An Advanced Measurement Placement Method for Power System Observability Using Semidefinite Programming

This paper presents an advanced method for joint placement of unsynchronized conventional measurements and synchronized phasorial measurements in unobservable power systems. Observability checking and determination of maximal observable islands are carried out either by a numerical procedure using the triangular factors of the gain matrix or by a binary semidefinite programming (BSDP) method that minimizes a linear objective function subject to linear matrix inequality constraints associated with the gain matrix representing the entire (unreduced) network and the existing measurement system. The minimal set of single measurements or groups of measurements that make the system observable is also determined by a BSDP-based placement algorithm which is applied on a reduced network and measurement set, whose size is governed by the rank deficiency of the Jacobian matrix resulting from the configuration of the existing conventional and phasorial measurements. The BSDP optimization problem is solved using an outer approximation scheme based on binary integer linear programming. Simulations are carried out on different IEEE benchmark systems to confirm the efficiency and effectiveness of the proposed approach.