infrastructure

“…These methods can be grouped as conventional methods and heuristic algorithms. Various conventional methods 8‐13 have been used for solving the OPP problem. Chakrabarti et al 8 have presented an integer quadratic programming approach for finding the optimal PMUs count and maximizing the measurement redundancy at power network buses.…”

“…A large‐scale system has also been analyzed to demonstrate the efficacy of the proposed algorithm to determine the global optimal solution. In Theodorakato et al, 12 an nonlinear programming model has been introduced wherein the equality constraints are lesser compared to design variables. This proposed model has been solved by employing a recursive quadratic programming method which aims to determine the guaranteed global minima.…”