Pascal Côté

Comparison of Stochastic Optimization Algorithms in Hydrological Model Calibration

AbstractTen stochastic optimization methods—adaptive simulated annealing (ASA), covariance matrix adaptation evolution strategy (CMAES), cuckoo search (CS), dynamically dimensioned search (DDS), differential evolution (DE), genetic algorithm (GA), harmony search (HS), pattern search (PS), particle swarm optimization (PSO), and shuffled complex evolution–University of Arizona (SCE–UA)—were used to calibrate parameter sets for three hydrological models on 10 different basins. Optimization algorithm performance was compared for each of the available basin-model combinations. For each model-basin pair, 40 calibrations were run with the 10 algorithms. Results were tested for statistical significance using a multicomparison procedure based on Friedman and Kruskal-Wallis tests. A dispersion metric was used to evaluate the fitness landscape underlying the structure on each test case. The trials revealed that the dimensionality and general fitness landscape characteristics of the model calibration problem are impo...

Water resources optimization method in the context of climate change

AbstractThis paper describes a method for water resources optimization in the context of climate change. The method takes into account the midterm variability or seasonality of inflows as well as the uncertainty in the climate change and resulting flows. The objective of the optimization algorithm is to find a compromise between the long-term planning of water resources systems and the midterm operations for optimum hydropower production. The proposed algorithm consists of the midterm dynamic programming formulation coupled with the use of the expected value of the cost-to-go function between two consecutive long-term periods. Future climate projections and transition probabilities between projections represent the stochastic nature of inflows and the nonstationarity of climate. The performance of the method was evaluated through the simulation of inflow projections for the Manicouagan River basin in Quebec, Canada. The results showed that the algorithm was able to adapt the operating policy to the climat...

Optimal Hydropower Generation Under Climate Change Conditions for a Northern Water Resources System

This paper examines climate change impacts on the water resources system of the Manicouagan River (Québec, Canada). The objective is to evaluate the performance of existing infrastructures under future climate projections and the associated uncertainties. The main purpose of the water resources system is hydropower production. A reservoir optimization algorithm, Sampling Stochastic Dynamic Programming (SSDP), was used to derive weekly operating decisions for the existing system subject to reservoir inflows reflecting future climate, for optimum hydropower production. These projections are simulations from the SWAT hydrologic model for climate change scenarios for the period from 2010 to 2099. Results show that the climate change will alter the hydrological regime of the study area: earlier timing of the spring flood, reduced spring peak flow, and increased annual inflows volume in the future compared to the historical climate. The SSDP optimization algorithm adapted the operating policy to the future hydrological regime by adjusting water reservoir levels in the winter and spring, and increasing the release through turbines, which in the end increased power generation. However, there could be more unproductive spills for some power plants, which would decrease the overall efficiency of the existing water resources system.

Stochastic short-term hydropower planning with inflow scenario trees

This paper presents an optimization approach to solve the short-term hydropower unit commitment and loading problem with uncertain inflows. A scenario tree is built based on a forecasted fan of inflows, which is developed using the weather forecast and the historical weather realizations. The tree-building approach seeks to minimize the nested distance between the stochastic process of historical inflow data and the multistage stochastic process represented in the scenario tree. A two-phase multistage stochastic model is used to solve the problem. The proposed approach is tested on a 31 day rolling-horizon with daily forecasted inflows for three power plants situated in the province of Quebec, Canada, that belong to the company Rio Tinto.

Self-Scheduling Short-Term Unit Commitment and Loading Problem

This paper presents a new method for solving the short-term unit commitment and loading problem for a specific hydropower system. Dynamic programming is used to compute maximum power output generated by a power plant. This information is then used as input of a two-phase optimization process. The first phase solves the relaxation of a nonlinear mixed-integer program in order to obtain the water discharge, reservoir volume and number of units working at each period in the planning horizon. The second stage solves a linear integer problem to determine which combination of turbines to use at each period. The goal is to maximize total energy produced over all periods of the planning horizon which consists of a week divided in hourly periods. Start-up of turbines are penalized. Numerical experiments are conducted on thirty different test cases for two Rio Tinto Alcan power plants with five turbines each.

Approximate stochastic dynamic programming for hydroelectric production planning

This paper presents a novel approach for approximate stochastic dynamic programming (ASDP) over a continuous state space when the optimization phase has a near-convex structure. The approach entails a simplicial partitioning of the state space. Bounds on the true value function are used to refine the partition. We also provide analytic formulae for the computation of the expectation of the value function in the “uni-basin” case where natural inflows are strongly correlated. The approach is experimented on several configurations of hydro-energy systems. It is also tested against actual industrial data.

Scenario-Tree Modeling for Stochastic Short-Term Hydropower Operations Planning

The authors investigate the complexity needed in the structure of the scenario trees to maximize energy production in a rolling-horizon framework. Three comparisons, applied to the stochastic short-term unit commitment and loading problem are conducted. The first one involves generating a set of scenario trees built from inflow forecast data over a rolling-horizon. The second replaces the entire set of scenario trees by the median scenario. The third replaces the set of trees by scenario fans. The method used to build scenario trees, based on minimization of the nested distance, requires three parameters: number of stages, number of child nodes at each stage, and aggregation of the period covered by each stage. The authors formulate the question of finding the best values of these parameters as a blackbox optimization problem that maximizes the energy production over the rolling-horizon. Numerical experiments on three hydropower plants in series suggest that using a set of scenario trees is preferable to using the median scenario, but using a fan of scenarios yields a comparable solution with less computational effort.

Controlled Approximation of the Stochastic Dynamic Programming Value Function for Multi-Reservoir Systems

We present an approximation of the Stochastic Dynamic Programming (SDP) value function based on a partition of the state space into simplices. The vertices of such simplices form an irregular grid over which the value function is computed. Under convexity assumptions, lower and upper bounds are developed over the state space continuum. The partition is then refined where the gap between these bounds is largest. This process readily provides a controllable trade-off between accuracy and solution time.

Comparing Model-Based and Model-Free Streamflow Simulation Approaches to Improve Hydropower Reservoir Operations

AbstractThis paper presents a comparison between an inflow model-based and an inflow model-free optimization method applied to a hydropower system. Widely used stochastic dynamic programming (SDP) ...

Evaluating Transition Probabilities for a Stochastic Dynamic Programming Model Used in Water System Optimization

AbstractStochastic dynamic programming is one of the most widely used optimization techniques for water system optimization. In this study, four methods for estimating transition probabilities have...