2022 Optimization Days
HEC Montréal, Québec, Canada, 16 — 18 May 2022
MA2 - Hydropower Optimization
May 16, 2022 10:30 AM – 12:10 PM
Location: Trudeau Corporation (green)
Chaired by Imene Benkalai
10:30 AM - 10:55 AM
A faster solution approach for the generator maintenance scheduling problem
The Generator Maintenance Scheduling Problem (GMSP) is a problem that combines a hydropower optimization problem with a scheduling problem. Both problems are known to be hard to solve and combining them leads to an even more challenging mathematical problem. Since the hydropower production functions are nonlinear, hyperplane curve fitting is used to linearize each power production function. The goal of the GMSP is to find an optimal schedule plan to decide when to shut down generators for maintenance. Therefore, one production function needs to be formulated per generator combination. Formulating so many power production functions with hyperplanes leads to a rather large number of constraints. To accelerate the solving time of the problem, a new heuristic based on the mean square algorithm is used to substitute some generator combinations based on a loss-of-power criterion. Thanks to this heuristic the number of constraints was substantially reduced and the solving time is almost ten times faster. Also, the power production and maintenance plannings are similar compared to those of the formulation without the heuristic.
10:55 AM - 11:20 AM
Long-term hydroclimatic persistence and the management of complex water resources systems
The operation of multireservoir systems is a challenging decision-making problem due to the presence of (i) multiple, often conflicting, objectives (e.g. hydropower generation versus irrigated agriculture), (ii) stochastic variables (e.g. inflows, water demands, commodity prices), (iii) nonlinear relationships, (e.g. hydropower production function) and (iv) trade-offs between immediate and future consequences. Stochastic Dual Dynamic Programming (SDDP) is one the few optimization techniques that largely remove these limitations. In SDDP, the hydrologic uncertainty is often captured by variants of a multi-site periodic autoregressive (MPAR) model. However, MPAR models are unable to capture the long-term persistence of the streamflow process found in some regions, which may lead to suboptimal reservoir operating policies. We propose an extension of the SDDP algorithm that can take handle the long-term persistence and provide reservoir operating policies that explicitly capture regime shifts. To achieve this, the state-space vector now includes a 'hidden' climate variable whose transition is governed by a Hidden Markov Model (HMM). The Senegal River Basin (SRB), whose flow regime is characterized by multiyear dry, normal, and wet periods, is used as a case study. To assess the economic value associated with the incorporation of the long-term persistence, we compared the performance of the water resources system with and without the additional climate state variable.
11:20 AM - 11:45 AM
Cluttering management during unit restoration in hydroelectric generating stations
Hydraulic turbine-generator units are made up of large parts. Like a stack, to have access to a part, one must first remove all the parts above it and store them inside the station. At the same time, new parts arrive and must also be stored in the station waiting to be lowered into the turbine pit. Storage space being limited, this creates a lot of clutter in the stations, which increases the restoring cost since the stored parts must be moved around repeatedly if not properly planned. An implicit enumeration approach will be presented in this talk to minimize the displacement of stored parts. Good performances are obtained since the problem is strongly constrained. Preliminary results will be presented.
11:45 AM - 12:10 PM
Stochastic optimization model for the short-term hydropower problem
We present an approach to solve the short-term unit commitment problem with uncertain inflow. The inflows are represented using scenario trees. The Backward reduction method is chosen to construct different scenario trees. This method seeks to minimize the number of scenarios of a fan tree based on historical and forecasted inflows. Different scenarios trees are obtained and a stochastic input process represented in the form of a scenario tree. A two-phase multistage stochastic model is implemented to solve the short-term unit commitment problem. The model is tested on a 10 day rolling-horizon with 14 forecasted days. Computational results are reported to evaluate the impact of the scenario tree reduction on the performance of the hydropower production.