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.
Highlights
Phasor measurement unit (PMU) is a metering device that can provide real-time voltage and current synchrophasor measurements with high accuracy
To prove the effectiveness of the Recursive Quadratic Programming (RQP) to achieve optimality, the obtained objective value is compared to the one found by solving the Integer Linear Programming (ILP) model with binary-valued variables for each benchmark test system
The pure ILP model is solved by using the branch-and-bound method (BBM)
Summary
Phasor measurement unit (PMU) is a metering device that can provide real-time voltage and current synchrophasor measurements with high accuracy. Authors of [12] proposed a nonlinear programming model for the solution of the OPP problem. 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]. A reduction in problem size typically translates to a reduction in total running time in comparison with past studies such as [11,12,17] The solution to such underdetermined systems is based on the Recursive Quadratic Programming (RQP) method [35]. The proposed nonlinear model is solved using a Recursive Quadratic Programming (RQP) method with super-linear convergence properties avoiding the Maratos effect.
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