OPTIMAL PREDICTIVE FLOOD CONTROL FOR RIVER-RESERVOIR OPERATION SYSTEM

ABSTRACT

During the real-time flood events, the operation of water surface system is very important and crucial to minimize the impacts of flood. The predictive reservoir operation method (PROM) provides optimal real-time operation of flood control systems with incorporation of current and forecasted storm events.
PROM utilizes a dynamic programming with successive algorithm, interacting with hydrologic routing method. The algorithm generates predictive control policies and system-wide feedback control under various hydrologic conditions. The developed methodology was embedded in PC-based decision support system (DSS) to evaluate alternatives up to desired convergence criteria. PROM is applied to Han River-Reservoir flood control project, which has 9 reservoir systems, as a case study. The results of case study for '1995 flood event in the Han River Basin have provided that the developed methodology and computer based DSS can operate water surface system to minimize flood impacts at the downstream while maintaining water for next hydrologic period water use during the real-time flood events.

Keywords: Predictive Flood Control, Multireservoir Operation, Dynamic programming, Hydrologic Routing Method, Decision Support System, Han River Basin

INTRODUCTION

One of the most important aspects of minimizing the impacts of floods is the operation of flood control systems. The forecasting of flood event is very important in order to operate these systems. The real-time reservoir operation problem involves the operation of a reservoir system by making decision on reservoir releases, as information becomes available, with relatively short time intervals that may vary between several minutes to several hours. Real-time operation of multireservoir systems involves various hydrologic, hydraulic, operational, technical, and institutional considerations (Mays, 1992).

There have been many reservoir operation models provided in the literature but only few have been presented at reservoir operation under flood control concerns. The U.S. Army Corps of Engineers (1973, 1979) developed HEC-5 and HEC-5C for reservoir operation for flood control. Windsor (1973) used recursive linear programming (LP) procedure for operation of flood control systems employing the Muskingum method for hydrologic routing and the mass balance equation for reservoir computations. Yazicigil (1980) developed an LP optimization model for the daily real-time operations of the Green River basin in Indiana, a system of four multipurpose reservoirs. The Tennessee Valley Authority (1974) developed an incremental dynamic programming and successive approximations technique for real-time operations with flood control and hydropower generation being the objectives.

One of methods to solve the computational burden of DP is using Dynamic Programming Successive Approximations (DPSA) which was suggested by Bellman and Dreyfus (1962) and generalized by Larson (1968). Trott and Yeh (1971), Yeh and Trott (1972), and Giles et al. (1981) have applied DPSA algorithm for multi-reservoir system operation. Recently, Yi (1996) successfully applied this method to the Lower Colorado River Basin scheduling of hydropower problem that has 27 state variables.

A predictive reservoir operation method (PROM) is presented that incorporates into a single algorithm to minimize the impacts of flood while maintaining water for next hydrologic period water use during the real-time flood events. PROM is applied to Han River-Reservoir flood control project, which has 9 reservoir systems, as a case study.

PREDICTIVE OPTIMAL CONTROL MODEL FORMULATION

CONTROL METHODOLOGY

The objectives of PROM are to minimize the impacts of floods along the downstream, while maintaining the target storages for the next hydrologic period. The overall methodology employed in real-time operation of multireservoir systems is represented in Fig. 1. The current status of the systems is measured, including inflows and stages of reservoirs, and stages along the downstream, and telemetered to the control center. The flood forecasting models initialize future river conditions and optimization model of multireservoir systems computes the optimal release policies for each reservoir for the current and future time steps over the operational forecast window. Only optimal release policies for the current time step are utilized for activating the control structures of the reservoirs. The current status of systems is again measured, telemetered and checked against computed values. A hydrologic flood routing model is reinitialized based on actual current system measurements. Optimization model of multireservoir systems is executed as needed to correct the predictive release polices, and process continues throughout the operational horizon.

FIG. 1. Predictive Reservoir Operation Model (PROM)

DYNAMIC PROGRAMMING WITH SUCCESSIVE APPROXIMATIONS

One way of alleviating the curse of dimensionality is using Bellman's concept of successive approximations. Instead of evaluating the optimal value function for all possible combinations of the state vector, only one component is changed at a time. The process of Dynamic Programming with Successive Approximations (DPSA) is as follows. Each component of the state vector is optimized one at a time with initial trajectory assumed as a starting point:

 (1)

where  is the dynamic programming optimal value function for stage , and  is a  state variable for stage . A superscript 0 is used to indicate the initial trajectory.

All the components are fixed to their initial values except the first.

 (2)

A one-dimensional dynamic programming problem is now solved over the first component only. That is,  are held constant in the objective function and all constraints and only  is allowed to vary. When an optimal solution is obtained over all stages , it is indicated with a superscript 1:

 (3)

Next, the second state component is varied, while maintaining all other components are present values, and a new solution is found

 (4)

which is designated with a superscript one.

 (5)

This process is continued until the final component is reached. At this point, the entire process is repeated starting with the new values found as the new trajectory. This process is terminated when no significant improvement is possible.

 (6)

FLOOD ROUTING METHOD

In state dynamics, the routing coefficients are successively calculated at current iteration  as

 (for ) (7)

where, flow rates at the upstream and downstream of reach  (, respectively) are obtained directly from the hydrologic flood routing model (Fig. 2).

This flood routing model simulates water discharges based on given status of system,  which are calculated from the optimization model in the previous iteration, . Labadie (1988) proposed this method in real-time urban storm water control using the optimal control theory then Flavio and Labadie (1997) successfully applied in optimal real-time control of irrigation canals with incorporation of current and forecasted demands.

FIG. 2 Typical reach illustrating calculation of routing coefficient

The Muskingum method is a commonly used hydrologic flood routing method for handling a variable discharge-storage relationship. The values of at the main channel reaches in the Han River Basin were selected by 0.2 (Yun, 1986). The parameter is the time of travel of the flood wave through the channel reach. The time of travel of the flood wave provided by KOWACO for So Yang Gang and Chung Ju Reservoir respectively. Based on the data, the parameters of channel reaches were determined.

CASE STUDY

PROBLEM FORMULATION

There are 9 reservoirs with hydropower plants in the Han River Basin. Flood control is one of the major purposes of multipurpose reservoirs in Korea. Two reservoirs, SoYangGang and ChungJu reservoirs were built and operation policies were established for these purposes in the Han River Basin. In addition, the HwaCheon reservoir can control the flood in some degree, while it is a power generation reservoir.

The objective function for the real-time operation of multireservoir system for flood control problem incorporates seven objectives: 1) the minimizes the downstream flooding effects through the basin, 2) maintenance of ideal target storage for water use of next hydrologic period, 3) avoidance the current storage exceeding the maximum storage at the flood control top resulting in endanger reservoir safety and backwater effect for upstream, 4) satisfaction of designed demands discharge rate for monthly water use, 5) assures optimal policies within the actual available release, 6) avoidance of rapid variation in controls resulting in unacceptable gate control, and 7) stability of final storage in the storage reservoirs at the end of the forecasted period, assuring recovery of control capacity in the next operational cycle.

The objective function is stated as follows:

 (8)

subject to:

  (9.a)

  (9.b)

  (9.c)

  (9.d)

  (9.e)

  (9. f)

  (9.g)

  (10.a)

  (10.b)

  (10.c)

   (11)

  (12.a)

  (12.b)

where,  = 1,..., node locations in the system, with a node representing any point of storage, control or flow confluence.  = 1... reaches locations in the system, with a reach representing any two point of node connection.  = 1...T time interval as a stage in DP formulation.  =  node storage at the beginning of time interval  (system state variables).  =  node storage at the end of time interval  (system state variables).  =  node release rate at the end of time interval  (decision variable).  = lower and upper bounds on  node storage. = lower and upper bounds on  node release.  = upper bounds on  node release at the end of time interval  (Note; only 1,2 and 3rd node will be estimated by storage-maximum available release relationship).  =  node forecasted inflows during period  (Note; for only 1,2 and 3rd node will be referred as a natural inflow while 4,5,6,7 and 8th node will be referred as a local inflow).  = node calculated discharges at the end of time interval ( Note; only 7 and 9th node will be calculated for evaluate the flooding effects of downstream).  = node designed top flood discharges (Note; only 7 and 9th node will be given by user for evaluate the flooding effects of downstream).  = node planned discharges for water supply (Note; only 8th node will be given by user for evaluate the satisfaction of water supply).  = node target storage (Note; only 1,2 and 3rd node will be given by user for evaluate the demand storage for the next hydrologic period).  = node limited storage for rainy season (Note; only 1,2 and 3rd node will be given by user for evaluate the assurance of the flood control capacity).  = routing coefficients of reach during period  (Note; accounting for attenuation and lagging of upstream releases to downstream nodes and system spills).  = downstream discharge of reach during period  (Note; accounting for effecting of upstream releases to downstream).  = node diversion or depletion for water supply (Note; only 8th node will be given by user for evaluate the satisfaction of water supply).  =  node weighting factor for the objective term (Note;).

SELECTION OF DPSA CONTROL DATA

For the upstream reservoir, the limitation storage at summer season and total storage capacity were set as the minimum and maximum storage respectively. Physically, the flood control capacity of downstream reservoirs is more than 0.0 MCM. However, those flood control capacities was set the no capacity since reservoirs were just opening their control gate at the flood. However, for the downstream reservoirs, the limitation storage at summer season was set as the minimum and maximum storage. Selection of DELX in CSUDP is extremely important because it affects execution time, computer storage requirements, and solution accuracy. Current dimensioning of CSUDP requires that the value of DELX must be determined less than the 101 (Labadie, 1990). Based on the criterion above, the DELX (DELXI and DELXF) was selected. The splicing factor was incorporated to reduce the execution time. In this study, the value of splicing factor was 2. The median value between the minimum and maximum storage used to set of the initial trajectory for the first execution only. The optimal solution or trajectory of the first execution was used to the initial trajectory in the next execution.

In the selection of weighting factors, for avoiding the flooding at downstream flood control point, objective 1, relatively large values were selected. For satisfied water demand for the Seoul Metropolitan Area, the weighting factor of objective 4 was also selected as the relatively large value. In addition, the weighting factors for objective 5 were also selected as the relatively large values since it is physical constraint. However, weighting factors for avoiding the unacceptable gate control, objective 6 were selected as the relatively small values because those related objectives always violate their restrictions. For weighting factor of maintain the water for next hydrologic period water use, the value were selected 0 since storages of upstream reservoirs were already over the their full of buffer zone. For the weighting factors of objective 3 and 7 should be ignored since objective 3 can be controlled by DPSA method as an boundary condition and objective 7 can be managed by DPSA method as an boundary condition of final stages respectively.

THE RESULTS AND DISCUSSION

Convergence of the routing coefficients required about seven executions. After seven executions of HRBSDP, the sum square error was 0.118514. This amount replied that mean variation of routing coefficient was 0.000617 (= 0.118514 / (24*8)). That is, if the simulated flood flow was 1000 CMS then 6.17 CMS are mean error of the simulated flood flow. Therefore, this convergence criterion was satisfied enough to terminate the HRBSDP run.

The Table 1 shows the comparison of peak storage of upstream reservoirs (Hwa Cheon, So Yang Gang and Chung Ju reservoir) between the observed operational data and simulated data by HRBSDP. Based on the two comparisons, the results of HRBSDP maintained more water than the past-observed operational data. This gives more benefits in water use for next hydrologic period. However, it can also have more risk in next flood control project since there is less room to control the following flood events.

Classified		Hwa Cheon	So Yang Gang	Chung Ju
Peak Storages	Observed	936.55	2638.07	2468.76
	Simulated	949.34	2643.16	2655.00
Maximum		1018.40	2872.00	2750.00

Table 1. The Comparison of Peak Storage

The comparison of peak discharges between the observed operational data and simulated data by HRBSDP. Most of simulated peak discharges by HRBSDP were less than the observed ones. The past observed data at Yeo Ju flood control point overflowed its capacity, 200-year flood. However, the peak discharges at Yeo Ju flood control was reduced a lot by the simulation of HRBSDP and never overflowed at all, which was shown in Fig. 3.

Fig. 3. The Flood Flow at Yeo Ju Flood Control Point

Therefore, the overall results showed that the decision by HRBSDP could minimize the downstream flood impacts while maintaining the water for next hydrologic use.

CONCLUSIONS

The Predictive Reservoir Operation Method is presented to minimize the impacts of floods along the downstream, while maintaining the water for the next hydrologic period. CSUDP, a generalized dynamic programming model (Labadie, 1988), was selected to develop the module based on the Dynamic Programming with Successive Approximation (DPSA) algorithm. In order to calculate the routing coefficients, the Muskingum method was utilized as a flood routing model. The power of using dynamic programming for reservoir operation should give the more assurance to the operational decision-maker providing quantitative information rather than qualitative information. In addition, the combining the optimization and simulation technique gives the user more reliable and realistic strategies in real-time operation of multireservoir system for flood control problem.

The developed methodology was embedded in PC-based decision support system (DSS) to evaluate alternatives up to desired convergence criteria. PROM is applied to Han River-Reservoir flood control project, which has 9 reservoir systems, as a case study. The results of case study for '1995 flood event in the Han River Basin have provided that the developed methodology and computer based DSS can operate water surface system to minimize flood impacts at the downstream while maintaining water for next hydrologic period water use during the real-time flood events.

KYU-CHEOUL SHIM

Ph. D.

Water Resources Planning and Management in Civil Engineering at Colorado State University, Fort Collins CO, USA 80526.

Phone: 1-970-491-8830

E-mail: skcpj94@lamar.colostate.edu

SOON-BO SHIM

Prof. and Director

The Institute of Water Resources and Quality Management, Chungbuk National University, San-48 GaeShin-Dong, Cheongju Korea

Phone: 82-431-61-2400

E-mail: wqshim@cbucc.chungbuk.ac.kr

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