A sequential quadratic programming method for contingency-constrained phasor measurement unit placement

Abstract

SUMMARYThe paper proposes a multi-objective based optimization problem to design the optimal placement of phasor measurement units (PMUs), which make the power system network completely observable. The optimization process tries to attain dual objectives: (i) to minimize the total number of PMUs required and (ii) to maximize the measurement redundancy at all buses in a power system. A sequential quadratic programming algorithm is used to determine the number of PMUs and their optimal locations. Existing conventional measurements and the limited PMU channel capacity can also be incorporated in the proposed PMU placement formulation. When a system is made observable with a minimum number of PMUs, lack of communication facilities in substations or a PMU loss will lead to unobservable buses in the power system. Hence, the communication constraints and loss of a PMU have to be considered in the design stage. The proposed method is successfully applied to IEEE test systems in MATLAB, and the simulation results are presented. The simulation results are compared with a binary integer linear programming (BILP) model, also implemented in MATLAB, in order to demonstrate the effectiveness and accuracy of the proposed methodology. The comparative study shows that the proposed model yields the same number of PMUs as the optimal one found by the BILP model for each case study. The advantage of the proposed optimization scheme is that, starting from an initial point, the method is able to yield different PMU placement sets each one having the same minimum number of PMUs, for each case study.

Optimal PMU placement for modeling power grid observability with mathematical programming methods

“…Therefore, the observability constraints of bus i and bus j are modified to be a joint observability constraint as the following 29 : Therefore, the observability constraints of bus i and bus j are modified to be a joint observability constraint as the following 29 :…”

“…The same method considering conventional measurements is developed in Esmaili et al 24 Zero injection redundancy limitation and global optimal solution considering mutual buses are presented in Khajeh et al 25 Chakrabarti et al 26 propose an integer quadratic programming approach. 29,30 In Almunif and Fan, 31 MILP and NLP comparison is conducted using a simple system, and limitation of zero injection formulation for NLP is discussed. 27 Nonlinear programming (NLP) formulations are introduced in Theodorakatos et al 28 This type of formulations has been explored under several contingencies in literature.…”

“…27 Nonlinear programming (NLP) formulations are introduced in Theodorakatos et al 28 This type of formulations has been explored under several contingencies in literature. 29,30 In Almunif and Fan, 31 MILP and NLP comparison is conducted using a simple system, and limitation of zero injection formulation for NLP is discussed. However, zero injection formulation in nonlinear programming-based PMU placement has not been properly solved in the literature.…”

Pragmatic approach for multistage phasor measurement unit placement: a case study of the Danish power system and inputs from practical experience

“…The cost-effective model proposed in [14] is adopted for determining optimal number of PMUs required, which are then scheduled over various stages as described in Section 4.3. Mathematical model of optimization problem for the cost-effective approach is given in (1)(2)(3)(4)(5).…”

Observability of nonlinear power system dynamics using synchrophasor data

“…PMU placement scenarios. Generators with PMU measurements 1 1 14 1, 8, 9, 10, 15, 16, 17, 18, 19, 20, 21, 22, 24, 27 15 (Scheme 1) 1, 4, 8,9,10,15,16,17,18,19,20,21,22,24,27 Table II. Calculate the observability for all these faults along system trajectories.…”