# An Effective Approach for the Probabilistic and Deterministic Multistage PMU Placement Using Cuckoo Search: Iran’s National Power System

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## Abstract

In recent years, phasor measurement units (PMUs) as vital elements have been widely increased in control, monitoring and protection of power systems. In practice, as the size of a power system is large, it is not possible to install all PMUs over a short period of time mainly due to the financial and technical barriers. One solution would be installing the PMUs over different stages. Accordingly, the paper presents an effective approach for multistage PMU placement (MSPP) in power systems, called dynamic MSPP. Furthermore, since the probabilistic concept of observability reflects a more realistic image of power system observability compared to deterministic ones, this paper, unlike most of the existing MSPP models, investigates the MSPP model in both probabilistic and deterministic frameworks. Compared to the existing approaches and results, the obtained ones in this paper show a considerable improvement in the observability level during PMU installation period. In the proposed approach, PMUs are installed at intermediate stages aimed at maximizing the cumulative network observability in a single optimization process, instead of several subsidiary optimizations in conventional approaches. Briefly, the proposed approach offers a complete search space for the problem, while the existing models lead to limited ones. Moreover, because of the nonlinearity posed by the probabilistic concept of observability as well as the proposed MSPP, cuckoo search optimization algorithm is used to handle the complexity and a new problem encoding/decoding technique for the proposed MSPP is utilized. Eventually, the suggested framework is implemented on different case studies as well as Iranian Transmission Network to reveal the performance of the presented model.

## Keywords

Cuckoo search Dynamic multistage planning Phasor measurement unit (PMU) Probability of observability## List of Symbols

## Predefined Sets

- \( I \)
Set of network buses

- SL
Set of network lines

- \( \tilde{S}^{M} \)
Set of buses that should be equipped with PMU after planning timetable

## Parameters

- \( \bar{A}_{ij} \)
Probability of observability of bus

*i*due to PMU at bus*j*- \( A_{ij}^{\text{Cm}} \)
Availability of current measurement at line

*i–j*- \( A_{ij}^{\text{Line}} \)
Availability of line

*i–j*- \( A_{i}^{\text{Link}} \)
Availability of communication link related to the PMU at bus

*i*- \( A_{i}^{\text{PMU}} \)
Availability of successful operation for PMU at bus

*i*- \( A_{i}^{\text{Vm}} \)
Availability of voltage measurement at bus

*i*- \( a_{ij}^{k} \)
Binary parameter related to the connectivity between buses

*i*and*j*at stage*k**i, j*Bus number indices

*t,k*Superscript relating to stage number

- \( n^{k} \)
Number of PMUs to be installed at stage

*k**M*Number of planning stages

- Nb
Total number of buses

## Functions

- C
Objective function of OPP

- \( f_{1} \)
Objective function of MSPP in deterministic point of view

- \( f_{2} \)
Objective function of MSPP in probabilistic point of view

- \( {\text{PO}}_{i}^{t} \)
Probability of observability of bus

*I*at stage*t*- \( {\text{APO}}^{t} \)
Average probability of the observability

- \( {\text{AUB}}^{t} \)
Average of unobserved buses at stage

*t*

## Variables

- \( x_{i}^{t} \)
Binary decision variable that is equal to 1 if bus

*i*at stage*t*is equipped with PMU and 0 otherwise- \( U_{i}^{t} \)
Binary variable representing the

*i*th bus observability at stage*t*, which is equal to 1 if bus*i*is observable and 0 otherwise- \( \tilde{S}^{t} \)
Set of buses to be equipped with PMU at stage

*t*

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