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\section{Abstract}
The integration of renewable energy sources has introduced greater volatility to the electricity market, making accurate imbalance forecasting increasingly important. The objective of this thesis is to explore the effectiveness of generative modeling techniques in forecasting imbalance prices and optimizing battery usage for energy trading in the Belgian electricity market. Various generative models were trained using data provided by Elia, the Transmission System Operator (TSO) in Belgium. The models incorporated different input features, including load, wind, photovoltaic power, and nominal net position. These models were evaluated using Mean Absolute Error (MAE), Mean Squared Error (MSE), and Continuous Ranked Probability Score (CRPS). The primary approach involved modeling Net Regulation Volume (NRV) values and generating multiple full-day NRV samples, which were then used to reconstruct imbalance prices. These reconstructed prices were used to optimize a simple policy for charging and discharging a battery, aimed at maximizing profit. Traditional evaluation metrics did not correlate well with the profitability of the models, necessitating evaluation based on profit generation. Among the tested models, the diffusion model achieved a profit of €218,170.75, representing a 9.74\% increase over the baseline policy, which used the previous day's NRV as a prediction. This demonstrates the potential benefits of advanced generative models for enhancing decision-making in energy trading. This thesis underscores the potential of generative modeling in forecasting imbalance prices and optimizing energy trading policies. Focusing on profitability as a key metric can lead to more practical and impactful applications in the energy market, particularly as the share of renewable energy continues to grow. Overall, this thesis highlights the importance of using profitability as a key metric for evaluating model performance and shows the potential of generative modeling in enhancing energy trading strategies. Furthermore, it shows that diffusion models can be particularly effective in improving energy trading policies and maximizing profit in the electricity market.

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\section{Conclusion}
During this thesis, multiple models were developed and trained to predict the Net Regulation Volume (NRV) values for specific days using data provided by Elia, the Transmission System Operator (TSO) in Belgium. The models incorporated various input features, including load, wind, photovoltaic power, and nominal net position. To evaluate their performance, the models were assessed using several metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), and Continuous Ranked Probability Score (CRPS).
The primary objective was to model imbalance prices and generate multiple predictions for these prices. These predictions were then utilized to optimize a simple policy for charging and discharging a battery to maximize profit. The optimization process followed a two-step approach: first, different models were used to predict NRV values and generate multiple full-day NRV samples. These samples were then used to reconstruct imbalance prices. Based on these reconstructed prices, the policy determined optimal charge and discharge thresholds for each prediction, with the mean of these thresholds serving as the final thresholds for a given day. The policy's effectiveness was measured by the profit it generated during the test period.
One significant finding is that traditional evaluation metrics like MAE, MSE, and CRPS do not correlate well with the profitability of the policy. This disconnect necessitates evaluating the models based on the profit they achieve during training, which increases computational complexity and duration. To mitigate this, a smaller validation set can be used to compare models based on maximum profit rather than conventional metrics. This approach revealed that better modeling performance does not always translate into higher profits.
Among the models tested, only the diffusion model surpassed the baseline policy, which used the previous day's NRV as a prediction. The diffusion model achieved a profit of €218,170.75, marking a 9.74\% increase over the baseline. This demonstrates the potential benefits of modeling imbalance prices and utilizing generated samples to optimize a simple policy for energy trading.
Future improvements to the diffusion model could involve more sophisticated implementations and advanced conditioning techniques. The current model is basic, and incorporating more complex policies could further enhance battery utilization and profitability.
In conclusion, this thesis underscores the potential of generative modeling in forecasting imbalance prices and optimizing energy trading policies. While traditional evaluation metrics have limitations, focusing on profitability as a measure of success can lead to more practical and impactful applications in the energy market.
In conclusion, this thesis shows that generative modeling can be very useful for predicting imbalance prices and improving energy trading strategies. Traditional metrics like MAE, MSE, and CRPS don't always reflect how profitable a model can be. Instead, evaluating models based on the profit they generate is more effective and practical. This approach can lead to better and more impactful applications in the energy market.

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@@ -84,7 +84,7 @@ Table \ref{tab:aqr_models_comparison} presents a comprehensive comparison of aut
(2 -256) & 20 & 108.84 & \textbf{218,141.31} & 283.94 & 428.6875 \\
(2 -256) & 20 & 105.31 & 215,862.35 & 283.06 & 440.2500 \\
(2 -512) & 20 & 103.41 & 216,411.79 & 282.56 & 450.3125 \\
(2 - 1024) & 20 & \textbf{100.36} & 215,686.32 & 282.69 & 463.6875 \\
(2 - 1024) & 20 & 100.36 & 215,686.32 & 282.69 & 463.6875 \\
(2 -256) & 50 & 117.81 & 216,632.39 & 282.75 & 421.3125 \\
(2 -512) & 50 & 180.83 & 210,769.03 & 282.06 & 446.4375 \\
(2 - 1024) & 50 & 179.59 & 212,793.94 & 282.88 & 454.5000 \\
@@ -125,8 +125,7 @@ Some examples of the generated samples from the model with the lowest CRPS and t
\label{fig:diffusion_policy_comparison_high_low_crps}
\end{figure}
A comparison of the baselines and the best-performing models is shown in Table \ref{tab:policy_comparison}. The best-performing model is the diffusion model with two layers consisting of 256 hidden units. Only the NRV values of yesterday are used as input features and 50 steps were used. The profit achieved using this model is €218,170.75 with 283.00 charge cycles. This is an improvement of 9.74\% compared to the baseline that uses the NRV of yesterday as a prediction. When the policy is evaluated using the real NRV data for the evaluated day, a total profit of €230,317.84 is achieved. This is the maximum profit that can be achieved using the simple policy that determines a buying and selling threshold for each day. The best-performing diffusion model achieves a profit of €218,170.75. This means that 94.78\% of the maximum profit is achieved using the diffusion model. This is a significant improvement compared to the baseline that uses the NRV of yesterday as a prediction. This baseline achieves a profit of €198,807.09 which is 94.72\% of the maximum profit. This shows that integrating the use of multiple full-day NRV samples into the policy can improve the profit significantly.
% TODO: Add linear model results
\begin{table}[H]
\centering
\begin{adjustbox}{max width=\textwidth}
@@ -143,7 +142,7 @@ A comparison of the baselines and the best-performing models is shown in Table \
\multicolumn{5}{l}{\textbf{Models}} \\
\midrule
NAQR: Linear & & & & \\
NAQR: Linear & All & 191,421.62 & 282.81 & -3.85\% \\
NAQR: Non-Linear (2 - 512) & NRV & 189,982.08 & 283.81 & -4.43\% \\
&&& \\
AQR: Linear & NRV & 190,501.34 & 282.94 & -4.17\% \\
@@ -159,5 +158,17 @@ A comparison of the baselines and the best-performing models is shown in Table \
\label{tab:policy_comparison}
\end{table}
\section{Conclusion}
In this thesis, generative methods are explored to model the NRV data of the Belgian electricity market. These methods are then used to improve the decision-making to charge and discharge a battery to make a profit.
A comparison of the baselines and the best-performing models is shown in Table \ref{tab:policy_comparison}. The most effective model is the diffusion model with two layers of 256 hidden units, utilizing only the NRV values from the previous day as input features and employing 50 steps. This model is unique in that it surpasses the Yesterday NRV baseline, achieving a profit of €218,170.75 with 283.00 charge cycles. This represents a 9.74\% improvement over the baseline that uses the NRV of the previous day for prediction. When the policy is evaluated using the actual NRV data for the evaluated day, the maximum achievable profit with a simple policy is €230,317.84. Thus, the best-performing diffusion model achieves 94.78\% of this maximum potential profit.
In contrast, all other evaluated models yielded lower profits compared to the Yesterday NRV baseline. Specifically, the NAQR models, both linear and non-linear, failed to outperform the baseline. The NAQR Non-Linear model, with two layers of 512 hidden units, achieved a profit of €189,982.08 with 283.81 charge cycles, resulting in a 4.43\% decrease compared to the Yesterday NRV baseline. Similarly, the NAQR Linear model did not yield competitive results.
The AQR models also underperformed relative to the baseline. The AQR Linear model, which used NRV features, achieved a profit of €190,501.34 with 282.94 charge cycles, representing a 4.17\% decrease. The AQR Non-Linear model, with four layers of 512 hidden units and using all features, achieved a slightly better profit of €196,999.03 with 284.88 charge cycles but still fell short by 0.91\%. The AQR GRU model, incorporating two layers of 256 hidden units and using NRV features, recorded a profit of €196,655.36 with 283.81 charge cycles, which is 1.08\% lower than the baseline.
Overall, the diffusion model is the only one that significantly improves upon the Yesterday NRV baseline, demonstrating its superior ability to predict and optimize for higher profits. These results show that using a generative model to generate samples of the NRV that can be used to optimize the buying and selling of electricity can be beneficial. The results are also visualized in Figure \ref{fig:profit_comparison}.
\begin{figure}[H]
\centering
\includegraphics[width=0.8\textwidth]{images/comparison/final_comparison.png}
\caption{Comparison of the profit achieved by the baselines and the best-performing models. The improvement is calculated compared to the baseline that uses the NRV of yesterday as a prediction.}
\label{fig:profit_comparison}
\end{figure}

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Reports/Thesis/verslag.tex
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@@ -179,6 +179,7 @@
% ------------ Introduction ---------
\include{sections/abstract}
\include{sections/introduction}
@@ -190,6 +191,8 @@
\input{sections/results}
\input{sections/conclusion}
\newpage
\printacronyms[display=all,sort=true]

67
Reports/Thesis/verslag.toc
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@@ -1,35 +1,36 @@
\acswitchoff
\babel@toc {english}{}\relax
\contentsline {section}{\numberline {1}Introduction}{2}{section.1}%
\contentsline {section}{\numberline {2}Electricity market}{4}{section.2}%
\contentsline {section}{\numberline {3}Generative modeling}{8}{section.3}%
\contentsline {subsection}{\numberline {3.1}Quantile Regression}{9}{subsection.3.1}%
\contentsline {subsection}{\numberline {3.2}Autoregressive vs Non-Autoregressive models}{12}{subsection.3.2}%
\contentsline {subsection}{\numberline {3.3}Model Types}{13}{subsection.3.3}%
\contentsline {subsubsection}{\numberline {3.3.1}Linear Model}{13}{subsubsection.3.3.1}%
\contentsline {subsubsection}{\numberline {3.3.2}Non-Linear Model}{14}{subsubsection.3.3.2}%
\contentsline {subsubsection}{\numberline {3.3.3}Recurrent Neural Network (RNN)}{14}{subsubsection.3.3.3}%
\contentsline {subsection}{\numberline {3.4}Diffusion models}{15}{subsection.3.4}%
\contentsline {subsubsection}{\numberline {3.4.1}Overview}{15}{subsubsection.3.4.1}%
\contentsline {subsubsection}{\numberline {3.4.2}Applications}{16}{subsubsection.3.4.2}%
\contentsline {subsubsection}{\numberline {3.4.3}Generation process}{16}{subsubsection.3.4.3}%
\contentsline {subsection}{\numberline {3.5}Evaluation}{18}{subsection.3.5}%
\contentsline {section}{\numberline {4}Policies}{20}{section.4}%
\contentsline {subsection}{\numberline {4.1}Baselines}{20}{subsection.4.1}%
\contentsline {subsection}{\numberline {4.2}Policies based on NRV generations}{20}{subsection.4.2}%
\contentsline {section}{\numberline {5}Literature Study}{22}{section.5}%
\contentsline {subsection}{\numberline {5.1}Day-Ahead Electricity Price Forecasting}{22}{subsection.5.1}%
\contentsline {subsection}{\numberline {5.2}Imbalance Price Forecasting}{23}{subsection.5.2}%
\contentsline {subsection}{\numberline {5.3}Policies for Battery Optimization}{23}{subsection.5.3}%
\contentsline {section}{\numberline {6}Results \& Discussion}{24}{section.6}%
\contentsline {subsection}{\numberline {6.1}Data}{24}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}Quantile Regression}{25}{subsection.6.2}%
\contentsline {subsubsection}{\numberline {6.2.1}Linear Model}{25}{subsubsection.6.2.1}%
\contentsline {subsubsection}{\numberline {6.2.2}Non-Linear Model}{32}{subsubsection.6.2.2}%
\contentsline {subsubsection}{\numberline {6.2.3}GRU Model}{35}{subsubsection.6.2.3}%
\contentsline {subsection}{\numberline {6.3}Diffusion}{39}{subsection.6.3}%
\contentsline {subsection}{\numberline {6.4}Comparison}{43}{subsection.6.4}%
\contentsline {subsection}{\numberline {6.5}Policies for battery optimization}{48}{subsection.6.5}%
\contentsline {subsubsection}{\numberline {6.5.1}Baselines}{48}{subsubsection.6.5.1}%
\contentsline {subsubsection}{\numberline {6.5.2}Policy using generated NRV samples}{49}{subsubsection.6.5.2}%
\contentsline {section}{\numberline {7}Conclusion}{53}{section.7}%
\contentsline {section}{\numberline {1}Abstract}{2}{section.1}%
\contentsline {section}{\numberline {2}Introduction}{3}{section.2}%
\contentsline {section}{\numberline {3}Electricity market}{5}{section.3}%
\contentsline {section}{\numberline {4}Generative modeling}{9}{section.4}%
\contentsline {subsection}{\numberline {4.1}Quantile Regression}{10}{subsection.4.1}%
\contentsline {subsection}{\numberline {4.2}Autoregressive vs Non-Autoregressive models}{13}{subsection.4.2}%
\contentsline {subsection}{\numberline {4.3}Model Types}{14}{subsection.4.3}%
\contentsline {subsubsection}{\numberline {4.3.1}Linear Model}{14}{subsubsection.4.3.1}%
\contentsline {subsubsection}{\numberline {4.3.2}Non-Linear Model}{15}{subsubsection.4.3.2}%
\contentsline {subsubsection}{\numberline {4.3.3}Recurrent Neural Network (RNN)}{15}{subsubsection.4.3.3}%
\contentsline {subsection}{\numberline {4.4}Diffusion models}{16}{subsection.4.4}%
\contentsline {subsubsection}{\numberline {4.4.1}Overview}{16}{subsubsection.4.4.1}%
\contentsline {subsubsection}{\numberline {4.4.2}Applications}{17}{subsubsection.4.4.2}%
\contentsline {subsubsection}{\numberline {4.4.3}Generation process}{17}{subsubsection.4.4.3}%
\contentsline {subsection}{\numberline {4.5}Evaluation}{19}{subsection.4.5}%
\contentsline {section}{\numberline {5}Policies}{21}{section.5}%
\contentsline {subsection}{\numberline {5.1}Baselines}{21}{subsection.5.1}%
\contentsline {subsection}{\numberline {5.2}Policies based on NRV generations}{21}{subsection.5.2}%
\contentsline {section}{\numberline {6}Literature Study}{23}{section.6}%
\contentsline {subsection}{\numberline {6.1}Day-Ahead Electricity Price Forecasting}{23}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}Imbalance Price Forecasting}{24}{subsection.6.2}%
\contentsline {subsection}{\numberline {6.3}Policies for Battery Optimization}{24}{subsection.6.3}%
\contentsline {section}{\numberline {7}Results \& Discussion}{25}{section.7}%
\contentsline {subsection}{\numberline {7.1}Data}{25}{subsection.7.1}%
\contentsline {subsection}{\numberline {7.2}Quantile Regression}{26}{subsection.7.2}%
\contentsline {subsubsection}{\numberline {7.2.1}Linear Model}{26}{subsubsection.7.2.1}%
\contentsline {subsubsection}{\numberline {7.2.2}Non-Linear Model}{33}{subsubsection.7.2.2}%
\contentsline {subsubsection}{\numberline {7.2.3}GRU Model}{36}{subsubsection.7.2.3}%
\contentsline {subsection}{\numberline {7.3}Diffusion}{40}{subsection.7.3}%
\contentsline {subsection}{\numberline {7.4}Comparison}{44}{subsection.7.4}%
\contentsline {subsection}{\numberline {7.5}Policies for battery optimization}{49}{subsection.7.5}%
\contentsline {subsubsection}{\numberline {7.5.1}Baselines}{49}{subsubsection.7.5.1}%
\contentsline {subsubsection}{\numberline {7.5.2}Policy using generated NRV samples}{50}{subsubsection.7.5.2}%
\contentsline {section}{\numberline {8}Conclusion}{55}{section.8}%

35
src/notebooks/thesis-visualizations.ipynb
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34
src/training_scripts/non_autoregressive_quantiles.py
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@@ -5,7 +5,7 @@ clearml_helper = ClearMLHelper(
project_name="Thesis/NrvForecast"
)
task = clearml_helper.get_task(
task_name="NAQR: Non Linear (2 - 256) + All"
task_name="NAQR: Linear"
)
task.execute_remotely(queue_name="default", exit_process=True)
@@ -31,16 +31,16 @@ from src.models.time_embedding_layer import TimeEmbedding
data_config = DataConfig()
data_config.NRV_HISTORY = True
data_config.LOAD_HISTORY = True
data_config.LOAD_FORECAST = True
data_config.LOAD_HISTORY = False
data_config.LOAD_FORECAST = False
data_config.WIND_FORECAST = True
data_config.WIND_HISTORY = True
data_config.WIND_FORECAST = False
data_config.WIND_HISTORY = False
data_config.PV_FORECAST = True
data_config.PV_HISTORY = True
data_config.PV_FORECAST = False
data_config.PV_HISTORY = False
data_config.NOMINAL_NET_POSITION = True
data_config.NOMINAL_NET_POSITION = False
data_config = task.connect(data_config, name="data_features")
@@ -75,17 +75,17 @@ model_parameters = {
model_parameters = task.connect(model_parameters, name="model_parameters")
# linear_model = LinearRegression(inputDim, len(quantiles) * 96)
linear_model = LinearRegression(inputDim, len(quantiles) * 96)
non_linear_model = NonLinearRegression(
inputDim,
len(quantiles) * 96,
hiddenSize=model_parameters["hidden_size"],
numLayers=model_parameters["num_layers"],
dropout=model_parameters["dropout"],
)
# non_linear_model = NonLinearRegression(
# inputDim,
# len(quantiles) * 96,
# hiddenSize=model_parameters["hidden_size"],
# numLayers=model_parameters["num_layers"],
# dropout=model_parameters["dropout"],
# )
model = non_linear_model
model = linear_model
model.output_size = 96
optimizer = torch.optim.Adam(model.parameters(), lr=model_parameters["learning_rate"])