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Updated thesis

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Victor Mylle
2024-05-09 20:46:54 +00:00
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Reports/Thesis/acronyms.tex Normal file
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% Training methods
\DeclareAcronym{QR}{
short = QR,
long = Quantile Regression
}
\DeclareAcronym{AQR}{
short = AQR,
long = Autoregressive Quantile Regression
}
\DeclareAcronym{NAQR}{
short = NAQR,
long = Non-Autoregressive Quantile Regression
}
% Metrics
\DeclareAcronym{MSE}{
short = MSE,
long = Mean Squared Error
}
\DeclareAcronym{MAE}{
short = MAE,
long = Mean Absolute Error
}
\DeclareAcronym{CRPS}{
short = CRPS,
long = Continuous Ranked Probability Score
}
% Electricity Market Terms
\DeclareAcronym{NRV}{
short = NRV,
long = Net Regulation Volume
}
\DeclareAcronym{PV}{
short = PV,
long = Photovoltaic
}
\DeclareAcronym{NP}{
short = NP,
long = Implicit Net Position
}

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\section{Policies for battery optimization}
The goal of this thesis is to model the NRV data and use this to optimize the buying and selling of electricity to make a profit. Different models and methods can be used to model the NRV data which can all result in different results. To evaluate the performance of the models, the generated profit on the test set can be used as a metric. First of all, baselines are needed to be able to compare the models to if adding NRV predictions to the policies improves the profit. The baselines are already discussed in the background section. It is very important to compare the baselines and other policies fairly. The profit depends on the number of charge cycles that are used. The more charge cycles a policy uses, the more profit it will be able to make. Using too many charge cycles is bad for the health of the battery. A penalty parameter can be used to penalize the policy when too many charge cycles are used in a day. To fairly compare the policies with different models and baselines, a maximum number of charge cycles is determined for the test period. The test period starts on 01-01-2023 and ends on (TODO: check the end date). Assuming a maximum of 400 charge cycles can be used in a year, only 293 charge cycles can be used during the test period. The penalty parameter is optimized using a simple gradient descent approach to make sure only 293 charge cycles are used during the test period. The profit is then calculated using the optimized penalty parameter.
To evaluate the policies, a battery of 2 MWh is used with a maximum charge and discharge power of 1 MW. The battery is charged and discharged in quarter-hour intervals at the price of that quarter-hour.
\input{sections/results/policies/baselines}
\input{sections/results/policies/nrv_samples_policy}

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\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.
% Updated table using acronyms
\begin{table}[H]
\centering
\begin{adjustbox}{width=\textwidth}
\begin{tabular}{@{}clcccccc@{}}
\toprule
Features & Method & Model & \ac{MSE} & \ac{MAE} & \ac{CRPS} & Parameters \\
\midrule
NRV & & & & & \\
& \acs{AQR} & Linear & 39222.41 & 152.49 & 91.56 & 1,261 \\
& \acs{NAQR} & Linear & 41219.98 & 152.26 & 73.97 & 121,056 \\
& & & & & \\
& \acs{AQR} & Non-Linear & 36346.57 & 144.80 & 84.51 & 422,925 \\
& \acs{NAQR} & Non-Linear & 40200.92 & 152.00 & 74.37 & 501,728 \\
& & & & & \\
& \acs{AQR} & GRU & 37681.71 & 146.62 & 83.08 & 11,829,261 \\
& \acs{NAQR} & GRU & 40917.24 & 152.04 & 76.06 & 3,007,200 \\
\midrule
NRV + Load + Wind + PV + NP (+ QE) & & & & & \\
& \acs{AQR} & Linear & 34031.71 & 142.29 & 79.99 & 6,850 \\
& \acs{NAQR} & Linear & 49132.26 & 167.37 & 78.75 & 1,079,520 \\
& & & & & \\
& \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 & 46448.90 & 164.50 & 81.06 & 14,229,344 \\
& & & & & \\
& \acs{AQR} & GRU & 35238.98 & 141.02 & 80.92 & 11,843,565 \\
& \acs{NAQR} & GRU & 40613.54 & 151.17 & 75.33 & 6,165,216 \\
\bottomrule
\end{tabular}
\end{adjustbox}
\caption{Comparison of the different models using the \ac{MSE}, \ac{MAE} and \ac{CRPS} metrics. The best-performing models for a certain type are selected based on the \ac{CRPS}.}
\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.

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@@ -56,7 +56,7 @@ In Figure \ref{fig:diffusion_intermediates}, multiple intermediate steps of the
& 300 & 3 & 1024 & 47815.13 & 167.22 & 81.16 \\
& 300 & 3 & 2048 & 46448.90 & 164.50 & 81.06 \\
& 300 & 4 & 1024 & 47483.05 & 166.97 & 81.32 \\
& 300 & 4 & 2048 & 47076.77 & 166.06 & 81.05 \\
& 300 & 4 & 2048 & 47076.77 & 166.06 & 81.06 \\
\bottomrule
\end{tabular}

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Reports/Thesis/sections/results/policies/baselines.tex
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\subsection{Baselines}
As discussed earlier, the most simple baseline that can be used is choosing two fixed thresholds. One threshold is used to buy electricity and the other threshold is used to sell electricity. The thresholds can be chosen based on the available historical data. A simple grid search is done over multiple combinations of thresholds. For each combination, the penalty parameter is optimized to make sure only 400 charge cycles are used in a year. The thresholds that achieve the highest profit on the training set are then used to evaluate the policy on the test set. The thresholds found that maximize the profit on the training set are 100€/MWh for buying and 200€/MWh for selling. Evaluating these thresholds on the test set results in a profit of €266,294.15 but using 492.0 charge cycles. This can not be used to fairly compare other policies. The thresholds can also be determined on the test set itself to find what the maximum possible profit is for the fixed thresholds policy. This can not be used in practice because the thresholds are determined on future data. It is, however, useful for the comparison of the other policies. The best thresholds found on the test set are 200€/MWh for buying and 250€/MWh for selling. The profit achieved using these thresholds is €143,004.34 with 287.12 charge cycles.
Another baseline that can be used is using the real NRV data of the previous day to determine the buying and selling thresholds for the next day. The NRV data of the previous day can be seen as a prediction for the NRV data of the next day. Now, the thresholds are not fixed anymore but are determined based on the NRV predictions. The thresholds are determined separately for each day using a simple grid search which allows the policy to adapt to the changing NRV data. The penalty parameter is also optimized to make sure only around 283 charge cycles are used. The profit achieved using this policy is €198,807.09 using 283.5 charge cycles.
Another baseline that can be used is using the real \ac{NRV} data of the previous day to determine the buying and selling thresholds for the next day. The \ac{NRV} data of the previous day can be seen as a prediction for the \ac{NRV} data of the next day. Now, the thresholds are not fixed anymore but are determined based on the \ac{NRV} predictions. The thresholds are determined separately for each day using a simple grid search which allows the policy to adapt to the changing \ac{NRV} data. The penalty parameter is also optimized to make sure only around 283 charge cycles are used. The profit achieved using this policy is €198,807.09 using 283.5 charge cycles.
The baseline policy using the NRV data of the day before as a prediction can be adapted to use the real NRV data of the day that is being optimized. This policy can show the maximum profit that can be achieved if a perfect NRV prediction is made. The profit for the policy using a perfect prediction of the NRV is €230,317.84 using 282.5 charge cycles. This policy can be seen as the upper bound for the other policies. To achieve better profit results than this, more complex policies need to be used. \\
The baseline policy using the \ac{NRV} data of the day before as a prediction can be adapted to use the real \ac{NRV} data of the day that is being optimized. This policy can show the maximum profit that can be achieved if a perfect \ac{NRV} prediction is made. The profit for the policy using a perfect prediction of the \ac{NRV} is €230,317.84 using 282.5 charge cycles. This policy can be seen as the upper bound for the other policies. To achieve better profit results than this, more complex policies need to be used. \\
\begin{table}[H]
\centering
\begin{tabular}{|l|l|l|l|}
\begin{tabular}{|l|c|c|}
\hline
\textbf{Policy} & \textbf{Profit (€)} & \textbf{Charge cycles} \\ \hline
\textbf{Baseline Policy} & \textbf{Profit (€)} & \textbf{Charge cycles} \\ \hline
Fixed thresholds & 143,004.34 & 287.12\\ \hline
Yesterday NRV & 198,807.09 & 283.5\\ \hline
Perfect NRV & 230,317.84 & 282.5\\ \hline
Yesterday \ac{NRV} & 198,807.09 & 283.5\\ \hline
Perfect \ac{NRV} & 230,317.84 & 282.5\\ \hline
\end{tabular}
\caption{Results of the baseline policies on the test set. }

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\usepackage{subcaption}
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\usepackage{tikz}
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\usetikzlibrary{positioning, calc}
% Electricity market
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% The last (bottom) infobox at bottom of titlepage
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