thesis: Add grid frequency measurement plots

1 files changed, 51 insertions, 1 deletions

diff --git a/ma/safety_reset.tex b/ma/safety_reset.tex
index a292458..f8c97f6 100644
--- a/ma/safety_reset.tex
+++ b/ma/safety_reset.tex
@@ -889,7 +889,7 @@ despite numerous distortions.
 \begin{figure}
     \centering
     \includegraphics{../lab-windows/fig_out/mains_voltage_spectrum}
-    \caption{Fourier transform of an 8 hour capture of mains voltage. Data was captured using our frequency measurement
+    \caption{Fourier transform of a 24 hour capture of mains voltage. Data was captured using our frequency measurement
     sensor described in section \ref{sec-fsensor} and FFT'ed after applying a blackman window. Vertical lines indicate
     $50 \text{Hz}$ and odd harmonics.}
     \label{mains_voltage_spectrum}
@@ -1055,6 +1055,44 @@ interface and its good tolerance of system resets due to unexpected power loss.
 
 \subsection{Frequency sensor measurement results}
 
+\begin{figure}
+    \centering
+    \includegraphics{../lab-windows/fig_out/freq_meas_trace_24h}
+    \caption{Trace of grid frequency over a 24 hour window. One clearly visible feature are large positive and negative
+    transients at full hours. Times shown are UTC. Note that the european continental synchronous area that this
+    sensor is placed in covers several time zones which may result in images of daily load peaks appearing in 1 hour
+    intervals. Fig.\ \ref{freq_meas_trace_mag} contains two magnified intervals from this plot.}
+    \label{freq_meas_trace}
+\end{figure}
+\begin{figure}
+    \begin{subfigure}{\textwidth}
+        \centering
+        \includegraphics{../lab-windows/fig_out/freq_meas_trace_2h_1}
+        \caption{A 2 hour window around 00:00 UTC.}
+    \end{subfigure}
+    \begin{subfigure}{\textwidth}
+        \centering
+        \includegraphics{../lab-windows/fig_out/freq_meas_trace_2h_2}
+        \caption{A 2 hour window around 18:30 UTC.}
+    \end{subfigure}
+    \caption{Two magnified 2 hour windows of the trace from fig.\ \ref{freq_meas_trace}.}
+    \label{freq_meas_trace_mag}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics{../lab-windows/fig_out/freq_meas_spectrum}
+    \caption{Fourier transform of the 24 hour grid frequency trace in fig. \ref{freq_meas_trace} with some notable peaks
+    annotated with the corresponding period in seconds. The $\frac{1}{f}$ line indicates a pink noise spectrum. We can
+    clearly see the noise spectrum flattens below some frequency around $\frac{1}{120 \text{s}}$. This effect is due to
+    primary control actively regulating grid frequency over such time intervals. Beyond the $\frac{1}{f}$ slope starting
+    at around $1 \text{Hz}$ we can make out a white noise floor in the order of $\frac{\mu\text{Hz}}{\text{Hz}}$.
+    % TODO: where does this noise floor come from? Is it a fundamental property of the grid? Is it due to limitations of
+    % our measurement setup (such as ocxo stability/phase noise) ???
+    }
+    \label{freq_meas_spectrum}
+\end{figure}
+
 Captured raw waveform data is processed in the Jupyter Lab environment\cite{kluyver01} and grid frequency estimates are
 extracted as described in sec. \ref{frequency_estimation} using the \textcite{gasior01} technique. Appendix
 \ref{grid_freq_estimation_notebook} contains the Jupyter notebook we used for frequency measurement.
@@ -1063,6 +1101,16 @@ extracted as described in sec. \ref{frequency_estimation} using the \textcite{ga
 
 \section{Channel simulation and parameter validation}
 
+To validate all layers of our communication stack from modulation scheme to cryptography we built a prototype
+implementation in python. Implementing all components in a high-level language builds up familiartiy with the concepts
+while taking away much of the implementation complexity. For our demonstrator we will not be able to use python since
+our target platform is a cheap low-end microcontroller. Our demonstrator firmware will have to be written in a low-level
+language such as C or rust. For prototyping these languages lack flexibility compared to python.
+% FIXME introduce project outline, specs -> proto -> demo above!
+
+To validate our modulation scheme we performed a series of simulations. We produced modulated frequency data that we
+superimposed with either of simulated pink noise or an actual grid frequency measurement series.
+% FIXME do test series with simulated noise emulating measured noise spectrum
 
 \section{Implementation of a demonstrator unit} 
 
@@ -1070,6 +1118,8 @@ extracted as described in sec. \ref{frequency_estimation} using the \textcite{ga
 
 \section{Lessons learned}
 
+
+
 \chapter{Future work}
 \section{Technical standardization}
 The description of a safety reset system provided in this work could be translated into a formalized technical standard