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Applications of metaheuristic algorithms for optimal operation of cascaded hydropower plants

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Abstract

In this paper, two optimal operation plans of a cascaded reservoir system with four hydropower plants are studied for reaching the highest power energy of all the power plants. In the first plan, called local optimization plan, optimal water discharge of each upstream hydropower plant is determined first and the optimal discharge is then used as input data for determining optimal water discharge of other downstream hydropower plants. In the second plan, called global optimization plan, optimal water discharge of all hydropower plants is simultaneously determined. For reaching the highest total power energy of the system, nine methods consisting of moth swarm algorithm, Harris hawks optimization, cuckoo search algorithm (CSA), snap drift cuckoo search algorithm (SD-CSA), stochastic fractal search algorithm, parasitism predation algorithm, marine predator algorithm, tunicate swarm algorithm, and the proposed improved cuckoo search algorithm (ICSA) are implemented. Among the methods, the proposed ICSA is first developed by improving the exploitation phase of CSA. The comparisons of power energy from each hydropower plant for the two plans indicate that local optimization plan is more useful for upstream plants but for downstream plants, whereas global optimization plan is more useful for downstream plants. For the purpose of reaching the highest total power energy for the whole system, the global optimization plan is more effective because it reaches higher power energy than local optimization plan. For investigating the improvement of the proposed method over CSA and SD-CSA, the three methods are run for seven benchmark functions and for the global optimization plan with different population sizes and different iteration numbers. As a result, it is recommended that global optimization plan should be applied for all hydropower plants in cascaded systems and downstream plants with higher power energy can share benefit to upstream ones. In addition, one of the most effective methods that should be recommended for implementing global optimization plan is the proposed ICSA.

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Data availability

Data of the whole system were taken from [24] and also reported in “Appendix”.

Abbreviations

Infh,m :

Inflow into the hth hydropower plant at the mth interval

M :

Number of intervals

N hp :

Number of hydropower plants in the cascaded system

NoS:

Population

Nestk, Nesth, Nestn, Nestm, Nestp, Nestq :

Randomly chosen solutions from current population

\( P_{h}^{\hbox{min} } ,\,P_{h}^{\hbox{max} } \) :

Lower limit and upper limit of power output of the hth hydropower plant

\( {\text{RV}}_{h}^{\hbox{min} } ,\,{\text{RV}}_{h}^{\hbox{max} } \) :

Lower limit and upper limit of water volume of the hth reservoir

RVh,m :

Water volume of the hth reservoir at the end of the mth interval

RVh,m−I :

Reservoir volume of the hth hydropower plant at the (m-1)th interval

S E :

Sum of energy obtained by four hydropower plants

SWh,m :

Spillage water from the hth hydropower plant at the mth interval

T m :

Number of hours for the mth interval

T j,h :

Traveling time of water from the jth reservoir to the hth reservoir

\( {\text{WD}}_{h}^{\hbox{min} } ,\,{\text{WD}}_{h}^{\hbox{max} } \) :

Lower limit and upper limit of water discharge via turbine of the hth hydropower plant

WDh,m :

Water discharge via turbine of the hth hydropower plant at the mth interval

\( \varphi_{1,h} ,\,\varphi_{2,h} ,\,\varphi_{3,h} ,\,\varphi_{4,h} ,\,\varphi_{5,h} ,\varphi_{6,h} \) :

Coefficients of power generation function of the hth hydropower plant

WDs,1,M, WDs,2,M, WDs,3,M, WDs,4,M :

Water discharge of four hydropower plants at the Mth interval corresponding to the sth solution

RVs,1,M, RVs,2,M, RVs,3,M, RVs,4,M :

Reservoir volume of the four hydropower plants at the Mth interval corresponding to the sth solution

P s,1,M, P s,2,M, P s,3,M, P s,4,M :

Power generation of the four hydropower plants at the Mth interval corresponding to the sth solution

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Authors and Affiliations

  1. Power System Optimization Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Thang Trung Nguyen

  2. Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

    Thuan Thanh Nguyen

  3. Institute of Research and Development, Duy Tan University, Danang, 550000, Vietnam

    Thai Dinh Pham

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  1. Thang Trung Nguyen
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  2. Thuan Thanh Nguyen
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  3. Thai Dinh Pham
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Correspondence to Thai Dinh Pham.

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Appendix

Appendix

See Tables 8, 9, 10, 11 and 12.

Table 8 Hydraulic limitations of four reservoirs (\( \times \) 104 m3)
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Table 9 Power output function coefficients of four hydropower plants
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Table 10 Inflows of four reservoirs (× 104 m3)
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Table 11 Travelling time (in hour) from upstream to downstream reservoirs
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Table 12 Optimal water discharge (× 104 m3) found by the proposed method
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Nguyen, T.T., Nguyen, T.T. & Pham, T.D. Applications of metaheuristic algorithms for optimal operation of cascaded hydropower plants. Neural Comput & Applic 33, 6549–6574 (2021). https://doi.org/10.1007/s00521-020-05418-0

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