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Optimal allocation and sizing of renewable distributed generation using ant lion optimization algorithm

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Abstract

Renewable sources can provide a clean and smart solution to the increased demands. Thus, photovoltaic and wind turbine are considered here as sources of distributed generation (DG). Allocation and sizing of DG have greatly affected the system losses. In this paper, ant lion optimization algorithm (ALOA) is proposed for optimal allocation and sizing of DG-based renewable sources for radial distribution system. First, the most candidate buses for installing DG are suggested using loss sensitivity factors. Then the proposed ALOA is employed to deduce the locations of DG and their sizing from the elected buses. The proposed algorithm is tested on 69 bus radial distribution system. The obtained results via the proposed algorithm are compared with others to highlight its benefits in reducing total power losses and consequently maximizing the net saving. Moreover, the results are introduced to verify the superiority of the proposed algorithm to enhance the voltage profiles for various loading conditions.

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Abbreviations

\(P_k ,Q_k \) :

The total effective active and reactive power supplied behind the bus ‘k’

\(V_k \) :

The magnitude of voltage at bus k

\(R_{ik} ,X_{ik} \) :

The resistance and reactance of transmission line between bus ‘i’ and ‘k’

\(V_i \) :

The magnitude of voltage at bus i

\(K_P \) :

The cost per kW-Hours

n :

The maximum number of ants

r(t):

A stochastic function

t :

The step of random walk (current iteration in this paper)

\(M_\mathrm{ant} \) :

The matrix for saving the position of each ant

\(\mathrm{Ant}_{i,j} \) :

The value of the jth variable of ith ant

d :

The number of variables

\(M_\mathrm{oa} \) :

The matrix for saving the fitness of each ant

\(M_{\text {ant lion}} \) :

The matrix for saving the position of each ant lion

\({\text {Ant lion}}_{i,j} \) :

The value of the jth variable of ith ant lion

\(M_\mathrm{oal} \) :

The matrix for saving the fitness of each ant lion

\(A_i \) :

The minimum of random walk of ith variable

\(C_i^t \) :

The minimum of ith variable at tth iteration

\(C^{t}\) :

The minimum of all variables at tth iteration

\(C_j^t \) :

The minimum of all variables for ith ant

\(D_i^t \) :

The maximum of ith variable at tth iteration

\(D^{t}\) :

The vector including the maximum of all variables at tth iteration

\(D_j^t \) :

The maximum of all variables for ith ant

\(\mathrm{Ant\, lion}_j^t \) :

The position of the selected jth ant lion at tth iteration

I :

This ratio equals to \(10^{w}\frac{t}{T}\)

T :

The maximum number of iterations

w :

To adjust the accuracy level of exploitation

\(r_a^t \) :

The random walk around the ant lion selected by the roulette wheel at tth iteration

\(r_e^t \) :

The random walk around the elite at tth iteration

\(\mathrm{Ant}_i^t \) :

The position of ith ant at tth iteration

\(P_\mathrm{Loss} \) :

The total power losses after compensation

\(F_t \) :

The total objective function

\(f_1 \) :

The part of \(F_t \) that express the minimization of power losses

\(f_2 \) :

The part of \(F_t \) that express the enhancement of voltage profiles

\(f_3 \) :

The part of \(F_t \) that express the improvement of VSI

\(w_1 ,w_2 ,w_3 \) :

The weighting factors

\(P_\mathrm{Swing} \) :

The active power of swing bus

\(Q_\mathrm{Swing} \) :

The reactive power of swing bus

L :

The number of transmission line in a distribution system

Pd(q) :

The demand of active power at bus q

Qd(q) :

The demand of reactive power at bus q

N :

The number of total buses

\(V_{\min } \) :

The minimum voltage at bus i

\(V_{\max } \) :

The maximum voltage at bus i

\(P_\mathrm{DG} \) :

The installed active power of the DG

\(Q_\mathrm{DG} \) :

The installed reactive power of the DG

\(N_\mathrm{DG} \) :

The number of installed unit of the DG

\(P_\mathrm{DG}^{\min }, P_\mathrm{DG}^{\max }\) :

The minimum and maximum real outputs of the DG unit

\(Q_\mathrm{DG}^{\min },Q_\mathrm{DG}^{\max } \) :

The minimum and maximum reactive outputs of the DG unit

\(S_\mathrm{Li} \) :

The actual complex power in line i

\(S_{\mathrm{Li}(\mathrm{rated})} \) :

The rated complex power in that line i

ALOA:

Ant lion optimization algorithm

DG:

Distributed generation

LSFs:

Loss sensitivity factors

PV:

Photovoltaic system

WT:

Wind turbine

GA:

Genetic algorithm

PSO:

Particle swarm optimization

PGSA:

Plant growth simulation algorithm

CSA:

Cuckoo search algorithm

ABC:

Artificial bee colony

ACO:

Ant colony optimization

FA:

Firefly algorithm

MINLP:

Mixed integer non-linear programming

HS:

Harmony search

ICA:

Imperialist competitive algorithm

BF:

Bacteria foraging

VSI:

Voltage Stability Index

MTLBO:

Modified teaching learning-based optimization

BB–BC:

Big Bang–Big Crunch

SGA:

Standard genetic algorithm

NR:

Not reported

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Author information

Author notes

  1. E. S. Ali

    Present address: Electrical Department, Faculty of Engineering, Jazan University, Jazan, Kingdom of Saudi Arabia

Authors and Affiliations

  1. Electric Power and Machine Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt

    E. S. Ali & S. M. Abd Elazim

  2. Electric Power and Machine Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt

    A. Y. Abdelaziz

Authors
  1. E. S. Ali
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  2. S. M. Abd Elazim
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  3. A. Y. Abdelaziz
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Corresponding author

Correspondence to E. S. Ali.

Appendix

Appendix

The pseudo code of the ALO algorithm is defined as follows:

Step 1: :

Initialize the first population of ants, ant lions randomly, LSFs and DG. Run load flow and calculate the fitness of ants and ant lions.

Step 2: :

Find the best ant lions and assume it as the elite.

Step 3: :

For each ant, select an ant lion using roulette wheel

3.1 Create a random walk and normalize it to keep it inside the search space,

3.2 Update the position of ant,

3.3 Update the values of c and d,

End for

Step 4: :

Run load flow and calculate the fitness of all ants,

Step 5: :

Replace an ant lion with its corresponding ant it if becomes fitter,

Step 6: :

Update elite if an ant lion becomes fitter than the elite,

Step 7: :

Repeat from step 3 until a stopping criteria is satisfied. ALOA parameters: Number of ant lions \(=\) 30, maximum number of iterations \(=\) 500.

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Ali, E.S., Abd Elazim, S.M. & Abdelaziz, A.Y. Optimal allocation and sizing of renewable distributed generation using ant lion optimization algorithm. Electr Eng 100, 99–109 (2018). https://doi.org/10.1007/s00202-016-0477-z

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  • DOI: https://doi.org/10.1007/s00202-016-0477-z

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