An Interval-Stochastic Programming Model for Distributed Photovoltaic Power Management under Uncertainty

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1 2016 7th nternatonal Conference on Bology, Envronment and Chemstry Volume 98 of PCBEE (2016) DO: /PCBEE V98. 4 An nterval-stochastc Programmng Model for Dstrbuted Photovoltac Power Management under Uncertanty Ronghua Xu 1 and Yanpeng Ca 1, 2, 3 1 State ey Laboratory of Water Envronment Smulaton, School of Envronment, Bejng Normal Unversty, Bejng, Chna 2 Bejng Engneerng Research Center for Watershed Envronmental Restoraton and ntegrated Ecologcal Regulaton, School of Envronment, Bejng Normal Unversty, Bejng, Chna 3 ey Laboratory of Wetland Ecology and Vegetaton Restoraton, Northeast Normal Unversty, Changchun, Chna Abstract. n ths study, an nterval-stochastc programmng model was formed for dentfyng optmal dstrbuted photovoltac development plannng wth lmted subsdes under uncertantes. The model was formulated through ncorporatng nterval and stochastc nto a general optmzaton framewor. t can deal wth uncertantes expressed as both probablty dstrbutons and ntervals. A soluton method was proposed to solve ths problem. The proposed model was then appled to a hypothetcal case of plannng future capacty of dstrbuted photovoltac power generaton n three regons of Chna where solar energy resources and proporton of electrcty consumpton were full of uncertantes. nterval solutons wth dfferent electrcty generaton patterns were obtaned. The results could be used for generatng decson alternatves for helpng decson-maers to dentfy optmal capacty allocaton scheme under lmted subsdes, avalable rooftop and grd access constrants. eywords: dstrbuted photovoltac power, subsdy, electrcty, uncertanty; plannng. 1. ntroducton Wth the growth of economy and enhancement of human actvtes, energy s playng an ncreasngly sgnfcant role n our world [1]. Tradtonal fossl energy resources le coal, petroleum and natural gas accounted for a very large proporton of the total energy use n many countres, especally for developng countres [2], [3]. Meanwhle, due to ncreasng populaton and rapd expanson of ndustry, the ncreasng energy consumpton result n much serous energy depleton and envronmental polluton [4], [5]. Consequently, t becomes more and more crucal to utlze renewable energy resources (.e. solar power, wnd power and geothermal energy) whch are benefcal to envronment and sustanable development [6]. n addton, applcaton and development of renewable energy for electrc power have also aroused ncreasngly concerns all around the world [7], [8]. As an mportant part of clean energy to cope wth the challenge of fossl fuel depleton, solar power has been developed rapdly. Dstrbuted photovoltac power generaton s defned as n partcularly constructed n the vcnty of the user ste, whch ntroducng user self-suffcency and surplus electrcty connected to the grd. t s a photovoltac power generaton facltes whch can balance the electrcty dstrbuton system. Dstrbuted photovoltac power generaton has some advantages: a) t has enormous envronmental protecton beneft wth scarcely polluton (.e. wthout nose, ar polluton or water polluton), b) t can allevate the stuaton of electrcty shortages n the local system to some degree, and c) electrcty generaton and electrcty consumpton wll be present n one system. n addton, dstrbuted photovoltac systems whch connected to Correspondng author. Tel.: +86(10) ; fax: +86(10) E-mal address: yanpeng.ca@bnu.edu.cn. 21

2 the grd can be nstalled to furnsh energy to a specfc consumer or drectly to the grd, ncreasng relablty of the systems [9]. Photovoltac power generaton technology was orgnated from Europe. Photovoltac power generaton technology can mae fully use of local solar power resource wth less conventonal energy sources consumpton. For a long tme, Europe sat at the heart of the global photovoltac maret where Germany, taly and Span manly accounted for a large proporton n the past. n recent years, wth rapd ncreasng photovoltac modules of Chna, Japan, the Unted States and other countres, the core areas of the global photovoltac maret gradually transfer from Europe to the outwards. Utlzaton of renewable energy resources s essental for many countres across the world partcularly for developng countres [10], [11]. n recent years, solar power whch s an mportant clean energy has been developed n electrc generaton. Recently, dstrbuted photovoltac power has been gradually developed n Chna. However, Photovoltac ndustry n Chna has suffered from many dffcultes durng development as t s stll n ts nfancy. Largescale producton and applcaton of photovoltac ndustry s from At the same tme, due to the hgh photovoltac power generaton effcency, energy conservaton and government powerful support, the capacty of photovoltac power ncrease rapdly lately. From 2012 to 2015, the correspondngly compound annual growth rate s 88.00% (Fg. 1). Cumulatve nstalled capacty(gw) capacty of photovoltac power staton capacty of dstrbutedphotovoltac power staton total capacty Fg. 1: Cumulatve nstalled capacty of photovoltac power n Chna (source: NEA [12]) n Amerca, the polcy of tax prvlege ncentves and Renewable Portfolo Standard (RPS) was ntroduced, and the government's fnancal subsdy s a crucal factor for the development of photovoltac power. n Germany, the polcy of feed-n tarffs whch could subsdze photovoltac power generaton was mplemented [9]. Smlarly, n Chna, the government has been subsdzng dstrbuted photovoltac generaton at 0.42 RMB per lowatt hour. n Chna, decson-maers are facng dffcultes of allocatng dstrbuted photovoltac staton quota wth lmted subsdes under multple uncertantes. Therefore, the objectve of ths research ams to form an nterval-stochastc programmng model for dstrbuted photovoltac power generaton plannng, through ntegratng the nterval programmng and stochastc programmng nto the general nterval lnear programmng (LP) framewor, taclng the multple uncertantes and complextes expressed as nterval numbers and dstrbuton nformaton. n addton, varous levels of electrcty demand, self-consumed electrcty rato as well as solar power resources can be ncorporated nto the developed model. A case study wll be provded for demonstratng applcablty of the developed model. n detal, ths study wll (a) formulate an nexact nterval-stochastc model whch can reflect uncertantes expressed as ntervals and probablty dstrbutons, (b) apply the model to support for plannng dstrbuted photovoltac power generaton, and (c) analyse the generated results and dscuss the applcablty of the developed model. 2. Methodology 22

3 2.1. Model Development n dstrbuted photovoltac power plannng, a manager wll face problems as programmng the electrc power generaton to generate the maxmum benefts. Such a problem can be formulated as maxmzng the economc benefts under lmted fnancal allowances. n ths process, multple uncertantes may exst, such as solar power resources, self-consumed electrcty rato and avalable rooftop area. The objectve s to acheve optmal plannng of dstrbuted photovoltac power generaton wth a maxmzed system benefts. The amount of electrcty generaton n the regon s uncertan (expressed as random varable), whle a plan for the allowable electrcty generaton levels must be made before the realzaton of the random varable. Therefore, the problem under consderaton can be formulated as an nterval stochastc programmng model. The model s based on the assumpton that a) ntal nvestment are the same, b) generated electrc power wll be fully used, c) hgh qualty rooftop wll be consdered frstly, and d) all the system effcency of dstrbuted PV power wll be a constant. Thus the model can be formulated as follows: Max f = L W H ( S A ) E[ M ] L W H ( N A )( E[1 M ]) subject to: L W R fnancal subsdes constrants, capacty constrants, demand constrants, L W H BC 1 1 (1a) W H T,, (1b) W D /100,, (1c) 1 1 W D / 30,, (1d) 1 1 W D /100,, (1e) W D / 30,, (1f) 1 1 W J,, (1g) Where f = economc beneft of all regons (RMB); = the name of regon; = the tme perod; W = capacty of regon n perod (MW); H = annual utlzaton hours of solar power (hour); α = effcency of system; S = electrcty prce(rmb); A = allowance of electrcty prce(rmb); M = self-consumed electrcty rato; N = Pool purchase prce; E [ ] = the expected value of a random varable; R = runnng costs (RMB/MW); B = 0.997g CO 2 / wh; C = carbon prce(rmb/g); T = total subsdes of electrcty power(wh); = avalable roof area(m 2 ); D =nstalled capacty on roof (MW) J = accessble capacty of power grd(mw); = the length of tme perod (year); Let each self-consumed electrcty rato tae a value M h wth the probablty p h (for h = 1, 2,, H), where h s denoted as the level of electrcty demand. Thus, we have: H E M = p M,,, h (2) h h h1 H E 1 M = p (1 M ),,, h (3) h h h1 2 D 100(W/m )* / (W/MW) (4) 23

4 subject to: H H Max f = LW H ( S A ) P M LW H ( N A ) P (1 M ) h h h h 1 1 h1 1 1 h1 L W R L W H BC (5a) W H T,, (5b) W / ,, (5c) 1 1 W / ,, (5d) 1 1 W / ,, (5e) W / ,, (5f) W J,, (5g) 1 1 nterval lnear programmng (LP) allows uncertantes to be drectly communcated nto the optmzaton process and resultng solutons, and t can reflect ndependent uncertantes n objectve coeffcents. Therefore, the model can be reformulated as follows: H H L h h L h h 1 1 h1 1 1 h1 Max f = W H ( S A ) P M W H ( N A ) P (1 M ) subject to: LW R LW H BC (6a) W H T,, (6b) W / ,, (6c) 1 1 W / ,, (6d) 1 1 W / ,, (6e) W / ,, (6f) 1 1 W J,, (6g) WhereW, H and are nterval parameters and varables; the superscrpts - and + represent lower and upper bounds Method of Soluton Accordng to Huang (1998), the submodel correspondng to the upper bound ( f ) should be frstly solved when the objectve functon s to maxmze f [13], and can be formulated as follows: H H L h h L h h 1 1 h1 1 1 h1 Max f = W H ( S A ) P M W H ( N A ) P (1 M ) LW R LW H BC (7a) 24

5 subject to: W H T,, (7b) 1 1 W / ,, (7c) 1 1 W / ,, (7d) 1 1 W / ,, (7e) W / ,, (7f) 1 1 W J,, (7g) Correspondngly, the lower bound objectve ( f ) can be presented as follows: H H L h h L h h 1 1 h1 1 1 h1 Max f = W H ( S A ) P M W H ( N A ) P (1 M ) subject to: LW R LW H BC (8a) W H T,, (8b) W / ,, (8c) 1 1 W / ,, (8d) 1 1 W / ,, (8e) W / ,, (8f) W J,, (8g) Case Study Table : Self-consumed electrcty rato under dfferent probabltes Level of electrcty demand Probablty Self-consumed electrcty rato =1 =2 =3 h = 1 (L = low) 0.2 [0.5,0.6] [0.6,0.7] [0.7,0.8] h = 2 (M = medum) 0.6 [0.6,0.7] [0.7,0.8] [0.8,0.9] h = 3 (H = hgh) 0.2 [0.7,0.8] [0.8,0.9] [0.9,1.0] Table : The electrcty prce under dfferent perod Regons The electrcty prce (RMB) =1 =2 =3 A B C Consder a hypothetcal case wheren a manager s n charge of plannng dstrbuted photovoltac power capacty over 3 years (wth three 1-year perods) n Chna. There are three regons whch wll be developed 25

6 dstrbuted photovoltac power generaton to satsfy electrcty demand, ncludng regon A, regon B, and regon C. The three regons would be gven 500 mllon fnancal subsdes from the government. Each regon has dfferent self-consumed electrcty rato n dfferent perods. n ths case, three levels are consdered whch are low, medum, and hgh [14], [15]. Each regon accepts dfferent level of lght from sunshne every day. Therefore, the annual utlzaton length of solar power n three regons are dfferent (.e. [1489, 1661], [1460, 1591], [1270, 1391] hours). Carbon prce would be 20 RMB/g and power subsdes would be 0.42 RMB/wh accordng to the natonal standards n the three regons. Pool purchase prce n each regon are 0.29, 0.35, 0.43 RMB/wh respectvely. Runnng cost of dstrbuted photovoltac power system n the three regons are [95000, ], [100000, ], [110000, ] RMB/ (MW Year) separately. The avalable rooftop area are [12, 15], [42, 45], [27, 30] m 2 n the three regons respectvely. Table shows the self-consumed electrcty rato and ther assocated probabltes. Table shows the electrcty prce n the three regons n dfferent perods. The objectve of the model s to maxmze the system benefts through effectvely allocatng the fnancal subsdes n the three areas. Snce there are multple uncertantes and complextes exstng n the system, the parameters and varables can be expressed as ntervals and probablty densty dstrbutons. Consequently, we have: L h h L h h 1 1 h1 1 1 h1 Max f = W H ( S A ) P M W H ( N A ) P (1 M ) subject to: LW R LW H BC (9a) W H T,, (9b) W / ,, (9c) 3 3 W / ,, (9d) 1 1 W / ,, (9e) W / ,, (9f) 3 3 W J,, (9g) 1 1 Where = the type of regon 1 for regon A, 2 for regon B, and 3 for regon C; h = the level of selfconsumed electrcty rato, 1 for low, 2 for medum, and 3 for hgh. 4. Result Analyss and Dscusson Fg. 2 and Fg. 3 present the upper and lower bounds of dstrbuted photovoltac power capacty respectvely. The capacty of dstrbuted photovoltac power was allocated on the base of total fnancal subsdes, regonal capacty constrant and regonal rooftop area constrant. t s revealed that regon B would have the most dstrbuted photovoltac power capacty durng the plannng perods. That s manly because t would generate the hghest benefts among the three regons. Durng perod 3, each regon wll acqure the largest capacty of dstrbuted photovoltac power than perod 1 and 2 as the perods passng by. n ths way, system benefts wll be optmzed, and t wll be [265, 359] mllons. 26

7 nstalled capacty(mw) Upper Bound A B C =1 =2 =3 Fg. 2: Lower bound of dstrbuted photovoltac capacty nstalled capacty(mw) Lower Bound A B C =1 =2 =3 5. Conclusons Fg. 3: Upper bound of dstrbuted photovoltac capacty A stochastc nterval lnear programmng method was formulated for facltatng dentfcaton of optmal dstrbuted photovoltac capacty development plannng wth lmted subsdes under uncertantes. Ths method can deal wth uncertantes expressed as both probablty dstrbutons and ntervals. The proposed model was then appled to a hypothetcal case of plannng future capacty of dstrbuted photovoltac power generaton plannng n three regons of Chna where solar energy resources and proporton of electrcty consumpton were full of uncertantes. The formulated model could be transformed nto two determnstc models, whch corresponded to the lower and upper bounds of the desred objectve. Solutons were obtaned by solvng the two submodels sequentally. Results of ths study could help:(a) facltate reflectons of multple forms of uncertantes wthn a subsdes allocaton system, (b) generate a number of cost-effectve decson alternatves under dfferent perods, allowng comprehensve analyss of trade-offs among system benefts and allocaton schemes, and (c) demonstrate the avalablty of the model through applyng to a case of dstrbuted photovoltac power plannng management wth the consderaton of self-consumed electrcty rato. The results could be used for generatng decson alternatves for helpng decson-maers to dentfy optmal capacty allocaton scheme under lmted subsdes, avalable rooftop and grd access constrants. 6. Acnowledgements Ths wor was supported by the Natonal Natural Scence Foundaton of Chna (Nos and ), and the Fundamental Research Funds for the Central Unverstes (No. 2014JJCB10). 7. References 27

8 [1] L.Q. Lu, C.X. Lu, Z.Y. Sun, et al. The development and applcaton practce of neglected tdal energy n Chna. Renew Sustan Energy. Rev. 2011, 15 (2): [2] L.M. Peala, R.R. Tan, D.C.Y. Foo, et al. Optmal energy plannng models wth carbon footprnt constrants. Appl. Energy. 2010, 86 (6): [3] Y. Zhu, Y.P. L, G.H. Huang. Plannng muncpal-scale energy systems under functonal nterval uncertantes. Renew. Energy. 2012, 39 (1): [4] Y. Zhu, Y.P. L, G.H. Huang. Plannng carbon emsson tradng for Bejng's electrc power systems under dual uncertantes. Renew. Sustan. Energy. Rev. 2013, 23: [5] Z. ravanja, L. Cuce. Mult-objectve optmzaton for generatng sustanable solutons consderng total effects on the envronment. Appl. Energy. 2013, 101: [6] C. Unshuay-Vla, J.W. Marangon-Lma, A.C. Z. De Souza, et al. Multstage expanson plannng of generaton and nterconnectons wth sustanable energy development crtera: a multobjectve model. nt. J. Elec. Power. 2011, 33 (2): [7] M.Q. Suo, Y.P. L, G.H. Huang. Multcrtera decson mang under uncertanty: An advanced ordered weghted averagng operator for plannng electrc power systems. Eng. Appl. Artf. ntel. 2012, 25 (1): [8] P. Stgson, E. Dotzauer, J. Yan. mprovng polcy mang through government - ndustry polcy learnng: The case of a novel Swedsh polcy framewor. Appl Energy. 2009, 86(4): [9] Chna Natonal Renewable Energy Centre (CNREC): [10] Y.P. Ca, G.H. Huang, Q. Tan, et al. Plannng of communty-scale renewable energy management systems n a mxed stochastc and fuzzy envronment. Renew. Energy. 2009, 34 (7): [11] L.M. Peala, R.R. Tan, D.C.Y. Foo, et al. Optmal energy plannng models wth carbon footprnt constrants. Appl. Energy. 2010, 86 (6) [12] Natonal Energy Admnstraton (NEA): [13] G. H. Huang. A hybrd nexact-stochastc water management model. Eur. J. Oper. Res. 1998, 107 (1): [14] M.A. Rosen. Energy consderatons n desgn for envronment: approprate energy selecton and energy effcency. nt J Green Energy. 2004, 1 (1): [15] L.G. Swan, V.. Ugursal,. Beausolel-Morrson. Hybrd resdental end-use energy and greenhouse gas emssons model - development and verfcaton for Canada. nt J Green Energy. 2013, 6 (1):