# AI-Based Scheduling Models, Optimization, and Prediction for Hydropower Generation: Opportunities, Issues, and Future Directions

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## Abstract

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## 1. Introduction

## 2. Hydropower Scheduling Models

#### 2.1. Approximating Hydropower Production

- The linear approximation of the water level produces more accurate results than the estimation of the turbine’s rotational speed.
- The mean absolute error (MAE) of the linear estimates for the rotational speed of the turbine is less than 10%, while the MAE of the linear estimates for the water level in the reservoir is less than 1%.
- When significant changes occur in the opening and closing of the valves, the performance of the estimations decreases.

#### 2.2. Scenario Tree

## 3. Hydropower Optimization Models, a Review

## 4. Applications of Artificial Intelligence Techniques for Optimization Problems

- What kinds of challenges in optimization can be solved using machine learning? What is it that makes them so challenging?
- When it comes to machine learning on a big scale, which optimization strategies have shown to be the most successful, and why?
- What new developments have been made recently in the design of solution algorithms, and what questions still need to be answered in this field of research?

#### 4.1. Optimization Algorithms in Machine Learning

#### 4.2. Unconstrained Optimization

#### 4.3. Machine Learning as an Optimization Problem

#### 4.4. Overview of Different Optimizers for Neural Networks

- AdaDelta/RMSProp: One of the problems with the AdaGrad method is that the learning rate tends towards zero when there is a large number of iterations. In order to avoid this fate, AdaDelta [31] and RMSProp [32] use only the gradients of the most recent iterations. Moreover, each iteration is subject to a degenerative average of the previous gradients, allowing the calculation of a cumulative momentum.
- Adam: Adaptive moment estimation (Adam) is a method reusing the advances of AdaDelta/RMSProp in a more efficient formula for problem solving [33].
- SAG: Stochastic Average Gradient (SAG) is an attempt to improve the convergence time compared to the previous methods [34]. As the name implies, the SAG method uses only a sample of the previous gradient history while keeping the totality of the gradients of the previous iterations computed this way.

#### 4.5. Adapting DNNs for Hessian-Free Optimization

#### 4.5.1. Damping

#### 4.5.2. Generalized Gauss–Newton Matrix

#### 4.5.3. Sub-Sampling

#### 4.5.4. Adapting Newton-CG

#### 4.6. Optimization with Reinforcement Learning

**Agent**making decisions a (actions) with respect to its

**state**and

**environment**s. The actions taken by the agent influence the environment.

**rewards**$r({s}_{t-1},{a}_{t-1},{s}_{t})$, which are obtained when the Agent performs a good action at time t.

**policies**$\pi \left(a\right|s)$ represent the functions allowing the Agent to decide according to its environment. The

**probability**$p\left({s}^{\prime}\right|s,a)$ represents the probability that the Agent performs an action transforming the current environment s to ${s}^{\prime}$. In contrast, $p({s}^{\prime},r|s,a)$ represents the probability that the state change ${s}^{\prime}$ results in a reward.

#### 4.7. Machine Learning Improvements

## 5. Machine Learning in Hydropower Production

#### 5.1. Linear Regression

#### 5.2. Random Forest

- The time at which the data were collected.
- The level of water in the reservoir.
- The volume of discharged water.
- The energy generated.
- One of the 15 plant schedules must reach its goal.

#### 5.3. Reinforcement Learning

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

P | Power produced for a turbine in Kilowatt |

$\eta $ | Efficiency of a turbine |

$\varphi $ | The energy loss approximated in meters |

${e}_{f}$ | The water level in the forebay |

${e}_{t}$ | The tailrace elevation |

g | Gravitational acceleration constant 9.8 m/s${}^{2}$ |

${h}_{net}$ | the net water head in meters of the dam |

${Q}_{tot}$ | total amount of water discharge in m${}^{3}$/s |

${Q}_{turb}$ | total amount of water discharge in m${}^{3}$/s |

${R}^{2}$ | R-Squared |

w and $\tau $ | Precision and recall variables |

AC | Alternating Current |

ACKTR | Actor-Critic using the Kronecker-Factored Trust Region |

AdaGrad | Adaptive Gradient Algorithm |

Adam | for adaptive moment estimation |

AI | Artificial Intelligence |

AWT | Adaptive Wavelet Transform |

BDTR | Boosted Decision Tree Regression |

BFGS | Broy-den–Fletcher–Goldfarb–Shanno |

BLR | Neural Network Regression |

DFR | Decision Forest Regression |

DNN | Deep Neural Networks |

DQN | Deep-Q Learning |

DRL | Deep Reinforcement Learning |

K-FAC | Kronecker-factored Approximate Curvature |

LMW | Linear Moving Window |

LR | Linear Regression |

LSTM | Long Short-Term Memory |

MAE | Mean Absolute Error |

MPD | Markov Decision Process |

MSE | Mean Square Error |

NAG | Nesterov Accelerated Gradient |

NNR | Bayesian Linear Regression |

RAE | Relative Absolute Error |

RF | Random Forest |

RMSE | Root Mean Square Error |

RMSprop | Root Mean Squared Propagation |

RNN | Recurrent Neural Network |

SAG | Stochastic Average Gradient |

SDP | Stochastic Dynamic Programming |

SGD | Stochastic Gradient Descent |

SWATS | Switching from Adam to SGD |

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**Figure 1.**An example of a hydropower system with three reservoirs and two powerhouses. The arrow shows the direction of water movement, which can be held and released when interacting with a reservoir (triangle) and a powerhouse (rectangle).

**Figure 2.**The dot at ${x}_{k}$ on a convex f moves towards the next iteration ${x}_{k+1}$ with a step size ${\alpha}_{k}$. The descent direction is given by the gradient $\nabla f\left({x}_{k}\right)$, which is equal to zero when $\nabla f\left({x}^{\ast}\right)$.

Name | Machine Learning Model | Year | Dataset | Objective |
---|---|---|---|---|

[51] | LR (LMW) | 2017 | 30 years of annual inflows in 30 regions. | Long-term annual prediction for water inflow prediction. |

[52] | LR | 2014 | Monthly data on the production of 132 power stations and the runoff from 1989 to 2008. | Project the trend of changes in hydroelectric production up to 2039 |

[50] | LR (BDTR) (DFR) (NNR) (BLR) | 2020 | 12,531 instances containing 34 years of historical data + a set of 82,057 h of data recorded between 2010 and 2019. | Predict water level one to seven days in advance by testing four machine learning algorithms (BDTR, DFR, NNR and BLR) for SC1 and SC2. |

[53] | LR | 2021 | 26 years of precipitation data from 1993 to 2019 measured at 6 different locations. | Predict the electricity production of a hydroelectric plant. |

[54] | RF | 2020 | Analyzing daily auction data for the sale of hydroelectricity from Norway, data based on [55]. | Observe if the data obtained in their previous work can be used in a machine learning classification or regression models. |

[56] | RF (C4.5, improved C4.5, ID3-IV, CHAID) | 2021 | Sample sets of each hydroplant production and divided into winter and summer. | Make quick decisions (24 h) for production. Comparison of 4 random forest algorithms. |

[57] | ACO-RF-AWT-LSTM | 2021 | 6205 daily data, from 2005 to 2019, retrieved from a power station in the western region of Azerbaijan. | Predicting short-term hydroelectric production. |

[58] | DRL (DQN) | 2020 | Daily precipitation and 10-day inflows of each reservoir from 1967 to 2015. | Optimize a system of three hydroplant. |

[59] | DRL | 2020 | Simplified historical dataset with Nordic European market price scenarios (2008 to 2019) and Water supply from four reservoirs of Norway between 1958 and 2019. | Optimize annual revenue based on water supply and electricity price. |

[60] | RL | 2022 | 1000 years of data simulated by Rio Tinto. | Compare a reinforcement learning model with traditional medium-term stochastic optimization methods in a three reservoirs system. Observe the behaviour of chance constraints. |

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**MDPI and ACS Style**

Villeneuve, Y.; Séguin, S.; Chehri, A.
AI-Based Scheduling Models, Optimization, and Prediction for Hydropower Generation: Opportunities, Issues, and Future Directions. *Energies* **2023**, *16*, 3335.
https://doi.org/10.3390/en16083335

**AMA Style**

Villeneuve Y, Séguin S, Chehri A.
AI-Based Scheduling Models, Optimization, and Prediction for Hydropower Generation: Opportunities, Issues, and Future Directions. *Energies*. 2023; 16(8):3335.
https://doi.org/10.3390/en16083335

**Chicago/Turabian Style**

Villeneuve, Yoan, Sara Séguin, and Abdellah Chehri.
2023. "AI-Based Scheduling Models, Optimization, and Prediction for Hydropower Generation: Opportunities, Issues, and Future Directions" *Energies* 16, no. 8: 3335.
https://doi.org/10.3390/en16083335