太陽能-風(fēng)-水-火熱發(fā)電系統(tǒng)外文文獻(xiàn)

Engineering Applications of Artificial Intelligence 86 2019 182 196 Contents lists available at ScienceDirect EngineeringApplicationsofArtificialIntelligence journal homepage Multi regiondynamiceconomicdispatchofsolar wind hydro thermal powersystemincorporatingpumpedhydroenergystorage M Basu Department of Power Engineering Jadavpur University Kolkata 700098 India A R T I C L EI N F O Keywords Cascaded reservoirs Wind power uncertainty Solar power uncertainty Pumped hydro energy storage Ramp rate limits Proscribed workable area A B S T R A C T This paper suggests chaotic fast convergence evolutionary programming CFCEP for solving multi region dynamic economic dispatch MRDED problem multi region economic dispatch MRED problem and economic dispatch ED problem MRDED problem is based on multi reservoir cascaded hydro plant with time delay thermal plants with nonsmooth fuel cost function wind and solar power units with uncertainty and pumped hydro energy storage MRED problem deals with tie line constraints transmission losses valve point effect and proscribed workable area of thermal generators ED problem deals with valve point effect proscribed workable area and ramp rate limits of thermal generators In the recommended technique chaotic sequences have been pertained for acquiring the dynamic scaling factor setting in fast convergence evolutionary programming FCEP The efficacy of the proposed technique has been verified on convoluted three area system for MRDED problem four area system for MRED problem and 140 unit Korean system for ED problem Test results acquired from the suggested CFCEP technique have been fit to that acquired from FCEP differential evolution DE and particle swarm optimization PSO It has been observed from the comparison that the recommended CFCEP technique has the capability to bestow with better quality solution 1 Introduction Economic dispatch ED seeks out the generation of all dedicated generators most cost effectively at the same time fulfilling a variety of physical and operational constraints in a single area system Gen erally generators are segregated into a number of generation areas interconnected by tie lines Multi region economic dispatch MRED is an escalation of single region economic dispatch MRED seeks out the generation level and interchange power between areas to minimize cost in all regions at the same time fulfilling power balance constraints generating limits constraints and tie line capacity constraints A variety of techniques Shoults et al 1980 Romano et al 1981 Helmick and Shoults 1985 Wang and Shahidehpour 1992 Streiffert 1995 Yalcinoz and Short 1998 Jayabarathi et al 2000 Chen and Chen 2001 Manoharan et al 2009 Wang and Singh 2009 Sharma et al 2011 Somasundaram and Jothi Swaroopan 2011 Ghasemi et al 2016 have been discussed for solving MRED problem Multi region dynamic economic dispatch MRDED is an escalation of multi region economic dispatch problem MRDED seeks out the gen eration level of dedicated generators and interchange power between areas with the forecasted load demands over a certain period of time so as to minimize cost in all areas at the same time fulfilling all operational constraints Multi region dynamic economic dispatch MADED with No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work For full disclosure statements refer to https doi org 10 1016 j engappai 2019 09 001 E mail address mousumibasu renewable energy resources has been discussed in Soroudi and Rabiee 2013 The hydrothermal scheduling problem has been explored for a number of decades Most of the techniques that have been utilized for solving the hydrothermal coordination problem generate a number of simplifying suppositions to aid the optimization problem well brought up Various classical techniques Nilsson and Sjelvgren 1996 Ferrero et al 1998 Yang and Chen 1989 Wood and Wollenberg 1996 Xia et al 1988 Braennlund et al 1986 Pereira and Pinto 1982 Yan et al 1993 Al Agtash and Renjeng 1998 and Ruzic and Rajakovic 1998 have been effectively utilized for solving this problem With the emergence of evolutionary computation techniques at tention has been gradually shifted to significance of such technology based approaches to knob the difficulty engrossed in actual world problems Stochastic search algorithms such as simulated annealing technique Wong and Wong 1994 evolutionary programming tech nique Yang et al 1996 Sinha et al 2003 genetic algorithm Orero and Irving 1998 Gil and Bustos 2003 differential evolution Lak shminarasimman and Subramanian 2006 particle swarm optimiza tion Hota et al 2009 clonal selection algorithm Swain et al 2011 teaching learning based optimization Roy 2013 etc have been per tained for optimal hydrothermal scheduling problem and eluded the https doi org 10 1016 j engappai 2019 09 001 Received 25 October 2018 Received in revised form 17 June 2019 Accepted 2 September 2019 Available online 12 September 2019 0952 1976 2019 Elsevier Ltd All rights reserved M BasuEngineering Applications of Artificial Intelligence 86 2019 182 196 Nomenclature P Cost function of th wind generator in area at time P Scheduled power output of th wind gener ator in area at time Available wind power of th wind power generator in area at time Pmin P max Lower and upper generation limits for th wind power generator in area P Rated wind power of th wind generator in area N Number of committed wind generators in area K Direct cost coefficient of th wind power generator in area KP Penalty cost coefficient of th wind power generator in area K Reserve cost coefficient of the th wind power generator in area Shape factor at a given location Scale factor at a given location Cut in wind speed Rated wind speed P Cost function of th solar PV plant in area at time P Scheduled power output of th solar PV plant in area at time P Power output from th solar plant in area at time P Rated power output of th solar PV plant in area Solar irradiation forecast Solar irradiation in the standard environ ment A certain irradiation point K Direct cost coefficient for th solar PV plant in area KP Penalty cost coefficient of th solar PV plant in area K Reserve cost coefficient of the th solar PV plant in area N Number of committed solar PV plants in area P Power generation of pumped storage plant in area at time P Pumping power of pumped storage plant at time Pmin P max Minimum and maximum power generation limits of pumped storage plant in area Pmin P max Minimum and maximum pumping power limits of pumped storage plant in area P Discharge rate of pumped storage plant in area at time P Pumping rate of pumped storage plant in area at time Watervolumeinupperreservoirof pumped storage plant in area at time limitations Hydrothermal scheduling integrating wind power has been discussed in Dubey et al 2016 and hydrothermal scheduling integrat ing solar power has been discussed in Singh Patwal et al 2018 min max Minimum and maximum upper reservoir storage limits of pumped storage plant in area Specified starting and final stored water vol umes in upper reservoir of pumped storage plant in area P Cost function of th thermal generator in area at time P Power output of th thermal generator in area at time Pmin Pmax Lower and upper generation limits for th thermal generator in area N Number of committed thermal generators in area Cost coefficients of th thermal generator in area Ramp up rate limit and ramp down rate limit of th thermal generator in area 1 2 3 4 5 6 Power generation coefficients of th hydro unit in area I Inflow rate of th reservoir in area at time Water discharge rate of th reservoir in area at time min max Minimum and maximum water discharge rate of th reservoir in area Number of upstream units directly above th hydro plant in area Spillage of th reservoir in area at time Water transport delay from reservoir to in area Storage volume of th reservoir in area at time min max Minimum and maximum storage volume of th reservoir in area 0 Initial storage volume of th reservoir in area T Final storage volume of th reservoir in area P Output power of th hydro unit in area at time Pmin P max Lower and upper generation limits for th hydro unit in area N Number of committed hydro generating units in area MNumber of areas P Power demand of area at time P Transmission line loss in area at time T Tie line real power transfer from area to area at time B Transmission loss coefficient TTime index and scheduling period T Set that contains all time intervals where pumped storage plant operated in genera tion mode T Set that contains all time intervals where pumped storage plant operated in pumping mode The quick increase of electric power demand day by day depletion of fossil fuel and the global warming caused by fossil fuel fired electric power plants have shoved energy based research in the direction of 183 M BasuEngineering Applications of Artificial Intelligence 86 2019 182 196 T Set that contains all time intervals where pumped storage plant operated in idle mode i e in between generating mode and pumping mode utilization of green energy across the globe Due to rising concern on climate change and clean energy solar and wind power are gaining acceptance for meeting energy demand at low cost without any harmful emissions The incorporation of climate driven electric power sources i e solar and wind power sources has upshot in larger uncertainties Solar irradiation and wind velocity are uncertain and their availability is immaterial to the load variation The variability and intermittency of these resources produce significant challenges to be trounced in the generation scheduling problem This blinking nature may have harmful effect on the entire grid This can be trounced by integrating pumped hydro energy storage which alleviates fluctuations in generation and supply The pumped storage hydraulic PSH unit is acquiring the enormous concentration throughout the globe Perez Diaz and Jim 2016 mostly because of its energy storage feature The major role of pumped storage hydraulic PSH units Fadil and Urazel 2013 in electric power systems is to hoard low cost surplus electric energy that is obtainable during off peak load levels as hydraulic potential energy which is done by pumping water from the lower reservoir of the unit into its upper reservoir The stored hydraulic potential energy is then used to generate electric energy during peak load levels The PSH unit is usually worked over daily or weekly periods Operation of a PSH unit over a period can decrease the total fuel cost in a power system Lagrangian multiplier and gradient search techniques Wood and Wollenberg 1984 is used to find the optimum hydrothermal gener ation scheduling with pumped storage hydraulic unit under practical constraints Khandualo et al 2013 have discussed evolutionary pro gramming technique for solving the generation pumping scheduling problem of hydrothermal system with pumped storage plants Ma et al 2015 have discussed the pumped hydro storage system for solar energy infiltration and mainly for small autonomous systems in remote areas Evolutionary algorithms are populace based self adaptive parallel searching techniques Evolutionary programming EP is one of the most reliable evolutionary algorithms based on the human inbred chro mosome operation It creates the global or close to the global optima of an optimization problem by generating many populaces over a number of iterations EP has three phases which are initialization creation of off spring by mutation and competition and selection In fast convergence evolutionary programming FCEP Basu 2017 Gaussian and Cauchy mutations to create offspring and one to one challenge are initiated in evolutionary programming EP to augment the convergence speed and quality of solution However FCEP has some disadvantage The triumphant applica tion of FCEP mostly depends on its scaling factor which is constant all through the whole search procedure So it is tricky to decide appropriate value of scaling factor in FCEP without the fine tuning development In recent years a number of triumphant applications of evolutionary algorithms jointed by chaotic sequences in optimization have been described in Caponetto and Fortuna 2003 It is observed that chaotic sequences utilized in evolutionary algorithms are capable for raising the exploitation ability of the evolutionary algorithm in the searching space and boost the convergence property due to the ergodicity stochastic chattels and irregularity of the chaotic technique In turn to shun the disadvantage of FCEP chaotic fast conver gence evolutionary programming CFCEP rooted in Tent equation for acquiring dynamic scaling factor control method is recommended This paper suggests chaotic fast convergence evolutionary program ming CFCEP for solving multi region dynamic economic dispatch MRDED problem comprising solar wind hydro thermal power sys tem incorporating pumped hydro energy storage multi region eco nomic dispatch MRED problem and economic dispatch ED problem Each area of MRDED problem comprises multi reservoir cascaded hy dro plant with time delay thermal plants with nonsmooth fuel cost functions wind power generating units with wind power uncertainty solar PV plant with solar power uncertainty and pumped hydro energy storage Three area test system for MRDED four area test system for MRED and 140 unit Korean system for ED is exploited here Simulation outcomes have been matched up to those acquired by fast conver gence evolutionary programming FCEP differential evolution DE and particle swarm optimization PSO It has been observed from the comparison that the developed CFCEP gives better solution 2 Problem formulation 2 1 Multi region dynamic economic dispatch The objective of multi region dynamic economic dispatch MRDED problem of solar wind hydro thermal power system incorporating pumped hydro energy storage is devised to minimize the total cost of supplying loads to all areas while fulfilling both equality and inequality constraints 2 1 1 Objective function With the insignificant marginal cost of hydroelectric plant opera tional cost of a solar wind hydro thermal system with pumped hydro energy storage essentially reduces to that of the fuel cost for thermal plants along with the cost of wind power generating units and solar PV plants The total cost can be stated as T 1 M 1 N 1 P N 1 P N 1 P 1 The fuel cost function of th committed thermal generator in area at th time taking into consideration the valve point effect Walters and Sheble 1993 is stated as P P P 2 sin Pmin P 2 The cost of wind power comprises three terms a direct cost an under estimation penalty cost for not using all the available wind power and a reserve cost due to over estimation of wind power when available wind power is less than the scheduled wind power So the wind power cost of th wind power generating unit in area at th time can be calculated as Hetzer et al 2008 P K P P P 3 P KP P P P 4 P K P 0 P 5 P 1 P 1 exp 1 P 6 184 M BasuEngineering Applications of Artificial Intelligence 86 2019 182 196 The wind power characterization is done by utilizing Weibul pdf Here 1 Detail description can be found in Hetzer et al 2008 The cost of solar power Liang and Liao 2007 comprises three terms a direct cost an under estimation penalty cost for not using all the available solar power and a reserve cost due to over estimation of solar power when available solar power is less than the scheduled solar power The solar power characterization is done by utilizing lognormal pdf Tian Pau 2010 So the solar power cost of th solar power plant in area at th time can be calculated as P K P P P P P 7 P P K P P P P P 8 P P is the probability of solar power surplus than the scheduled power and P P is the expectation of solar power than the scheduled power P P K P P P P P 9 P P is the probability of solar power shortage than the scheduled power and P P is the expectation of solar power below the scheduled power 2 1 2 Constraints i Power balance constraints N 1 P N 1 P N 1 P N 1 P P P P T M and T 10 N 1 P N 1 P N 1 P N 1 P P P P T M and T 11 N 1 P N 1 P N 1 P N 1 P P P T M and T 12 where T is the tie line real power transfer from area to area T is positive when power flows from area to area and T is negative when power flows from area to area The hydroelectric generation is a function of water discharge rate and reservoir water head which in turn is a function of storage P 1 2 2 2 3 4 5 6 N M T 13 Wind power model The power output Hetzer et al 2008 of th wind power generat ing unit at time for a given wind speed is expressed as P 0 for P P for P P for 14 Solar power model The power output Liang and Liao 2007 from PV cell is expressed by P P 2 for 0 15 Total transmission loss P can be computed by using B coefficient stated as P N 1 N 1 P B P N 1 B0 P B00 16 Here total number of plants N N N N N and P is the respective thermal hydro wind and solar power generation in area at time ii Pumped storage constraints Here pure pumped storage hydraulic PSH unit is used which re lies entirely on water that has been pumped to an upper reservoir from a lower reservoir When the PSH unit operates in the generating mode and decides to change its situation to pumping mode or vice versa the unit should be off for an hour due to the physical limitation of the PSH unit and this is known as changeover time 1 P M and T 17 1 P M and T 18 1 M and T 19 Pmin P Pmax M and T 20 Pmin P Pmax M and T 21 min max M T 22 Since the initial and final water volume of the upper reservoir of the PSH unit are taken as the same in this problem the total net water amount utilized by the PSH unit must be equal to zero 0 T 23 iii Generation limits Pmin P Pmax N M T 24 Pmin P Pmax N M T 25 Pmin P Pmax N M T 26 iv Thermal generator ramp rate limits constraints The ramp rate limits of each thermal generator should be within its ramp up rate limit a