Water Science and Engineering, 2010, 3(4):443-453 doi:10.3882/j.in.1674-2370.2010.04.007 http://www.waterjournal.cn e-mail: we2008@vip.163.com Etablihment and evaluation o operation unction model or cacade hydropower tation Chang-ming JI 1, 2, Ting ZHOU* 1, Hai-tao HUANG 1 1. Buine Adminitration School, North China Electric Power Univerity, Beijing 102206, P. R. China 2. Renewable Energy School, North China Electric Power Univerity, Beijing 102206, P. R. China Abtract: Toward olving the actual operation problem o cacade hydropower tation under hydrologic uncertainty, thi paper preent the proce o extraction o tatitical characteritic rom long-term optimal cacade operation, and propoe a monthly operation unction algorithm or the actual operation o cacade hydropower tation through the identiication, proceing, and creening o available inormation during long-term optimal operation. Applying the operation unction to the cacade hydropower tation on the Jinhajiang-Yangtze River ytem, the modeled long-term electric generation i hown to have high preciion and provide beneit. Through comparion with optimal operation, the imulation reult how that the operation unction propoed retain the characteritic o optimal operation. Alo, the inadequacie and attribution o the algorithm are dicued baed on cae tudy, providing deciion upport and reerence inormation or reearch on large-cale cacade operation work. Key word: actual operation; independent variable; multiple tepwie regreion; attribution analyi; cacade hydropower tation 1 Introduction With global climate change, hydrological complication have become increaingly igniicant contraint during the proce o water reource development and management. In the ield o water reource development and utilization, the uncertainty o hydrological condition ha been the primary retriction in actual operation o hydropower tation. Nowaday, the operation chart i the mot popular tool or guiding reervoir and hydropower tation operation. The operation chart ha it own advantage: it i imple, practical, and eay to operate. It alo ha ome obviou diadvantage (Zhang 2004): the normal area range o the operation chart i too large, and output deciion do not take into conideration uture reervoir inlow, which may lead to the ame deciion in period with imilar tatu but dierent uture inlow ituation. Thee diadvantage are incompatible with the actual operation. With the bloom o intelligent algorithm in recent year, ome cholar have introduced Thi work wa upported by the National Natural Science Foundation o China (Grant No. 40971300), and the Fundamental Reearch Fund or the Central Univeritie (Grant No.10QX43). *Correponding author (e-mail: zhouting02@gmail.com) Received Sep. 9, 2010; accepted Nov. 24, 2010
neural network, genetic algorithm, upport vector machine, and ant colony optimization algorithm into olution o the operation problem o reervoir and hydropower tation (Wardlaw and Shari 1999; Zhou et al. 2009; Eogbue and Liu 2006; Zhao et al. 2009). However, intelligent algorithm alo have diadvantage in guiding reervoir operation, including poor viual impreion and too much reliance on ample inormation, which decreae their eaibility and eiciency in guiding cacade operation. Becaue the output o a hydropower tation ha a cloe relationhip with reervoir water level and inlow, and the relationhip ha been proven to be linear (Li et al. 2005), the operation unction ha been adopted to guide actual cacade operation. Lu and Guo (1998) imulated the dynamic operation unction o the Danjiangkou Reervoir by conidering reervoir torage and inlow to be independent variable and outlow to be a dependent variable. Liu et al. (2006) propoed the optimization-regreion-optimization algorithm or the Qingjiang cacade hydropower tation, and Ding (2005) made coniderable progre in the etablihment o independent variable et. Meanwhile, intelligent algorithm uch a artiicial neural network are ueul a an alternative to multiple regreion analyi or determining optimal guidance (John 2004). Thi paper propoe principle or chooing variable o the operation unction, and integrate tepwie regreion into the model. Through application in large-cale cacade operation, it can be demontrated that, compared with the traditional operation chart, the operation unction more ully retain the beneit o electric power quantity, guaranteed output, and utilization rate o reervoir in the optimal operation model. Compared with intelligent algorithm, the operation unction i more intuitive and concie. Additionally, through analyi o the tructure o the operation unction we can better undertand the principle o optimal operation. 2 Operation unction development baed on tepwie regreion algorithm The operation unction thi paper propoe i baed on the optimal operation reult. A variable ytem o operation unction i contructed by extracting characteritic o optimal operation procee, and then the operation unction i etablihed according to tepwie regreion theory to achieve guideline purpoe. The ormulation o the operation unction will be dicued below. 2.1 Independent variable ytem etablihment o operation unction In the ormulation o the operation unction, the initial etting o the independent variable ytem i eential; regreion can only provide a tatitical relationhip, but can neither ully explain the phyical or caual relationhip between dependent and independent variable in the operation unction, nor completely rule out ale correlation between dependent and independent variable. Thereore, the eaibility and phyical meaning o the independent variable 444 Chang-ming JI et al. Water Science and Engineering, Dec. 2010, Vol. 3, No. 4, 443-453
hould be taken into conideration in the ormulation o the independent variable ytem. The primary principle or ormulating independent variable i computability. Computability principle mut be relected in the election and calculation procee, epecially in the cae o cacade. For example, the current inlow or a leading reervoir can be adopted by an independent variable ytem becaue the current inlow i equal to natural inlow, which i known inormation, but or the ollowing reervoir the current inlow cannot be adopted; or thoe ollowing reervoir, reervoir inlow i the um o natural inlow and outlow rom the upper reervoir. Obviouly, the outlow rom the upper reervoir i decided through operation deciion, which are unknown beorehand, o the reervoir inlow cannot be adopted by the independent variable ytem or the whole cacade, but we can ue natural inlow intead to relect inlow inormation in thi period. In the tructure o the independent variable ytem, the initial reervoir water level (Z) and inlow (Q) are undoubtedly two important actor. However, Z and Q are in dierent dimenion, and the proce by which Q tranorm Z i a nonlinear proce decribed by a torage capacity curve. Thereore, thi paper additionally relie on a uperpoition water level, a virtual water level that aume additional inlow o water into the current reervoir. The proce can be explained by the ollowing ormula: Z = φ V + TQ (1) ( ) where Z i the uperpoition reervoir water level, φ i an operator repreenting the interpolation calculation obtained by the reervoir torage capacity curve, V i the initial torage o the reervoir, and T i a period o one month (T = 2.63 10 6 ). Obviouly, Z include inormation not only on Z but alo on Q, while avoiding the nonlinear relationhip between Q and Z, and providing a more comprehenive decription o reervoir tatu. Beide, in order to decribe the electric power potential o cacade hydropower tation, energy actor are adopted by the independent variable ytem. The baic energy variable are inlow energy E and torage energy E, which decribe reervoir inlow and water level rom another apect. The interaction o E and E i alo adopted (Ding 2005), denoted by EE. E i the electric quantity that current inlow can totally generate baed on the current reervoir water level. The calculation ormula i a ollow: E = 9.81η QhT (2) in which h = φv ϕq (3) In Eq. (2) and (3), η i power generation eiciency; T repreent the unit length o time, here hour; ϕ i an operator repreenting the interpolation calculation between downtream low and downtream water level; and h repreent the average hydraulic head o reervoir between Z and Z. E i the maximum electric power the reervoir can generate in current torage tatu. The calculation ormula i a ollow: Chang-ming JI et al. Water Science and Engineering, Dec. 2010, Vol. 3, No. 4, 443-453 445
( ) E = 9.81η h V V0 (4) V0 + V h = ϕ Z0 2 (5) where V 0 i the minimum torage o the reervoir, h i the average hydraulic head between Z and the minimum dead torage level o reervoir, and Z 0 i the contant hydraulic head downtream. It ha to be realized that optimal operation mut take the whole cacade into conideration. Thu, any ingle hydropower tation operation deciion ha a cloe relationhip with total inlow energy and torage energy o the cacade, o it i neceary to integrate inlow energy E and torage energy E o the whole cacade ytem into the independent variable ytem. Through urther analyi it can be indicated that or thoe period whoe E value are large but whoe E value are mall, and thoe whoe E value are large but whoe E value are mall, the optimal operation will lead to the ame deciion. In ummary, the independent variable ytem o the operation unction include the ollowing: initial reervoir water level, uperpoition water level, inlow, torage energy and inlow energy o the cacade hydropower tation, and the interaction o torage energy and inlow energy. 2.2 Deciion variable determination in operation unction More than one index (dependent variable) can be choen to decribe the deciion o the operation unction, including output, terminal water level, and outlow. According to the operation eature o the hydropower tation, thi tudy elected output a the deciion variable, and, combined with reervoir operation contraint, conidered the terminal water level o the reervoir the tandby deciion variable ued to achieve greater regreion preciion. The reaon or chooing output but not water level a the main deciion variable i that the itting error o output i relatively mall. Thi tudy ued the leading hydropower tation a an example. The water level i no lower than 2 065 m; i water level i choen a the deciion variable, each 1% deviation lead to a 20-m water level error, and the output deviation magniied by the ollowing ormula: where Δ N i Δ N = 9.81η qδ h (6) Δ h i the water level deviation. We aume q (outlow) i no le than 1 000 m 3 /, and the value o η i commonly et around 0.8, o Δ N i greater than 100 MW, which i much greater than the value obtained by chooing the output a the deciion variable. That i why we did not conider water level the main deciion variable. However, in certain period, uch a the end o the lood eaon or dry eaon, the water level o the reervoir will be maintained at the normal torage level or dead torage level, which make it more appropriate to adopt the terminal water level a a deciion variable. In concluion, the determination o the deciion 446 Chang-ming JI et al. Water Science and Engineering, Dec. 2010, Vol. 3, No. 4, 443-453
variable i dependent on the itting error and the operation contraint o the reervoir. 2.3 Stepwie regreion algorithm The deciion variable and independent variable ytem were dicued above, but, or any one period, not all independent variable have relevance to the deciion, o there i a quetion o how to pick out the real relevant variable in each period to decreae the itting error to within the minimum range. The tepwie regreion algorithm i propoed or uch requet. It main unction i introducing independent variable one by one into the unction by their igniicant extent (contribution) ize. On the other hand, thoe introduced already may loe importance and thu be deleted rom the unction. Every tep o the introduction into the unction or the deleting rom it mut include an F-tet to enure that new variable combination are alway improving the goodne o it o unction. Huang and Liang (2006), Luo et al. (2008), Li et al. (2008), and Ji et al. (2010) introduced peciic principle o the tepwie regreion algorithm. Thereore, the baic ormat o the operation unction can be decribed a y = a + a x + a x + + a x (7) 0 1 1 2 2 m m where y repreent a dependent variable (output or reervoir water level), x 1, x 2,, xm repreent independent variable provided through tepwie regreion baed on hitorical ample, a 0 i a contant, and a1, a2,, am repreent coeicient o independent variable. 3 Simulation proce o operation unction guiding cacade operation Operation unction are independent o each other in ormulation, o the guidance eiciency in actual operation cannot be judged by a ingle tatitical evaluation, but rather through imulation operation that traner mathematical reult into cacade operation eature. Thi ection introduce the method or implementing operation unction guiding long-term cacade operation to check the reliability and operability o the model, and ully veriy every apect o the eiciency the operation unction ha generated. The general conideration o imulation o the operation unction guiding cacade operation i to regard each operation unction a the initial deciion o the operation, combined with other contraint uch a characteritic reervoir water level, output curve o the hydraulic turbine, and comprehenive utilization demand. Then, rolling imulation are conducted rom the beginning o the operation period month by month. During the imulation proce o the operation unction there are everal principle to which we need to pay attention: (1) When the operation unction conlict with the contraint o the reervoir or hydropower tation, priority hould be given to the tation own contraint. Speciically, when the output judged by the operation unction cannot meet the reervoir water level contraint, guaranteed output, outlow, or other contraint, while the power generation capacity can meet the contraint, the initial output mut be appropriately adjuted to meet all Chang-ming JI et al. Water Science and Engineering, Dec. 2010, Vol. 3, No. 4, 443-453 447
it own contraint. (2) The ytem-guaranteed output hould be enured to the maximum extent. Maximization o the ytem-guaranteed output i one o the mot important objective in optimal operation. Whether or not the guaranteed output o optimal operation can be preerved i alo important or cacade operation. Thereore, thi tudy added the iterative module in dry period (rom June to October) to the imulation proce (Fig. 1) to maintain the ytem output at an average level (which i alo accordant with the optimal output proce) in dry period, thu improving the ytem-guaranteed output. Fig. 1 Simulation proce o long-term cacade hydropower tation (3) In the reliability validation proce o operation deciion making, the low-ranking priority contraint hould be veriied beore high-ranking priority contraint; the higher the ranking o the contraint i, the later it i validated. I the order i revered, contraint o higher-ranking priority may be replaced by contraint o lower-ranking priority, which i contrary to operational common ene. For example, the guaranteed output o the hydropower tation mut be placed beore the reervoir water level contraint, or the guaranteed output contraint damage i permitted within the cope o damage, but the reervoir water level contraint i rigid and hould be aured anytime, o it hould be placed ater the guaranteed output contraint. Operation unction, together with the principle above, mut be incorporated into the cacade operation imulation proce to guide the cacade operation. The imulation proce i 448 Chang-ming JI et al. Water Science and Engineering, Dec. 2010, Vol. 3, No. 4, 443-453
implemented in a VC++ 6.0 environment. Fig. 1 illutrate the imulation proce o a long-term cacade hydropower tation. 4 Cae tudy In order to demontrate the imulation theory and check the eiciency o the operation unction in guiding cacade operation, thi tudy took a large-cale cacade including 14 hydropower tation rom the Jinhajiang River to the Yangtze River a it reearch object. Thi cacade originate at Qizong Hydropower Station in Yunnan Province and end at Gezhouba Hydropower Station in Hubei Province. The Qizong-Gezhouba cacade i a rich hydropower reource, with an enormou intalled capacity, which play an important role in the outhern part o the power grid (Zhou 2009). Thi cacade ytem ha ive outtanding regulating hydropower tation with monthly or higher regulating ability, thu providing or high demand with actual optimal operation. Regarding the Qizong-Gezhouba cacade a the reearch object i a way to ully check the eiciency o the operation unction algorithm and the imulation proce. Firt, thi tudy took the cacade optimal operation proce calculated by Wu (2009) with the improved progreive optimization algorithm (IPOA) or the year rom 1953 to 2001 a the tatitical ample o the operation unction. According to the principle introduced in ection 2 and 3, the operation unction or each hydropower tation were etablihed. Some o the operation unction or the leading hydropower tation are given in Table 1. For October and May, the dependent variable wa choen to be the terminal reervoir water level, becaue it wa maintained at the normal level and minimum level in October and May. The dependent variable or the ret wa output, and the tructure and coeicient o the operation unction were judged according to the tepwie regreion theory. Table 1 Monthly operation unction o cacade leading hydropower tation Month Dependent variable Coeicient o independent variable o operation unction a 0 Q Z Z E E EE E E October Terminal water level 2150 January Output 4 714.75 0.148 54.252 April Output 25 725.6 0.032 12.402 3.066 0.171 May Terminal water level 2 065 4.1 Evaluation o ytem-generated energy Comparion o the annual and eaonal generated energy o the cacade ytem or imulation operation and optimal operation can help evaluate the ytem-generated energy. Firtly, the annual generated energy o imulation operation i 3 10 5 MW h, 0.08% le than that o optimal operation annually, o the energy lo i very little. Secondly, comparion o the lood eaon how that the energy generated by imulation operation i 8 10 5 MW h, 0.39% le than that o optimal operation; comparion o dry eaon how that generated Chang-ming JI et al. Water Science and Engineering, Dec. 2010, Vol. 3, No. 4, 443-453 449
energy o imulated operation i 5 10 5 MW h, 0.26% more than that o optimal operation. Seaonal generated energy comparion how that the imulated reult retained the generated energy optimal operation achieved, while the ditribution between the lood eaon and dry eaon i more even, which beneit the operation o the power ytem. 4.2 Evaluation o ytem output curve Comparion o the output curve between the imulation operation and optimal operation i hown in Fig. 2. It can be een rom the general trend that imulation operation ha good conitency with optimal operation, epecially or the guaranteed output o the dry eaon, which, due to the iterative module in the dry eaon, aured guaranteed output maintenance. Fig. 2 Output comparion between imulation operation and optimal operation during year rom 1953 to 2000 4.3 Evaluation o leading reervoir water level curve Qizong, the leading hydropower tation, i a multi-annual regulating reervoir whoe dead torage level i 2 065 m and whoe normal torage level i 2 150 m. The reervoir water level curve o the leading hydropower tation can relect the general eiciency o utilization o the whole cacade ytem to a certain extent. It can be een in Fig. 3 that the trend o the reervoir water level curve are quite accordant, and the torage and adjutment ability i ully utilized, which how a high imulation preciion and eiciency. Fig. 3 Reervoir water level comparion between imulation operation and optimal operation during year rom 1953 to 2000 450 Chang-ming JI et al. Water Science and Engineering, Dec. 2010, Vol. 3, No. 4, 443-453
5 Dicuion o inadequacie o operation reult and attribution analyi Section 4.1, 4.2, and 4.3 have decribed tet o the operational eiciency guided by the operation unction rom the apect o ytem-generated energy, ytem output, and the leading reervoir water level. Generally peaking, the eiciency o imulation o the operation proce i atiactory. However, thi algorithm alo ha it inevitable hortcoming, leading to everal deiciencie during the imulation proce, a decribed below: (1) Both the period o time and the depth o output damage increaed. The ytem i uually regulated uch that the depth o output damage hould not be 20% greater than the guaranteed output in order to acilitate the load arrangement in the power grid. However, operation ometime cannot meet the damage depth requirement, becaue the uture inlow i unknown and the output cannot be pre-adjuted, while inlow i quite mall, o there may appear a phenomenon o greatly decreaing output at the end o the dry eaon, uch a in the year 1959, 1992, and 1994, which i obviouly detrimental to the overall operation o the power grid ytem. (2) The phenomenon o leading reervoir drawdown reaching the dead torage level in advance o the dry eaon i becoming more requent, a i inuicient torage in the lood eaon. In condition o optimal operation o the Qizong Reervoir, the operation i baed on acknowledgement o the total inlow or the period, o the deciion can adjut the long-term output to avoid ucceive dead torage level or inuicient torage to a maximum extent. However, or the imulation operation, the water level drawdown reache the dead torage level rom March to the end o the dry eaon, epecially in extremely dry year (1959, 1992, and 1994). Meanwhile, the torage i not uicient in the lood eaon in thee year. That i alo the explanation a to why the guaranteed output were greatly damaged in the three year. (3) Abandoned water o the leading reervoir in wet year i igniicant. It can be een rom Fig. 3 that in wet year (1973, 1980, and 1983), the reervoir torage wa at a normal level in advance o optimal operation, inevitably cauing abandoned water during the period in which the reervoir wa at a normal level. However, optimal operation may increae the output in advance in order to clear part o the torage to decreae the abandoned water, while on the other hand enuring the ull torage o the reervoir by the end o the lood eaon. The deiciencie mentioned above relect ome diadvantage o the operation unction algorithm rom certain point o view. In act, uture inlow uncertainty will inevitably reduce beneit or any actual operation method, epecially in unuual inlow condition. In view o the operation unction algorithm propoed in thi paper, we conclude with reaon or reduction o eiciency and tability: (1) Retricted by inlow orecating accuracy, the actual operation cannot obtain uture inlow inormation, o the operation deciion can only be made baed on current inormation but ignoring the coherence characteritic o the hydrological cycle, which i bound to lead to Chang-ming JI et al. Water Science and Engineering, Dec. 2010, Vol. 3, No. 4, 443-453 451
deciion deviation. For example, or the ame period in dierent year, i the initial tatu period i the ame, the operation unction will generate the ame output deciion. However, the optimal operation deciion in act take all uture inlow inormation into conideration, not only current inormation. Thi i an important reaon why the operation unction deciion deviate rom the optimal operation. (2) In the development proce o the operation unction, the particularly dry or wet year produce unuual ample, o the itting error o the operation unction i larger than in normal year rom a tatitical point o view. The theory o the operation unction i baed on long-term tatitical characteritic. Thu, or period in which inlow deviate greatly rom the average level, the regreion error are inevitably larger than the normal average. Moreover, the application o the operation unction to guide the actual operation in unuual year alo involve greater error. Beide, the optimal operation in unuual year i more dependent on uture inlow inormation combined with conideration o guaranteed output, abandoned water, generated power, etc., requiring a number o iteration to achieve the inal deciion. However, imulation operation cannot ue the uture inlow inormation, not to mention long-term iteration, to chooe the bet deciion. Thereore, or lood eaon in extremely wet year, abandoned water will increae more in the lood eaon than during optimal operation; or the dry eaon in extremely dry year, guaranteed output during imulation operation will be adverely aected more than in optimal operation. In ummary, there remain ome deect in the operation unction algorithm thi paper propoe in detail o imulation reult. Attribution analyi how that the deect are mainly caued by orecating preciion problem and the contradiction between the univeral and peciic nature o optimal operation reult. Thee are alo the limitation o actual cacade operation with unolved inlow orecating preciion, which hould be another uture reearch direction. 6 Concluion Thi tudy introduced the tepwie regreion principle into actual cacade operation deciion making analyi, and carried out monthly operation unction or the Jinhajiang-Yangtze River cacade hydropower ytem. Through comprehenive conideration o reervoir water level contraint, guaranteed output, and comprehenive water reource utilization contraint, thi paper imulated the cacade operation proce guided with operation unction through computer project. Comparion between imulation and optimal operation howed that imulation operation retained mot o the beneit o optimal operation in cacade generated power, output proce, and leading reervoir water level, and relected ine operability. Further analyi o the inadequacie o imulation proce detail and attribution were made to guide uture reearch, while oering an important reerence or reearch on the actual cacade operation ield. 452 Chang-ming JI et al. Water Science and Engineering, Dec. 2010, Vol. 3, No. 4, 443-453
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