Stochastic Dynamic Programming with Risk Consideration for Transbasin Diversion System Tawatchai Tingsanchali, F.ASCE1; and Thana Boonyasirikul2 Abstract: An optimization procedure called SDPR that includes dynamic programming, stochastic dynamic programming ͑SDP͒, simulation, and trial and error adjustment of risk coefficient is developed and applied to determine the optimal operation policy of the proposed Kok-Ing-Nan transbasin diversion system in Thailand. Subject to hydrologic uncertainty, transition probabilities of inflows and its related uncertainty were considered. Due to dimensionality problems, the system is decomposed into three serially linked subsystems: two for the proposed upstream Kok and Ing diversion storages and one for the existing Sirikit reservoir. Optimization of each subsystem is done sequentially from upstream to downstream with specified sets of hydrologic state variables and diversion/release targets. The targets of the three subsystems are interrelated and link the subsystems together. From the derived optimal operation policies, simulation results show that the transbasin diversion increases the Sirikit reservoir release, irrigation reliability and net benefit of the system each by about 50–60%. Compared to SDP, the SDPR optimal operation policy increases both the maximum irrigation reliability and maximum system net benefit by about 10%. DOI: 10.1061/͑ASCE͒0733-9496͑2006͒132:2͑111͒ CE Database subject headings: Stochastic models; River basins; Irrigation; Hydroelectric power generation; Risk management; Optimization. Introduction to the Nan River. The transbasin diversion will increase inflow to the Sirikit Reservoir and hence its releases for irrigation, hydro- The Chao Phraya River Basin, the largest and most important power generation and other domestic uses. river basin in Thailand, covers approximately 180,000 km2. The The study presented in this paper is conducted to determine an main stream, the Chao Phraya River, and its four major tributar- optimal operation policy for the transbasin diversion system. In ies, Ping, Wang, Yom, and Nan Rivers, yield an annual river such tropical regions as the Southeast Asian peninsula, hydrologic runoff of 30,300 million cubic meters ͑mcm͒ on average. There conditions have large seasonal fluctuations and high uncertainty are two regulating reservoirs: the Bhumibol Reservoir which has that significantly affect reservoir operation and increase risk of an active storage of 9,662 mcm on the Ping River and the Sirikit water shortage. Therefore, inflow uncertainty must be incorpo- Reservoir of 6,660 mcm on the Nan River. The increase of up- rated into optimization when determining the optimal operation stream water use has reduced runoff from the upstream catchment policy. areas whereas the downstream water requirement has increased Many related studies have been reported in the literature. For ͑ ͒ due to growth in irrigation area, population, and urbanization. example, Stedinger et al. 1984 developed a stochastic dynamic ͑ ͒ Therefore, water shortages have occurred frequently in the last programming SDP model employing the best forecast of current decade, especially in the downstream irrigation area of the Chao period inflows to define a reservoir operation policy. Karamouz ͑ ͒ Phraya river basin. In order to solve this water shortage, the and Vasiliadis 1992 used Bayesian decision theory to develop Kok-Ing-Nan transbasin diversion system, as shown in Fig. 1, Bayesian stochastic dynamic programming for reservoir optimi- was proposed by the Electricity Generating Authority of Thailand zation for Bayesian interpretation of transition probabilities. ͑ ͒ ͑EGAT͒͑1983͒ and by the Royal Irrigation Department of Loaiciga and Marino 1986 introduced the interaction between Thailand ͑1993͒ to divert water from the Kok and Ing river basins the expected value and variance of the objective function as a means of analyzing the risk averse nature of decision making in reservoir operations. Yeh ͑1985͒ and Simonovic ͑1992͒ provided 1Professor, School of Civil Engineering, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani, Thailand 12120. an extensive literature review and evaluation of various models E-mail: [email protected] used in reservoir management and operations. Several of these 2Senior Water Resources Engineer, Electricity Generating Authority studies applied stochastic optimization to examine the perfor- of Thailand, Nonthaburi, Thailand; formerly, Doctoral Graduate, Asian mance or to determine the operational policy of an existing Institute of Technology. system. Some incorporated reliability constraints to evaluate an Note. Discussion open until August 1, 2006. Separate discussions existing system operation or to determine the heuristic operating must be submitted for individual papers. To extend the closing date by rule based on deterministic approaches. However, fully incorpo- one month, a written request must be filed with the ASCE Managing rating the risk due to inflow uncertainty in stochastic optimization Editor. The manuscript for this paper was submitted for review and pos- sible publication on August 6, 2001; approved on July 15, 2005. This in determining optimal operational policies for water resource paper is part of the Journal of Water Resources Planning and Manage- systems continues to be a challenging problem. ment, Vol. 132, No. 2, March 1, 2006. ©ASCE, ISSN 0733-9496/2006/ In this study, stochastic dynamic programming with a multi- 2-111–121/$25.00. objective function and consideration of risk due to inflow uncer- Fig. 2. Schematic diagram of Kok-Ing-Nan transbasin diversion system Fig. 1. Map of proposed Kok-Ing-Nan transbasin diversion system SDPR to determine the optimal operation policy of Kok-Ing-Nan transbasin diversion system. The optimization is based on maxi- mizing system net benefits. The performance of the transbasin tainty is applied to determine optimal operational policies for the diversion system is evaluated under the optimal operational poli- proposed Kok-Ing-Nan transbasin diversion system in Thailand. cies obtained from both SDPR and SDP by simulation using input Since the multistorage transbasin diversion system is large scale time series of generated monthly inflows. Finally, the simulation and complex, the SDP algorithm is inhibited by the large state- results with and without the proposed transbasin diversion system space dimensionality of the problem. Many attempts have been based on SDPR and SDP policies are compared to determine the made to simplify this problem by using combined optimization improvement in the system performance. techniques such as linear programming, dynamic programming ͑DP͒, simulation, regression, and search techniques to evaluate system performance. A DP model was sequentially applied by Stochastic Dynamic Programming with Risk Boehle et al. ͑1982͒ to optimize reservoir system operation. Consideration Hla ͑1991͒ formulated an SDP model for optimizing annual hydropower energy generation from Ubol Ratana reservoir in Uncertainty due to random characteristics and stochastic pro- Thailand. Braga et al. ͑1991͒ developed a DP-SDP model for cesses of hydrologic parameters is involved in optimization of optimization of hydropower production of a multiple storage- operation policies of diversion systems. Some policies may offer reservoir system with correlated inflows and applied it to the a relatively high expected benefit but at the expense of an in- Brazilian hydroelectric system. Karamouz et al. ͑1992͒ extended creased variability or risk on outcomes. Therefore, the expected implicit stochastic optimization to a three-step cyclic procedure value and variability of the objective function are to be carefully including DP, regression and simulation to improve initial oper- considered in the optimization formulation. Since the stochastic ating rules of a multiple reservoir system. Niedda and Sechi processes of inflow are also reflected in the objective function, the ͑1996͒ developed a mixed optimization procedure based on net- Markov chain approximation model is applied to determine the work linear programming and subgradient method to deal with expected value of the objective function. The variability of the large design problems for water resources systems. However, objective function due to random inflows introduces uncertainty most of these studies emphasized deterministic approaches to in the system output. For a single reservoir subsystem, the objec- evaluate system performance rather than to determine an explicit tive function of expected utility function u in terms of net mon- ͑ ͒ operation stochastic policy for the system. To overcome the high etary benefit b rt can be written as dimensionality of multistorage operation problems, the transbasin m diversion system is decomposed into three sequentially linked Max Eͭu͚ͫ b͑r ͒ͬͮ ͑1͒ single reservoir subsystems, namely Kok-Ing, Ing-Nan, and t t=1 Sirikit ͑Fig. 2͒, with each subsystem then individually optimized sequentially from upstream to downstream. The total net benefit is where rt =a decision variable, i.e., the release of a storage dam or ͑ ͒ ͑ ͒ the sum of the net benefits of the three subsystems. Although the diverted flow of a diversion dam in month t mcm ; b rt =net decomposition method does not fully guarantee the overall benefit b as a function of rt due to implementation and operation optimal result of the entire system, it provides an approximate of the transbasin diversion system ͑in millions of U.S. dollars͒; ͕ ͓͚m ͑ ͔͖͒ solution for practical