American Journal of Environmental Sciences 4 (3): 178-184, 2008 ISSN 1553-345X © 2008 Science Publications Hydropower System Management Considering the Minimum Outflow M. L. Arganis and R. Domínguez Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria Circuito Escolar s/n Edificio 5, Delegación Coyoacán. México 04510, D.F. Abstract: This paper deals with the operating rules of the Grijalva River hydropower serial system obtained by means of stochastic dynamic programming and its subsequent simulation using historical records and synthetic series. Penalties in spills and deficit were considered in optimum policies. During simulation several restrictions were added to the original problem, particularly to ensure minimum outflow so as to guarantee the ecological river flow, which enables operators to adjust energy at daily demands peak and consider the existing autocorrelation between biweekly volume data Keywords: stochastic dynamic programming, operating rules, serial dams, autocorrelation INTRODUCTION MATERIALS AND METHODS Ecological hydrology has become an important tool Site description: The Grijalva River rises in Guatemala to be taken into account in water management[1,2]. and flows through Mexico’s Chiapas State and into Hydropower management has several implications: on Tabasco State where it joins the Usumacinta River, and one hand, it produces clean power, few greenhouse it finally empties into the Gulf of Mexico (Fig.1). emissions, no fossil fuel is used, etc. On the other hand, E.. E.U it also generates ecological changes and damages the .U. surrounding environment before, during, and after its Mexico operation[3,6]. Gulf of Mexico Several research projects have been undertaken P ac Tabasco ifi over the last two decades, so as to develop qualitative c O ce an techniques to generate the minimum flow required for Chiapas acceptable ecologic survival, if such a term is Gulf of Mexico acceptable. This multidisciplinary subject is expanding and more people in the world are increasingly [7-11] concerned about it . Peñitas r Malpaso e v i Hydropower systems in developing countries are R a v l a j i Chicoasen r commonly used mainly for daily peak demands. If the G La Angostura G rij alv a R dam is located upstream, a set of rural and urban areas ive r or even green areas or crop areas, as well as ecosystems Fig. 1: Grijalva River, Mexico could suffer significant damage due to river flow, which is subject to the dam’s operating rules. Operating rules depend on the random nature of Before the fifties, the Grijalva River caused reservoir inflows, the time of year, dry and rainy continuous flooding in Tabasco’s plain zone. seasons, dam operating design levels, etc., but they are However, the Operator Organism Comisión Federal de Electricidad (CFE) has performed studies related to the strongly related to political issues involving decision- Grijalva River’s hydroelectric potential since 1958. In makers and operators’ needs. A lot of studies can be coordination with Secretaría de Recursos Hidráulicos performed, but if they are not put into practice, they (known today as the Comisión Nacional remain as mere theoretical responses to real problems del Agua, CONAGUA), the CFE subsequently drew up and almost tantamount to doing nothing at all. the Grijalva Comprehensive Plan. Corresponding Author: M. L. Arganis, N Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria Circuito Escolar s/n Edificio 5 Cub.414-F, Delegación Coyoacán. México 04510, D.F. Tel 52 55 5623 36 00 Ext. 8636 Fax: 56 16 27 98. 178 Am. J. Environ. Sci., 4 (3): 178-184, 2008 The hydropower serial system is comprised of the The intended function was to maximize the La Angostura Dam (Belisario Domínguez), built expected value of a long term benefit, imposing some between 1969 and 1975; the Chicoasen Dam (Manuel penalty coefficients in each spill or deficit of an Moreno Torres), built between 1977 and 1983, as well equivalent system consisting of two reservoirs with the as the Malpaso Dam (Netzahualcoyotl), built between greatest useful reservoir capacity (UC), in this case, La 1959 and 1964, and the Peñitas Dam (Angel Albino Angostura and Malpaso dams[24]. The following was Corzo), which was completed in 1987. Figure 2 shows proposed: a schematic profile of these dams. FO = MaxE(GAng + GMalp − C1DerrAng − (1) K I L O M E T E R S 108.00 104.00 81.00 72.00 C2 DerrMalp − C3 Def Ang − C4 DefMalp ) M NMOL 533.00 U.C.=13169 hm3 E Where: FO objective function, E() expected operator, 500 T G generated energy from the La Angostura dam, NMOL 392.00 Ang 400 ANGOSTURA E GMalp generated energy from the Malpaso dam, U.C.=251 hm3 R C1DerrAng penalty coefficient from the spills in La 300 S Angostura, C2DerrMalp penalty coefficient from spills in NMOL 182.50 200 Malpaso, C3DefAng, penalty coefficient from the deficit 3 A. CHICOASEN U.C.=9600 hm NMOL 87.40 S. in La Angostura, C4DefMalp, penalty coefficient from the 100 U.C.=130 hm3 L. MALPASO deficit in Malpaso. PEÑITAS Fig. 2: Profile of the Grijalva hydropower serial Each dam is subject to: continuity: j = i+x-k; estates: 1 system, Mexico ≤ j ≤ NS, inflows: 1 ≤ x ≤ nx; extraction: kmin ≤ k ≤ kmax. The dams produced very significant changes in the Stochastic dynamic programming assumes a) flow of water through the riverbed, flooded very big random inflows associated to a probability density areas while artificial reservoirs were created. This brought the most important benefits to the country for function f(x), b) dependent operation in system electric purposes; but with their consequential changes reservoirs. To get the maximum expected value from to the environment and surrounding areas. benefit equations, 2 and 3 are applied: Stochastic dynamic programming: There are various NS1 NS2 useful optimization techniques in literature intended to BK1 ,K2 (i ,i ) = ƒƒ q (i , j )q (i , j ) n 1 2 n,K1 1 1 n,k2 2 2 { gain optimal control over a system, such as linear j1 =1 j2 =1 (2) programming[12-14], nonlinear programming[15], dynamic b (i , j ) + b (i , j ,i , j ) +B* ( j , j ) programming, special forms in dynamic programming, n,K 1 1 n,K1 ,K2 1 1 2 2 n+1 1 2 } 1 ⁄ deterministic or stochastic dynamic programming, evolutive computing, simulated annealing, dynamic And: programming with fuzzy rules [16-23], etc., but many of B* (i ,i ) = max Bk, ,k2 (i ,i (3) n 1 2 k1 ,k2 { n 1 2 } these methods are not actually used for practical K1 ,K2 purposes. This poses a challenge which engineers and Where: Bn (i1,i2 ) benefits up to stage n, given decision-makers have to take into account if really they operating rules K1, K2, q (i , j )q (i , j ) , transition intend to solve nature and human needs. n,K1 1 1 n,k2 2 2 In this document, stochastic dynamic programming probability, B* ( j , j ) , optimum was applied based on variables n+1 1 2 involved in the problem. This method defines the feasible optimum control based on Bellman’s optimum expected value, up to stage n+1, corresponding to the principle, “An optimum policy has the next property: optimal extraction K*. no matter whatever state or initial decisions has been In order to optimize the number of calculations, taken, the remaining decisions must equation 2 is reexpressed by equations 4 and 5: constitute an optimum policy independently of the resulting state of the first decision”. This sequential nature, marked by interdependent decisions, allows the K ,K B 1 2 = φ (i ,i ) + operating rules of storage dams to take full advantage n n,K1 ,K2 1 2 of the algorithm methodology, through the use of NS1 NS2 (4) + ƒ ƒ q (i , j )q (i , j )B* ( j , j ) dynamic programming. n,Kl 1 1 n,K2 2 2 n+1 1 2 j =1 J =1 1 2 179 Am. J. Environ. Sci., 4 (3): 178-184, 2008 NS1 φ (i ,i ) = q (i , j )b (i , j ) + n,K1 ,K2 1 2 n,K1 1 1 n,K1 1 1 DELVOLdam,i = CDVdam PENDdam,i-2 j1 =1 (8) (5) NS2 (INGHQdam, year,i-2 −VIMEDdam,i-2 ) + q (i , j )b (i , j ,i , j ) n,K2 2 2 n,K1 ,K2 1 1 2 2 j2 =1 Where CDVdam is a coefficient greater or equal to zero In order to solve the system form by equations 3 that multiplies extraction volume DELVOL applied to and 4, the next steps are followed: the La Angostura or Malpaso dam. 1. Expected values from benefit, from each stage φ (i ,i ) are calculated with equation 5 (they Table 1: Over storage comparison n,K1 ,K2 1 2 Dam Real over storage Simulated over storage are cyclic). in 1999 in 1999 (hm3) 3 2. A very big N value is assumed (hm ) n=N La Angostura 3059.0 1219.1 3. The calculations begins with the last year ( ) Malpaso 356 727.7 assuming B*=0 when n=N 4. Equation 4 is applied several times up to the sum RESULTS AND DISCUSSION of benefit increments between two consecutive stages that are practically the same. In 1993 the Instituto de Ingeniería of the 5. Computing K* for each dam with the B* is Universidad Nacional Autónoma de Mexico (II- calculated in step 5. UNAM) developed a study[25] defining optimal operating rules for the La Angostura and Malpaso Variation in extraction volume in terms of the dams. Later, that analysis was complemented[26] in autocorrelation between inflows: Intending to get order to obtain whole operating rules; that is, policies better answers given by simulation in Malpaso spills were monthly extractions that were defined in both with synthetic longer than the historical records, a dams, as a function in both reservoirs of the ending coefficient affecting the added or extracted volume storage in the prior month.