Integer Linear Programming Based Optimal Placement of Phasor Measurement Units for Power System Observability in Khouzestan Province in Iran

Nowadays, phasor measurement units are used in power networks for different purposes, such as Linearization of state estimation equations and speed improvement of controlling and protecting systems. Optimization of position and number of these equipments is considerably important because of their high costs. Effective parameters on position and number of PMUs optimization are: Network topology and zero injection buses in power networks. In this paper an objective function based on integer linear programming (ILP) is presented to determine the number and optimized position of PMUs, in order to complete observability of power systems. The effect of zero injection buses on objective function in power networks is evaluated. Simulation results are implemented in MATLAB software on the IEEE 14 buses system, and also 230kv and 400kv networks in Khouzestan province. © 2017 Elixir All rights reserved. Elixir Elec. Engg. 112 (2017) 49003-49007 Electrical Engineering Available online at www.elixirpublishers. com (Elixir International Journal) Behrouz Moarref / Elixir Elec. Engg. 112 (2017) 49003-49007 49004 In this paper positioning the PMU with the minimum number of them and making them displayable is done with ILP (integer linear programming). This method is simple, understandable and applicable with high calculation speed. ILP gives the best total answers for all the systems. This method is simulated on standard IEEE with MATLAB and it is compared with other positioning methods for PMU. These comparisons show that this method is a sufficient and acceptable one. The 230 and 400 KV network form Khouzestan province is chosen as a case study. II.Observability Analysis with Pmu A PMU installed on a certain bus is able to measure the voltage magnitude and phase angle of the local bus and the branch current phasor of all branches emerging from this bus. Fig 1. PMU Observability Analysis. The voltage magnitude and phase angle of the neighboring bus can be computed using voltage drop equations. Thus the buses monitored by a PMU are directly observable, the neighboring buses connected to the PMU buses are indirectly observable and the other buses which are not associated with the PMU buses are unobservable. The following graph explains the bus observability in a system[9]. In Fig. 1, the network has 7 buses from A to bus G. Assume two PMUs are located on bus B and bus F, so bus B and F are directly observable. Bus A, C, E and G are all connected to bus B and F so they are indirectly observably. Bus D is not associated with any PMU bus, so bus D is unobservable. So in this 7-bus system example, 6 buses are observable and 1 bus is not observable. Thus, this system is not a completely observed system. A completely observed system means all the buses in this system should be directly or indirectly observed with a proper PMU placement scheme. III. PMU PLACEMENT PROBLEM FORMULATION A PMU is able to measure the voltage phasor of the installed bus and the current phasors of all the lines connecting to this bus. That is to say, a PMU can make the installed bus and its neighboring buses observable. The objective of placing PMUs in power systems is to determine a minimal set of PMUs such that the whole system is observable. Therefore the placement of PMUs makes a problem that is to find a minimal set of PMUs such that a bus must be reached at least once by the set of the PMUs. Now the optimal placement of PMUs can be formulated as a problem of Integer Linear Programming (ILP) [10]: