system using system dynamics-based simulation

International Conference on Flood Resilience: Experiences in Asia and Europe 5-7 September 2013, Exeter, United Kingdom

FLOOD CONTROL OPERATION OF A MULTI-RESERVOIR SYSTEM USING SYSTEM DYNAMICS-BASED SIMULATIONOPTIMIZATION MODEL ‫به نام‬

M. Hosseini1, S. Jamshid Mousavi1*, A. Ardeshir1, K. Behzadian1, 2 1Amirkabir

University of Technology, Iran; 2University of Exeter, United Kingdom of Civil and Environmental Engineering, Amirkabir University of Technology, Hafez street, Tehran, Iran; Tel: +98 (0)21 64543014; E-mail: [email protected]

*School

ABSTRACT This paper presents a multi-objective optimisation model for multi-purpose reservoir operation model. Two conflicting objectives are to minimize downstream damage by reducing flood peaks at selected downstream control points and to maximize hydropower generation. The obtained Pareto optimal solution is a compromise between optimal alternatives of downstream and hydropower damages. The proposed model is applied to the reservoirs system of Karkheh river basin in southwest of Iran. The proposed model includes VENSIM simulation model based on system dynamics approach coupled with multi-objective particle swarm optimization (MOPSO) algorithm. The MOPSO-VENSIM model is employed to optimize the operation of cascaded reservoirs during flood through allocating an optimal initial flood control capacity to each reservoir in the river basin. The results indicate that an improved reservoir operation as flood peak reduction, distribution of initial flood control capacity among the cascaded reservoirs in the basin, optimal distribution of downstream damage between vulnerable areas and optimal distribution of hydropower generation. Furthermore, the optimal allocation of flood control capacity among the reservoirs represents planning instruction for flood control capacity in the reservoirs system of Karkheh river basin. The results show that maximum damage in vulnerable areas would happen at some point of Karkheh downstream.

KEYWORDS Simulation, Optimization, Flood, System Dynamics, PSO.

1. INTRODUCTION Most reservoirs are currently operated as multi-purpose such as irrigation, drinking water supply, power generation, flood control. Flood control is typically one of the most significant purposes due to its role in reducing flood damage particularly in vulnerable areas. Linear and Nonlinear programming are two conventional approaches for the development of optimal operational policy rules in reservoirs. One more optimization model for reservoir flood-control operation is dynamic programming (DP) that can accommodate the nonlinear and stochastic features. However, DP suffers from the problem of “curse of dimensionality” although some researchers such as Wasimi and Kitanidis (1983) and Kumar and Baliarsingh (2003) proposed employed some techniques to overcome this difficulty. In the last decade meta-heuristic optimization techniques have been extensively used for operation of reservoir flood control systems. Evolutionary algorithms (EAs) such as Genetic algorithm (GA) (Karamouz et al. 2003; Malekmohammadi et al. 2011) and Differential evolution (DE), Ant Colony Optimization (ACO) (Afshar et al. 2009), Simulated Annealing (SA) (Ahmed and Mays 2013), Tabu Search (TS), Particle Swarm Optimization (PSO) and Artificial Neural Networks (ANN) are examples of these methods. Particle Swarm Optimization (PSO) has been also used in many applications (Bayat et al. 2011). Other meta-heuristic optimization techniques were also used by other researchers such as Karaboga et al. (2007) for Tabu search algorithm, Wei and Hsu (2008) for feed-forward backpropagation neural network, and Mehta and Jain (2009) for Neuro-Fuzzy technique. In present paper, a multi-objective simulation- optimization model has been presented by integrating VENSIM as simulation model with PSO algorithm as an optimization tool and consequently, multiobjective particle swarm optimization- VENSIM simulation (MOPSO- VENSIM) model has been developed. The main purpose of this study is to examine the applicability of MOPSO-VENSIM model to a case study of Karkheh river basin in order to achieve optimal operating policy for flood control.

International Conference on Flood Resilience: Experiences in Asia and Europe 5-7 September 2013, Exeter, United Kingdom

2. METHODOLOGY 2.1 Multiobjective optimisation model When a reservoir is operated for multiple purposes such as irrigation, drinking water supply, power generation, flood control, a multi-objective optimisation model will be required to derive operational policies of the reservoir system. Among these purposes, flood control is usually the most important as it may cause irreparable damages. To aim this purpose, the flood storage capacity is an essential need in reservoirs to control flood control and prevent/reduce any damages to downstream points. On the other hand, the flood storage capacity can reduce potential hydropower generation in dry seasons. Therefore, finding an appropriate compromise between these two conflicting objectives is important. In flood control reservoirs, coordinated operation of the flood control capacity of reservoirs will be needed in order to decrease probable flood damages. The present study mainly deals with optimal allocation of flood control capacity in a series of cascaded reservoirs in Karkheh river basin with respect to reducing downstream damages and increasing the benefits of hydropower generation. Having said the abovementioned purposes for reservoir operation, a multi-objective optimization model is required in addition to simulation model. Therefore, a multi objective approach is developed here by considering two objective functions, flood damage in vulnerable areas and hydropower damage due to initial flood control capacity in reservoir. The final result of this optimisation model is a Pareto-optimal front of the optimal solutions. In the following, the structure of the optimisation model including the objectives, constrains and the simulation model is described in more detail.

2.1.1 MOPSO-VENSIM model VENSIM as a system dynamic modelling tool is used here to simulate the flood control of a reservoir operation. VENSIM is simulation software developed by Ventana System, Inc, for improving the performance of real systems. VENSIM is a visual modelling tool that enables user to conceptualize, document, simulate, analyse, and optimize models of dynamic systems and provides a simple and flexible way of building simulation models from causal loop or stock and flow diagrams (Ventana System 2007). The main reasons for the popularity of System Dynamics are the increased speed of model development, the trust developed in the model due to user participation, the possibility of group model development, the effective communication of model results, the ease of model modification in response to changes in the system and the ability to perform sensitivity analysis. PSO algorithm is used here as an intelligent search technique for optimisation model. This algorithm was selected here because of some advantages such as simple running and its high speed in finding the optimal solution. Therefore, the proposed model here is called MOPSO-VENSIM model which is a combination of VENSIM model with multiobjective PSO algorithm.

2.1.2 Objective functions Two main objectives are modelled here to develop optimal operation of multi-purposes cascaded reservoirs. The first objective is to minimise a function of peak discharges at some control points as a measure of flood damages as follows:

(1)

where t is the index of time step; k is the index of downstream damage centre; m is the number of downstream damage centres; is the total damage of downstream damage centres; is the outflow hydrograph of the reservoir and is the flood damage associated with the peak of the outflow hydrograph of the reservoir at damage centre k during time period t. The second objective is to minimize the total loss due to reduction of hydropower generation as follows: (2)

International Conference on Flood Resilience: Experiences in Asia and Europe 5-7 September 2013, Exeter, United Kingdom

where i is the index of reservoir; n is the number of reservoirs; is the total loss due to the reduction of hydropower generation; is the amount of control volume allocated to reservoir i and is the loss of reduction of hydropower generation associated with flood control capacity of reservoir i.

2.1.3 Constraints There are a number of constrains in the proposed optimisation model. The most important one is the mass balance equation of the reservoir operation which is developed according to the principle of continuity. Assuming that the flow varies linearly during each discrete time period, the finite difference formula of continuity equation for reservoir i at time period t can be expressed as: (3) where is a time interval on hour basis for routing; is the set of reservoirs; is the starting time for operation and T is the flood duration. The whole planning horizon is the time length between and T. The flood control operations have to comply with operating regulations, with regard to the permissible bounds of release and storage, as well as the reservoir water balance. The first limitation is the upper and lower limits of reservoir storage volume ranging from maximum storage capacity ( ) to minimum storage ( ) over a planning horizon. This constraint for reservoir i can be expressed as: (4) A reservoir with gated outlets may have a rating curve between volume and outflow rate that is generated based on the outlets of the reservoir. These curves are can be stated as constraints in the optimization model as follows: (5) (6) where is the release of reservoir i at period t; is the storage volume of reservoir i at period t; is the maximum outflow capacity of the reservoir i at period t which is calculated based on the storage volume; is the minimum required release of reservoir i at period t and is the rating curve of reservoir i. In addition, another physical constraint is the release incremental amount between the adjacent periods (t-1) and t that is restricted by a constant value ). (7) River routing is a procedure for simulating the movement of flows through a river reach. In this paper the Muskingum linear channel routing method is used for river routing. This method is based on the solution of continuity equation and approximates the storage volume in a channel by a combination of prism storage and wedge storage. The general form of Muskingum routing equation used in this paper can be found in Windsor (1973).

3. DESCRIPTION OF CASE STUDY Karkheh River is the third largest river in Iran. Karkheh River basin, covering 50,000 km², is situated in south and southwest of Iran. Six reservoirs were planned to be located on the basin, including; Garsha, Koran Bozan, Sazbon, Seymareh, Tang Mashoreh, and Karkheh reservoirs (Figure 1). Garsha, Koran Bozan, Sazbon and Seymareh reservoirs are going to be located on the Seymareh River, and Tang Mashoreh and Karkheh reservoirs on Kashkan and Karkheh River respectively. 8 vulnerable areas are shown in Figure 1 as control points. Karkheh River Basin and its multi-purpose reservoir system have active storage capacity of about 14 billion cubic-meters and 1,827 MW potential of hydropower generation. The reduction in potential hydropower generation represented as the amount of reduction in hydropower generation (in MW) that is replaced with flood control capacity in reservoir. Karkheh river reservoir system is used to investigate the applicability of MOPSO-VENSIM model. The developed model is formulated for two

International Conference on Flood Resilience: Experiences in Asia and Europe 5-7 September 2013, Exeter, United Kingdom

different scenarios in order to evaluate the effects of increasing storage capacity in the basin on reducing damage during flood condition.

Garsha Tang Mashureh Kuran Buzan Sazbon Seymare h I2 I1 Karkheh

Figure. 1. Map of Karkheh River basin, Iran.

4. DATA COLLECTION MOPSO-VENSIM is applied to deal with 2% frequency flood (50-year return period flood). The flood hydrograph developed here is based on the analyses of possible storms and a rainfall-runoff simulation model using HEC-1. The other main datum used in this study is flood control capacitypotential hydropower generation reduction function that is considered for all reservoirs in the basin. The potential hydropower generation in hydroelectric power plants is a linear function of hydroelectric power plant efficiency, effective water head and water discharge flowing through the turbines. The relation of potential hydropower generation can be represented as:

(8)

International Conference on Flood Resilience: Experiences in Asia and Europe 5-7 September 2013, Exeter, United Kingdom

Where P is potential hydropower generation in MW; η is hydroelectric power plant efficiency; H is effective water pressure head and R is water discharge flowing through the turbines of the hydroelectric power plant. In order to estimate potential hydropower generation, it is necessary that the difference between the assigned control volume and the volume for which hydropower generation is maximum is estimated based on reservoir height-volume relationship. In other words, when the total active volume of reservoir is assigned to flood control there will be no hydropower generation and the maximum reduction (loss) of hydropower generation will be resulted. Volume. By changing the assigned flood control volume from this maximum amount to a minimum volume, we can obtain a curve relating the assigned flood control capacity and the associated reduction in potential hydropower generation. Figure 2 illustrates such curves obtained for two of reservoirs.

Figure. 2. Curve between reduction in potential hydropower generation and flood control capacity for two reservoirs Similarly, the relation between financial downstream loss and peak flow rate of hydrograph is developed. Again, due to the limited space of the paper, these functions are presented in figure 3 only for two vulnerable downstream section defined in Figure 1.

Figure. 3. Relation between financial downstream loss and peak flow rate for two downstream sections

5. APPLICATION OF THE METHODOLOGY

International Conference on Flood Resilience: Experiences in Asia and Europe 5-7 September 2013, Exeter, United Kingdom

The main aim of the proposed methodology is to find optimal reservoir operation rule curves by using MOPSO- VENSIM model. We consider a step-wise parametric operating rule with five discrete levels (volumes) for each of ones (steps) the optimum release volume should be defined. Therefore, the number of steps (parameters) represents the number of decision variables for which the optimal release volumes need to be determined by the optimization algorthm. In addition to parameters of the rule curves, initial flood control capacity of each reservoir is also considered as one more decision variable. The method used here to identify the solutions on the Pareto optimal curve adopts a constrained approach to convert multiple objectives into single objective without considering all the objectives simultaneously. In this study, the objective function of hydropower generation is considered as a constraint. Therefore, the only objective is to minimize the total damage in vulnerable areas in the river basin. The assumed reservoir storage volume is divided into five parts with different decision variables for each part. In cases where the amount of water stored in a reservoir exceeds the maximum storage capacity of the reservoir, the fifth decision variable is used. At first, depending on the number of population, new rule-curves are produced in PSO algorithm and are transferred to VENSIM using MS EXCEL. At the beginning of each time-step, depending on reservoir water level and the amount of flow entering the reservoir, the present storage volume is calculated and the proposed rule curve is used in order to compute reservoir release and to simulate the model for each member of the population. Next, objective function values are transferred to PSO algorithm using MS EXCEL. This type of modelling is a practical way to decrease the number of decision variables. This iterative process will continue until it converges into an optimal solution. The rule curves, equivalent to a best solution, are used as operational rule curves for reservoirs under flood condition.

6. RESULTS AND DISCUSSION The proposed model is solved using a 4-hour flow routing time step for 240-hour duration. Maximum fluctuation of reservoir release is considered as a constraint so that the peak release does not exceed the maximum amount between two successive time steps. As mentioned earlier, five decision variables are considered in each reservoir in order to control the amount of reservoir release. One decision variable is also used for defining initial flood control capacity. The number of decision variables is shown in Table 1. Table. 1. Number of decision variable in different scenarios

Scenario

Decision variable name

Non-developed

Reservoir volume Initial flood control capacity

Number of decision variables 10 2

The results in this paper are to specify downstream damage between vulnerable areas, hydropower loss and initial flood control capacity corresponding to the reservoirs. The proposed model was run 5 times and was set to iterate 250 times during each run. Once the model was run five times, only the points on the Pareto curve were drawn and extracted. The time required to run the model for a system of Pentium IV processor and 4G memory is approximately two hours.

6.1 Non-developed scenario of Karkheh river-reservoir system This scenario, only Karkheh and Seymareh reservoirs have been considered for system operation which are the current state of system where other reservoir is under planning or contruction. The Pareto optimal curve of operational system alternatives of this scenario is shown in figure 4. According to figure 4, the diagram is quite symmetrical. In this curve, the minimum downstream damage is equal to 435 billion Rials beyond which no further reduction in downstream damage can be envisaged. Furthermore,

International Conference on Flood Resilience: Experiences in Asia and Europe 5-7 September 2013, Exeter, United Kingdom

if no capacity is assumed for flood control in reservoirs, the system will experience considerable downstream damage.

Figure.4. Pareto optimal operating curves, non-developed scenario.

Figures 5 and 6 respectively represent distribution of damage in vulnerable areas and distribution of flood control capacity between the current reservoirs of the basin.

Figure. 5. Trend of downstream damage increment in vulnerable areas with increase in total downstream damage, non-developed scenario.

International Conference on Flood Resilience: Experiences in Asia and Europe 5-7 September 2013, Exeter, United Kingdom

Figure. 6. Change Trend of required flood control capacity of reservoirs with increase in total downstream damage, non-developed scenario. These curves represent planning instructions for flood control capacity of Karkheh river-reservoir system in non-developed scenario.

7. CONCLUSIONS This paper two conflicting objectives including minimizing downstream damage by reducing flood peaks at selected downstream control points and maximizing hydropower generation were analysed by using a multi-objective simulation-optimization model known as MOPSO-VENSIM model. This model has been developed to optimize the reservoir flood control operation and initial flood control capacity of reservoirs in Karkheh river basin. VENSIM simulation model is based on system dynamics approach and has been chosen in this study due to some effective benefits. The new model is formulated and solved for a non-developed scenario where the current state of the systems (business as usual) is available. MOPSO-VENSIM model is demonstrated through its appcalition on a case study of Karkheh river reservoir system in south and southwest of Iran. In this study, because of using stair-shaped of drainage curve, parametric operation rules are considered and the parameters of these rules in addition to initial flood control capacity of each reservoir have been chosen as operating decision variables. Results indicate that in non-developed scenario, the minimum amount of downstream damage is equal to 435 billion Rials and there is no possibility of further reduction. The distribution of downstream damage between vulnerable areas and distribution of hydropower damage and corresponding initial flood control capacity between the reservoirs were presented. Furthermore, the distribution of initial flood control capacity between reservoirs represents planning instructions for flood control capacity in the reservoirs system of Karkheh river basin. As results show, the maximum amount of damage between vulnerable areas is allocated to vulnerable area of Karkheh downstream in each scenario.

8. ACKNOWLEDGEMENTS The required information of this study is provided by mahab ghodss Consulting Engineering Company. Great Appreciation goes to Dr. Salavitabar who contributed to the development of this study by his constructive comments.

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International Conference on Flood Resilience: Experiences in Asia and Europe 5-7 September 2013, Exeter, United Kingdom

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