A Generalized Pattern Search Algorithm Methodology for solving an Under-Determined System of Equality Constraints to achieve Power System Observability using Synchrophasors

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.

Generalized Pattern Search Algorithm for Crustal Modeling

In computational seismology, receiver functions represent the impulse response for the earth structure beneath a seismic station and, in general, these are functionals that show several seismic phases in the time-domain related to discontinuities within the crust and the upper mantle. This paper introduces a new technique called generalized pattern search (GPS) for inverting receiver functions to obtain the depth of the crust–mantle discontinuity, i.e., the crustal thickness H, and the ratio of crustal P-wave velocity Vp to S-wave velocity Vs. In particular, the GPS technique, which is a direct search method, does not need derivative or directional vector information. Moreover, the technique allows simultaneous determination of the weights needed for the converted and reverberated phases. Compared to previously introduced variable weights approaches for inverting H-κ stacking of receiver functions, with κ = Vp/Vs, the GPS technique has some advantages in terms of saving computational time and also suitability for simultaneous determination of crustal parameters and associated weights. Finally, the technique is tested using seismic data from the East Africa Rift System and it provides results that are consistent with previously published studies.