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

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.

Approximate Optimal Trajectories for Flexible-Link Manipulator Slewing Using Recursive Quadratic Programming

The method of recursive quadratic programming, coupled with a homotopy method, has been used to generate approximate minimum-time and minimum tracking-error tip trajectories for two-link flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for a multi-link, multi-joint system with bending only in the horizontal-plane. Constraints on the trajectory include boundary conditions on link tip position, final joint velocities, accelerations and torque inputs to complete a rest-to-rest maneuver, straight-line tip tracking between boundary positions, and motor torque limits. Trajectory comparisons demonstrate the impact of torque input smoothness on structural mode excitation. Applied torques retain much of the qualitative character of rigid-body slewing motion with alterations for energy dissipation.