Multiagent Genetic Algorithm: An Online Probabilistic View on Economic Dispatch of Energy Hubs Constrained by Wind Availability

Multiagent Genetic Algorithm: An Online Probabilistic View on Economic Dispatch of Energy Hubs Constrained by Wind Availability
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  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 1 Multiagent Genetic Algorithm: An OnlineProbabilistic View on Economic Dispatch of EnergyHubs Constrained by Wind Availability Moein Moeini-Aghtaie  , Student Member, IEEE  , Payman Dehghanian  , Student Member, IEEE  ,Mahmud Fotuhi-Firuzabad  , Senior Member, IEEE  , and Ali Abbaspour   Abstract—  Multiple energy carriers (MECs) have been broadlyengrossing power system planners and operators toward amodernstandpoint in power system studies. Energy hub, though playingan undeniable role as the intermediate in implementing theMECs, still needs to be put under examination in both modelingand operating concerns. Since wind power continues to be oneof the fastest-growing energy resources worldwide, its intrinsicchallenges should be also treated as an element of crucial role inthe vision of future energy networks. In response, this paper aimsto concentrate on the online economic dispatch (ED) of MECsfor which it provides a probabilistic ED optimization model. Thepresented model is treated via a robust optimization technique,i.e., multiagent genetic algorithm (MAGA), whose outstandingfeature is to  Þ nd well the global optima of the ED problem. EDonce constrained by wind power availability, in the cases of windpower as one of the input energy carriers of the hub, faces aninevitable uncertainty that is also probabilistically overcome in theproposed model. Ef  Þ ciently approached via MAGA, the presentedscheme is applied to test systems equipped with energy hubs andas expected, introduces its applicability and robustness in the EDproblems.  Index Terms—  Economic dispatch (ED), energy hub, multiagentgenetic algorithm (MAGA), multiple energy carriers (MECs),probabilistic modeling, wind power. I. I  NTRODUCTION  A. Motivation and Problem Description E  NERGY ef  Þ ciency has been so far interestedly triggeredaround the world and approached through various multi-energy carrier (MEC) frameworks [1], [2]. In providing a power system with a considerable pro Þ ciency when dealing with en-ergy resources, MEC, unlike a single energy carrier, focuses onnot only electricity energy, but also natural gas, district heating,and so on. Composed of various carriers, MECs would be ableto be stored and converted via an integrated system, referred toas an  energy hub  [2]. Manuscript received April 30, 2012; revised December 21, 2012; acceptedJune 22, 2013.The authors are with the Center of Excellence in Power System Manage-ment and Control, Department of Electrical Engineering, Sharif University of Technology, Tehran 11365-11155, Iran (e-mail:;;; versions of one or more of the  Þ gures in this paper are available onlineat Object Identi Þ er 10.1109/TSTE.2013.2271517 An energy hub aims at feeding the loads via hybrid inputand output energy carriers. The inputs, as illustrated in Fig. 1,can be electricity, natural gas, and district heat, while the outputwould be both electricity and heat loads. Various forms of en-ergy at the energy hub’s input port gives the decision maker more  ß exibility in satisfying the energy loads at different times.Hence,anenergyhubprovidesthepossibilityofbene Þ tingfroma number of prospective advantages over conventional decou- pled energy supply, e.g., more  ß exibility in load supplying or  peak shaving in prices [3]. Within the energy hubs, some de-vices such as transformers, power-electronic devices, combinedheat and power technologies (CHP), heat exchangers, and other equipment, which are so-called  convertors , converts and con-trols the  ß ow of energy.Today’s trend in employing the current supportive mecha-nisms applied in different countries, such as renewable port-folio standard (RPS), has lead to the rapid progress of renew-able energies in power system generation [4]. As a result, windenergy, as a promising renewable source of power generation,can be regarded as a main input energy carrier in the hub struc-ture. Although wind energy, as an environmentally friendly andcost-predictablerenewableenergy,can untanglesomeof theex- periencedchallengesassociatedwithenergyproblem,itsuniquecharacteristics, i.e., intermittency and uncontrollability of its production, will force the hub’s operator in utilizing other en-ergy carriers. This will compensate the imposed uncertaintiesof wind turbines’ production.The customers’ willingness to pay the possible minimumcosts for energy is another crucial factor in the operation studiesof the MEC systems and mainly contributes to their economicsuccess. In response, it calls for a suitable economic model of energy hubs. Due to the fact that various inputs or a combina-tion of them are incorporated in an energy hub, the questionconcerning how to manage their economic dispatch (ED) would be brought up [5]. Subject to various operational/economicconstraints, online ED let the committed input carriers econom-ically participate in  Þ nding the optimal point where variouskinds of hub’s loads would be ef  Þ ciently met.  B. Literature Review Studies on the MEC and energy hub concept, modeling, andoptimization have recently seen a growing trend. This not onlyincludesthetechnical concerns,e.g.,power  ß ow,reliability,andso on, but also encompasses the economic analysis. In [5], theoptimalpower  ß owofMECsispursuedandageneraloptimality 1949-3029/$31.00 © 2013 IEEE  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 2 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY Fig. 1. MEC system structure. condition for their dispatch is derived. Reference [6] conducteda Monte Carlo valuation approach to study the  ß exibility of thehubs output to the uncertain and volatile market prices. A long-term, multiarea, and multistage model for the supply expansion planning of hubs is presented in [7], where the authors offer a mixed integer linear optimization problem to minimize theassociated investment and operation costs.The issue of ED in power systems has been also the sub- ject of keen considerations in the past papers, through whichsomeheuristicapproachesareintroduced.Animprovedparticleswarm optimization model is proposed in [8] for nonconvex ED problems. Reference [9] proposes a practical approach basedon quadratic programming which is able to solve the real-timeED problem. Several other techniques also have been used todealwiththeEDproblem;amongst,linearprogrammingin[10],weighted sum based methods in [11], and -constrained methodin [12] can be itemized. However, some methods consider oneobjective at a time, some fail to get any information regardingthe tradeoff front, some require a large number of runs to gen-erate the desired Pareto set, and most of them could not guar-antee the global optima of the ED problem.When it comes to modeling the ED problem in MECs andenergy hubs, a main problem arises in  Þ nding the global optimaof the optimization model at a low computational burden. Onthe other hand, the unavoidable uncertainties imposed by therenewable integrations have to be thoroughly addressed [13] inthe decision making under study. C. Paper Contribution To the best of authors’ knowledge, none of the past re-searchers have investigated the effects of two upcoming andunavoidable energy policies, i.e., energy hubs and renewableenergies, on the operation studies of energy networks. Mo-tivated by the aforementioned facts, this paper endeavors tooutline an optimization and modeling framework for MECs’online economic dispatch. Exploiting the innovative concept of energy hubs, the interaction between different energy carriers,especially in the presence of renewable energies, is pinpointed.In doing so, a decomposed ED of MECs is proposed to simul-taneously solve the bilevel optimization both within a hub andthe whole energy system. This model also aims to overcomethe imposed computational labor of the at hand large-scaleoptimization problem. Multiagent genetic algorithm (MAGA)is considered as a promising approach when dealing with such aglobal numerical optimization problem, i.e., ED in the cases of energy hubs. The MAGA is chosen since it proves its ef  Þ ciencyin reaching the high-quality solutions at a low computational burden [14].  D. Paper Organization The rest of the paper is organized as follows. Section II isdevoted to the MEC systems where the energy hubs and windturbine production models are addressed. Economic dispatch of MECs is conducted in Section III, where the formulations areoffered and the optimization framework is constructed. MAGAis introduced as the robust optimization toolbox in this sectionand its instructions in dealing with the problem are presented.SectionIVdealswiththenumericalanalysiswheretheproposedframework is implemented on the test systems. In doing so, anillustrative example is  Þ rst outlined. The proposed scheme isalso simulated through an 11-hub case study to investigate var-ious aspects of the decomposed ED model. And Þ nally, the con-clusion is summarized in Section V.II. M ODELING  P ROCEDURE OF  MEC S YSTEMS In this paper, an MEC system is considered as a system com- posingofinterconnectedenergyhubswhoseconceptdetermines prosperity of the future energy networks. As a result, the proper modeling of these energy hubs as well as utilizing the accuratemodels of energy carrier systems would be of great importanceintheoperationstudiesofMECs.Thissectionprovidesthemain principles associated with the modeling outlines of energy hubsas well as wind turbine production characteristics.  A. Energy Hub Modeling Outlines As noted earlier, an energy hub represents an interface between power producers, consumers, and the transportationinfrastructure [5]. Some real facilities which can be modeledthrough the energy hub concept are, for example, big buildingcomplexes (airports, hospitals, and shopping malls), rural and  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. MOEINI-AGHTAIE  et al. : MAGA: ONLINE PROBABILISTIC VIEW ON ED OF ENERGY HUBS CONSTRAINED BY WIND AVAILABILITY 3 Fig. 2. Proposed energy hub structure. urban domains, industrial plants (steel works, paper mills), andsmall isolated systems (trains, ships, aircrafts). The convertorsof an energy hub establish a redundant connection between theinput and output ports. For instance, the electricity load can bemet by the power received directly from the grid or providingall or part of the load by consuming the natural gas in CHP (seeFig. 2). This redundancy in supply means more  ß exibility inmeeting different energy loads.Fig. 2 illustrates the structure of an energy hub which is the basis of the MEC systems in this paper. The input energy car-riers of this energy hub are considered as wind-srcinated elec-trical energy, network-received electrical energy , and thegas .The input carriers mapping to the outputs, established by anenergy hub, can be mathematically modeled through the cou- pling matrix . The entry of this matrix, , which is knownas  coupling factor  , relates the th input to the th output. Equa-tion (1) represents the mathematical description of an energyhub [2](1.a)(1.b)where and , respectively, denote the th load at the huboutput port and th energy carrier at its input port. and are,respectively, representatives of the sets associated with inputcarriers and output loads.The coupling factor for a single-input–single-output relationstands for the converter ef  Þ ciency. When an input carrier of the energy hub splits up to more than one converter, the cou- pling factors are no longer equal to the converter ef  Þ ciencies.So, other coupling factors, namely  dispatch factors , have to beintroduced.Thesefactorsidentifyhowpower  ß owfromaninputcarrier is distributed between the hub’s convertors. Taking intoaccount these conjunctive factors in the MEC models, the en-ergy hub input–output relation can be de Þ ned as(2.a)(2.b)(2.c)where and , respectively, represent the input carrier vector ofthehubandvectoroftheenergycarriersreceivedtoinputportof the hub converters; and are the ef  Þ ciency and dispatchfactor matrices of an energy hub. For the sake of simplicity, theconverter ef  Þ ciencies are assumed to be constant which also re-sults in a constant ef  Þ ciency matrix . In this paper, the dis- patch matrix is the point where the proposed multicarrier ED method can justify its novelty and necessity in the oper-ating studies of MEC systems. This key point is introduced asthe basis of the proposed method and will be discussed more inSection III.The other consideration demanding issue deals with the un-certain behavior of wind energy,as an input carrier,and calls for employingaprobabilisticframeworkinMECsystemstudies.Inresponse, the proposed ED model of MECs and energy hubs isso organized to clearly demonstrate the hubs’ ability in dealingwith the imposed uncertainties.  B. Wind Turbine Modeling Outlines In order to be able to consider the stochastic output of windturbines,anef  Þ cientcharacterizationapproachisrequired.Withsuitably modeling the wind speed variations, one can simulatethe real model of wind turbines’ power production. Hence, the Þ rst step in wind power characterization is to model the windspeed.Among the several introduced methods in prior works [15],[16], employing the probability distribution functions (pdfs) iscommonly adopted to represent the wind speed variations in powersystemstudies[17] – [19].Ithasbeenshownthatthewind speed pro Þ le at a speci Þ ed site closely follows the Weibull dis-tribution over time [17]. The Weibull pdf of wind speed is given by(3)  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 4 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY where istheshapefactor; denotesthescalefactor; and rep-resents the random variable related to the wind speed. Parame-ters of this pdf (scale and shape factors) can be estimated usingthe wind speed historical data. These parameters are here pre-dicted utilizing the Weibull  Þ t function in the MATLAB envi-ronment. The wind speed Weibull cumulative distribution func-tion (cdf), which will be used in wind power probability func-tion characterization, is given by(4)Once these parameters are calculated, the th order momentof wind speed can be computed as follows:(5)Also, the average and standard deviation of the Weibull func-tion can be estimated using (6.a) and (6.b)(6.a)(6.b)where the  gamma function  is given by(7)The output power of a wind turbine is a nonlinear functionof wind speed. This relation relies on several factors, such astype of turbine, turbine rotor, gearbox, etc. In the past works,the researchers have utilized a simpli Þ ed linear formulation, asshown in the following, to characterize this relation in power system studies [17] – [19]: (8)where and are, respectively, representatives of the windturbine produced power and turbine rated power; is the windspeed; and , , and are the cut-in speed, cut-out speed,and the rated speed of wind turbine, respectively.The above model will be adopted in the proposed multicar-rier ED in this paper. According to (8), the power output of awind turbine is a mixed random variable, which is continuous between zero and rated power, and becomes a discrete variableat values of zero and rated power.The concept of probability theory associated with the randomvariables can ef  Þ ciently help in the transformation process of wind speed pdf to wind power pdf. This process can be accom- plished in the following manner; in the continuous interval of wind power variable, i.e., , the pdf of is asfollows [17]:(9)In order to present the transformation a bit less burdensome,two virtual ratios ( and ) are de Þ ned as follows.(10.a)(10.b)With regards to the wind speed-power transformation proce-dure and the wind speed pdf introduced in (3), the discrete partsof wind power function get the following values [17]:(11.a)(11.b)Havingobtainedthewindpowerpdf,generalattributesofthisstochastic variable (its average and its standard deviation) can be easily derived. These two basic and imperative indices aregiven as follows:(12.a)(12.b)(12.c)The interested readers are referred to [19] for more details andinformation.III. E CONOMIC  D ISPATCH OF  MEC S YSTEMS Intheoperationstageofanenergyhubandbasedonthehub’sstructure, some challenges have to be addressed [5].1) How much of which energy carriers should be applied?2) Howshouldtheinputenergiesbedispatchedandconvertedin the hub?3) How should power   ß ow between the hubs be controlled?4) How should other energy producers be dispatched in re-sponse to the wind energy  ß uctuations?Insuchcircumstances,theMECoperationstudiescanbecon-ducted in two separate parts: economic dispatch within and be-tween the hubs. These two optimization steps can lend the deci-sion maker a hand in operating the energy systems at the mostoptimalcondition.Thissectionprovidesadetailedinvestigationof the proposed ED model on the MECs. The general structureof the proposed method and its formulation are  Þ rst introduced.  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. MOEINI-AGHTAIE  et al. : MAGA: ONLINE PROBABILISTIC VIEW ON ED OF ENERGY HUBS CONSTRAINED BY WIND AVAILABILITY 5 The heuristic optimization approach, employed in this paper, isthen discussed in detail.  A. General Structure of the Multicarrier Economic Dispatch To formulate the proposed ED model of energy hubs, the ob- jective function has to be comprised of the electrical and gascosts to be minimized. Different forms of energy loads in eachhour within the study period should be met as an equality con-straint in the optimization process. The lower and upper boundsof the hub’s input carriers, inputs of hub’s converters, as well asthe dispatch matrices are incorporated in the proposed model asthe inevitable constraints. They are presented in the following:(13.a)(13.b)(13.c)(13.d)(13.e)where the following nomenclature is applied:Generation cost of the th unit.Generation cost of gas energy.Electrical load at hour .Heat load at hour .The wind-srcinated electrical power at hour . Number of generating units.Time period of studies.Theimposed costassociatedwitheachinputenergy carrierof the hubs is modeled as a quadratic function of its corresponding power  [5](14)where and are the cost coef  Þ cients; is the produced power; and are,respectively,representativesofelectricalandgas input carriers.The main goal pursued on the proposed optimization modelis, therefore, to determine the optimal operation of each energyhub in order to meet the various loads available. The inherentcomputation burden imposed to solve such a numerical opti-mization will be aggravated once dealing with large-scale en-ergy systems. This will adversely affect the practicality of themethods employed in the past works [5]. In response, the pro- posed method within the scope of this paper aims to simultane-ously provide the possibility of energy hubs internal optimiza-tionaswellasdecomposingtheoptimizationprocedureforeach Fig. 3. Proposed procedure pursued in ED of the MEC systems. carrier network. Fig. 3 fully depicts the decomposed method-ology proposed in this paper.This bilevel ED model proposes how to coordinate the dis- patchofeachenergyhubandtheef  Þ cientoperationofthewholeenergy system. Composing from two main blocks, it, in the  Þ rst block, employs a well-organized heuristic method in order to prespecify the dispatch factor of each hub. As shown in Fig. 2,this variable determines how the received gas energy would bedispatched between furnace and CHP unit. As long as the CHPunit supplies a portion of the energy hub electrical load, thedispatch factor couples the power and gas networks. As aconsequence, in operation studies of MEC systems, the oper-ator needs to simultaneously model power system together withthe gas networks. This method of MEC modeling results in alarge-scale optimization problem which is computationally in-ef  Þ cient. In response, setting the dispatch factors by MAGA de-couples the model of energy networks and then more ef  Þ cientlythe optimization process can obtain the optimal operating pointof each network.The second block is comprised of two stages. In Stage 1, theoptimal dispatch of the hub would be reached by setting the dis- patchfactorsofeachhubviaMAGA,outliningtheonlinemodelof wind turbine production, and then identifying the predictedamount of energy loads. Consequently, the electrical and gasloads of MECs in each bus would be set.The second stage deals with the ED of each energy carrier separately and endeavors toward  Þ nding the optimum genera-tion amount of the committed units as well as the total cost of energies as economically as possible.Investigating different possible dispatch factors on the inputcarriers,producedbyMAGA,theeconomicconditionofenergycarriers together with the optimal dispatch of each energy hubwould be found. The lower computational burden and higher  probability of reaching the global optima are among the superi-orities of the proposed model.In the following, the formulation associated with the second block of the proposed method is presented.
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