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Efficient hybrid algorithm for transmission expansion planning

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Abstract

This work presents an efficient hybrid algorithm (EHA) that consists of a search space reducer (SSR) and a modified bat-inspired algorithm (MBA) to solve the transmission network expansion planning (TNEP). The contribution of the proposal is to consider, at the same time, the security constraints criterion ‘N − 1’, load scenarios and network losses to give a more comprehensive approach in an efficient manner, which allows applying the EHA to large-scale real system. Discrete variables in the TNEP are handled by the MBA, and an optimal power flow is used to evaluate the fitness function as well as planning options. By using the SSR to define the initial candidate set for the MBA, the solution search space is reduced improving the computational performance of the proposed MBA. To validate the proposed method and show its efficiency in comparison with others in the literature, tests are conducted on Garver and IEEE 24-bus test system, in addition to an equivalent Brazilian system.

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Abbreviations

E :

Set of branches with existing transmission lines

C :

Set of branches with candidate transmission lines

F :

Set of branches with fictitious transmission lines

L :

Set of operational conditions, including the base case and contingencies

S :

Set of load scenarios

B :

Set of load buses

Z :

Set of generation buses

R ij :

Set of candidate reinforcements for branch ij

E ij :

Set of existing transmission lines of branch ij

F ij :

Set of fictitious transmission lines of branch ij

ΩE i :

Set of existing lines connected to bus i

ΩC i :

Set of candidate lines connected to bus i

N L :

Number of operational conditions, including the base case and contingencies

N S :

Number of load scenarios

N C :

Number of candidate transmission lines

N pg :

Number of active power generation buses

N pd :

Number of buses with active power deficit

N B :

Number of system buses

u :

Index for load scenario

c :

Index for operational condition

k :

Index for existing or reinforcement transmission line

pgi,u,c :

Active power generation at bus i (MW), load scenario u and operation condition c

pdi,u,c :

Active power deficit at bus i (MW), load scenario u and operation condition c

EPk,ij :

Expansion parameter for reinforcement k in branch ij, which is a binary variable 0/1

θ ij,u,c :

Angular difference between terminal buses i and j at scenario u and operation condition c

SI1 k, SI2k :

Sensitivity indices for candidate line k

fE k,u,c :

Active power flow (MW) of existing transmission line k in branch ij, at scenario u and operation condition c

fC k,u,c :

Active power flow (MW) of candidate transmission line k for branch ij, at scenario u and condition c

fF k,u,c :

Active power flow (MW) of fictitious line k for branch ij, at scenario u and condition c

p u :

Probability of scenario u

dci :

Specific deficit generation cost at bus i ($/MW)

pci :

Specific generation cost at bus i ($/MW)

pg min i , pg max i :

Inferior and superior limits of pgi,u,c (MW), respectively

d i,u, c :

Demand at bus i (MW) load scenario u and operational condition c

fE max k :

Active power flow limit of an existing transmission line k (MW)

fC max k :

Active power flow limit of a candidate transmission line k (MW)

ce k :

Investment cost of a candidate transmission line k ($)

b k :

Susceptance of line k

γ k :

Susceptance of fictitious line k, considered as 0.001 per unit (pu)

g k :

Conductance of line k

in:

An individual or virtual bat

x in :

Position of each individual or virtual bat

f in :

Frequency of each individual or virtual bat

v :

Mean sound propagation speed (360 m/s)

v*:

Speed of the receiver (current optimal solution)

v in :

Speed of an individual or virtual bat

η :

Population size

f Din :

Apparent frequency with the Doppler effect of bat

t :

Iteration index

x t * :

Position of the best bat at iteration t

x Cin :

Continuous position value of bat

A in :

Sonic pulse amplitude

r in :

Sonic pulse rate

t max :

Maximum number of iterations

x lim :

Boundary of the search space

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Acknowledgements

The authors thank the ‘Foundation for Supporting Research in Minas Gerais’ (FAPEMIG), ‘Coordination for the Improvement of Higher Education Personnel’ (CAPES), ‘Brazilian National Research Council’ (CNPq) and ‘Electric Power National Institute’ (INERGE) for supporting this work.

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Authors and Affiliations

  1. Department of Electrical Energy, Federal University at Juiz de Fora (UFJF), Juiz De Fora, MG, Brazil

    E. J. De Oliveira, C. A. Moraes, L. W. Oliveira & L. M. Honório

  2. Department of Electrical Engineering, Federal Center of Technological Education of Rio de Janeiro, Rio De Janeiro, Brazil

    R. P. B. Poubel

Authors
  1. E. J. De Oliveira
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  2. C. A. Moraes
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  3. L. W. Oliveira
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  4. L. M. Honório
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  5. R. P. B. Poubel
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Correspondence to E. J. De Oliveira.

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De Oliveira, E.J., Moraes, C.A., Oliveira, L.W. et al. Efficient hybrid algorithm for transmission expansion planning. Electr Eng 100, 2765–2777 (2018). https://doi.org/10.1007/s00202-018-0744-2

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