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Reconfiguration and Optimal Micro-Phasor Unit Placement in a Distribution System Using Taguchi-Binary Particle Swarm Optimization

  • Research Article-Electrical Engineering
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Abstract

The concepts of smart grid and microgrid require new monitoring systems to support automation functionalities in control centers at electrical distribution system (EDS) level. The availability of micro-PMUs (\(\upmu \)PMUs) nowadays equips the control centers with the necessary information, which improves the accuracy of distribution system state estimation, for its various applications. Further, a non-configured EDS involves a significant amount of active power losses that causes additional costs to utilities. The work presented in this paper introduces a generalized, two-stage robust methodology for optimal \(\upmu \)PMU placement considering reconfiguration of the EDS. This hybrid method combines the Taguchi method and upgraded version of binary particle swarm optimization (BPSO) that ultimately provides fast and accurate global optimum. The Taguchi method engenders a more diversified population, which eventually evades premature convergence, and consequently, it makes BPSO more robust. The proposed methodology provides optimal solution for any radial distribution system. Here, for illustration, results obtained for standard IEEE-33 nodes feeder system have been given to demonstrate the behavior and viability of the referred methodology. Various case studies under complex conditions along with the comparative analysis with the existing methods have been carried out to corroborate the superiority and versatility of the proposed methodology.

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Abbreviations

TIBPSO:

Taguchi integrated binary particle swarm optimization

DSSE:

Distribution system state estimation

EDS:

Electrical distribution system

OA:

Orthogonal array

APLM:

Active power loss minimization

\(\upmu \)PMU:

Micro-phasor measurement unit

OmPP:

Optimal micro-PMU placement

TM:

Taguchi method

BPSO:

Binary particle swarm optimization

\(F_\mathrm{T}\) :

EDS total power loss in configuration

y :

Position of particle

J :

Cost function

T :

Represents configuration

H :

Vector matrix for 7-node feeder

\(c_{mk}\) :

\(m-k\) switch state

\(g_{mk}\) :

\(m-k\) branch conductance

\(A^{\mathrm{in}}\) :

Bus incidence matrix

StNR:

Signal to noise ratio

\(N_T\) :

Branch numbers on T configuration

p :

Number of particles

d :

Dimension of search space

P :

Bus real power injection

D, E :

Denotes 2 levels of OA

M :

Number of experiments

m, k :

Bus indices

\(\theta \) :

Bus phase angle

N :

Number of nodes

\({\hat{\mathrm{fit}}}\) :

Fitness function

v :

Velocity of particle

\('\) :

Transpose

\({\hat{b}}\) :

Vector of 1s or greater than 1

\(c_1,c_2\) :

Acceleration constant

\(f_\mathrm{v}\) :

Fitness value

pbest:

Particle best

gbest:

Global best

\(\gamma \) :

Penalty factor

i, j :

Indices

\(r_1\),\(r_2\) :

Random variables

A :

Connectivity matrix

R :

Redundancy level

Y :

Position vector

W :

Cost vector

C :

Measurement redundancy

l :

Number of levels

\(K,\phi \) :

Constants

f :

Observability constraint

V :

Bus voltage

G :

Initial population matrix

t :

Iteration number

\(\omega m\) :

Set of buses neighbors to m

g :

Variable

\(N_{\mathrm{NO}}\) :

unobservable nodes

Q :

Bus reactive power injection

w :

Inertia weight

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Authors and Affiliations

  1. Electrical Engineering Department, National Institute of Technology Hamirpur, Hamirpur, Himachal Pradesh, 177005, India

    Sukriti Tiwari & Ashwani Kumar

Authors
  1. Sukriti Tiwari
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  2. Ashwani Kumar
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Correspondence to Sukriti Tiwari.

Appendix

Appendix

An orthogonal array with seven factors and each factor consisting of two levels denoted by letters D and E with symbolization as \(L_8(2^7)\) is given in Table 10.

Table 10 Orthogonal array
Full size table

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Tiwari, S., Kumar, A. Reconfiguration and Optimal Micro-Phasor Unit Placement in a Distribution System Using Taguchi-Binary Particle Swarm Optimization. Arab J Sci Eng 46, 1213–1223 (2021). https://doi.org/10.1007/s13369-020-04973-x

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