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Electricity generation cost reduction for hydrothermal systems with the presence of pumped storage hydroelectric plants

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Abstract

This paper presents the applications of novel metaheuristic algorithms including equilibrium optimization (EO), coot optimization, and slime mould optimization together with three Particle swarm optimization variants for optimal power generation cooperation of power systems with conventional hydroelectric power plants, thermal power plants and especially pumped-storage hydroelectric plants (PHPs). Three different power systems are applied to run these algorithms to prove that PHPs have a significant contribution to the generation cost reduction. In the first two systems, there are not inflows to the upper reservoirs of the PHPs and these plants only produce electricity by using pumped water. In the third system, inflows to PHPs are considered. The requirement is that the volume of reservoir at the beginning and the end of a day must be the same. However, the generation cost for the cases with the operation of PHPs is much less than other cases without the PHPs or without the pump mode of PHP. About the generation cost of three systems, PHPs support to reach the saving cost of $1,222.1998, $89,091.16, and $94,449.2 corresponding to 0.45%, 3% and 3.4%, respectively. So, the PHPs should be run in power systems. Among the six applied methods, EO is the best since it can reach less cost than others from higher than 2% to under 8%. Hence, it is recommended that EO is a potential method for finding optimal operation parameters of power systems with the PHPs.

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Abbreviations

\(PT_{t,k}\) :

Generation of the tth TP at the kth period

\(a_{1t}\), \(a_{2t}\), \(a_{3t}\) :

Cost coefficients of the tth TP

\(N_{1}\) :

Number of TPs

\(N_{2}\) :

Number of periods

\(PT_{t}^{min}\), \(PT_{t}^{max}\) :

Minimum and maximum generations of the tth TP

\(PH_{i,k}\), \(PH_{j,k}^{Gen}\) :

Generation of the ith CHP and the jth PHP at the kth period

\(PL_{k}\) :

Power loss of the power system at the kth period

\(PD_{k}\) :

Load at the kth period

\(N_{3}\), \(N_{4}\) :

Number of CHPs and PHPs

\(PH_{j,k}^{Pum}\), ON pumj,k :

Pump power and pump status of the jth PHP at the kth period

Q j,k and V j,k :

Discharge and volume of the jth PHP at the kth period

\(Q_{j}^{min}\), \(Q_{j}^{max}\) :

Lower and upper discharge limits of the jth PHP

\(V_{j}^{min}\), \(V_{j}^{max}\) :

Lower and upper volume limits of the jth PHP

\(b_{1j}\), \(b_{2j}\), \(b_{3j}\) :

Generation function coefficients of the jth PHP

\(PH_{j}^{Genmin}\), \(PH_{j}^{Genmax}\) :

Minimum and maximum generations of the jth PHP

\(I_{j,k}\), \(S_{j,k}\) :

Inflow and spillage of the jth PHP at the kth period

\(x_{ad}^{new}\) :

Newly updated value of the dth control variable in the ath solution

N D, N M :

Number of control and dependent variables.

x ad , y am :

The dth control and the mth dependent variables in the ath solution

\(x_{d\min } ,x_{d\max }\) :

Minimum and maximum limits of the dth control variable

\(y_{m\min } ,y_{m\max }\) :

Minimum and maximum limits of the mth dependent variable

rnd :

Random number within 0 and 1

N S :

Population

It, It max :

Present iteration and maximum iteration.

\(\Delta Q_{{j,k^{{\prime }} }}\) :

Discharge violation of the jth PHP at the k′th period

\(\Delta V_{j,k}\), \(\Delta V_{i,k}\) :

Volume violation of the jth PHP and the ith CHP at the kth period

\(\Delta Q_{{i,k^{{\prime }} }}\) :

Discharge violation of the ith CHP at the k′th period

\(PT_{1,k}\), \(\Delta PT_{1,k}\) :

Generation and generation violation of the first TP at the kth period

\(PT_{1}^{min} {,} PT_{1}^{max}\) :

Minimum and maximum generation of the first TP

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Authors and Affiliations

  1. Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Phu Trieu Ha

  2. Division of MERLIN, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh, Vietnam

    Dao Trong Tran

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

    Thang Trung Nguyen

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Appendix

Appendix

See Fig. 15, Tables 6 and 7.

Fig. 15
figure 15

Load and inflow of Systems 2 and 3

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Table 6 Data of TPs for the three applied systems
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Table 7 Data of PHP and CHP in three applied systems
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Ha, P.T., Tran, D.T. & Nguyen, T.T. Electricity generation cost reduction for hydrothermal systems with the presence of pumped storage hydroelectric plants. Neural Comput & Applic 34, 9931–9953 (2022). https://doi.org/10.1007/s00521-022-06977-0

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