Modeling of joint water-supply scheduling with multi-source in Beijing under uncertain conditions

Transcription

1 MATEC Web of Conferences 246, 112 (218) Modelng of ont water-supply schedulng wth mult-source n Beng under uncertan condtons Xaoun Dou 1,2,*, Hea Wang 2 1 Insttute of Water Resources for Pastoral Area, MWR, 12 Hohhot, Chna 2 Chna Insttute of Water Resources and Hydropower Research, 138 Beng, Chna Abstract. After the Mddle Route of outh-to-north Water Transfer Proect (NWTP) fnshed, a pattern of ont water-supply ncludng NWTP water, the surface water of Myun reservor and underground water has been formed n Beng. In vew of the uncertanty n water-supply schedulng, ths study takes 22 as the plannng year, and the nfluence of uncertan factors on the system cost was fully consdered by nterval two stages plannng method. In order to mnmze the total water-supply cost, a ont water-supply schedulng model n Beng has been establshed, whch reflects the actual stuaton of the ont watersupply system wth multple sources. The results llustrate that the mnmum water-supply cost of Beng wll be [14.6, 25.4] bllon yuan n 22, and the optmal water-supply of Myun reservor, groundwater and NWTP water expected to be.54, 2.5 and.95 bllon m³, respectvely. 1 Introducton The mddle route of the outh-to-north Water Transfer Proect (NWTP) was formally fnshed n 214, whch means that Danangkou reservor can provde Beng wth domestc and ndustral water. It effectvely allevates the scarcty of Beng's water resources, whle t wll have a certan mpact on the exstng pattern of water supply. After completon, Beng formed a ont schedulng modelng wth Myun reservor, NWTP water and groundwater [1]. However, there are some uncertantes on both sdes of supply and demand n the mult-source combned water supply dspatchng modelng. In terms of water supply, the change of clmate such as precptaton, temperature and so on wll cause the uncertanty of Myun reservor and upstream water of Danangkou reservor, and subsequently affect the water supply of Myun reservor and NWTP water dverson. At the same tme, the change of precptaton and evaporaton wll affect the quantty of groundwater, and subsequently cause the change of groundwater quantty. In terms of water demand, changes n the future populaton, rapd soco-economc development, adustment of the ndustral structure and transformaton n farmland types and rrgaton patterns wll affect the water consumpton of domestc, ndustral, agrcultural and envronmental water, leadng to uncertanty about total water demand n the future. Meanwhle, as a result of the dfferent dstrbuton characterstcs of surface water and groundwater, the rule of movement transformaton between them has a certan nfluence on the mult-source ont management [2, 3]. Therefore, t s of great practcal sgnfcance to analyze the water supply and demand balance and fully consder the possble uncertantes by constructng the mult-source water supply dspatchng model n Beng, whch s of great mportance to the comprehensve management of water resources n Beng and the adustment and gudance to the operaton proect of NWTP [4]. In ths background, the study takes 22 years as the plannng year to establsh a mult-source water supply dspatchng model n Beng. 2 Modelng and methods The purpose of the mult-source ont dspatchng s to determne the most reasonable water supply of each water sources [5] and meet the demand of water supply, and acheve the lowest water cost [6]. Consderng the uncertanty n water supply dspatchng, ths study takes two-stage programmng model [7, 8] to fnd the optmal soluton. In the frst stage, accordng to the Beng water demand and supply capacty n 22, the water supply of each source n the future s predcted and a penalty coeffcent was brought n. If the actual water supply cannot meet the demand, t wll lead to economc punshment. In the second stage, the unreasonable loss n the frst stage decson s mnmzed to acheve the optmal water supply quantty by dealng wth the uncertan events. In order to solve the uncertanty of parameters, ths study brngs n the nterval number [9]. The upper lmt of the nterval ndcates the maxmum value that the parameter may take, and the lower lmt ndcates the mnmum value that the parameter may take. Thus the nterval two stage programmng s formed to solve the * Correspondng author: douxun@163.com The Authors, publshed by EDP cences. Ths s an open access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense 4. (

2 uncertanty problem n the optmal allocaton of multsource water supply. (5) Constrants of water balance For surface water Qm = Q q W Q 2.1 Obectve functon Qm Q = q W The model s to mnmze the total cost of water supply to the cty durng the year, that s, C W mn f = p L water source at 25%, 5%, 75% frequency. pre-udgment the amount of water supply. C W W s to s the unt s a defnte value, the water supply s also a defnte value, whch can be solved by lnear programmng. The decson varables z can obtan the best value by L model. Therefore, the orgnal obectve functon can be transformed nto: the net nflow water s. The of each parameter n ths study ndcates the upper and lower lmts of the parameters, and when the upper and lower bounds are equal, the parameter becomes a defnte number. W,, 2,, (W (2) W Q q Q Q q,, 2,, (11) (12) (13) W ΔW z (3) Q q W ΔW z Q Q mn Q q W ΔW z Q mn z 1 (4) W max s the maxmum avalable water. (4) Constrants of the mnmum water storage capacty W max W ΔW z water s. s the water loss. (3) Constrants of the maxmum water wthdrawal Q Q mn,, 2,, (1) Q s the net nflow. m Δ W z ) W mn W ΔW z Q q Q,, 2,, s ntal water storage, the ntal NWTP W max W W mn s the mnmum total water demand n Beng. (2) Constrants of water avalable The correspondng constrants are: s.t. Wmn (9) mn f = C (W ΔW z ) p L The obectve functon should meets the followng 6 constrants: (1) Constrants of the mnmum water supply When the water supply s a defnte value, the model can be dvded nto two sub-models, whch meet the lower and the upper lmts of the target functon values. One of sub-model s obectve functon can be expressed as: 2.2 Constrants mn f = C (W ΔW z ) p L s the probablty of q W (8) The model needs to pre-udgment the water supply quantty of each water source at frst, as t s uncertan, the study adds a decson varable z, z [,1 ]. As t ddn t meet the predct water. s the penalty coeffcent when the actual water supply does not reach p,, 2,, 2.3 Model solvng s the shortage water whch the antcpated water quantty. (7) (6) Constrants of non-negatve (1) ( = 1, 2, 3) s the Myun reservor, surface water and groundwater. ( = 1, 2, 3) s the flow of each cost of water supply. (6) For underground water zopt opt, the (5), best (14) (15) (16) (17) and z are the decson varables, and f opt are the soluton of the lower sub-model, water supply target s Wopt = W ΔW zopt m. The other sub-model s obectve functon can be expressed as: Q s the storage water volume at the end of water supply. Q mn s the mnmum storage water volume that mantan the ecologcal needs. 2

3 C (W mn f = ΔW z ) p L derved from the Beng tatstcal Yearbook and the Water Resources Bulletn. (18) The correspondng constrants are: s.t Growth Rate Method opt W ΔW zopt W ΔW z Q q Q Q q W ΔW zopt Q Q mn Q q W ΔW zopt Q mn s the decson varable, The water consumpton of agrcultural, ndustral and envronmental were calculated by the growth rate method [11], usng the formula: = (1d)n, where s the water consumpton n 22, s the water consumpton of Beng n 216, d s the growth rate, n s the number of years. It s calculated about the water consumpton of agrcultural, ndustral and envronmental of Beng n 22 are 455 mllon m³, 583 mllon m³ and 735 mllon m³ n 22, respectvely. The Beng tatstcal Yearbook 217 shows the resdent populaton n 216 s mllon [12]. Accordng to Beng Cty master plan ( ), the resdent populaton scale of Beng wll be controlled wthn 23 mllon n 22 [13], and keep t at ths level n a long term. The data from the Beng Muncpal Water Conservaton Management Center ndcates the daly water consumpton per capta s 21L. Thus, the domestc water consumpton of Beng wll be 1.76 bllon m³ n 22. (19) f opt (2) (21) (22) and opt are the solutons of the upper lmt sub-model. Consequently, the solutons of the entre model are f opt = [ f opt, f opt ] opt = [opt, opt ], And the optmal allocaton scheme s: Aopt = W opt opt (23) (24) 3 Results Multvarate regresson method The method combned Multvarate Regresson and Prncpal Component Analyss (PCA) [14] was used to forecast agrcultural water, ndustral water, domestc water and envronmental water, respectvely [15]. By revewng the Beng tatstcal Yearbook, the varables related to agrcultural water, ndustral water, domestc water and envronmental water are selected for analyss, as shown n Table Predcton of Water demand Water demand of Beng s conferred from domestc water, ndustral water, agrcultural water and envronmental water. The growth rate method and multvarate regresson method [1] were used to forecast water demand n 22, and the basc data Domestc water Household populaton Per capta GDP Resdental consumer prce ndex Commodty retal prce ndex Table 1. Water demand-related varables of Beng Industry water Agrculture water Gross output value of The actual cultvated area at ndustral above year-end desgnated sze Producton of maor Enterprse number agrcultural products The total output value of Average number of agrculture, forestry, anmal employees husbandry and fshery Producer prce ndex of Assets total agrcultural products Takng agrcultural water as an example, there are four related varables about agrcultural water, the PCA method llustrates that there s a prncpal component Number of loads Coeffcents n the lnear combnaton Envronment water Fecal removal volume Urban greenng coverage Park green area per capta ewage treatment capacty related to agrcultural water usng, the results of analyss are shown n Table 2. Table 2. PCA of agrcultural water usng Related varables The actual cultvated area at year-end Producton of maor agrcultural products The total output value of agrculture, forestry, anmal husbandry and fshery Producer prce ndex of agrcultural products Characterstc roots of prncpal components The actual cultvated area at year-end Producton of maor agrcultural products The total output value of agrculture, forestry, anmal husbandry and fshery 3 Prncpal component F

4 Producer prce ndex of agrcultural products As ndcated n Table 2, the expresson of prncple component F1 s: F1 =.549* The actual cultvated area at year-end.569* Producton of maor agrcultural products -.55* The total output value of agrculture, forestry, anmal husbandry and fshery - 27* Producer prce ndex of agrcultural products. Accordng to ths, the F1 of years can be obtaned, then usng -.27 the multvarate regresson analyss n P, the expresson of agrcultural water s as follows: agrcultural water *F1. The change trend of F1 can be obtaned by F1 scatter plot, as shown n Fgure 1, whch can be deduced that agrcultural water s 53 mllon m³ n 22. Fg. 1. The trend of prncple component F1 over tme n agrcultural water Therefore, n 22, domestc water, ndustral water, agrcultural water and envronmental water n Beng wll be 1.92,.26,.53 and.88 bllon m³, respectvely. Consderng the uncertanty, the domestc water, ndustral water, agrcultural water and envronmental water range are [1.76, 1.92], [.26,.46], [.53,.58], [.74,.88] bllons m³ n 22 by combnng the results of the above two methods. The total water consumpton range s [32.94, 38.36] bllon m³. groundwater storage s mantaned n [1.38, 2.16] bllon m³. In accordance wth Myun reservor engneerng characterstcs, t s cognzed that the reservor capacty s 4.38 bllon m³, the maxmum water supply s 3.94 bllon m³, and the mnmum storage s.44 bllon m³. By queryng the relevant data of groundwater n Beng, t s known that the stored groundwater s 1.68 bllon m³ at normal level, and the maxmum mnng volume s 2.8 bllon m³ n hstory. 3.2 Forecast of Water supply 3.3 Cost of water supply and penalty coeffcent By nvestgatng the water supply system n Beng, t s found that the water supply rato of Myun reservor, groundwater and surface waters s about 1:4:2. Accordng to the rato, the water supply targets of Myun reservor water, groundwater and surface water are [.47,.55], [1.88, 2.19], [.94, 1.1] bllon m³, respectvely. The total water supply volume s not less than 3.55 bllon m³ n 22 on the bass of the hstorcal water supply. Accordng to the Master plan of Beng NWTP [16] and Beng Cty Conservaton Plannng tudy on the water resources n 22, the results of the forecast, obtaned 25%, 5% and 75% of the frequency of Myun reservor are [197, 245], [34, 373], [435, 442] mllon m³ [17], the correspondng probablty s.25,.5,.25. Groundwater resources n Beng plan area [18] at 25%, 5% and 75% frequency are [2.23, 2.41], [2.75, 3.6], [3.22, 3.65] bllon m³. On the bass of the weekly update of water transfer nformaton from the Beng NWTP Constructon Commttee offce, the 25%, 5%, and 75% frequency of the water nflow volume are [.7,.71], [.91,.94], [1.24, 1.25] bllon m³. The maxmum water supply for the water transfer s 4.31m³/s one day, as a result the annual maxmum water supply volume s 1.27 bllon m3. Accordng to Beng Water Resources Bulletn [19], the Myun reservor s mantaned n [.72, 1.24] bllon m³, The cost of water supply n Myun reservor and NWTP s the sum of the water resources fee, sewage treatment charge and water conveyance cost, and the cost of groundwater s the sum of water resources charge, sewage treatment and water extracton cost [2]. Accordng to Beng Waterworks Group announced the prce about 216, we do know that the cost of Myun reservor, groundwater, NWTP water are as shown n Table 3. Table 3. Table of water supply cost yuan/m³ NWTP Myun Groundwater water reservor The cost of conveyance (extracton) Water resources charge ewage treatment charge Cost of water supply [.53,.58] [2, 3] [.74,.96] [1.57, 2.3] [1.57, 2.3] [1.57, 2.3] [1.36, 3] [1.36, 3] [1.36, 3] [3.46, 5.88] [4.93, 8.3] [3.67, 6.26] The penalty coeffcent s 1.5 tmes of the cost of water supply[21], the penalty coeffcents of Myun reservor, groundwater and NWTP water are [5.19, 8.82], [5.51, 9.39], [7.4, 12.45](yuan/m³), respectvely. The statstcs parameters are shown n Table 4. 4

5 Table 4. Parameter table of mult-source combned water supply dspatchng model Parameters Myun reservor Mnmum total volume of water dverson bllon m³ Maxmum volume of water dverson bllon m³ Water transfer targets nterval bllon m³ Penalty coeffcent nterval yuan/m³ Cost of water supply nterval yuan/m³ Groundwater NWTP water [.47,.55] [1.88, 2.19] [.94, 1.1] [5.19, 8.82] [5.51, 9.39] [7.4, 12.45] [3.46, 5.88] [3.67, 6.26] [4.93, 8.3] 4.38 Reservor capacty bllon m³ Quantty of reservor nterval bllon m³ The maxmum of reservor storage(dead storage) bllon m³ The storage volume of groundwater(nterval) bllon m³ The storage volume of groundwater at normal level bllon m³ The amount of water n 25% probablty (nterval) (bllon m³ The amount of water n 5% probablty (nterval) (bllon m³ The amount of water n 75% probablty (nterval) (bllon m³ [.72, 1.24].44 [1.38, 2.16] 1.68 [.2,.25] [2.23, 2.41] [.7,.71] [.3,.37] [2.75, 3.6] [.91,.94] [.44,.45] [3.22, 3.65] [1.24, 1.25] results are shown n Table 5, and Fgure 2 shows the target of optmal water supply. 4 Conclusons The obtaned parameters are taken nto the model and calculated by Lngo software [22]. The calculaton Table 5. The results of the optmal water supply volume under dfferent frequences Myun Water resource Probablty Ground water NWTP water reservor Optmal water-supply bllon m³ Water scarcty n dfferent nflows bllon m³ 25%.25 [,.7] [,.18] [.24,.25] 5%.5 [.1,.4] 75%.25 Actual water supply n dfferent nflows bllon m³ 25%.25 [.48,.55] [1.93, 2.1] [.7,.71] 5% [.91,.94] 75% Z1opt, Z2opt=.52, Z3opt=, the mnmum system cost fopt=[14.6, 25.4]bllon yuan 5

6 Fg. 2. Map of optmal water supply n dfferent frequences As ndcated n Table 5, the lowest water supply cost s [14.6, 25.4] bllon n 22, and the decson varable Z1opt, Z2opt=.52, Z3opt=, and the optmal water supply target of Myun reservor, groundwater and NWTP water are.55, 2.5 and.95 mllon m³, respectvely. For Myun reservor, compared to.55 bllon m³ of the optmal supply target, at 25% frequency, Myun reservor exsts [,.7] bllon m³ water shortage, n 5% and 75% frequency, Myun reservor s not lack of water. mlarly, for groundwater, compared to 2.5 bllon m³ of the optmal water supply target, n the 25% frequency, there s [,.12] bllon m³ of water shortage, and n the 5% and 75% frequency, groundwater s not short of water. For NWTP water, at 25% and 5% frequency, there s [.24,.25], [.1,.4] bllon m³ water shortage, and n the 75% frequency, NWTP water s not lackng. When the water supply s relatvely adequate, the water shortage s relatvely mnor. When the water supply s relatvely small, prorty s gven to local water, and prorty s gven to the NWTP water as t has a hgher cost when shortage References Y.N. Zhang, F.Q. Tan, H.C. Hu, Journal of Hydraulc Engneerng, 45, (214) I.R. Wlls, P. Lll, Journal of Water resource plannng and management, 3 (1984) W. Yu, Y.Y. Hams, Water resource research, 4 (1974) C.M. Lu, H.R. Wang, Journal of Natural Resources, 18, (23) J.J. You, H. Gan, H. Wang, Journal of Hydraulc Engneerng, 36, (25) J. Zhang, G.H. Huang, Y. Lu, Journal of Hydraulc Engneerng, 4, (29) Y.P. L, G.H. Huang,.L. Ne, Advances n Water Resources, 29, (26) Ahmed, A.J. Kng, G. Para, Kluwer Academc Publshers (23) I. Maqood, G.H. Huang, J.. Yeomans, European Journal of Operatonal Research, 167, (25) A.M. Kshrsagar, R. Khattree, Multvarate Regresson, (Chemometrcs wth R, prnger Berln Hedelberg, 211) Y.Z. Zha, J.. Wang, J.Q. Zheng, Journal of Natural Resources, 4, (211) Beng Muncpal Bureau of tatstcs, Beng tatstcal Yearbook 217 (Chna tatstcs Press, Beng, 217) People's Government of Beng Muncpalty, Beng urban master plan ( ) (217) X.J. Dou, J. Lv, H.Q. un, Journal of Chna Insttute of Water Resources and Hydropower Research, 2 (218) L.W. h, P 19. tatstcal Analyss from Entry to Mastery (Tsnghua Unversty Press, Beng, 212) Beng Constructon Commttee Offce of NWTP, Master plan of Beng NWTP (Chna Water Power Press, Beng, 28) Y.C. Han, Beng Normal Unversty (29) G.P. He, D. Zhou, Z.. Yang, Hydrogeology & Engneerng Geology, 2, (25) Beng Hydrologcal taton, Beng Water Resources Bulletn (217) J. Zhang, North Chna Electrc Power Unversty (28).H. Mo, H.N. Duan, B. hen, Journal of Hydraulc Engneerng, 45, (214) J.X. Xe, Y. Xue, Optmze Modelng wth LINDO/LINGO oftware (Tsnghua Unversty Press, Beng, 25)