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6
Reports/Thesis/acronyms.tex
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@@ -83,6 +83,10 @@
long = Cumulative Distribution Function
}
\DeclareAcronym{QE}{
short = QE,
long = Quarter Embedding
}
@@ -99,7 +103,7 @@
\DeclareAcronym{NP}{
short = NP,
long = Implicit Net Position
long = Nominal Net Position
}
\DeclareAcronym{TSO}{

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Reports/Thesis/sections/appendix.aux
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Reports/Thesis/sections/appendix.tex
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% horizontal page with one big figure
\begin{landscape}
\section{Appendix}
\begin{figure}[H]
\centering
% sample 864
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_864.jpeg}
\end{subfigure}
% sample 4320
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_4320.jpeg}
\end{subfigure}
% sample 6336
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_6336.jpeg}
\end{subfigure}
% sample 7008
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{AQR linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{AQR non-linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{AQR GRU model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_7008.jpeg}
\caption{Diffusion model}
\end{subfigure}
\caption{Comparison of the autoregressive models with the diffusion model}
\label{fig:ar_linear_gru_comparison}
\end{figure}
\begin{figure}[H]
\centering
% sample 864
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_linear_model_samples/NAQR_NRV_Load_Wind_PV_NP-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_gru_model_examples/NAQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_864.jpeg}
\end{subfigure}
% sample 4320
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_linear_model_samples/NAQR_NRV_Load_Wind_PV_NP-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_gru_model_examples/NAQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_4320.jpeg}
\end{subfigure}
% sample 6336
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_linear_model_samples/NAQR_NRV_Load_Wind_PV_NP-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_gru_model_examples/NAQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_6336.jpeg}
\end{subfigure}
% sample 7008
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_linear_model_samples/NAQR_NRV_Load_Wind_PV_NP-Sample_7008.png}
\caption{NAQR linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{NAQR non-linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_gru_model_examples/NAQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{NAQR GRU model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_7008.jpeg}
\caption{Diffusion model}
\end{subfigure}
\caption{Comparison of the non-autoregressive models with the diffusion model}
\label{fig:ar_linear_gru_comparison}
\end{figure}
\end{landscape}

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Reports/Thesis/sections/results.tex
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@@ -26,11 +26,11 @@ The data useful to model the NRV is scattered over multiple categories. The data
\item \textbf{Photovoltaic power production estimation and forecast on Belgian grid (Historical)} \\
% https://opendata.elia.be/explore/dataset/ods032/table/?sort=datetime
The photovoltanic power production is also available in a quarter-hour interval. The production is also forecasted day-ahead and week-ahead. The data is provided for each of the provinces in Belgium. Forecasts are also available for the 3 Belgian regions (Flanders, Wallonia, Brussels) and the total Belgian production. The photovoltanic data has been provided since 01-04-2018 and is available to the present day. \cite{noauthor_photovoltaic_nodate}
The photovoltaic power production is also available in a quarter-hour interval. The production is also forecasted day-ahead and week-ahead. The data is provided for each of the provinces in Belgium. Forecasts are also available for the 3 Belgian regions (Flanders, Wallonia, Brussels) and the total Belgian production. The photovoltaic data has been provided since 01-04-2018 and is available to the present day. \cite{noauthor_photovoltaic_nodate}
\item \textbf{Wind power production estimation and forecast on Belgian grid (Historical)} \\
% https://opendata.elia.be/explore/dataset/ods031/information/
Just as the photovoltanic power production data, wind power production is available in a quarterly-hour interval for each of the provinces and regions in Belgium. This data also includes the real production and the forecasts. An additional column is available that shows if the power is generated offshore or onshore. During this thesis, the offshore and onshore data will be combined. The wind power production data has been provided since 01-01-2015 and is available to the present day. \cite{noauthor_wind_nodate}
Just as the photovoltaic power production data, wind power production is available in a quarterly-hour interval for each of the provinces and regions in Belgium. This data also includes the real production and the forecasts. An additional column is available that shows if the power is generated offshore or onshore. During this thesis, the offshore and onshore data will be combined. The wind power production data has been provided since 01-01-2015 and is available to the present day. \cite{noauthor_wind_nodate}
\item \textbf{Day-ahead implicit net position (Belgium's balance)} \\
% https://opendata.elia.be/explore/dataset/ods022/information/?sort=datetime

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Reports/Thesis/sections/results/models/comparison.tex
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@@ -1,5 +1,5 @@
\subsection{Comparison}
After training the different models and experimenting with various hyperparameters, the performance differences between the model architectures and methods can be compared using the \ac{MSE}, \ac{MAE}, and \ac{CRPS} metrics. Visual comparisons of some examples are also provided.
After training the different models and experimenting with various hyperparameters, the performance differences between the model architectures and methods can be compared using the \ac{MSE}, \ac{MAE}, and \ac{CRPS} metrics This is shown in Table \ref{tab:model_comparison}. Visual comparisons of some examples are also provided.
% Updated table using acronyms
\begin{table}[H]
@@ -15,6 +15,7 @@ After training the different models and experimenting with various hyperparamete
& & & & & \\
& \acs{AQR} & Non-Linear & 36346.57 & 144.80 & 84.51 & 422,925 \\
& \acs{NAQR} & Non-Linear & 40200.92 & 152.00 & 74.37 & 501,728 \\
& Diffusion & Non-Linear & 42984.02 & 157.54 & 77.92 & 3,116,896 \\
& & & & & \\
& \acs{AQR} & GRU & 37681.71 & 146.62 & 83.08 & 11,829,261 \\
& \acs{NAQR} & GRU & 40917.24 & 152.04 & 76.06 & 3,007,200 \\
@@ -25,7 +26,7 @@ After training the different models and experimenting with various hyperparamete
& & & & & \\
& \acs{AQR} & Non-Linear & 32447.41 & 137.24 & 79.22 & 524,013 \\
& \acs{NAQR} & Non-Linear & 42588.16 & 157.20 & 73.75 & 673,760 \\
& Diffusion & Non-Linear & 47178.91 & 166.89 & 80.30 & 3,116,896 \\
& Diffusion & Non-Linear & 47178.91 & 166.89 & 80.30 & 3,782,496 \\
& & & & & \\
& \acs{AQR} & GRU & 35238.98 & 141.02 & 80.92 & 11,843,565 \\
& \acs{NAQR} & GRU & 40613.54 & 151.17 & 75.33 & 6,165,216 \\
@@ -36,45 +37,173 @@ After training the different models and experimenting with various hyperparamete
\label{tab:model_comparison}
\end{table}
A first recurring conclusion that can be made is that the \ac{NAQR} models have higher \ac{MSE} and \ac{MAE} errors but higher \ac{CRPS}. The reason for this behavior is not immediately clear. One reason for this could be the way the autoregressive quantile regression works. Autoregressive models use the previous predicted value as input to predict the next value. The autoregressive model does not know that it will be used to predict multiple values in the future. In the case of NRV modeling, a value is sampled as input for the next day. The sampling introduces an error which the model is not trained for. Because of this, the NRV distribution outputted by the model will be further away from the expected distribution. This error propagates further in the full-day NRV samples which results in a higher CRPS. The non-autoregressive models do not have this problem because they predict all values at once. The non-autoregressive models, however, have a higher \ac{MSE} and \ac{MAE} error. The model outputs a distribution for each quarter of the day. The full-day NRV sample is then generated by sampling from each of the distributions. The sampled values are independent of each other. This can result in unrealistic samples with large peaks which impact the \ac{MSE} and \ac{MAE} metrics.
A first recurring conclusion that can be made is that the \ac{NAQR} models have higher \ac{MSE} and \ac{MAE} errors but lower \ac{CRPS}. The reason for this behavior is not immediately clear. One reason for this could be the way the autoregressive quantile regression works. Autoregressive models use the previous predicted value as input to predict the next value. The autoregressive model does not know that it will be used to predict multiple values in the future. In the case of NRV modeling, a value is sampled as input for the next day. The sampling introduces an error which the model is not trained for. Because of this, the NRV distribution outputted by the model will be further away from the expected distribution. This error propagates further in the full-day NRV samples which results in a higher CRPS. The non-autoregressive models do not have this problem because they predict all values at once. The non-autoregressive models, however, have a higher \ac{MSE} and \ac{MAE} error. The model outputs a distribution for each quarter of the day. The full-day NRV sample is generated by sampling from each of the distributions. The sampled values are independent of each other. This can result in unrealistic samples with large peaks which impact the \ac{MSE} and \ac{MAE} metrics.
Comparing the Linear model with the GRU model, the GRU model has a better performance when only using the NRV data. The autoregressive linear quantile regression model, however, outperforms the model using all available features. Some examples of the test set are shown in \ref{fig:ar_linear_gru_comparison}. A comparison is made between the autoregressive linear and GRU models. A clear difference in the confidence intervals can be observed. The confidence intervals almost have the same width over the whole day. This is not the case for the GRU model. The confidence intervals are wider in the middle of the day. This gives a more realistic insight into the uncertainty.
A comprehensive comparison of the test set examples is shown in Figure \ref{fig:ar_linear_gru_diffusion_comparison} and Figure \ref{fig:naqr_linear_gru_diffusion_comparison}. Figure \ref{fig:ar_linear_gru_diffusion_comparison} shows the best performing autoregressive models and the diffusion model while Figure \ref{fig:naqr_linear_gru_diffusion_comparison} shows the best performing non-autoregressive models and the diffusion model.
\begin{figure}[H]
\centering
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{Autoregressive linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{Autoregressive GRU model}
\end{subfigure}
When comparing the autoregressive models using all input features, the non-linear model performs the best. It has the lowest MSE, MAE and lowest CRPS. The GRU model performs the worst and is even outperformed by the linear model. When looking at the plots shown in Figure \ref{fig:ar_linear_gru_diffusion_comparison}, the GRU model does not seem bad and even seems to perform better than the linear model. Not many conclusions can be made by looking at four examples but it shows that the GRU model is capable of generating realistic samples. The GRU model is the most complex and has the most parameters but performs the worst when looking at the metrics. The examples in the figure show that the confidence intervals generated by the GRU model are wider than the confidence intervals for the linear and non-linear models. In each of the examples, the confidence intervals of the GRU model are wider during the day and narrower during the night. This shows the NRV distribution is more uncertain during the day than during the night. This observation can not easily be made when looking at the linear and non-linear models. For each of the models, a slight trend can be observed during the day. This shows the model is not just generating random or fixed samples.
\caption{Comparison of the autoregressive linear and GRU model}
\label{fig:ar_linear_gru_comparison}
\end{figure}
Comparing the autoregressive models with the diffusion model using all features, the diffusion model performs the worst in terms of the metrics in the table. All metrics are worse than each autoregressive model. Comparing the samples in Figure \ref{fig:ar_linear_gru_diffusion_comparison}, the diffusion model seems to model the NRV reasonably well but the confidence intervals are very narrow. There is not a lot of variance in the generated samples. This can explain why the metrics perform much worse. A reason for this worse performance is overfitting on the training data.
% other conclusion:
Next, the non-autoregressive models can be compared. Again, the non-linear model performs the best based on the CRPS metric. When looking at the examples shown in Figure \ref{fig:naqr_linear_gru_diffusion_comparison}, the non-linear and GRU model seems to perform very similar. The confidence intervals have almost the same width and for both models, no real trend can be observed. The mean hovers around zero. The examples of the non-autoregressive linear model, on the other hand, look completely different. There, wider confidence intervals can be observed with large peaks. Again, no big trends can be observed. The mean NRV hovers around zero again. Comparing these models against the samples from the diffusion model, the diffusion model seems to perform the best. There, a real trend can be observed but the confidence intervals are very narrow. The generated samples of the diffusion model look more realistic than the samples of the non-autoregressive models. The diffusion model, however, performs the worst based on the metrics. Again, overfitting can be a reason for this worse performance.
% horizontal page with one big figure
\begin{landscape}
\begin{figure}[H]
\centering
% sample 864
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_864.jpeg}
\end{subfigure}
% sample 4320
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_4320.jpeg}
\end{subfigure}
% sample 6336
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_6336.jpeg}
\end{subfigure}
% sample 7008
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_linear_model_samples/AQR_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{AQR linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_non_linear_model_samples/AQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{AQR non-linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/aqr_gru_model_examples/AQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{AQR GRU model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_7008.jpeg}
\caption{Diffusion model}
\end{subfigure}
\caption{Comparison of the autoregressive models with the diffusion model}
\label{fig:ar_linear_gru_diffusion_comparison}
\end{figure}
\begin{figure}[H]
\centering
% sample 864
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_linear_model_samples/NAQR_NRV_Load_Wind_PV_NP-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_gru_model_examples/NAQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_864.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_864.jpeg}
\end{subfigure}
% sample 4320
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_linear_model_samples/NAQR_NRV_Load_Wind_PV_NP-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_gru_model_examples/NAQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_4320.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_4320.jpeg}
\end{subfigure}
% sample 6336
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_linear_model_samples/NAQR_NRV_Load_Wind_PV_NP-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_gru_model_examples/NAQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_6336.png}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_6336.jpeg}
\end{subfigure}
% sample 7008
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_linear_model_samples/NAQR_NRV_Load_Wind_PV_NP-Sample_7008.png}
\caption{NAQR linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_non_linear_model_samples/NAQR_NL_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{NAQR non-linear model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/quantile_regression/naqr_gru_model_examples/NAQR_GRU_NRV_Load_Wind_PV_NP_QE-Sample_7008.png}
\caption{NAQR GRU model}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.38\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/results/samples/Diffusion_Test_Example_7008.jpeg}
\caption{Diffusion model}
\end{subfigure}
\caption{Comparison of the non-autoregressive models with the diffusion model}
\label{fig:naqr_linear_gru_diffusion_comparison}
\end{figure}
\end{landscape}

4
Reports/Thesis/sections/results/models/diffusion.tex
View File

@@ -56,13 +56,13 @@ In Figure \ref{fig:diffusion_intermediates}, multiple intermediate steps of the
& 300 & 3 & 4096 & 39943.93 & 151.62 & 77.59 \\
& 300 & 4 & 256 & 56939.68 & 185.07 & 81.16 \\
& 300 & 4 & 512 & 46225.72 & 164.74 & 79.19 \\
& 300 & 4 & 1024 & 42984.02 & 157.54 & 77.92 \\
& 300 & 4 & 1024 & 42984.02 & 157.54 & \textbf{77.92} \\
& 300 & 4 & 2048 & 41145.32 & 154.14 & 78.18 \\
\midrule
NRV + Load + Wind + PV + NP & & & & & & & \\
& 300 & 2 & 256 & 63337.36 & 196.21 & 84.29 \\
& 300 & 2 & 512 & 52745.92 & 177.16 & 81.57 \\
& 300 & 2 & 1024 & 47178.91 & 166.89 & 80.30 \\
& 300 & 2 & 1024 & 47178.91 & 166.89 & \textbf{80.30} \\
& 300 & 3 & 256 & 66148.13 & 200.34 & 85.31 \\
& 300 & 3 & 512 & 53159.99 & 178.46 & 81.95 \\
& 300 & 3 & 1024 & 47815.13 & 167.22 & 81.16 \\

7
Reports/Thesis/sections/results/models/gru.tex
View File

@@ -1,9 +1,8 @@
\subsubsection{GRU Model}
Another popular architecture to model sequential data is a recurrent neural network. There exist two main types of recurrent neural networks, the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The GRU is a simplified version of the LSTM, which has fewer parameters and is computationally less expensive. The GRU model can be trained for quantile regression in the same way as the linear and non-linear models using the pinball loss. There is, however, a difference in how the input data is structured and provided to the model. For linear and non-linear models, the data is provided in the shape of $(batch\_size, num\_features)$. The recurrent neural network, on the other hand, expects the input data to be structured as $(batch\_size, time\_steps, num\_features\_per\_timestep)$. This is also explained in the background section about the recurrent neural network.
Another popular architecture to model sequential data is a recurrent neural network. There exist two main types of recurrent neural networks, the Long Short-Term Memory (LSTM) \cite{hochreiter_long_1997} and the Gated Recurrent Unit (GRU) \cite{cho_learning_2014}. The GRU is a simplified version of the LSTM, which has fewer parameters and is computationally less expensive. The GRU model can be trained for quantile regression in the same way as the linear and non-linear models using the pinball loss. There is, however, a difference in how the input data is structured and provided to the model. For linear and non-linear models, the data is provided in the shape of $(batch\_size, num\_features)$. The recurrent neural network, on the other hand, expects the input data to be structured as $(batch\_size, time\_steps, num\_features\_per\_timestep)$. This is also explained in the background section about the recurrent neural network.
The GRU model architecture to predict the NRV quantiles is shown in Table \ref{tab:gru_model_architecture}. The model starts with an embedding layer that converts the quarter of the day into an embedding. This layer concatenates the other input features with the quarter embedding. The input of the TimeEmbedding is of shape (Batch Size, Time Steps, Input Features Size). The output of this layer is then passed to the GRU layer. The GRU layer outputs the hidden state for every time step. This results in a tensor of shape (Batch Size, Time Steps, Hidden Size). Only the last hidden state is relevant for the prediction of the NRV quantiles for the next quarter. The last hidden state should contain all the necessary information from the previous quarters to make the prediction. The last hidden state is then passed through a linear layer to output the quantiles for the NRV prediction. The input and output of the model depend if the model is trained using an autoregressive or non-autoregressive way. The non-autoregressive variant of the GRU model has two days worth of time steps. This results in $92*2$ time steps. The model then needs to output $(96 * \text{number\_of\_quantiles})$ NRV quantile values.
The GRU model architecture to predict the NRV quantiles is shown in Table \ref{tab:gru_model_architecture}. The model starts with an embedding layer that converts the quarter of the day into an embedding. This layer concatenates the other input features with the quarter embedding. The input of the TimeEmbedding is of shape (Batch Size, Time Steps, Input Features Size). The output of this layer is then passed to the GRU layer. The GRU layer outputs the hidden state for every time step. This results in a tensor of shape (Batch Size, Time Steps, Hidden Size). Only the last hidden state is relevant for the prediction of the NRV quantiles for the next quarter. The last hidden state should contain all the necessary information from the previous quarters to make the prediction. The last hidden state is then passed through a linear layer to output the quantiles for the NRV prediction. The input and output of the model depend if the model is trained using an autoregressive or non-autoregressive way.
TODO: Zielige visualisatie van model nu
\begin{table}[H]
\centering
\begin{tabularx}{\textwidth}{Xr} % Set the table width to the text width
@@ -57,7 +56,7 @@ NRV + Load + PV\\ + Wind & & & & & & & & & \\
NRV + Load + PV\\ + Wind + Net Position \\+ QE (5 dim) & & & & & & & & & \\
& 4 & 256 & 39906.53 & 40881.92 & 149.78 & 152.34 & 84.88 & 76.15 \\
& 8 & 256 & 37675.15 & 40159.91 & 145.39 & 150.42 & 83.37 & 75.89 \\
& 4 & 512 & & 40613.54 & & 151.17 & & 75.33 \\
& 4 & 512 & 38564.57 & 40613.54 & 147.23 & 151.17 & 85.48 & 75.33 \\
& 8 & 512 & 35238.98 & 39896.57 & 141.02 & 149.96 & 80.92 & 75.92 \\
\bottomrule
\end{tabular}

9
Reports/Thesis/sections/results/models/linear.tex
View File

@@ -29,10 +29,9 @@ Comparing the results of the autoregressive and non-autoregressive linear models
The MSE and MAE of the non-autoregressive model are higher than the autoregressive model. This can be explained by the fact that the non-autoregressive model does not take into account the previous sampled value. Sampling is done for every quarter of the day independently. This can lead to large differences between the sampled values and thus can increase the MSE and MAE. The autoregressive model does take into account the previous sampled value and can adapt its quantile predictions based on this value so a smoother and more accurate sample can be generated.
% TODO: Check listing of features -> hoofdletters en shit
Another thing to note is the influence of the input features on the non-autoregressive linear model. When increasing the number of input features, the evaluation metrics are a lot worse in comparison with only using the NRV history of the previous day. A reason for this behavior could be that the model is not able to capture the patterns in the data because of the huge amount of input parameters. When using the NRV, Load, Photovoltanic power production, Wind power production, and the Net Position as input features, the non-autoregressive model has an input size of 864. This increases the complexity of the model as well. The total number of trainable parameters becomes 1,079,520. This is a huge number of parameters and the model is not able to learn the patterns in the data anymore.
Another thing to note is the influence of the input features on the non-autoregressive linear model. When increasing the number of input features, the evaluation metrics are a lot worse in comparison with only using the NRV history of the previous day. A reason for this behavior could be that the model is not able to capture the patterns in the data because of the huge amount of input parameters. When using the NRV, load, photovoltaic power production, wind power production, and the nominal net position as input features, the non-autoregressive model has an input size of 864. This increases the complexity of the model as well. The total number of trainable parameters becomes 1,079,520. This is a huge number of parameters and the model is not able to learn the patterns in the data anymore.
The performance of the autoregressive linear model, however, improves with the addition of more input features. When using the NRV, Load, Photovoltanic power production, Wind power production, and the Net Position as input features, the autoregressive model has an input size of 484. This is almost half the size of the non-autoregressive model. The total number of trainable parameters becomes 6,305 which is way less than the non-autoregressive model.
The performance of the autoregressive linear model, however, improves with the addition of more input features. When using all available features, the autoregressive model has an input size of 484. This is almost half the size of the non-autoregressive model. The total number of trainable parameters becomes 6,305 which is way less than the non-autoregressive model.
An important thing to note is that the autoregressive model needs an additional feature to know which quarter of the day it is modeling. The quarter of the day also influences the value of the NRV. This can easily be seen in Figure \ref{fig:nrv_mean_std_over_quarter}. The figure shows the mean and standard deviation of the NRV values over the quarter of the day. These values change over the day which means the quarter is very valuable information for the model. The non-autoregressive on the other hand does not need this information because it models all the quarters of the day at once.
@@ -49,7 +48,7 @@ Providing the autoregressive model with the quarter of the day can be done in mu
\text{sin}(\frac{2\pi}{96} \times \text{quarter}) \quad \text{and} \quad \text{cos}(\frac{2\pi}{96} \times \text{quarter})
\end{equation}
The sine and cosine values are then concatenated with the input features. Another method that can be used is adding an embedding layer to the model. The discrete quarter of the day value can then be mapped to a vector. The embedding layer itself is learned during the training process which allows the model to learn patterns between quarters. The length of the embedding vector can be chosen and experimented with. The quarter-of-the-day information is then concatenated with the input features. Other information (eg. day of the week, month, year) can also easily be added to the model using this method by just increasing the size of the embedding layer. The results of the linear model with the quarter information are shown in Table \ref{tab:autoregressive_linear_model_quarter_embedding_baseline_results}.
The sine and cosine values are then concatenated with the input features. Another method that can be used is adding an embedding layer to the model. The discrete quarter of the day value can then be mapped to a vector. The embedding layer itself is learned during the training process which allows the model to learn patterns between quarters. The length of the embedding vector can be chosen and experimented with. The quarter-of-the-day information is then concatenated with the input features. Other information (eg. day of the week, month, year) can also easily be added to the model using this method by just increasing the size of the embedding layer. The results of the linear model with the quarter information are shown in Table \ref{tab:autoregressive_linear_model_quarter_embedding_baseline_results}. QT stands for Quarter Trigonometric and QE stands for Quarter Embedding.
\begin{table}[ht]
\centering
@@ -75,7 +74,7 @@ NRV + Load + PV + Wind + NP + QE \textbf{(5 dim)} & \textbf{34031.71} & \textbf{
The results show that adding the quarter embedding to the model improves all evaluation metrics for the autoregressive linear model. The quarter embedding is a valuable feature for the model.
Some examples of the generated full-day NRV samples are shown in Figure \ref{fig:autoregressive_linear_model_samples}. The examples are taken from the test set. The figure shows the confidence intervals of the NRV generations and the mean NRV prediction. The confidence intervals and mean are calculated based on 1000 generated full-day NRV samples. The samples were generated using the input features NRV, Load, Wind, PV, Net Position, and the quarter embedding for the autoregressive model.
Some examples of the generated full-day NRV samples are shown in Figure \ref{fig:autoregressive_linear_model_samples}. The examples are taken from the test set. The figure shows the confidence intervals of the NRV generations and the mean NRV prediction. The confidence intervals and mean are calculated based on 1000 generated full-day NRV samples. The samples were generated using the input features NRV, load, wind, photovoltaic power and the nominal net position. For the autoregressive model, the quarter embedding is also used as input.
\begin{figure}[H]
\centering

6
Reports/Thesis/sections/results/models/non-linear.tex
View File

@@ -49,9 +49,9 @@ While this non-linear model is still quite simple, it offers the flexibility in
& 4 & 256 & 37817.78 & 40200.92 & 146.90 & 152.00 & 85.63 & 74.37 \\
& 8 & 256 & 36346.57 & 38746.81 & 144.80 & 148.82 & 84.51 & 74.55 \\
& 16 & 256 & 38624.83 & 39328.47 & 148.61 & 149.19 & 87.05 & 75.38 \\
\midrule
NRV + Load + PV\\ + Wind & & & & & & & & \\
& 2 & 256 & 42983.21 & 42950.17 & 156.65 & 156.88 & 92.15 & 76.21 \\
% \midrule
% NRV + Load + PV\\ + Wind & & & & & & & & \\
% & 2 & 256 & 42983.21 & 42950.17 & 156.65 & 156.88 & 92.15 & 76.21 \\
\midrule
NRV + Load + PV\\ + Wind + Net Position\\ + QE (dim 5) & & & & & & & & \\
& 2 & 256 & 37785.49 & 42828.61 & 146.99 & 157.03 & 85.22 & 76.36 \\

88
Reports/Thesis/sections/results/policies/nrv_samples_policy.tex
View File

@@ -3,17 +3,36 @@ The generated full-day samples can be used to improve the profit of the policy.
A low CRPS value does not necessarily mean the policy will generate a high profit. Because of this, the CRPS metric can not be used to evaluate the model during the training phase and use this metric to do early stopping. To fairly evaluate and compare the models, a validation set is split off from the training set. The validation set is used to evaluate the profit of the policy during the training and use this to do early stopping. The last two months of the training set are used as the validation set. This range starts on 01-11-2022 and ends on 31-12-2022. Two months are chosen to make sure enough data is available to have a good estimate of the profit while making sure the validation set is not too large. The policy can be evaluated quite fast on the validation set which is feasible to do during the training after a certain number of epochs.
Early stopping is done because the models are prone to overfitting. When training the models too long, the models will start to overfit the training data which results in a lower profit on the test set. An example of the overfitting can be seen in Figure \ref{fig:early_stopping}. There the CRPS value of the validation set is shown together with the profit on the validation set. The CRPS value keeps improving during the training while the profit on the validation set is already decreasing. If early stopping was done based on the CRPS, the model would have been trained for too long and the profit on the test set would have been lower.
\begin{figure}[ht]
% 2 figures next to each other
\centering
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/policies/comparison/crps.png}
\caption{CRPS}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\includegraphics[width=\textwidth]{images/diffusion/policies/comparison/profit.png}
\caption{Profit}
\end{subfigure}
\caption{CRPS and profit on the validation set during training.}
\label{fig:early_stopping}
\end{figure}
\begin{table}[ht]
\centering
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{lccccc}
\toprule
Layers & Test CRPS & Test Profit (€) & Test Charge Cycles & Test Penalty \\
Model (layers - hidden size) & Test CRPS & Test Profit (€) & Test Charge Cycles & Test Penalty \\
\midrule
\multicolumn{5}{l}{\textbf{Only NRV}} \\
\midrule
Linear & 79.73 & 190501.34 & 282.93 & 570.11 \\
Non-Linear (2 - 256) & 86.67 & 190,521.14 & 282.69 & 694.37 \\
Non-Linear (4 - 256) & \textbf{84.64} & 191,305.88 & 283.25 & 904.63 \\
Non-Linear (4 - 256) & 84.64 & 191,305.88 & 283.25 & 904.63 \\
Non-Linear (4 - 512) & 87.77 & 191,374.56 & 282.88 & 1095.56 \\
Non-Linear (8 - 256) & 87.93 & 192,110.72 & 282.56 & 1034.63 \\
Non-Linear (2 - 512) & 87.03 & 190,924.44 & 282.94 & 621.38 \\
@@ -25,8 +44,9 @@ A low CRPS value does not necessarily mean the policy will generate a high profi
\midrule
\multicolumn{5}{l}{\textbf{All Features}} \\
\midrule
Linear & 81.23 & 188007.07 & 283.44 & 638.01 \\
Non-Linear (2 - 256) & 79.33 & 190,466.07 & 282.56 & 689.89 \\
Non-Linear (4 - 256) & \textbf{80.20} & 192,269.40 & 283.88 & 614.49 \\
Non-Linear (4 - 256) & 80.20 & 192,269.40 & 283.88 & 614.49 \\
Non-Linear (8 - 256) & 84.83 & 192,655.81 & 282.69 & 1029.75 \\
Non-Linear (4 - 512) & 107.99 & \textbf{196,999.03} & 284.88 & 819.43 \\
Non-Linear (8 - 512) & 90.63 & 193,654.29 & 282.69 & 1173.56 \\
@@ -37,37 +57,38 @@ A low CRPS value does not necessarily mean the policy will generate a high profi
\bottomrule
\end{tabular}
\end{adjustbox}
\caption{Comparison of AQR: Non-linear and GRU models using different hyperparameters. Early stopping is done based on the profit using the validation set.}
\label{tab:aqr_model_comparison}
\caption{Comparison of AQR: Linear, Non-linear and GRU models using different hyperparameters. Early stopping is done based on the profit using the validation set.}
\label{tab:aqr_models_comparison}
\end{table}
Table \ref{tab:aqr_models_comparison} presents a comprehensive comparison of autoregressive quantile regression (AQR) models, including Linear, Non-Linear, and GRU architectures, evaluated on various performance metrics such as Test CRPS, Test Profit, Test Charge Cycles, and Test Penalty. The models are tested using only Net Regulation Volume (NRV) and all features as input. The key observations from this comparison indicate that the Non-Linear model with 4 hidden layers and 512 units per layer achieves the highest profit of €196,999.03 when all features are used. This suggests that deeper non-linear models with a larger capacity to learn complex patterns perform better in terms of profitability. Among the models trained with only NRV, the GRU with 2 layers and 256 units per layer achieves the highest profit of €196,655.36, suggesting that GRU models are effective in capturing temporal dependencies when fewer features are considered. It is not easy to make concrete conclusions. There is not a single hyperparameter that influences the model to perform better. The difference between the best-performing models is often very small which makes it difficult to conclude.
\begin{table}[ht]
\centering
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{lccccc}
\toprule
Layers & Steps & Test CRPS & Test Profit (€) & Test Charge Cycles & Test Penalty \\
Model (layers - hidden size) & Steps & Test CRPS & Test Profit (€) & Test Charge Cycles & Test Penalty \\
\midrule
\multicolumn{6}{l}{\textbf{Only NRV}} \\
\midrule
256 - 256 & 5 & 275.03 & 191,221.97 & 282.50 & 315.6875 \\
256 - 256 & 20 & 113.27 & 215,946.13 & 283.13 & 421.8125 \\
256 - 256 & 50 & 139.61 & \textbf{218,170.75} & 283.00 & 449.2750 \\
512 - 512 & 50 & 167.23 & 209,625.07 & 282.25 & 449.1875 \\
1024 - 1024 & 50 & 100.72 & 217,560.20 & 283.75 & 455.5625 \\
256 - 256 & 80 & 201.15 & 209,761.89 & 283.50 & 457.2500 \\
(2 - 256) & 5 & 275.03 & 191,221.97 & 282.50 & 315.6875 \\
(2 - 256) & 20 & 113.27 & 215,946.13 & 283.13 & 421.8125 \\
(2 - 256) & 50 & 139.61 & \textbf{218,170.75} & 283.00 & 449.2750 \\
(2 - 512) & 50 & 167.23 & 209,625.07 & 282.25 & 449.1875 \\
(2 - 1024) & 50 & 100.72 & 217,560.20 & 283.75 & 455.5625 \\
(2 -256) & 80 & 201.15 & 209,761.89 & 283.50 & 457.2500 \\
\midrule
\multicolumn{6}{l}{\textbf{All Features}} \\
\midrule
256 - 256 & 20 & 108.84 & \textbf{218,141.31} & 283.94 & 428.6875 \\
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512 - 512 & 20 & 103.41 & 216,411.79 & 282.56 & 450.3125 \\
1024 - 1024 & 20 & \textbf{100.36} & 215,686.32 & 282.69 & 463.6875 \\
256 - 256 & 50 & 117.81 & 216,632.39 & 282.75 & 421.3125 \\
512 - 512 & 50 & 180.83 & 210,769.03 & 282.06 & 446.4375 \\
1024 - 1024 & 50 & 179.59 & 212,793.94 & 282.88 & 454.5000 \\
256 - 256 & 80 & 242.68 & 205,374.94 & 283.13 & 451.3125 \\
(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 -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 \\
(2 -256) & 80 & 242.68 & 205,374.94 & 283.13 & 451.3125 \\
\bottomrule
\end{tabular}
\end{adjustbox}
@@ -109,24 +130,27 @@ A comparison of the baselines and the best-performing models is shown in Table \
\begin{table}[H]
\centering
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{lccc}
\begin{tabular}{lcccc}
\toprule
Model & Test Profit (€) & Test Charge Cycles & Yesterday Baseline Improvement \\
Model (layers - hidden size) & Features & Test Profit (€) & Test Charge Cycles & Yesterday Baseline Improvement \\
\midrule
\multicolumn{4}{l}{\textbf{Baselines}} \\
\multicolumn{5}{l}{\textbf{Baselines}} \\
\midrule
Fixed thresholds & 143,004.34 & 287.12 & \\
Yesterday NRV & 198,807.09 & 283.5 & \\
Perfect NRV & 230,317.84 & 282.5 & \\
Fixed thresholds && 143,004.34 & 287.12 & \\
Yesterday NRV && 198,807.09 & 283.5 & \\
Perfect NRV && 230,317.84 & 282.5 & \\
\midrule
\multicolumn{4}{l}{\textbf{Models}} \\
\multicolumn{5}{l}{\textbf{Models}} \\
\midrule
AQR: Linear & 190,501.34 & 282.94 & -4.17\% \\
AQR: Non-Linear (4 - 512, All) & 196,999.03 & 284.88 & -0,91\% \\
AQR: GRU (2 - 256, Only NRV) & 196,655.36 & 283.81 & -1.08\% \\
Diffusion (2 - 256, 50 steps, Only NRV) & 218,170.75 & 283.00 & \textbf{+9.74\%} \\
NAQR: Linear & & & & \\
NAQR: Non-Linear (2 - 512) & NRV & 189,982.08 & 283.81 & -4.43\% \\
&&& \\
AQR: Linear & NRV & 190,501.34 & 282.94 & -4.17\% \\
AQR: Non-Linear (4 - 512) & All & 196,999.03 & 284.88 & -0.91\% \\
AQR: GRU (2 - 256) & NRV & 196,655.36 & 283.81 & -1.08\% \\
& & & \\
Diffusion (2 - 256, 50 steps) & NRV & 218,170.75 & 283.00 & \textbf{+9.74\%} \\
\bottomrule
\end{tabular}

59
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1
Reports/Thesis/verslag.out
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@@ -31,4 +31,3 @@
\BOOKMARK [3][-]{subsubsection.6.5.1}{\376\377\000B\000a\000s\000e\000l\000i\000n\000e\000s}{subsection.6.5}% 31
\BOOKMARK [3][-]{subsubsection.6.5.2}{\376\377\000P\000o\000l\000i\000c\000y\000\040\000u\000s\000i\000n\000g\000\040\000g\000e\000n\000e\000r\000a\000t\000e\000d\000\040\000N\000R\000V\000\040\000s\000a\000m\000p\000l\000e\000s}{subsection.6.5}% 32
\BOOKMARK [1][-]{section.7}{\376\377\000C\000o\000n\000c\000l\000u\000s\000i\000o\000n}{}% 33
\BOOKMARK [1][-]{appendix.A}{\376\377\000A\000p\000p\000e\000n\000d\000i\000x}{}% 34

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9
Reports/Thesis/verslag.toc
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@@ -29,8 +29,7 @@
\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}{46}{subsection.6.5}%
\contentsline {subsubsection}{\numberline {6.5.1}Baselines}{46}{subsubsection.6.5.1}%
\contentsline {subsubsection}{\numberline {6.5.2}Policy using generated NRV samples}{47}{subsubsection.6.5.2}%
\contentsline {section}{\numberline {7}Conclusion}{51}{section.7}%
\contentsline {section}{\numberline {A}Appendix}{58}{appendix.A}%
\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}%

135
src/notebooks/thesis-visualizations.ipynb
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@@ -314,6 +314,141 @@
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Final Profits Overview"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"models_final = [\n",
" \"NAQR: Non-Linear\",\n",
" \"AQR: Linear\",\n",
" \"AQR: Non-Linear\",\n",
" \"AQR: GRU\",\n",
" \"Diffusion\",\n",
"]\n",
"\n",
"profits_final = [189982.08, 190501.34, 196999.03, 196655.36, 218170.75]\n",
"\n",
"improvement_final = [-4.43, -4.17, -0.91, -1.08, 9.74]\n",
"\n",
"# Yesterday and Perfect baselines for reference lines\n",
"yesterday_baseline = 198807.09\n",
"perfect_baseline = 230317.84\n",
"\n",
"# Create the final bar plot with the Yesterday NRV Baseline line changed to an even darker orange\n",
"fig, ax = plt.subplots(figsize=(14, 10))\n",
"\n",
"# Choose an even darker orange color for the Yesterday NRV Baseline line\n",
"yesterday_baseline_color = \"#FF4500\" # Darker orange color\n",
"\n",
"# Add horizontal striped lines for final baselines with larger line widths behind the bars\n",
"ax.axhline(\n",
" y=yesterday_baseline,\n",
" color=yesterday_baseline_color,\n",
" linestyle=\"--\",\n",
" linewidth=2,\n",
" zorder=0,\n",
" label=\"Yesterday NRV Baseline\",\n",
")\n",
"ax.axhline(\n",
" y=perfect_baseline,\n",
" color=\"green\",\n",
" linestyle=\"--\",\n",
" linewidth=2,\n",
" zorder=0,\n",
" label=\"Perfect NRV Baseline\",\n",
")\n",
"\n",
"# Bar plot for final profits with a single color and smaller bar width\n",
"bars_final = ax.bar(models_final, profits_final, color=\"skyblue\", width=0.5, zorder=2)\n",
"\n",
"# Annotate the final bars with the improvement percentages and profit values inside the bars at the top\n",
"for bar, profit, imp in zip(bars_final, profits_final, improvement_final):\n",
" if not np.isnan(profit):\n",
" height = bar.get_height()\n",
" ax.annotate(\n",
" f\"{imp:.2f}%\",\n",
" xy=(bar.get_x() + bar.get_width() / 2, height),\n",
" xytext=(\n",
" 0,\n",
" -10,\n",
" ), # 10 points vertical offset to place inside the bar at the top\n",
" textcoords=\"offset points\",\n",
" ha=\"center\",\n",
" va=\"top\",\n",
" fontsize=12,\n",
" color=\"black\",\n",
" fontweight=\"bold\",\n",
" )\n",
" ax.annotate(\n",
" f\"€{profit:,.2f}\",\n",
" xy=(bar.get_x() + bar.get_width() / 2, height / 2),\n",
" xytext=(0, 0), # No offset\n",
" textcoords=\"offset points\",\n",
" ha=\"center\",\n",
" va=\"center\",\n",
" color=\"black\",\n",
" fontsize=10,\n",
" fontweight=\"bold\",\n",
" )\n",
"\n",
"# Add price labels next to the horizontal lines with adjusted positions to avoid overlap\n",
"ax.text(\n",
" 0,\n",
" yesterday_baseline,\n",
" f\"€{yesterday_baseline:,.2f}\",\n",
" color=yesterday_baseline_color,\n",
" ha=\"left\",\n",
" va=\"bottom\",\n",
" fontsize=12,\n",
" fontweight=\"bold\",\n",
" bbox=dict(facecolor=\"white\", edgecolor=\"none\", pad=3),\n",
")\n",
"ax.text(\n",
" 0,\n",
" perfect_baseline,\n",
" f\"€{perfect_baseline:,.2f}\",\n",
" color=\"green\",\n",
" ha=\"left\",\n",
" va=\"bottom\",\n",
" fontsize=12,\n",
" fontweight=\"bold\",\n",
" bbox=dict(facecolor=\"white\", edgecolor=\"none\", pad=3),\n",
")\n",
"\n",
"# Set labels and title with larger font size\n",
"ax.set_ylabel(\"Test Profit (€)\", fontsize=14)\n",
"ax.set_title(\n",
" \"Comparison of Test Profits and Improvements over Yesterday NRV Baseline\",\n",
" fontsize=16,\n",
")\n",
"ax.legend(loc=\"upper right\", bbox_to_anchor=(1, 1.15), fontsize=12)\n",
"\n",
"# Add grid lines\n",
"ax.grid(True, which=\"both\", linestyle=\"--\", linewidth=0.5, alpha=0.7, zorder=1)\n",
"\n",
"# Rotate x-axis labels for better readability in the final plot\n",
"plt.xticks(rotation=45, ha=\"right\", fontsize=12)\n",
"plt.yticks(fontsize=12)\n",
"\n",
"# Adjust bar width and layout\n",
"plt.tight_layout()\n",
"\n",
"# Show the final plot with the Yesterday NRV Baseline line changed to an even darker orange\n",
"plt.show()\n"
]
}
],
"metadata": {

20
src/training_scripts/non_autoregressive_quantiles.py
View File

@@ -5,7 +5,7 @@ clearml_helper = ClearMLHelper(
project_name="Thesis/NrvForecast"
)
task = clearml_helper.get_task(
task_name="NAQR: Non Linear (4 - 512)"
task_name="NAQR: Non Linear (2 - 256) + All"
)
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 = False
data_config.LOAD_FORECAST = False
data_config.LOAD_HISTORY = True
data_config.LOAD_FORECAST = True
data_config.WIND_FORECAST = False
data_config.WIND_HISTORY = False
data_config.WIND_FORECAST = True
data_config.WIND_HISTORY = True
data_config.PV_FORECAST = False
data_config.PV_HISTORY = False
data_config.PV_FORECAST = True
data_config.PV_HISTORY = True
data_config.NOMINAL_NET_POSITION = False
data_config.NOMINAL_NET_POSITION = True
data_config = task.connect(data_config, name="data_features")
@@ -68,8 +68,8 @@ else:
model_parameters = {
"learning_rate": 0.0001,
"hidden_size": 512,
"num_layers": 4,
"hidden_size": 256,
"num_layers": 2,
"dropout": 0.2,
}