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Optimal allocation of static VAR compensator by a hybrid algorithm

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Abstract

Flexible AC transmission system (FACTS) devices are gaining popularity in electrical transmission networks for the last few years due to their ability to improve a system’s performance without restructuring or expanding the existing network. But, placing the FACTS device at any arbitrary location in the network may not be optimally beneficial. Also, judging the optimally beneficial location of these devices becomes necessary prior to investment owing to their high expense of installation and maintenance. In this paper, a novel hybrid algorithm combining Cuckoo Search Algorithm (CSA) and Chemical Reaction Optimization (CRO) is proposed to solve the problem of optimally allocating a static VAR compensator (SVC) for the standard IEEE 14-bus, 30-bus and 57-bus transmission systems under heavily loaded condition. The optimal allocation of SVC is done by considering technical aspects like voltage stability, power generation minimization and line loss reduction and also by considering commercial facets like savings on annual cost of power generation and return-on-investment (ROI) time period for the expenditure incurred on the SVC. The ROI calculation is a novel addition to the problem formulation which adds a practical outlook to the feasibility of investment. Thus, a holistic approach is followed for determining the optimal location of the SVC in the power network and the results validate the superior performance of the proposed algorithm.

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Abbreviations

N :

Total number of buses

\(Q_i \) :

Reactive power at the bus ‘i’

\(V_k \) :

Voltage at the bus ‘k’

\(B_{ik} \) :

Susceptance between buses ‘i’ and ‘k’

\(\delta _i \) :

Load angle in degrees at bus ‘i’

\(P_g \) :

Generated active power within \(P_g ^{\min }\) and \(P_g ^{\max }\)

\(Q_p^{SVC} \) :

Reactive power injection by SVC at bus ‘p’

\(B_p^{SVC} \) :

Susceptance of SVC at bus ‘p’

\(P_{D_i } \) :

Active power demand at bus ‘i’

\(Q_{G_i } \) :

Generated reactive power at bus ‘i’ within \(Q_{G_i } ^{\min }\) and \(Q_{G_i } ^{\max }\)

\(Y_{ij} \) :

Y-bus admittance matrix between buses ‘i’ and ‘j’

\(Q_{SVC} \) :

Reactive power consumed by SVC within \(Q_{SVC}^{\min }\) and \(Q_{SVC}^{\max }\)

\(S_{Li} \) :

Complex power flow from/to bus ‘i’ within \(S_{Li}^{\max }\)

\(N_G \) :

Total number of generators

\(N_{TL} \) :

Number of transmission lines

\(C_p \) :

Cost of active power generation (in $/h)

\(a_m ,b_m ,c_m \) :

Cost coefficients of generator at ‘m’ generator bus

\(C_T \) :

Total cost of power generation (in $/h)

\(C_{mnt}\) :

Cost of SVC maintenance (in $)

EMI:

Equated monthly instalment

\(\tau \) :

Recovery time

\(Q_{L_k } \) :

Reactive power transmission loss at bus ‘k’

\(Q_{loss} \) :

Total reactive power loss over all buses

\(C_T^{total} \) :

Total cost of active and reactive power generation across all buses

\(FF_{without\_SVC} \) :

Fitness function without SVC in the system

pe :

Potential energy

ml :

Specified molecule

\(G^{prev}\) :

Solution of previous generation

\(G^{best}\) :

Global best solution across all generations

rand :

Random number in specified limits

\(\Gamma \) :

Gamma distribution function

\(\sigma _x \) :

Standard deviation of “x” variables

g :

Specified number of solution

FACTS:

Flexible AC transmission system

SVC:

Static VAR compensator

SQP:

Sequential quadratic programming

PSO:

Particle swarm optimization

IPSO:

Immune particle swarm optimization

CSA:

Cuckoo search algorithm

TSC:

Thyristor switched capacitor

\(P_i \) :

Active Power at the bus ‘i’

\(V_i \) :

Voltage at the bus ‘i’

\(G_{ik} \) :

Conductance between buses ‘i’ and ‘k’

\(\theta _{ik} \) :

Difference in load angle between buses ‘i’ and ‘k’

\(\delta _k \) :

Load angle in degrees at bus ‘k’

\(Q_g\) :

Generated reactive power within \(Q_g ^{\min }\) and \(Q_g ^{\max }\)

\(V_p \) :

Voltage at bus ‘p’ where SVC is connected

\(P_{G_i } \) :

Generated active power at bus ‘i’ within \(P_{G_i } ^{\min }\) and \(P_{G_i } ^{\max }\)

\(P_{SVC} \) :

Active power consumed by SVC

\(Q_{D_i } \) :

Reactive power demand at bus ‘i’

\(V_{G_i } \) :

Voltage at generator bus within \(V_{G_i } ^{\min }\) and \(V_{G_i } ^{\max }\)

\(T_i \) :

Transformer tap at bus ‘i’ within \(T_i ^{\min }\) and \(T_i ^{\max }\)

\(V_{D_i } \) :

Voltage demand at bus ‘i’ within \(V_{D_i } ^{\min }\) and \(V_{D_i } ^{\max }\)

\(N_T \) :

Number of transformers

\(N_D \) :

Number of load buses

\(C_Q \) :

Cost of reactive power generation (in $/h)

\(\phi \) :

Power factor angle

\(C_{SVC} \) :

Cost of SVC installation (in $)

S :

Operating range of the SVC (in MVAr)

r :

Monthly rate of interest

\(P_{L_k } \) :

Active power transmission loss at bus ‘k’

\(P_{loss} \) :

Total active power loss over all buses

\(FVSI_{sum}\) :

Summation of FVSI over all transmission lines

\(FF_r \) :

Fitness function at rth vulnerable bus location

\(\omega _q \) :

Coefficient of preference for criteria where \(0\le \omega _q \le 1\)

ke :

Kinetic energy

\(G^{new}\) :

Created solution

\(\Delta G^{new}\) :

Difference between the current and previous generation

\(\beta \) :

Distribution factor, where \(0.3\le \beta \le 1.99\)

\(\chi \) :

Step size for each generation

\(G^{dis}\) :

Current solution obtained by discovery

\(\sigma _y \) :

Standard deviation of “y” variables

\(\Delta G^{dis}\) :

Difference between current and previous discovered solutions

OPF:

Optimal power flow

ABC:

Artificial bee colony algorithm

DE:

Differential evolution

IGA:

Immune genetic algorithm

ROI:

Return on investment

CRO:

Chemical reaction optimization

TCR:

Thyristor controlled reactor

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Authors and Affiliations

  1. Department of Electrical Engineering, National Institute of Technology, Durgapur, India

    Deepro Sen & Parimal Acharjee

  2. Department of Electrical Engineering, KIIT University, Bhubaneshwar, India

    Sriparna Roy Ghatak

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  1. Deepro Sen
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Correspondence to Deepro Sen.

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Sen, D., Ghatak, S.R. & Acharjee, P. Optimal allocation of static VAR compensator by a hybrid algorithm. Energy Syst 10, 677–719 (2019). https://doi.org/10.1007/s12667-017-0247-7

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