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

Rampup and rampdown 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
 \( v_{\text{in}} \) :

Cutin wind speed
 \( v_{\text{out}} \) :

Cutout 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 pumpedstorage plant at time \( t \)
 \( P_{\text{phjt}} \) :

Pumping power of \( j \)th pumpedstorage plant at time \( t \)
 \( P_{\text{ghj}}^{\hbox{min} } ,P_{\text{ghj}}^{\hbox{max} } \) :

Minimum and maximum power generation limits of \( j \)th pumpedstorage plant
 \( P_{\text{phj}}^{\hbox{min} } ,P_{\text{phj}}^{\hbox{max} } \) :

Minimum and maximum pumping power limits of \( j \)th pumpedstorage plant
 \( Q_{\text{ghjt}} \left( {P_{\text{ghjt}} } \right) \) :

Discharge rate of \( j \)th pumpedstorage plant at time \( t \)
 \( Q_{\text{phjt}} \left( {P_{\text{phjt}} } \right) \) :

Pumping rate of \( j \)th pumpedstorage plant at time \( t \)
 \( Q_{{{\text{spent}},{\text{TOT}},j}} \) :

Total water amount spent for generation of \( j \)th pumpedstorage plant
 \( Q_{{{\text{pump}},{\text{TOT}},j}} \) :

Total pumped water amount of \( j \)th pumpedstorage plant
 \( Q_{{{\text{net}},{\text{spent}},j}} \) :

Net spent water amount by \( j \)th pumpedstorage hydraulic unit during operation cycle
 \( V_{{{\text{res}},jt}} \) :

Water volume in upper reservoir of \( j \)th pumpedstorage 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 pumpedstorage 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 pumpedstorage plant
 \( t,T \) :

Time index and scheduling period
 \( T_{\text{gen}} \) :

Set that contains all time intervals where pumpedstorage plant operated in generation mode
 \( T_{\text{pump}} \) :

Set that contains all time intervals where pumpedstorage plant operated in pumping mode
 \( T_{{{\text{change\_over}}}} \) :

Set that contains all time intervals where pumpedstorage 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 pumpedstorage plants
References
Attavriyanupp P, Kita H, Tanaka T, Hasegawa J (2002) A hybrid EP and SQP for dynamic economic dispatch with nonsmooth fuel cost function. IEEE Trans Power Syst 17(2):411–416
Bakirtzis AG, Gavanidou ES (1992) Optimum operation of a small autonomous system with unconventional energy sources. Electr Power Syst Res 23(1):93–102
Basu M (2017) Fast convergence evolutionary programming for economic dispatch problems. IET Gener Transm Distrib 11(16):4009–4017
Cai J, Ma X, Li L (2007) Chaotic particle swarm optimization for economic dispatch considering the generator constraints. Energy Convers Manag 48(2):645–653
Caponetto R, Fortuna L (2003) Chaotic sequences to improve the performance of evolutionary algorithms. IEEE Trans Evol Comput 7(3):289–304
Cheng W, Zhang H (2015) A dynamic economic dispatch model incorporating wind power based on chance constrained programming. Energies 8(1):233–256
Dubey HM, Pandit M, Panigrahi BK (2016) Ant lion optimization for shortterm wind integrated hydrothermal power generation scheduling. Electr Power Energy Syst 83(1):158–174
Elattar EE (2015) A hybrid genetic algorithm and bacterial foraging approach for dynamic economic dispatch problem. Electr Power Energy Syst 69:18–26
Fadil S, Urazel B (2013) Solution to security constrained nonconvex pumpedstorage hydraulic unit scheduling problem by modified subgradient algorithm based on feasible values and pseudo water price. Electr Power Compon Syst 41:111–135
Fogel LJ, Owens AJ, Walsh MJ (1966) Artificial intelligence through simulated evolution. Wiley, New York
Fogel LJ, Fogel DB, Angeline PJ (1994) A preliminary investigation on extending evolutionary programming to include selfadaptation on finite state machines. Informatica 18:387–398
Giorsetto P, Utsurogi KF (1983) Development of a new procedure for reliability modeling of wind turbine generators. IEEE Trans Power Appar Syst 102(1):134–143
Han XS, Gooi HB, Kirschen DS (2001) Dynamic economic dispatch: feasible and optimal solutions. IEEE Trans Power Syst 16(1):22–28
Khan NA, Awan AB, Mahmood A, Razzaq S, Zafar A, Sidhu GAS (2015) A Combined emission economic dispatch of power system including solar photo voltaic generation. Energy Convers Manag 92(1):82–91
Liang RueyHsun, Liao JianHao (2007) A fuzzyoptimization approach for generation scheduling with wind and solar energy systems. IEEE Trans PWRS 22(4):1665–1674
Lu Y, Zhou J, Qin H, Wang Y, Zhang Y (2011) Chaotic differential evolution methods for dynamic economic dispatch with valvepoint effects. Eng Appl Artif Intell 24:378–387
Mondal S, Bhattacharya A, Nee Dey SH (2013) “Multiobjective economic emission load dispatch solution using gravitational search algorithm and considering wind power penetration. Electr Power Energy Syst 44(1):282–292
Pan S, Jian J, Yang L (2018) A hybrid MILP and IPM approach for dynamic economic dispatch with valvepoint effect. Electr Power Energy Syst 97:290–298
Patwal RS, Narang N, Garg H (2018) A novel TVACPSO based mutation strategies algorithm for generation scheduling of pumped storage hydrothermal system incorporating solar units. Energy 142:822–837
PerezDiaz J, Jim J (2016) Contribution of a pumpedstorage hydropower plant to reduce the scheduling costs of an isolated power system with high wind power penetration. Energy 109(1):92–104
Ross DW, Kim S (1980) Dynamic economic dispatch of generation. IEEE Trans Power Appar Syst PAS99(6):2060–2068
Shilaja C, Ravi K (2017) Optimization of emission/economic dispatch using Euclidean affine flower pollination algorithm (eFPA) and binary FPA (BFPA) in solar photo voltaic generation. Renew Energy 107:550–566
Travers DL, Kaye RJ (1998) Dynamic dispatch by constructive dynamic programming. IEEE Trans Power Syst 13(1):72–78
Walters DC, Sheble GB (1993) Genetic algorithm solution of economic dispatch with valve point loading. IEEE Trans Power Syst 8(3):1325–1332
Wood AJ, Wollenberg BF (2012) Power generation, operation and control. Wiley, Hoboken
Xiong G, Shi D (2018) Hybrid biogeographybased optimization with brain storm optimization for nonconvex dynamic economic dispatch with valvepoint effects. Energy 157:424–435
Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3:82–102
Yuan Xiaohui, Wang Liang, Zhang Yongchuan, Yuan Yanbin (2009) A hybrid differential evolution method for dynamic economic dispatch with valvepoint effects. Expert Syst Appl 36:4042–4048
Zhang Y, Gong* D, Geng N, Sun X (2014) Hybrid barebones PSO for dynamic economic dispatch with valvepoint effect. Appl Soft Comput 18:248–260
Zou D, Li S, Kong X, Ouyang H, Li Z (2018) Solving the dynamic economic dispatch by a memorybased global differential evolution and a repair technique of constraint handling. Energy 147:59–80
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Basu, M. Dynamic economic dispatch incorporating renewable energy sources and pumped hydroenergy storage. Soft Comput (2019). https://doi.org/10.1007/s00500019042373
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Keywords
 Tent equation
 Solar–wind–thermal system
 Pumpedstorage hydraulic unit
 Ramp rate limits