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Dynamic economic dispatch incorporating renewable energy sources and pumped hydroenergy storage

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Abstract

Due to mounting infiltration of solar and wind energy sources, it becomes essential to investigate its brunt on the dynamic economic dispatch. Here, solar–wind–thermal system integrating pumped-storage hydraulic unit has been considered. This work recommends chaotic fast convergence evolutionary programming (CFCEP) rooted in Tent equation for solving dynamic economic dispatch problem incorporating renewable energy sources and pumped-storage hydraulic unit. Chaotic sequences increase the exploitation ability in the searching space and enhance the convergence property. In the recommended technique, chaotic sequences have been pertained for acquiring the dynamic scaling factor setting in fast convergence evolutionary programming (FCEP). The efficiency of the recommended technique is revealed on two test systems. Simulation outcomes of the suggested technique have been matched up to those acquired by FCEP, differential evolution and particle swarm optimization. It has been observed from the comparison that the recommended CFCEP technique has the capability to confer with better quality solution.

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Abbreviations

\( F_{C} \) :

Cost function

\( a_{\text{si}} ,b_{\text{si}} ,c_{\text{si}} ,d_{\text{si}} ,e_{\text{si}} \) :

Cost coefficients of \( i \)th thermal generator

\( P_{\text{sit}} \) :

Output power of \( i \)th thermal unit at time \( t \)

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

Lower and upper generation limits for \( i \)th thermal generator

\( {\text{UR}}_{i} ,{\text{DR}}_{i} \) :

Ramp-up and ramp-down rate limits of the \( i \)th thermal generator

\( P_{\text{wkt}} \) :

Available wind power of \( k \)th wind turbine generator at time \( t \)

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

Lower and upper generation limits for \( k \)th wind turbine generator

\( P_{\text{wrk}} \) :

Rated wind power of \( k \)th wind turbine generator

\( K_{\text{wk}} \) :

Direct cost coefficient for the \( k \)th wind turbine generator

\( v_{\text{in}} \) :

Cut-in wind speed

\( v_{\text{out}} \) :

Cut-out wind speed

\( v_{r} \) :

Rated wind speed

\( v_{\text{wt}} \) :

Forecasted wind speed at time \( t \)

\( P_{\text{PVmt}} \) :

Power output from \( m \)th solar PV plant at time \( t \)

\( P_{\text{PVrm}} \) :

Rated power output of \( m \)th solar PV plant

\( G \) :

Solar irradiation forecast

\( T_{\text{ref}} ,T_{\text{amb}} \) :

Reference and ambient temperature

\( \alpha \) :

Temperature coefficient

\( K_{\text{sm}} \) :

Direct cost coefficient for the \( m \)th solar PV plant

\( P_{\text{Dt}} \) :

Load demand at time \( t \)

\( P_{\text{Lt}} \) :

Total transmission line losses at time \( t \)

\( P_{\text{ghjt}} \) :

Power generation of \( j \)th pumped-storage plant at time \( t \)

\( P_{\text{phjt}} \) :

Pumping power of \( j \)th pumped-storage plant at time \( t \)

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

Minimum and maximum power generation limits of \( j \)th pumped-storage plant

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

Minimum and maximum pumping power limits of \( j \)th pumped-storage plant

\( Q_{\text{ghjt}} \left( {P_{\text{ghjt}} } \right) \) :

Discharge rate of \( j \)th pumped-storage plant at time \( t \)

\( Q_{\text{phjt}} \left( {P_{\text{phjt}} } \right) \) :

Pumping rate of \( j \)th pumped-storage plant at time \( t \)

\( Q_{{{\text{spent}},{\text{TOT}},j}} \) :

Total water amount spent for generation of \( j \)th pumped-storage plant

\( Q_{{{\text{pump}},{\text{TOT}},j}} \) :

Total pumped water amount of \( j \)th pumped-storage plant

\( Q_{{{\text{net}},{\text{spent}},j}} \) :

Net spent water amount by \( j \)th pumped-storage hydraulic unit during operation cycle

\( V_{{{\text{res}},jt}} \) :

Water volume in upper reservoir of \( j \)th pumped-storage plant at time \( t \)

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

Minimum and maximum upper reservoir storage limits of \( j \)th pumped-storage plant

\( V_{{{\text{res}},j}}^{\text{start}} ,V_{{{\text{res}},j}}^{\text{end}} \) :

Specified starting and final stored water volumes in upper reservoir of \( j \)th pumped-storage plant

\( t,T \) :

Time index and scheduling period

\( T_{\text{gen}} \) :

Set that contains all time intervals where pumped-storage plant operated in generation mode

\( T_{\text{pump}} \) :

Set that contains all time intervals where pumped-storage plant operated in pumping mode

\( T_{{{\text{change\_over}}}} \) :

Set that contains all time intervals where pumped-storage plant operated in idle mode, i.e., in between generating mode and pumping mode

\( N_{t} \) :

Number of thermal generating units

\( N_{w} \) :

Number of wind power generating units

\( N_{\text{PV}} \) :

Number of solar PV plant

\( N_{\text{Pump}} \) :

Number of pumped-storage plants

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Authors and Affiliations

  1. Department of Power Engineering, Jadavpur University, Kolkata, 700098, India

    Mousumi Basu

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  1. Mousumi Basu
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Appendix

Appendix

See Tables 6 and 7.

Table 6 Thermal generator characteristics of test system 1
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Table 7 Hourly temperature and load demand of test system 1
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Basu, M. Dynamic economic dispatch incorporating renewable energy sources and pumped hydroenergy storage. Soft Comput 24, 4829–4840 (2020). https://doi.org/10.1007/s00500-019-04237-3

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