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Placement of Dg, Cb, and Tcsc in radial distribution system for power loss minimization using back-tracking search algorithm

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Abstract

The back-tracking search algorithm (BSA) is a new heuristic algorithm. BSA has two especially important properties: it is not sensitive to the initial value and has a single control parameter. This study presents the BSA-based optimal sizing and placement of distributed generations (DGs), capacitor banks (CBs), and thyristor-controlled series compensator (TCSC) in a radial distribution system (RDS). These elements are integrated separately and simultaneously in RDS. The objective function is power loss. The BSA is executed on IEEE 33 bus RDS. The obtained results are compared to a genetic algorithm (GA) and other algorithms in the literature. The results demonstrate that the BSA is more efficient and has the potential to find optimal solutions with less power loss. In this paper, optimal placement and sizing of DGs, TCSC, and CBs in a RDS is solved simultaneously using BSA for the first time.

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Abbreviations

DG:

Distributed generation

f :

Fitness function

g :

Equality constraint

h :

Inequality constraint

x :

Control variables

u :

State variables

\(P_\mathrm{loss} \) :

Total power loss

\(P_\mathrm{feeder} \) :

Feeder active power

\(Q_\mathrm{feeder} \) :

Feeder reactive power \(P_{DG,i} \)DG active power output at ith bus

\(DG_i^\mathrm{placement} \) :

DG placement at ith bus

\(P_{\mathrm{Load},i} \) :

Active load at ith bus

\(Q_{\mathrm{Load},i} \) :

Reactive load at ith bus

N :

Total bus number

\(N_{DG} \) :

Total number of DG

\(N_{CB} \) :

Total number of CB

\(CF_i \) :

Status (on/off) of the feeder

\(CDG_i \) :

Status (on/off) of the distributed generation at ith bus

\(CCB_i \) :

Status (on/off) of the capacitor bank at ith bus

\(V_i \) :

Voltage magnitude at ith bus

\(\delta _{ij} \) :

The voltage angle difference between buses i and j

\(Q_{cb,i} \) :

CB reactive power output at ith bus

\(G_{ij} \) :

Transfer conductance between buses i and j

CB:

Capacitor bank

SN :

Number of population size

D :

The number of optimization parameters

\(\mathrm{Randshuff}\) :

Random mixing function

\(\mathrm{Rand}\,(\mathrm{low,up})\) :

Produce a random number between low and up

\(\mathrm{Pop}\) :

Population

oldPop:

Old population

\(\sim \) :

Produce

Crossoverpop:

Crossover population

\(P_{DG,i}^{\min } \) :

Minimum DG active power output at ith bus

\(P_{DG,i}^{\max } \) :

Maximum DG active power output at ith bus

\(I_{ij} \) :

Current magnitude at branch ij

\(I_{ij}^{\max } \) :

Allowable maximum current magnitude at branch ij

a, b :

\(\mathrm{Rand} ( {0,1})\)

\(:=\) :

Update operator

\(\hbox {mutant}\mathrm{Pop}\) :

Population of mutation

map:

Matrix (\(SN{*}D)\)

\(Q_{cb,i}^{\min } \) :

Minimum CB reactive power output at ith bus

\(Q_{cb,i}^{\max } \) :

Maximum CB reactive power output at ith bus

\(B_{ij} \) :

Transfer susceptance between buses i and j

map:

Matrix (\(SN{*}D)\)

TCSC :

Thyristor-controlled series compensator

Ls :

TCSC reactor

\(\alpha _{ij}^{\max } \) :

The maximum range of thyristor firing angle \(\pi \)

\(\alpha _{ij}^{\min } \) :

The minimum range of thyristor firing angle \(\pi /2\)

\(X_{CL}\) :

TCSC reactance

\(TCSC_{ij}^\mathrm{placement} \) :

TCSC placement between buses i and j

\(Q_{cb,i}^\mathrm{placement} \) :

CB placement at ith bus

\(\alpha _{ij} \) :

firing angle of \(X_{CL}\) between buses i and j

\(I_{c}\) :

TCSC capacitor current

\(I_{T}\) :

Thyristor current

\(\varpi \) :

Constant

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Authors and Affiliations

  1. Engineering Faculty, Department of Electrical and Electronics, Ege University, Izmir, Turkey

    Waleed Fadel & Ulas Kilic

  2. Engineering Faculty, Department of Electrical and Electronics, Manisa Celal Bayar University, Manisa, Turkey

    Sezai Taskin

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  1. Waleed Fadel
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  2. Ulas Kilic
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Correspondence to Waleed Fadel.

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Fadel, W., Kilic, U. & Taskin, S. Placement of Dg, Cb, and Tcsc in radial distribution system for power loss minimization using back-tracking search algorithm. Electr Eng 99, 791–802 (2017). https://doi.org/10.1007/s00202-016-0448-4

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