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Swarm-Inspired Artificial Bee Colony Algorithm for Solving Optimal Power Flow with Wind Farm

  • Research Article - Electrical Engineering
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Abstract

In this paper, an enhanced artificial bee colony (ABC)-based algorithm is proposed for solving optimal power flow (OPF) with wind farm. The OPF calculations determine optimal values of control variables and system quantities for secure and economic system operation considering various limitations with wind farm. In the OPF problem, wind farm is modeled as an aggregate permanent magnet synchronous generator and subsequently modeled as an aggregate squirrel cage induction generator. The proposed algorithm is developed by the combined application of Gaussian and Cauchy probability distributions in ABC algorithm and hence termed as swarm-inspired artificial bee colony (SIABC) algorithm. The performance of the proposed SIABC algorithm is compared with particle swarm optimization (PSO) and ABC algorithms. The optimal solutions for adopted IEEE 30-bus system with wind farm and adopted Indian Utility 66-bus system obtained by these algorithms are compared and analyzed. The analysis reveals that the proposed SIABC algorithm is relatively simple, reliable and faster in convergence than PSO and ABC algorithms.

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Abbreviations

F T :

Total fuel cost ($/h)

a Gi ,b Gi ,c Gi :

Fuel cost coefficients of ith committed thermal generator

a Gs ,b Gs ,c Gs :

Fuel cost coefficients of slack bus generator

P Gi :

Active power generation of ith committed thermal generator

P Gs :

Active power generation of slack bus generator

\({P_{\rm Gi}^{\min} ,P_{\rm Gi}^{\max} }\) :

Active power generation limits of ith committed thermal generator

\({Q_{\rm Gi}^{\min} ,Q_{\rm Gi}^{\max} }\) :

Reactive power generation limits of ith committed thermal generator

\({P_{\rm Gs}^{\min} ,P_{\rm Gs}^{\max} }\) :

Active power generation limits of slack bus generator

\({Q_{\rm Gs}^{\min} ,Q_{\rm Gs}^{\max} }\) :

Reactive power generation limits of slack bus generator

V Ci :

Voltage magnitude of ith voltage controllable bus

nvcb:

Number of voltage controllable buses

\({V_{\rm Ci}^{\min} ,V_{\rm Ci}^{\max} }\) :

Voltage magnitude limits of ith voltage controllable bus

V Lj :

Voltage magnitude of jth load bus

\({V_{\rm Lj}^{\min} ,V_{\rm Lj}^{\max} }\) :

Voltage magnitude limits of jth load bus

nlb:

Number of load buses

\({P_{\rm Ri} =P_{\rm Gi}^{\max} -P_{\rm Gi} }\) :

Available reserve of ith committed thermal generator

\({P_{\rm Rs} =P_{\rm Gs}^{\max} -P_{\rm Gs} }\) :

Available reserve of slack bus generator

P Wi :

Active power generation of ith wind farm

χ :

Reserve requirement expressed as fraction of total load (generally 10 %)

P D :

Total system load

\({{\rm LF}_k ;{\rm LF}_k^{\max} }\) :

Power flow in the kth line and its corresponding limit (p.u MVA)

nl:

Number of transmission lines

rand(0,1):

Uniformly distributed random number between (0, 1)

Nrand(0,1):

Gaussian distributed random number with μ = 0 and σ = 1

Crand(0,1):

Cauchy distributed random number with L =  0 and S =  1

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Authors and Affiliations

  1. Department of EEE, SSN College of Engineering, Chennai, India

    M. Devesh Raj & N. B. Muthuselvan

  2. Department of EEE, College of Engineering, Guindy, Chennai, India

    P. Somasundaram

Authors
  1. M. Devesh Raj
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  2. N. B. Muthuselvan
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  3. P. Somasundaram
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Correspondence to M. Devesh Raj.

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Raj, M.D., Muthuselvan, N.B. & Somasundaram, P. Swarm-Inspired Artificial Bee Colony Algorithm for Solving Optimal Power Flow with Wind Farm. Arab J Sci Eng 39, 4775–4787 (2014). https://doi.org/10.1007/s13369-014-1084-9

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  • DOI: https://doi.org/10.1007/s13369-014-1084-9

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