Generalized Formulation for Optimal Placement of
PMUs Considering Single Unit or Single Branch
Outage
Nima Amin, Mahdi Banejad
Faculty of Electrical & Robotic Engineering
Shahrood University of Technology
Shahrood, Iran
ni.amin@yahoo.com, m.banejad@shahroodut.ac.ir
Abstract—Phasor Measurement Units (PMUs) are being
considered as the essential tools in modern power system studies.
In this paper a general approach is proposed to place the PMUs
optimally in a power system and minimize the total installation
cost to make the entire system completely observable. In this
paper, the placement of PMUs is performed with respect to the
maximum measurement redundancy, considering both cases of
single PMU loss or single branch outages as just one problem.
The proposed approach employs Binary Integer Linear
Programming (BILP) to formulate the objective function. In
order to consider more practical assumptions, with and without
considering of zero injections buses, this method does not utilize
the existing conventional measurement units in the power
network. In addition, to show the effect of unequal PMU
installation in each bus, modified cost matrix is added to the
problem. The proposed approach is then applied to several
standard IEEE test systems (14-bus, 30-bus and 57-bus) to find
the optimal placement of the PMUs. The simulation results
approve the capability of the proposed method in finding the
optimal place of the PMUs with minimizing the installation cost.
I. INTRODUCTION
Phasor Measurement Units (PMUs) are important devices
in Wide Area Measurement, Protection and Control
(WAMPAC) system studies. PMU is a monitoring device,
which can provide synchronized measurement of voltage and
current phasor in a power system. Synchronized signals are
achieved from Global Positioning System (GPS) satellites [1].
PMU measurements, in compare with SCADA system, are
taken at higher speed. Time stamping of each measurement;
provides the precise view of the entire network
interconnections. The most phasor-based applications of
PMUs in industries are: visualization, monitoring,
control/protection, disturbance analysis, system dynamic and
state estimation [2]. In recent years, due to high cost of having
PMU at each node of the network, several research activities
have been performed to locate minimal set of PMUs in order
to make the power system completely observable, with
considering different operation conditions.
Phasor measurement placement method, using graph
theoretical observability analysis has been formulated in [3]
and to solve the minimum number of PMUs problem, both
modified bisecting search and simulated annealing has been
implemented. However possible measurement loss and branch
outage is not considered. In [4], the optimal PMU placement
proposed with Nondominated Sorting Genetic Algorithm
(NSGA). Optimal solution of objective function has been
solved with graph theory and simple GA and just single
branch Contingency has been considered. The proposed
method requires more complexity computation and restricted
by the size of the problem.
Reference [1] has introduced techniques for optimal PMU
placement based on incomplete observability, using simulated
annealing. In accordance to incomplete observability, depth of
observability was introduced in this paper. PMU placement
method for power system state estimation based on the
minimum number of the normalized measurement matrix has
been presented in [5]. Presented method in [6] is exhaustive
search- based to find minimum number and optimal placement
of PMUs for complete network observability. This method
gives a global optimal solution for the PMU placement, but it
becomes computationally intensive for large systems.
Optimal PMU placement algorithm by using nonlinear
integer programming, under the existence of conventional
power flow or power injection measurement has been
presented in [7]. An integer quadratic programming approach
to maximize the measurement redundancy was used in [8]. In
[9] and [10], a similar formulation of PMU placement problem
was proposed. This algorithm with and without considering
conventional power flow and power measurement in system is
always linear.
Presented method in this paper proposes an approach to
place PMUs in a power system optimally, not only to make
the entire network completely observable in normal operating
condition, but also it maintains observable in the case of loss
of any single PMU or single branch from the network. In this
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