89 lines
4.2 KiB
TeX
89 lines
4.2 KiB
TeX
\documentclass[paper=A4]{article}
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\usepackage[utf8]{inputenc}
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\usepackage[a4paper, left=2cm, right=2cm, top=2cm, bottom=2cm]{geometry}
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\usepackage{siunitx}
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\sisetup{
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group-separator = {.},
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input-decimal-markers={.},
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output-decimal-marker = {.},
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group-minimum-digits=9}
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\usepackage{graphicx}
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\usepackage{fancyhdr}
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\usepackage{lastpage}
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\usepackage{subfigure}
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\usepackage{float}
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\usepackage{wrapfig}
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\usepackage{multicol}
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\usepackage{amsmath, amssymb}
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\usepackage{hyperref}
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\hyphenpenalty=10000 %to stop cutting words in a paragraph
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\pagestyle{fancy}
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\fancyhf{}
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\rhead{\includegraphics*[scale=0.013]{./Pictures/FaSTTUBe_Logo_ohneAuto.png}}
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\rfoot{Page \thepage \hspace{1pt} of \pageref{LastPage}}
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\lhead{Car 313, 23.04, Rev. 1}
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\chead{\large TS Discharge Circuit Schematic}
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\begin{document}
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\begin{figure}[H]
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\centering
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\includegraphics[width=0.98\textwidth]{./Documents/DC.pdf}
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\caption{Schematic of the Discharge Circuit PCB}
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\end{figure}
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\section*{Discharge Time}
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As seen in the Schematic, for our discharge circuitry a PTC (PTCEL13R251NxE) is used. The total capacitance of the DC-link capacitor from the two inverters that we are using is \SI{200}{\micro\farad}, and the maximum voltage of the accumulator is 403.2V. Using the RC discharging circuit equation, we obtain the highest resistance that the PTC can have so that we are still within the 5s discharge limit.
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\begin{align}
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V_C = & V_0 \cdot e^{-t/RC} \\
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\SI{60}{\volt} = & \SI{403.2}{\volt} \cdot e^{-\SI{5}{\second}/(R_{PTC} \cdot \SI{200}{\micro\farad})} \\
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R_{PTC} \approx & \SI{13123}{\ohm}
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\end{align}
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\begin{wrapfigure}{r}{0.4\textwidth}
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\includegraphics[width=1\linewidth]{./Pictures/PTC-R-T.png}
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\caption{Resistance vs. Temperature for PTCEL13 (typical)}
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\label{fig:PTC_T_R}
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\end{wrapfigure}
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To Calculate how much discharge attempts we can have before the discharge reaches 5s, we first see at what temperature the PTC the resistance of \SI{13123}{\ohm} have. We can get this from the datasheet of the PTC (fig. \ref{fig:PTC_T_R}).
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As seen in the datasheet, the temperature is about \SI{165}{\celsius}. Assuming that the temperature rises instantly after the discharge, and the heat dissipation is negligible (since the thermal time constant $\tau_{th}$ is \SI{130}{\second}). As we are calculating the lest amount of precharge allowed, we assume the temperature of the environment to be \SI{45}{\celsius}. Since the thermal capacity $C_{th}$ is \SI{1.45}{\joule/\kelvin}, we can see that the total energy that we can generate from discharge is $E = \SI{120}{\kelvin} \cdot \SI{1.45}{\joule/\kelvin} = \SI{174}{\joule}$.
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We then calculate how much energy in produced in one discharge:
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\begin{align}
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E = & \frac{1}{2} \cdot C \cdot V^2 \\
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= & \SI{16.26}{\joule}
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\end{align}
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Therefore, the total amount of discharge we can carry out before the time exceeds \SI{5}{\second} is $\SI{174}{\joule} / \SI{16.26}{\joule} = 10.7$ --- ten times.
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\section*{Permanent TS Voltage}
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We can find the equilibrium temperature by finding the temperature at which the heat loss is equal to the power emitted. Using the model for LTSpice from Vishay, we can see what the heat loss is at equilibrium. (fig. ) We can see that it is about \SI{2.56}{\watt} Since the dissipation factor is \SI{19.5}{\milli\watt/\kelvin}, we can calculate what the temperature difference $\Delta T$ is.
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\begin{align}
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(T_{eq} - \SI{45}{\celsius}) & \cdot \SI{19.5}{\milli\watt/\kelvin} = \SI{2.56}{\watt} \\
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T_{eq} & \approx \SI{176.3}{\celsius}
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\end{align}
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\bibliographystyle{plain}
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\renewcommand\refname{Reference}
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\begin{thebibliography}{00}
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\bibitem{lem_datasheet} \textit{Current Transducer HO-S series}. \href{https://www.lem.com/sites/default/files/products_datasheets/ho-50__250-s_v7.pdf}{https://www.lem.com/sites/default/files/products\_datasheets/ho-50\_\_250-s\_v7.pdf}, 03.2022
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\bibitem{adz_datasheet} \textit{ADZ SME 200bar}. \href{https://www.adz.de/fileadmin/user_upload/downloads/produkte/SME/ADZ_SME_OperatingManual_DE-EN_A.pdf}{https://www.adz.de/fileadmin/user\_upload/downloads/produkte/SME/ADZ\_SME\_
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OperatingManual\_DE-EN\_A.pdf}, 12.2010
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\end{thebibliography}
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\end{document}
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