Comparing stochastic optimization methods to solve the medium-term operation planning problem

Abstract

Abstract. The Medium-Term Operation Planning (MTOP) of hydrothermal systems aimsto define the generation for each power plant, minimizing the expected operating cost over the planning horizon. Mathematically, this task can be characterized as a linear, stochastic, large-scale problem which requires the application of suitable optimization tools. To solve this problem, this paper proposes to use the Nested Decomposition, frequently used to solve similar problems (as in Brazilian case), and Progressive Hedging, an alternative method, which has interesting features that make it promising to address this problem. To make a comparative analysis between these two methods with respect to the quality of the solution and the computational burden, a benchmark is established, which is obtained by solving a single Linear Programming problem (the Deterministic Equivalent Problem). An application considering a hydrothermal system is carried out.Mathematical subject classification: Primary: 06B10; Secondary: 06D05.

Medium-Term Hydrothermal Scheduling of the Infiernillo Reservoir Using Stochastic Dual Dynamic Programming (SDDP): A Case Study in Mexico

“…Officially, the deterministic approach has been employed in Mexico to solve the MTHS problem. Although this approach is the basis for the stochastic programming approach, its main drawback is that it does not model the stochastic nature of the problem due to its assumption that only one scenario will occur [12]; therefore, through this approach, it is not possible to obtain a decision that considers the other possible scenarios that can also happen, and one can only obtain a decision that is optimal for a particular realization [13]. Given the stochastic nature of the MTHS problem, it is essential to consider this ingredient in the optimization model in order to obtain more accurate solutions and reduce the expected total cost.…”

“…It is a large-scale problem because the number of scenarios grows exponentially with the number of stages [13]. Since the hydrothermal scheduling problem is coupled in time, before making present decisions it is therefore necessary to estimate their future consequences.…”

Day‐ahead unit commitment for hydro‐thermal coordination with high participation of wind power

“…Progressive hedging presents some remarkable features to solve high-dimensional problems with implicit stochastic models. This method was proposed originally by Rockafellar and Wets [44] and it has been used recently to solve operational planning for different term periods [45][46][47][48][49][50]. Real-time dispatching has been solved with progressive hedging in Ref.…”

A computational study of a stochastic optimization model for long term hydrothermal scheduling

“…In order to deal with this task, a chain of models is normally used, dividing the main problem into a hierarchy of smaller subproblems with different planning horizons and degrees of detail. Then, some information from the long-term scheduling problem [1,2] is used as input to the more detailed mid-term problem [3][4][5] which, in turn, feed their results into the short-term scheduling problem [6][7][8][9][10][11]. The information transferred from one problem to other can be some target of generation [12] or a function that describes the future operation cost with respect the storage level of water in the reservoirs [13].…”