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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/models/diffusion.tex
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@@ -132,4 +132,4 @@ The examples of the test dataset are shown in Figure \ref{fig:diffusion_test_set
\label{fig:diffusion_test_set_example_only_nrv_vs_all} \label{fig:diffusion_test_set_example_only_nrv_vs_all}
\end{figure} \end{figure}
The plots in Figure \ref{fig:diffusion_test_set_example_only_nrv_vs_all} show the difference in generated samples when only the NRV data is used as input and when all available input features are used. The model that is only conditioned on the NRV data generates samples that do not have much variance. The confidence intervals are quite smooth and do not contain many peaks. The model trained using all available input features, on the other hand, has another behavior. The confidence intervals contain more peaks and the generated samples have more variance. This proves the model does indeed take the other input features into account when generating the samples. When looking at the metrics, the performance of the model that uses all input features is worse than the model that only uses the NRV data. The most obvious reason for this behavior is overfitting. The plots in Figure \ref{fig:diffusion_test_set_example_only_nrv_vs_all} show the difference in generated samples when only the NRV data is used as input and when all available input features are used. The model that is only conditioned on the NRV data generates samples that do not have much variance. The confidence intervals are quite smooth and do not contain many peaks. The model trained using all available input features, on the other hand, has another behavior. The confidence intervals contain more peaks and the generated samples have more variance. This proves the model does indeed take the other input features into account when generating the samples. When looking at the metrics, the performance of the model that uses all input features is worse than the model that only uses the NRV data. The most obvious reason for this behavior is overfitting. Another reason could be the way the input features are used in the model. The input features are concatenated with the NRV data at every layer of the neural network. This could result in the model not using the input features in the best way possible.

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Reports/Thesis/sections/results/policies/nrv_samples_policy.tex
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@@ -1,8 +1,24 @@
\subsection{Policy using generated NRV samples} \subsection{Policy using generated NRV samples}
The generated full-day samples can be used to improve the profit of the policy. For each day, the generated samples can be used to determine the buying and selling thresholds. Assume that there are 100 generated full-day NRV samples for the day for which the profit needs to be optimized. The thresholds are determined for each generated sample separately using a simple grid search. All these thresholds can then be reduced by taking the mean to get one value for the buying threshold and one value for the selling threshold. Again, the penalty parameter is optimized for the test set to make sure around 283 charge cycles are used for fair comparison. The policy is evaluated for the different types of models that were trained and discussed in the previous sections. The generated full-day samples can be used to improve the profit of the policy. For each day, the generated samples can be used to determine the buying and selling thresholds. Assume that there are 100 generated full-day NRV samples for the day for which the profit needs to be optimized. The thresholds are determined for each generated sample separately using a simple grid search. All these thresholds can then be reduced by taking the mean to get one value for the buying threshold and one value for the selling threshold. Again, the penalty parameter is optimized for the test set to make sure around 283 charge cycles are used for fair comparison. The policy is evaluated for the different types of models that were trained and discussed in the previous sections. To reduce the computational cost, the policy is only evaluated for the best-performing models based on the CRPS metric.
\begin{table}
\centering
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{lcccccc}
\toprule
Model & Type & CRPS & Profit (€) & Charge Cycles & Penalty \\
\midrule
\acs{AQR} & Non-Linear & & 189,717.74 & 282.06 & 566.4 \\
\bottomrule
\end{tabular}
\end{adjustbox}
\caption{Comparison of the different models using the profit metric. The best-performing models for a certain type are selected based on the profit.}
\label{tab:policy_comparison}
\end{table}
% TODO: Explain the results of the different models % TODO: Explain the results of the different models
% TODO: Compare with baselines % TODO: Compare with baselines
% TODO: explain further % TODO: explain further
An observation that can be made is that the metrics used to evaluate the NRV predictions, do not necessarily correlate with the profit that can be made using the predictions. This means the best model in terms of the metrics does not necessarily result in the best profit. During the training, the profit should be used as a metric to evaluate the models but this becomes computationally expensive. Because of this, the policy now will only be evaluated after the training is done. The profit can give a better insight if the model improves the profit compared to the baselines. An observation that can be made is that the metrics used to evaluate the NRV predictions, do not necessarily correlate with the profit that can be made using the predictions. This means the best model in terms of the metrics does not necessarily result in the best profit. During the training, the profit should be used as a metric to evaluate the models but this becomes computationally expensive. Because of this, the policy now will only be evaluated after the training is done. The profit can give a better insight if the model improves the profit compared to the baselines.

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\ACRO{usage}{QR=={0}} \ACRO{usage}{QR=={0}}
\ACRO{usage}{AQR=={0}} \ACRO{usage}{AQR=={0}}
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@@ -146,4 +149,4 @@
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[48
] [49]) (./verslag.aux (./sections/introduction.aux) (./sections/background.aux) (./sections/policies.aux) (./sections/literature_study.aux) (./sections/appendix.aux))
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1
Reports/Thesis/verslag.out
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@@ -29,3 +29,4 @@
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\BOOKMARK [2][-]{subsection.7.1}{\376\377\000B\000a\000s\000e\000l\000i\000n\000e\000s}{section.7}% 30 \BOOKMARK [2][-]{subsection.7.1}{\376\377\000B\000a\000s\000e\000l\000i\000n\000e\000s}{section.7}% 30
\BOOKMARK [2][-]{subsection.7.2}{\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}{section.7}% 31 \BOOKMARK [2][-]{subsection.7.2}{\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}{section.7}% 31
\BOOKMARK [1][-]{appendix.A}{\376\377\000A\000p\000p\000e\000n\000d\000i\000x}{}% 32

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Reports/Thesis/verslag.tex
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@@ -30,6 +30,7 @@
\usepackage{booktabs} \usepackage{booktabs}
\usepackage{tikz} \usepackage{tikz}
\usepackage{acro} \usepackage{acro}
\usepackage{pdflscape}
\usetikzlibrary{positioning, calc} \usetikzlibrary{positioning, calc}
% Electricity market % Electricity market
@@ -193,4 +194,9 @@
% bibliography % bibliography
\printbibliography \printbibliography
% appendix
\appendix
\include{sections/appendix}
\end{document} \end{document}

1
Reports/Thesis/verslag.toc
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@@ -31,3 +31,4 @@
\contentsline {section}{\numberline {7}Policies for battery optimization}{43}{section.7}% \contentsline {section}{\numberline {7}Policies for battery optimization}{43}{section.7}%
\contentsline {subsection}{\numberline {7.1}Baselines}{43}{subsection.7.1}% \contentsline {subsection}{\numberline {7.1}Baselines}{43}{subsection.7.1}%
\contentsline {subsection}{\numberline {7.2}Policy using generated NRV samples}{44}{subsection.7.2}% \contentsline {subsection}{\numberline {7.2}Policy using generated NRV samples}{44}{subsection.7.2}%
\contentsline {section}{\numberline {A}Appendix}{48}{appendix.A}%

3
src/models/diffusion_model.py
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@@ -39,7 +39,6 @@ class SimpleDiffusionModel(DiffusionModel):
hidden_sizes: list, hidden_sizes: list,
other_inputs_dim: int, other_inputs_dim: int,
time_dim: int = 64, time_dim: int = 64,
dropout_rate: float = 0.2,
): ):
super(SimpleDiffusionModel, self).__init__(time_dim) super(SimpleDiffusionModel, self).__init__(time_dim)
@@ -49,7 +48,6 @@ class SimpleDiffusionModel(DiffusionModel):
nn.Linear(input_size + time_dim + other_inputs_dim, hidden_sizes[0]) nn.Linear(input_size + time_dim + other_inputs_dim, hidden_sizes[0])
) )
self.layers.append(nn.ReLU()) self.layers.append(nn.ReLU())
self.layers.append(nn.Dropout(dropout_rate))
for i in range(1, len(hidden_sizes)): for i in range(1, len(hidden_sizes)):
self.layers.append( self.layers.append(
@@ -58,7 +56,6 @@ class SimpleDiffusionModel(DiffusionModel):
) )
) )
self.layers.append(nn.ReLU()) self.layers.append(nn.ReLU())
self.layers.append(nn.Dropout(dropout_rate))
self.layers.append( self.layers.append(
nn.Linear(hidden_sizes[-1] + time_dim + other_inputs_dim, input_size) nn.Linear(hidden_sizes[-1] + time_dim + other_inputs_dim, input_size)

32
src/training_scripts/autoregressive_quantiles.py
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@@ -2,7 +2,9 @@ from src.utils.clearml import ClearMLHelper
#### ClearML #### #### ClearML ####
clearml_helper = ClearMLHelper(project_name="Thesis/NrvForecast") clearml_helper = ClearMLHelper(project_name="Thesis/NrvForecast")
task = clearml_helper.get_task(task_name="AQR: Non Linear + Load + Wind + PV + QE + NP") task = clearml_helper.get_task(
task_name="AQR: GRU (8 - 512) + Load + Wind + PV + QE + NP"
)
task.execute_remotely(queue_name="default", exit_process=True) task.execute_remotely(queue_name="default", exit_process=True)
from src.policies.PolicyEvaluator import PolicyEvaluator from src.policies.PolicyEvaluator import PolicyEvaluator
@@ -44,7 +46,7 @@ data_config.NOMINAL_NET_POSITION = True
data_config = task.connect(data_config, name="data_features") data_config = task.connect(data_config, name="data_features")
data_processor = DataProcessor(data_config, path="", lstm=False) data_processor = DataProcessor(data_config, path="", lstm=True)
data_processor.set_batch_size(512) data_processor.set_batch_size(512)
data_processor.set_full_day_skip(False) data_processor.set_full_day_skip(False)
@@ -67,7 +69,7 @@ else:
model_parameters = { model_parameters = {
"learning_rate": 0.0001, "learning_rate": 0.0001,
"hidden_size": 256, "hidden_size": 512,
"num_layers": 8, "num_layers": 8,
"dropout": 0.2, "dropout": 0.2,
"time_feature_embedding": 5, "time_feature_embedding": 5,
@@ -81,25 +83,25 @@ time_embedding = TimeEmbedding(
# time_embedding = TrigonometricTimeEmbedding(data_processor.get_time_feature_size()) # time_embedding = TrigonometricTimeEmbedding(data_processor.get_time_feature_size())
# lstm_model = GRUModel( lstm_model = GRUModel(
# time_embedding.output_dim(inputDim),
# len(quantiles),
# hidden_size=model_parameters["hidden_size"],
# num_layers=model_parameters["num_layers"],
# dropout=model_parameters["dropout"],
# )
non_linear_model = NonLinearRegression(
time_embedding.output_dim(inputDim), time_embedding.output_dim(inputDim),
len(quantiles), len(quantiles),
hiddenSize=model_parameters["hidden_size"], hidden_size=model_parameters["hidden_size"],
numLayers=model_parameters["num_layers"], num_layers=model_parameters["num_layers"],
dropout=model_parameters["dropout"], dropout=model_parameters["dropout"],
) )
# non_linear_model = NonLinearRegression(
# time_embedding.output_dim(inputDim),
# len(quantiles),
# hiddenSize=model_parameters["hidden_size"],
# numLayers=model_parameters["num_layers"],
# dropout=model_parameters["dropout"],
# )
# linear_model = LinearRegression(time_embedding.output_dim(inputDim), len(quantiles)) # linear_model = LinearRegression(time_embedding.output_dim(inputDim), len(quantiles))
model = nn.Sequential(time_embedding, non_linear_model) model = nn.Sequential(time_embedding, lstm_model)
model.output_size = 1 model.output_size = 1
optimizer = torch.optim.Adam(model.parameters(), lr=model_parameters["learning_rate"]) optimizer = torch.optim.Adam(model.parameters(), lr=model_parameters["learning_rate"])

40
src/training_scripts/diffusion_training.py
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@@ -2,7 +2,7 @@ from src.utils.clearml import ClearMLHelper
clearml_helper = ClearMLHelper(project_name="Thesis/NrvForecast") clearml_helper = ClearMLHelper(project_name="Thesis/NrvForecast")
task = clearml_helper.get_task( task = clearml_helper.get_task(
task_name="Diffusion Training: hidden_sizes=[2048, 2048, 2048] (300 steps), lr=0.0001, time_dim=8" task_name="Diffusion Training (GRUs): hidden_sizes=[1024, 1024] (300 steps), lr=0.0001, time_dim=8 + NRV + L + W + PV + NP",
) )
task.execute_remotely(queue_name="default", exit_process=True) task.execute_remotely(queue_name="default", exit_process=True)
@@ -19,20 +19,20 @@ from src.policies.PolicyEvaluator import PolicyEvaluator
data_config = DataConfig() data_config = DataConfig()
data_config.NRV_HISTORY = True data_config.NRV_HISTORY = True
data_config.LOAD_HISTORY = False data_config.LOAD_HISTORY = True
data_config.LOAD_FORECAST = False data_config.LOAD_FORECAST = True
data_config.PV_FORECAST = False data_config.PV_FORECAST = True
data_config.PV_HISTORY = False data_config.PV_HISTORY = True
data_config.WIND_FORECAST = False data_config.WIND_FORECAST = True
data_config.WIND_HISTORY = False data_config.WIND_HISTORY = True
data_config.NOMINAL_NET_POSITION = False data_config.NOMINAL_NET_POSITION = True
data_config = task.connect(data_config, name="data_features") data_config = task.connect(data_config, name="data_features")
data_processor = DataProcessor(data_config, path="", lstm=False) data_processor = DataProcessor(data_config, path="", lstm=True)
data_processor.set_batch_size(64) data_processor.set_batch_size(64)
data_processor.set_full_day_skip(True) data_processor.set_full_day_skip(True)
@@ -42,28 +42,28 @@ print("Input dim: ", inputDim)
model_parameters = { model_parameters = {
"epochs": 15000, "epochs": 15000,
"learning_rate": 0.0001, "learning_rate": 0.0001,
"hidden_sizes": [2048, 2048, 2048], "hidden_sizes": [1024, 1024],
"time_dim": 8, "time_dim": 8,
} }
model_parameters = task.connect(model_parameters, name="model_parameters") model_parameters = task.connect(model_parameters, name="model_parameters")
#### Model #### #### Model ####
model = SimpleDiffusionModel( # model = SimpleDiffusionModel(
96,
model_parameters["hidden_sizes"],
other_inputs_dim=inputDim[1],
time_dim=model_parameters["time_dim"],
)
# model = GRUDiffusionModel(
# 96, # 96,
# model_parameters["hidden_sizes"], # model_parameters["hidden_sizes"],
# other_inputs_dim=inputDim[2], # other_inputs_dim=inputDim[1],
# time_dim=model_parameters["time_dim"], # time_dim=model_parameters["time_dim"],
# gru_hidden_size=128,
# ) # )
model = GRUDiffusionModel(
96,
model_parameters["hidden_sizes"],
other_inputs_dim=inputDim[2],
time_dim=model_parameters["time_dim"],
gru_hidden_size=512,
)
### Policy Evaluator ### ### Policy Evaluator ###
battery = Battery(2, 1) battery = Battery(2, 1)
baseline_policy = BaselinePolicy(battery, data_path="") baseline_policy = BaselinePolicy(battery, data_path="")