Evaluation on Intelligent Energy Management System for PHEVs/PEVs Using Monte Carlo Method

Transcription

1 Evaluatio o Itelliget Eergy Maagemet System for PHEVs/PEVs Usig Mote Carlo Method Wecog Su, Studet Member, IEEE Departmet of Electrical ad Computer Egieerig North Carolia State Uiversity Raleigh, NC, USA wsu@csu.edu Mo-Yue Chow, Fellow, IEEE Departmet of Electrical ad Computer Egieerig North Carolia State Uiversity Raleigh, NC, USA Abstract-- The large peetratio of Plug-i Hybrid Electric Vehicles (PHEVs) ad Plug-i Electric Vehicles (PEVs) brigs up may techical problems that eeds to be addressed ad reassured o. There is also a eed for i-depth study o PHEVs i term of Smart Grid eviromet. I this paper, we itroduced the existig testbed of a Large-scale PHEV chargig ifrastructure developed by FREEDM/ATEC ceter to achieve the optimal power allocatio. The we applied Mote Carlo method to simulate the myriad real-world scearios at a muicipal parkig deck. Case studies were performed to aalyze the system performace of itelliget chargig algorithms for a large amout of PHEVs usig Mote Carlo simulatio. Accordigly, the simulatio results characterized the optimizatio performace i terms of the optimal electricity cosumptio ad the PHEV battery Stateof-Charge at plug-out. Idex Terms-- PHEV, Smart Grid, Mote Carlo Method, Itelliget Eergy Maagemet. E I. INTRODUCTION CONOMIC ad evirometal icetives, as well as advaces i techology, are reshapig the traditioal view of power systems. Plug-i Hybrid Electric Vehicles (PHEVs) have received icreasig attetio because of their low pollutio emissios ad high fuel ecoomy. Ultimately, PHEVs will shift eergy demads from crude oil to electricity for the persoal trasportatio sector []. By drawig o ad supplyig power to the power grid, electric vehicles could displace the use of petroleum. This would reduce pollutio ad alleviate security issues related to oil extractio, importatio, ad combustio. Alog with the utilizatio of grid power, PHEVs also have the potetial to trasfer power to the grid to alleviate peak power demad ad provide acillary services to the grid []. The U.S. Departmet of Eergy projects that approximately millio PHEVs will be o the road by 5 ad 45, PHEVs will be sold i 5 aloe. At this peetratio rate, PHEVs would accout for.5% of all ew vehicle sales i 5 [3]. The Electric Power Research Istitute (EPRI) projects that 6% of the etire U.S. vehicle fleet will cosist of PHEVs by 5 usig a moderate peetratio sceario [4]. Accordigly, there is a growig eed to address the implicatios of this techology o the power grid. Large umbers of PHEVs have the potetial to threate the stability of the power system. For example, the aggregated load i a muicipal parkig deck eeds to be maaged very carefully i order to avoid iterruptio whe several thousad PHEVs are itroduced ito the system over a short period of time (e.g., durig the early morig hours whe people arrive at work). Moreover, due to variatios i the eeds of the PHEVs parked i the deck at ay give time, the demad patter will also have a sigificat impact o the electricity market. A theoretical system of PHEVs i a muicipal parkig deck has bee well studied i [5-7]. The iitial algorithms have bee implemeted i Matlab/Simulik ad Labview. Commuicatio betwee the cetral cotroller, PHEV chargers, ad vehicles was achieved usig the ZigBee protocol [6]. A Particle Swarm Optimizatio (PSO) based cotrol algorithm was put forward i [8] to optimally allocate power to PHEVs at a muicipal parkig deck. I [9], a EDA-based optimizatio algorithm was proposed to achieve real-time eergy maagemet at a large-scale PHEV/PEV parkig deck. I [], authors evaluated the large peetratio of PHEVs uder various chargig scearios. I [], authors performed sesitivity aalysis o battery modelig to large-scale chargig algorithms. This paper is orgaized as follows: sectio II will preset the existig Itelliget Eergy Maagemet System (iems) architecture ad each system compoet. Sectio III will briefly itroduce Mote Carlo Method i mathematical term ad show how it could cotribute to evaluatio o the existig iems. There are a large variatio of the arrival ad departmet time of PHEVs ito a PHEV parkig deck. The umber of PHEVs i a parkig deck at a time also has a large variatio with limited amout power supplied from the utilities. I sectio IV, we will simulate real-world parkig deck scearios with radom vehicles arrivals, iitial PHEVs states, time of availability etc. ad aalyze the optimizatio results (e.g. the State-of-Charge at plug-out) usig Mote Carlo method. Sectio V will implemet the Mote Carlo simulatio ad aalyze the results. Sectio VI will summarize the paper ad briefly discuss the future work.

2 II. SYSTEM ARCHETECTURE Based o the existig iems algorithm, our ultimate goal is to optimally allocate the power eergy to PHEVs at a muicipal parkig deck over a large operatig sceario with cosiderig multi-objective optimizatio ad demad side maagemet through local iformatio ad a limited amout of commuicatio. The model aims at reflectig the real world sceario uder a certai itelliget cotrol philosophy. Fig. illustrates the basic architecture of the whole system. The system is composed of the power grid, eergy maagemet system ad the PHEVs/PEVs. Each parkig deck comprises of multiple loads (PHEVs/PEVs) ad is cotrolled by a iems. May distributed iems may be coected to the utility, actig as a iterface betwee the grid ad loads. Figure. Itelliget PHEVs Chargig System Architecture III. OVERVIEW OF MONTE CARLO METHOD Mote Carlo method has revolutioized scietific computig ad bee frequetly employed to solve problems i various fields of egieerig. The moder Mote Carlo algorithms have bee well preseted i George Fishma's books [-3], alog with a buch of egieerig applicatios. Most real world problems are complex ad highly oliear. I additio, it ivolves more tha just a couple ucertai parameters. Whe the determiistic methods are computatioally impossible to imitate real-life problems or make predictios, Mote Carlo method might provide approximate solutios. More specifically, Mote Carlo method is a approach of solvig problems usig radom umbers ad statistics tools. Radom samplig is a essetial compoet of Mote Carlo simulatio. Geerally speakig, the pricipal steps i Mote Carlo simulatio ca be summarized as:. Geerate radom sample data from a domai of impossible iput variables. Covert the sample data to a estimate of the solutio i order to evaluate the system 3. Aalyze the results ad access the error of approximatio We will give a overview of Mote Carlo method i mathematical terms. The expected value of a fuctio g is expressed i both discrete ad cotiue time domai: E ( g ( X ) ) g ( x ) f ( x ) ( ) x A E ( g ( X ) ) g ( x ) f ( x ) ( ) x A Where f ( x ) is the probability desity fuctio of radom values X. The if we draw -sample of X's, ( x,... x ), the the Mote Carlo estimate of E( g( X )) is described as g ( x) g( x ) (3) i i The the weak law of large umbers tells us that for ay arbitrarily small lim P ( g ( x ) E ( g ( X )) ) (4) It meas that as is gettig much larger, there is a smaller probability that g ( x) deviates much from E( g( X )). I other words, a large umber of trials ca guaratee a decet estimatio. The we ca compute the variace by the stadard formulas: Var ( g( X)) Var ( g ( x)) Var( g( xi )) [ g( x) E( g( X))] f ( x) (5) i xa Var ( g( X)) Var g x Var g x g x E g X f x dx ( ( )) ( ( i)) [ ( ) ( ( ))] ( ) (6) i xa However, E(g(X)) i these two equatios above is usually ukow ad the sum or the itegral is ot feasibly computed [4]. Whe we are actually implemetig Mote Carlo method, we eed to approximate the variace to obtai a ubiased estimator for Var(g(x)): ˆ Var( g( x)) ( g( xi ) g ( x)) (7) i If the umber of samples is large eough, Ad the ubiased estimate of the variace of g ( x) is of Var ˆ ( g( x)) Var g x g x g x ˆ ( ( )) ( ( i ) ( )) (8) ( ) i The coefficiet of variatio idicates the accuracy level of Mote Carlo simulatio ad is defied as: Var ˆ ( g ( )) ˆ x Var( g( x)) / g ( x) g ( x) Vˆ a r ( g ( x ) ) [ g ( x ) ] (9) ( ) Thus it tells that a large umber of trials ca reduce the variatio so as to produce a better estimate of the

3 probability. But as the umber of samples keeps goig up, the techical computig is more time-cosumig. I order to make the Mote Carlo simulatio more efficiet, a certai Variace Reductio techiques ca be applied to a geeral/straightforward Mote Carlo method (e.g., Bootstrappig, Importace Samplig). The fudametal descriptios ad discussio of the correspodig advaced techiques ca be foud i [-5]. IV. SIMULATION I order to test the eergy allocatio to PHEVs i realtime with utility costraits ad varyig iputs, we ca apply Mote Carlo simulatio to model pheomea with predictable ucertaity i iputs. This is obviously useful whe the dimesio of iputs icreases. Cosequetly, Mote Carlo method, with its relatively meager requiremets, has cosiderable appeal i iems project. It makes it possible to simulate ad moitor the real-world parkig deck scearios uder certai eergy optimizatios. I iitial work we have developed a simulator to help develop effective distributed cotrol algorithms for the iems for PHEV muicipal parkig deck. Fig. shows the simulator for five charger statio which has bee used for testig ad aalysis of the proposed algorithms. Fig. 3 shows the Matlab/Simulik based large-scale chargig ifrastructure digit testbed. Mote Carlo method ca brig us may beefits if the model we focus o is complex, oliear, or ivolves more tha just a couple ucertai parameters, especially i iems project. To ame a few [-3]:. Mote Carlo method produces a umerical estimate with error of approximatio decreasig as o matter how little kowledge of the system we have. It is especially true as the dimesio m icreases.. The chief advatage of Mote Carlo simulatio, compared to other umerical methods that ca solve the same problem, it is coceptually simple. 3. It allows several iputs to be geerated at the same time to create the probability distributio of several outputs. I curret iems testbed, we geerate 4 iput variables uder differet distributio. 4. Differet types of probability distributios ca be assiged to each iput. Whe the distributio is ukow, the oe that represets the best fit could be chose. 5. The amout of work to achieve the same precisio is idepedet of the dimesio of the radom variables. 6. Mote Carlo simulatio ca fit Matlab Parallel Computig Toolbox very well. May computer processors ca be participatig i a Mote Carlo simulatio simultaeously. Each simulatio is idepedet of aother. Figure 4. 4-D Iput Space Figure. Simulik Based Testbed for 5 PHEV/PEV s Figure 3 Large-scale Chargig Ifrastructure Digital Testbed We first costruct a 4-dimesio space where each directio represets a iput variable, which is show i Fig. 4. So, we try to select a distributio for the iput that most closely matches data we already have, or best represets our curret state of kowledge. Accordigly, differet types of probability distributios ca be assiged to each of 4 iputs of the system. I this case, we assume each iput is idepedet of aother. Markov Chai Mote Carlo is beyod the scope of our work at this stage. Mote Carlo simulatio is categorized as a samplig method because the iputs are radomly geerated from probability distributios to simulate the process of samplig from a actual populatio.

4 Fig. 5 shows that the iems is give four iputs, amely, State-of-Charge at plug-i (SOC_plug-i), Plug-i Time (Time_plug-i), Time of Availability, ad Battery Capacity. Time of Availability: cotiuous uiform radom umber betwee 6 ad 4. U (6, 4).35.3 Percetage of Vehicles Figure 5. Mote Carlo Simulatio i iems SOC_plug-i: cotiuous uiform radom umber betwee. ad.75. U (.,.75) Percetage of Vehicles State of Charge Figure 6. Plot of SOC at Plug-i Time_plug-i: Poisso distributio Pois(8) or Pois (9). k e Pois( k) () k! Where is the expected plug-i time of most vehicles over a period of 4 hours. It is a reasoable assumptio that PHEVs/PEVs are expected to start chargig aroud 9:AM or 8:AM at a muicipal parkig deck. Poisso is useful for modelig cout data with measuremets takig oegative iteger values:,,, There is o obvious upper limit for the possible values. Mea ad stadard deviatio is expressed μ = λ ad σ = Frequecy K Figure 7. Theoretical Probability Desity Fuctio of PHEVs Plug-i time at A Muicipal Parkig Deck Time of Availability (hrs) Figure 8. Distributio of Time of Availability Battery Capacity: cotiuous uiform radom umber betwee 6Ah ad 5Ah. U (6,5) or costat value. There are five chargers i the existig iems model. We first geerate radom 5x vectors for each iput, followig the desired distributio; From each trail, we radomly resample each 5x vector times from the origial dataset usig bootstrappig. Thus fially each charger is give, iput variables. Accordig to Cetral Limit Theorem (CLT) N (,) as () S / CLT guaratees good approximatio to the samplig distributio for ay populatio model, provided that satisfies the ambiguous requiremet of beig large. A geeral rule of thumb is that the CLT applies whe 5. If the populatio is symmetric, 5 is sufficiet. The figure below shows the histogram of Time_plug-i at 5 chargers Figure 9. Plug-i Time at 5 s Cofidece Itervals (CI) provides a mea of assessig ad reportig the precisio of a poit estimate, such as a frequecy of PHEVs plug-i. 95% CI meas that we have 95% probability of coverig the true value or we ca be 95% cofidet that the true expected plug-i time of all

5 PHEVs at a muicipal parkig deck is time T. The followig hypothesis test is set up to evaluate whether the geerated radom iput Time_Plug-i is followig the Poisso distributio with a desired parameter. The level test of H : versus H a : We rejects H if is ot i the ( )% cofidece iterval for. A ( )% cofidece iterval for cosists of all claims for which the size test of H : versus H a : is ot rejected. I this case, let's say H : 8 versus H a : 8. Sice all 5 true values i Table I fall withi the iterval, we fail to reject H : 8. It meas that all the 5 set of iput variables follow the prescribed distributio. Table I Cofidece Iterval of 5 Iput Variables CI_Lower True Value CI_Upper We also could use p-value to do hypothesis test ad obtai the same results. The p-value of a hypothesis test is the largest for which H is ot rejected, based o observed sample data. Computers ca do all the calculatios ad report the p- value, thus elimiatig the eed for tables. Decisio rule for hypothesis testig usig p-value: - Reject H if the p-value α - Fail to reject H if the p-value > α V. RESULTS ANALYSIS Boxplot i Fig. graphically depicts the SOC at plugout through five-umber summaries: sample miimum, lower quartile, media, upper quartile, ad the sample maximum. It is a quick way of examiig SOC at plug-out amog PHEV chargers. The 5 sets of data look very similar. Thus we oly eed to look ito oe of them istead of all the five chargers i order to aalyze the simulatio results. Pricipal compoets aalysis ivolves a mathematical procedure that trasforms a umber of possibly correlated variables ito a smaller umber of ucorrelated variables called pricipal compoets. We assume x is a vector of SOC at plug-i; x is a vector of Time_Availability; x3 is a vector of plug-i time; x4 is a vector of plug-out time. X X X3 X4 Coefficiets with Error Bars Coeff. t-stat p-val e e Figure. Coefficiets Aalysis o SOC at Plug-out Now Fig. idicates that PHEV SOC at plug-out at a muicipal parkig deck maily depeds o x ad x rather tha x3 ad x4. Also we try to fid a simple liear mappig betwee some of iput variables ad the output of our iterest. y = x +.858x The particular relevace of a R value must be iterpreted i a subject-matter cotext. For example, R values above.9 are ofte eeded i egieerig applicatios, while i some sociology experimets a R value as large as.3 would be impressive. But i this case, R is about.6. Thus this mappig ca somehow represet the system behavior. Percetage of Vehicles State of Charge Figure. Distributio of SOC at Plug-out Figure. Boxplot of the SOC at Plug-out Table II State-of-Charge at Plug-out SOC % Number of vehicles

6 I optiaml allocatio for SOC Maximizatio algorithm results, most PHEV leave a parkig deck with SOC 55% - 75%. Desity OutSOC data fit Figure 3. Actual ad Fitted Distributio of SOC at Plug-out The let's look ito the distributio of actual SOC_plugout alog with the fitted oe i Fig. 3. The actual SOC_plug-out ca fit the ormal distributio very well. I reality, it is a rule that provides the umber of bis i the histogram, ad is give by the followig formula. K log Here k is the umber of bis ad is the umber of sample data. Fig. 4 displays a cumulative probability plot of the data. Idepedet Mote Carlo Method geerates the output as a rage istead of a fixed value ad shows how likely the output value is to occur i the rage (95% Cofidece Iterval here). Cumulative probability OutSOC data fit Data Figure 4. Cumulative Probability Distributio of SOC at Plug-out VI. CONCLUSION AND FUTURE WORK I order to achieve the optimal eergy allocatio to PHEVs/PEVs with utility costraits ad varyig iputs, we have applied Mote Carlo simulatio to model real-world parkig deck scearios. It makes it possible to simulate ad moitor the real-world parkig deck scearios uder a certai eergy usage optimizatios. At this stage, we are assumig all the iput variables are idepedet based o the curret state of kowledge. Selectig a distributio for each idepedet variable is quite simple ad straightforward. As iput dimesios icrease ad iems ivolves i more ucertai variables, idepedet Mote Carlo method might ot be suitable. VII. ACKNOWLEDGEMENT This work was supported i part by the Natioal Sciece Foudatio, Award umber: EEC-8 ad this project is i collaboratio of the FREEDM (Future Reewable Electric Eergy Delivery ad Maagemet) systems ceter with ADAC (Advaced Diagosis Automatio ad Cotrol) Lab ad ATEC (Advaced Trasportatio Eergy Ceter). VIII. REFERENCES [] K. Parks, P. Deholm, ad T. Markel, Cost ad Emissios Associated with Plug-i Hybrid Vehicle Chargig i the Xcel Eergy Colorado Service Territory, Techical Report, Natioal Reewable Eergy Laboratory (NREL), May 7 [] W. Kempto ad J. Tomic, Vehicle-to-Grid Power Implemetatio: From Stabilizig the Grid to Supportig Large Scale Reewable Eergy, Joural of Power Resources, vol. 44, 5 [3] K. Sikes, T. Gross, Z. Li, J. Sulliva, T. Cleary, ad J. Ward, Plugi Hybrid Electric Vehicle Market Itroductio Study: Fial Report, ORNL/TM-9/9, U.S. Departmet of Eergy, [4] M. Duvall ad E. Kippig, Evirometal Assessmet of Plug-I Hybrid Electric Vehicles, EPRI, July 7. [Olie]. Available: olio/pdm/phev-execsum-vol.pdf [5] P. Kulshrestha, L. Wag, M.-Y. Chow, ad S. Lukic, "Itelliget Eergy Maagemet System Simulator for PHEVs at Muicipal Parkig Deck i a Smart Grid Eviromet," i Proc. 9 IEEE Power ad Eergy Society Geeral Meetig, Calgary, Caada, 9. [6] P. Kulshrestha, K. Swamiatha, M.-Y. Chow, ad S. Lukic, "Evaluatio of ZigBee Commuicatio Platform for Cotrollig the Chargig of PHEVs at a Muicipal Parkig Deck," i Proc. IEEE Vehicle Power ad Propulsio Coferece, Dearbor, Michiga, U.S.A, Sept 7-, 9 [7] W. Su, ad M.-Y. Chow, A Itelliget Eergy Maagemet System for PHEVs Cosiderig Demad Respose, i Proc. FREEDM Aual Coferece, Tallahassee, Florida, U.S.A. May [8] W. Su, ad M.-Y. Chow, Performace Evaluatio of A PHEV Parkig Statio Usig Particle Swarm Optimizatio, i Proc. IEEE Power ad Eergy Society Geeral Meetig, Detroit, Michiga, U.S.A. July 4-9, [9] W. Su, ad M.-Y. Chow, Performace Evaluatio of A EDA-based Large-scale Plug-i Hybrid Electric Vehicle Chargig Algorithm, IEEE Tras. Smart Grid, Special Issue o Trasportatio Electrificatio ad Vehicle-to-Grid Applicatio, [] W. Su, ad M.-Y. Chow, Ivestigatig a Large-scale PHEV/PEV Parkig Deck i a Smart Grid Eviromet, Proc. 43rd North America Power Symposium, Bosto, MA, August 4-6,. [] W. Su, ad M.-Y. Chow, Sesitivity Aalysis o Battery Modelig to Large-scale Chargig Algorithms, i Proc. 37th Aual Coferece of theieee Idustrial Electroics Society, Melboure, Australia, November 7-, [] George S. Fishma, A first course i Mote Carlo, Duxbury Press; editio (October 5, 5) [3] George S. Fishma, Mote Carlo: cocepts, algorithms, ad applicatios, New York: Spriger [4] Mote Carlo Methods ad Importace Samplig", Lecture Notes for Stat 578C, Statistical Geetics, Eric C. Aderso, UC Berkeley, Oct 999 [5] Malvi H. Kalos, Mote Carlo methods, Joh Wiley & Sos, Ic.; st editio (October 5, 986)