jaseg/master-thesis
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

modulation, freq estimation: add some blurb, citations

Browse source
This commit is contained in:
jaseg 2020-05-13 13:22:17 +02:00
parent 7e1a6f24af
commit 7368a30d66
1 changed files with 48 additions and 23 deletions
Download patch file Download diff file Expand all files Collapse all files

71
ma/safety_reset.tex
View file

@ -1011,30 +1011,45 @@ controllable load:
\item[Modulation amplitude] proportionally related to modulation power. In a practical setup we might realize a
modulation power up to a few hundred \si{\mega\watt} which would yield maybe a few tens of \si{\milli\hertz} of
frequency amplitude.
\item[Modulation pre-emphasis and slew-rate control]. Pre-emphasis might be necessary to ensure an adequate SNR at
the receiver. Slew-rate control and other shaping measures might be necessary to reduce the impact of these
sudden load changes on the transmitter's primary function (say, aluminium smelting) and to prevent disturbances
to grid components.
\item[Modulation pre-emphasis and slew-rate control]. Pre-emphasis might be necessary to ensure an adequate
Signal-to-Noise ratio (SNR) at the receiver. Slew-rate control and other shaping measures might be necessary to
reduce the impact of these sudden load changes on the transmitter's primary function (say, aluminium smelting)
and to prevent disturbances to grid components.
\item[Modulation frequency]. For a practical implementation a careful study would be necessary to determine an
optimal frequency band for operation. On one hand we need to prevent disturbances to the grid such as through
excitation of some local or inter-area modes. On the other hand we need to optimize SNR and data rate to achieve
optimal latency between transmission start and successful reception and to reduce the overall burden on
transmitter and grid.
excitation of some local or inter-area modes. On the other hand we need to optimize Signal-to-Noise ratio (SNR)
and data rate to achieve optimal latency between transmission start and successful reception and to reduce the
overall burden on transmitter and grid.
\item[Further modulation parameters]. The modulation itself has numerous parameters that are discussed in sec.\
\ref{mod_params} below.
\end{description}
\section{From grid frequency to a reliable communications channel}
% FIXME
\section{From grid frequency to a reliable communication channel}
\subsection{Channel properties}
% FIXME
In this section we will explore how we can construct a reliable communication channel from the analog primitive we
outline in the previous section. Our load control approach to grid frequency modulation leads to a channel with the
following properties.
\begin{description}
\item[Slow-changing.] Accurate grid frequency measurements need several periods of the mains sine wave. Faster
sampling rates can be achieved with more complex specialized synchrophasor estimation algorithms but this will
result in a tradeoff between sampling rate and accuracy\cite{belega01}.
\item[Analog.] Grid frequency is an analog signal.
\item[Noisy.] While stable over long periods of time thanks to Load-Frequency Control\cite{entsoe04} it shows
considerable random short-term variations. In addition our modulation amplitude is limited by technical and
economic constraints so we have to find a system that will work at poor SNRs.
\item[Polarized.] Grid frequency measurements have an inherent sense of \emph{up} (higher frequencies). We can use
this in a polarized modulation scheme to encode information without first transmitting some reference signal to
establish this polarization.
\end{description}
\subsection{Modulation and its parameters}
\label{mod_params}
In this section we will consider how to select a good set of parameters for a modulation scheme fitting grid frequency
modulation.
The sensitivity of the grid to oscillation at particular frequencies described above means we should avoid any
modulation technique that would concentrate a lot of energy in a small bandwidth. Taking this principle to its extreme
provides us with a useful pointer towards techniques that might work well: Spread-spectrum techniques. By employing
@ -1285,12 +1300,12 @@ required precision for manageable averaging times--we would need either a ADC sa
for a reconstruction through interpolated readings an impractically high ADC resolution.
Detail on the inner workings of commercial phasor measurement units is scarce but given their essential role to SCADA
systems there is a large amount of academic research on such algorithms\cite{narduzzi01,derviskadic01}. A popular
approach to these systems is to perform a Short-Time Fourier Transform (STFT) on ADC data sampled at high sampling rate
(e.g. \SI{10}{\kilo\hertz}) and then perform some analysis on the frequency-domain data to precisely locate the strong peak
around \SI{50}{\hertz}. A key observation here is that FFT bin size is going to be much larger than required frequency
resolution. This fundamental limitiation follows from the nyquist criterion %FIXME maybe cite? and if we had to process
an \emph{arbitrary} signal this would highly limit our practical measurement accuracy
systems there is a large amount of academic research on such algorithms\cite{narduzzi01,derviskadic01,belega01}. A
popular approach to these systems is to perform a Short-Time Fourier Transform (STFT) on ADC data sampled at high
sampling rate (e.g. \SI{10}{\kilo\hertz}) and then perform some analysis on the frequency-domain data to precisely
locate the strong peak around \SI{50}{\hertz}. A key observation here is that FFT bin size is going to be much larger
than required frequency resolution. This fundamental limitiation follows from the nyquist criterion %FIXME maybe cite?
and if we had to process an \emph{arbitrary} signal this would highly limit our practical measurement accuracy
\footnote{
Some software packages providing FFT or STFT primitives such as scipy\cite{virtanen01} allow the user to
super-sample FFT output by specifying an FFT width larger than input data length, padding the input data with zeros
@ -1351,12 +1366,22 @@ resolution and despite numerous distortions.
Published grid frequency estimation algorithms such as \textcite{narduzzi01} or \textcite{derviskadic01} are rather
sophisticated and use a combination of techniques to reduce numerical errors in FFT calculation and peak fitting. Given
that we do not need reference standard-grade accuracy for our application we chose to start with a very basic algorithm
instead. We chose to use a general approach developed by experimental physicists at CERN that is described by
\textcite{gasior01}. This approach assumes a general sinusoidal signal superimposed with harmonics and broadband noise.
Applicable to a wide spectrum of practical signal analysis tasks it is a reasonable first-degree approximation of the
much more sophisticated estimation algorithms developed specifically for power systems. Some algorithms have components
such as kalman filters\cite{narduzzi01} that require a phyiscal model. As a general algorithm from \textcite{gasior01}
does not require this kind of application-specific tuning, eliminating one source of error.
instead. We chose to use a general approach to estimate the precise fundamental frequency of an arbitrary signal that
was developed by experimental physicists at CERN and that is described by \textcite{gasior01}. This approach assumes a
general sinusoidal signal superimposed with harmonics and broadband noise. Applicable to a wide spectrum of practical
signal analysis tasks it is a reasonable first-degree approximation of the much more sophisticated estimation algorithms
developed specifically for power systems. Some algorithms have components such as kalman filters\cite{narduzzi01} that
require a phyiscal model. As a general algorithm from \textcite{gasior01} does not require this kind of
application-specific tuning, eliminating one source of error.
The \textcite{gasior01} algorithm passes the windowed input signal through a DFT, then interpolates the signal's
fundamental frequency by fitting a wavelet such as a gaussian to the largest peak in the DFT results. The bias parameter
of this curve fit is an accurate estimation of the signal's fundamental frequency. This algorithm is similar to the
simpler interpolated DFT algorithm used as a reference in much of the synchrophasor estimation
literature\cite{borkowski01}. The three-term variant of the maximum sidelobe decay window often used there is a blackman
window with parameter $\alpha = \frac{1}{4}$. Analysis has shown\cite{belega01} that the interpolated DFT algorithm is
worse than algorithms involving more complex models under some conditions but that there is \emph{no free lunch} meaning
that more complex perform worse when the input signal deviates from their models.
\subsection{Frequency sensor hardware design}
\label{sec-fsensor}