Short-Term Hourly Hydropower Prediction: Evaluating Long Short-Term Memory (LSTM) and Mixed-Integer Linear Programming (MILP)-Based Methods

Technical Summary: Short-Term Hourly Hydropower Prediction via LSTM and MILP

Problem Statement
The paper addresses the Short-Term Hydropower Scheduling (STHS) problem, specifically focusing on the prediction of hourly water discharge for two interconnected hydropower plants (Chute-du-Diable and Chute-à-la-Savane) on the Péribonka River in Quebec, Canada. The core challenge involves managing water resources to meet energy demands while adhering to reservoir constraints and operational realities. Traditional approaches rely on Mixed-Integer Linear Programming (MILP) to optimize production, but these models face scalability issues and computational complexity, particularly when dealing with nonconvexities and large-scale systems. While machine learning (ML) has shown promise in medium- and long-term forecasting, its application to short-term, hourly scheduling remains underexplored, particularly for run-of-river influenced systems where water discharge is heavily dependent on upstream flow and natural inflow variability.

Methodology
The study proposes and evaluates an autoregressive Long Short-Term Memory (LSTM) model designed to predict the total water discharge (sum of discharge flow and spillage) for a 96-hour horizon.

• Data Source: The model utilizes 12 years of historical data (December 2010 – December 2022) provided by Rio Tinto. The dataset includes hourly features such as reservoir volume, turbine unit states, natural inflow, and energy production.
• Preprocessing: Data cleaning involved smoothing outliers in natural inflow and discharge values. A moving average (MA) was applied to future inflow features to reduce noise and represent deterministic scenarios for training. For the downstream plant (CalS), the total inflow was calculated by adding the upstream plant's (CdD) predicted outflow to the local natural inflow, acknowledging the lack of travel time delay between the two plants.
• Model Architecture: The proposed solution is a supervised, autoregressive LSTM.
  • Input: A window of the previous 48 hours of data (including reservoir volume, active units, and inflow forecasts).
  • Mechanism: The model operates in a feedback loop where the prediction for one time step is fed back as input for the next, allowing it to generate a sequence of 96 future hours.
  • Configuration: The model uses 256 LSTM cells, the NADAM optimizer, and a Mean Squared Error (MSE) loss function. It was trained on 80% of the data (84,000 instances) and tested on 20% (20,938 instances).
• Benchmarking: The LSTM performance was compared against:
  1. A deterministic MILP model (previously developed for this specific system) that maximizes energy generation subject to reservoir and unit commitment constraints.
  2. Historical operational decisions (real-world data).
• Evaluation Metrics: Performance was assessed using Mean Absolute Error (MAE), MSE, and Root Mean Squared Error (RMSE). Crucially, feasibility was evaluated by analyzing whether predicted reservoir volumes respected physical bounds (minimum and maximum levels) and by calculating the resulting energy production.

Key Results

• Prediction Accuracy: The LSTM model successfully captured temporal patterns in water discharge. The CalS plant (downstream) showed better performance metrics (lower MSE and MAE) than the CdD plant, likely due to the inclusion of upstream discharge features which helped correlate operations.
• Comparison with MILP and Reality:
  • In 2021 (lower inflow years), the LSTM predictions generally fell between the optimized MILP decisions and historical real-world decisions, suggesting a compromise behavior.
  • In 2020 (high inflow years), the LSTM tended to predict lower discharge values compared to both reality and the MILP optimization.
• Feasibility and Constraints: A significant limitation identified was the model's inability to explicitly enforce reservoir constraints.
  • While the MILP model strictly adhered to volume bounds, the LSTM model produced infeasible solutions in several instances, particularly during high inflow periods (e.g., 2020), where predicted reservoir volumes exceeded maximum capacity.
  • The model struggled to adapt to sudden, abrupt changes in water discharge, often adjusting predictions gradually rather than instantaneously, which led to volume accumulation errors over the 96-hour horizon.
• Horizon Limitations: The authors observed a degradation in prediction accuracy after approximately 72 hours, suggesting that the 96-hour horizon used for comparability with the MILP model may be too long for the current autoregressive setup.

Significance and Claims
The paper claims to be the first application of a supervised autoregressive LSTM model specifically designed to predict future water flow decisions for a hydropower system using previous plant states. Its primary contributions are:

1. Benchmarking: It provides a clear, direct comparison between a data-driven Recurrent Neural Network (RNN) approach and a traditional MILP optimization method for the STHS problem, a gap noted in existing literature.
2. Proof of Concept: It demonstrates that ML models can approximate operational decisions and capture the sequential dependencies inherent in hydropower scheduling, offering a potential alternative to computationally heavy optimization models.
3. Limitations as Future Direction: The authors modestly conclude that while the LSTM offers a viable, fast alternative for short-term management, it currently lacks the explicit constraint handling of MILP. They identify the need for future work to incorporate constraint mechanisms (e.g., post-prediction correction or hybrid models), reduce the prediction horizon to improve accuracy, and better model inflow uncertainty.

The study positions the LSTM not as a replacement for optimization in all contexts, but as a promising tool for rapid, adaptive decision-making that complements traditional methods, provided that feasibility constraints are addressed in future iterations.