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Assessing Trade-offs Between Hydropower Production And Flood Control In The Dal<auml C>lven River Basin, Sweden

Congress: 2015
Author(s): Andrea Bottacin-Busolin, Anders Wrman
University of Manchester1, KTH Royal Institute of Technology2

Keyword(s): Sub-theme 10: Management of water resources,
AbstractIntroduction
The operation of high-head hydropower systems made of multiple interconnected reservoirs and power stations is affected by economic, social, environmental and technological constraints, and depends on the stochastic variability of correlated hydrologic inflows and energy prices. A main challenge for the planning and management of these systems is the assessment of trade-offs between multiple competing objectives using uncertain information. Although several methods have been suggested [2,3,5-7], the derivation of optimal operating rules for water resources systems is often plagued by the high dimensionality of the state space and by the complex interaction between mutually correlated random variables.

This work presents a methodology for the stochastic analysis of trade-offs in large-scale water reservoir networks and demonstrates its application to a multi-reservoir system in the Dalälven River basin, Sweden. The river Dallven is located in central Sweden and has an average hydropower potential of 1420 MW, of which 2/3 is utilized. The hydropower system comprises 13 main regulation units and over 40 power plants. The system is regulated for the purpose of electricity production and to provide protection against floods. Due to the late spring and summer peak discharges, the lowland areas adjacent to the river are often flooded during the summer period, resulting into the excessive production of mosquitoes that proliferate in the waterlogged areas. In recent years, the local County Administrative Board has been considering different solutions to the problem, including the use of chemical pesticides as a preventive countermeasure. However, pesticides have been proven to be a very expensive and partly ineffective solution that also carries significant adverse environmental impacts. The question therefore arises as to whether the multi-reservoir system in the Dallven River basin can be regulated in such a way that the risk of flood is minimized at a reasonable cost for the power companies.

Methods
The objectives considered in the trade-off analysis are the maximization of power production and the minimization of flood risk. In the absence of accurate data on the energy prices, the total power production is here taken as a surrogate for the total revenue, which is a more relevant target for the power companies. The operation of the reservoir system is optimized using three different approaches. The first approach assumes perfect foreknowledge of the inflow series, and uses linear programming to optimize the sequence of reservoir releases. Constraints on the releases and the discharge at a control station are imposed using penalty functions. In the second approach, optimal operating rules are derived using model predictive control (MPC) in combination with an autoregressive model that is calibrated against weekly inflow series. The third approach is based on approximate dynamic programming (ADP) [1,4] and allows the determination of an approximate value function, which can be used for online operation of the system under stochastic inflow scenarios. A multiobjective analysis is performed by combining the ADP model with a weighting technique that is consistent with the convex approximations of the value function generated by the algorithm.

Results and Discussion
When complete foreknowledge of the inflows is assumed, the performance of the ADP model is found to be slightly superior to that of linear programming. Similarly, the ADP model outperforms the MPC approach when the system is operated with uncertain information about the future inflows. The application of the model to the trade-off analysis of flood risk and power production in the Dallven River basin shows that it is possible to significantly reduce flood risk at the expense of a loss of production, and the optimal trade-off between the two objectives is defined by a specific Pareto frontier, which has been determined. In particular, the stochastic analysis shows that the risk of flood during the summer period is almost 70% when the flood risk reduction objective is not considered, but can be decreased down to 12% at the cost of a production loss of 3.2%. However, flood risk significantly increases when additional constraints due to water court decisions are incorporated in the model.

Conclusion
We have demonstrated a multiobjective methodology for trade-off analysis to help make balanced decisions in complex reservoir networks under uncertain inflow scenarios. The application of the model to a multiobjective study in Dallven allowed deriving optimal operating policies that can significantly reduce the risk of flood while minimizing the loss of production. In the numerical simulations, the approximate dynamic programming approach outperformed linear programming in the deterministic case, and MPC in the stochastic case, and therefore appears to be a reliable method for stochastic optimization of multi-reservoir operation. The ADP approach provides an explicit formulation of the stochastic flow of information to the decision maker while keeping the computational costs within reasonable limits. Furthermore, the combination of the ADP model with the weighting method for multiobjective optimization allows the determination of the Pareto frontier, which provides an immediate visualization of costs and benefits associated with different operating policies. Although the study was limited to two objectives, the method can also be applied to many-objective optimization problems that often arise in water resource management. 1. Bertsekas, D. P. (2007) Dynamic Programming and Optimal Control, Vol. II, 3rd ed., Athena Scientific.
2. Castelletti, A., Pianosi, F., and Restelli, M. (2013) A multiobjective reinforcement learning approach to water resources systems operation: Pareto frontier approximation in a single run, Water Resour. Res. 49, 3476–3486.
3. Labadie, J. (2004) Optimal Operation of Multireservoir Systems: State-of-the-Art Review, J. Water Resour. Plan. Manag. 130, 93–111.
4. Powell, W. B. (2011) Approximate Dynamic Programming: Solving the Curses of Dimensionality, John Wiley & Sons.
5. Teegavarapu, R. S. V., Ferreira, A. R., and Simonovic, S. P. (2013) Fuzzy multiobjective models for optimal operation of a hydropower system, Water Resour. Res. 49, 3180–3193.
6. Tilmant, A., and Kelman, R. (2007) A stochastic approach to analyze trade-offs and risks associated with large-scale water resources systems, Water Resour. Res. 43, W06425.
7. Zhao, T., Zhao, J., and Yang, D. (2014) Improved Dynamic Programming for Hydropower Reservoir Operation, J. Water Resour. Plan. Manag. 140, 365–374.

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