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AliAbdelwanisAliAbdelwanis
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‎exercise/fig/ex07/Fig_subtask1.1_modulation.tex

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height=0.3\textwidth,
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% x-Ticks
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xtick={0,60,120,180,240, 300, 360},
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xticklabels={0,60,120,180,240, 300, 360},
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xticklabels={0,$\frac{\pi}{3}$,$\frac{2\pi}{3}$,$\pi$,$\frac{4\pi}{3}$, $\frac{5\pi}{3}$, $2\pi$},
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xticklabel style = {anchor=north},
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% y-Ticks
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ytick={-1,-0.5,0,0.5,1},

‎exercise/fig/ex07/Fig_subtask1.2.tex

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height=0.3\textwidth,
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% x-Ticks
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xtick={0,60,120,180,240, 300, 360},
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xticklabels={0,60,120,180,240, 300, 360},
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xticklabels={0,$\frac{\pi}{3}$,$\frac{2\pi}{3}$,$\pi$,$\frac{4\pi}{3}$, $\frac{5\pi}{3}$, $2\pi$},
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xticklabel style = {anchor=north},
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% y-Ticks
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ytick={-200,-100,0,100,200},
@@ -42,7 +42,7 @@
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% internal load voltage u
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\addplot[blue, domain= 0:360, solid] {150*sin(x-(180/6))};
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% Label of u
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\node[black, fill=white, inner sep = 1pt, anchor = south] at (axis cs:120,160) {$u_\mathrm{1e}$};
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\node[black, fill=white, inner sep = 1pt, anchor = south] at (axis cs:120,160) {$u_{2\mathrm{i}}(t)$};
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\end{axis}
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\begin{axis}[
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% x/y range adjustment
@@ -71,7 +71,7 @@
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]
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\end{axis}
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\end{tikzpicture}
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\caption{Internal load voltage $u_\mathrm{1e}$, fundamental voltage and current components $u^\mathrm{(1)}_\mathrm{2}(t)$
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\caption{Internal load voltage $u_{2\mathrm{i}}(t)$, fundamental voltage and current components $u^\mathrm{(1)}_\mathrm{2}(t)$
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and $i^\mathrm{(1)}_\mathrm{2}(t)$, respectively. }
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\label{sfig:ex07_sub1.2_fund_components}
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\end{figure}

‎exercise/fig/ex07/Fig_subtask1.3.tex

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height=0.3\textwidth,
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% x-Ticks
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xtick={0, 45, 90, 135, 180, 225, 270, 315, 360, 405, 450,495, 540},
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xticklabels={0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360},
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xticklabels={0, $\frac{\pi}{6}$,$\frac{\pi}{3}$, $\frac{\pi}{2}$, $\frac{2\pi}{3}$, $\frac{5\pi}{6}$, $\pi$, $\frac{7\pi}{6}$, $\frac{4\pi}{3}$, $\frac{3\pi}{2}$, $\frac{5\pi}{3}$, $\frac{11\pi}{6}$, $2\pi$},
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xticklabel style = {anchor=north},
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% y-Ticks
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ytick={-400,-200,0,200,400},
@@ -45,9 +45,9 @@
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\addplot[blue, domain= 0:540, solid] {-155.5*sin(x/1.5)+200};
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\addplot[blue, domain= 0:540, solid] {-155.5*sin(x/1.5)-200};
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% Label of u
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\node[black, fill=white, inner sep = 1pt, anchor = south] at (axis cs:120,160) {$u(t)$};
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% \node[black, fill=white, inner sep = 1pt, anchor = south] at (axis cs:120,160) {$u_{2\mathrm{i}}(t)$};
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% Start point
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\filldraw[black] (3,-195) circle (2pt) node[anchor=west]{\textbf{s}};
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\filldraw[black] (3,-195) circle (2pt) node[anchor=west]{\textbf{x}};
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\end{axis}
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\begin{axis}[
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% x/y range adjustment

‎exercise/fig/ex07/Fig_subtask1.4.tex

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height=0.3\textwidth,
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% x-Ticks
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xtick={0,60,120,180,240, 300, 360},
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xticklabels={0,60,120,180,240, 300, 360},
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xticklabels={0,$\frac{\pi}{3}$,$\frac{2\pi}{3}$,$\pi$,$\frac{4\pi}{3}$, $\frac{5\pi}{3}$, $2\pi$},
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xticklabel style = {anchor=north},
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% y-Ticks
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ytick={-200,-100,0,100,200},
@@ -42,7 +42,7 @@
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% internal load voltage u
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\addplot[blue, domain= 0:360, solid] {150*sin(x-(180/6))};
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% Label of u
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\node[black, fill=white, inner sep = 1pt, anchor = south] at (axis cs:120,160) {$u_\mathrm{1e}$};
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\node[black, fill=white, inner sep = 1pt, anchor = south] at (axis cs:120,160) {$u_{2\mathrm{i}}(t)$};
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\end{axis}
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\begin{axis}[
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% x/y range adjustment
@@ -72,6 +72,6 @@
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\end{axis}
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\end{tikzpicture}
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\caption{Output current $i_\mathrm{2}(t)$, its fundamental wave $i^\mathrm{(1)}_\mathrm{2}(t)$
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and its harmonics $i^\mathrm{(n)}_\mathrm{2}(t)$. }
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and its harmonics $i^{(k)}_\mathrm{2}(t)$. }
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\label{sfig:ex07_sub1.4_current_and_components}
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\end{figure}

‎exercise/fig/ex07/Single-phase_DC_Inverter.tex

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% Add connection to u2 inductor
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(jmu2) to [short,-] ++(0,2) coordinate (ju2x)
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% Add u2ae
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(ju2e) to [sV=$u_\mathrm{1e}$] ++(0,-1.5) coordinate (ju2n)
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(ju2e) to [sV=$u_{2\mathrm{i}}(t)$] ++(0,-1.5) coordinate (ju2n)
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% Add connection of u2in
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(ju2n) to [short,-*] (jT4c);
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@@ -50,7 +50,8 @@
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\draw (jT1e) ++(3,0) node[currarrow](i2){}
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(i2) node[anchor=south,color=black]{$i_\mathrm{2}(t)$}
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% Add voltage arrows u2
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(ju2) ++(-0.5,0) to [open,v^=$u_\mathrm{2}(t)$,voltage = straight] ++(0,-1.5);
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(ju2) ++(-0.5,0) to [open,v^=$$,voltage = straight] ++(0,-1.5)
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(ju2) ++ (0.1,-0.5) node[anchor=north,color=black]{$u_\mathrm{2}(t)$};
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% (ju2x) ++(0,-0.8) to [open,v^=$u_\mathrm{2}(t)$,voltage = straight] ++(3.8,0);
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\end{circuitikz}
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\end{center}

‎exercise/tex/exercise07.tex

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%% Task 1: Single-phase inverter: %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\task{Single-phase DC inverter}
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The following ideal single-phase DC inverter
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\task{Single-phase DC converter}
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The following ideal single-phase DC converter
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\input{fig/ex07/Single-phase_DC_Inverter.tex}
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configured in a bridge topology and supplies a load consisting of an inductor and an internal load voltage. The inverter consists
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of four thyristors arranged in H-bridge configuration.
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of four transistors arranged in H-bridge configuration.
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\begin{table}[ht]
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\centering % Zentriert die Tabelle
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\begin{tabular}{ll}
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\toprule
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Input DC voltage: & $U_{\mathrm{1}}=\SI{200}{\volt}$ \\
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Inductance: & $L = \SI{4.8}{\milli \henry}$ \\
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Internal load voltage: & $u_\mathrm{1e}(t) = 150 \sin(\omega t - \frac{\pi}{6})$ \\
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Internal load voltage: & $u_{2\mathrm{i}}(t) = 150 \sin(\omega t - \frac{\pi}{6})$ \\
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Reference angular frequency: & $\omega_2 = 2\pi \cdot \SI{50}{\hertz}$ \\
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\bottomrule
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\end{tabular}
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\caption{Parameters of the single-phase DC inverter.}
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\caption{Parameters of the single-phase DC converter.}
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\label{table:ex07_Task1_ParametersOfTheCircuit}
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\end{table}
30-
The inverter is modulated using PWM with a modulation index of M=0.75. Assuming ideal operation of the switching components:
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The inverter is modulated using PWM with a modulation index of $m=0.75$. Assuming ideal operation of the switching components, perform the following tasks:
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% Subtask1
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\subtask{Draw the inverter output voltage $u_\mathrm{2}(t)$ belonging to figure \ref{sfig:ex07_sub1.1_modulation}.
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and its fundamental component $u^\mathrm{(1)}_\mathrm{2}(t)$. How large is the phase difference $\delta$ of the voltage
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fundamental component $u^\mathrm{(1)}_\mathrm{2}(t)$ compared to the internal load voltage $u_\mathrm{1e}$?}
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\subtask{Draw the inverter output voltage $u_\mathrm{2}(t)$ belonging to Fig. \ref{sfig:ex07_sub1.1_modulation}.
33+
and its fundamental component $u^\mathrm{(1)}_\mathrm{2}(t)$. How large is the phase difference $\varphi_{2\mathrm{i}}$ of the voltage
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fundamental component $u^\mathrm{(1)}_\mathrm{2}(t)$ compared to the internal load voltage $u_{2\mathrm{i}}(t)$?}
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% Subtask2
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\subtask{Calculate the amplitude $\hat{i}^\mathrm{(1)}_\mathrm{2}$ and the phase angle $\varphi^\mathrm{(1)}$ of the
38-
current fundamental wave $i^\mathrm{(1)}_\mathrm{2}(t)$ compared to $u_\mathrm{1e}$ and draw $u^\mathrm{(1)}_\mathrm{2}(t)$
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current fundamental component $i^\mathrm{(1)}_\mathrm{2}(t)$ compared to $u_{2\mathrm{i}}(t)$ and draw $u^\mathrm{(1)}_\mathrm{2}(t)$
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and $i^\mathrm{(1)}_\mathrm{2}(t)$ in Fig. \ref{sfig:ex07_sub1.2_fund_components}.}
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% Subtask3
42-
\subtask{In Fig. \ref{sfig:ex07_sub1.3_Harmonics}, draw the voltage harmonics $u^\mathrm{(n)}_\mathrm{2}(t)$. Try to sketch, approximately,
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the current harmonics $i^\mathrm{(n)}_\mathrm{2}(t)$ by counting the voltage time area squares.
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One square corresponds to a voltage time area of $\SI{17.8}{\milli \volt \second}$. The starting point is marked with \textbf{s}.\\
42+
\subtask{In Fig. \ref{sfig:ex07_sub1.3_Harmonics}, draw the voltage harmonics $u^{(k)}_\mathrm{2}(t)$. Try to sketch, approximately,
43+
the current harmonics $i^{(k)}_\mathrm{2}(t)$ by counting the voltage time area squares.
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One square corresponds to a voltage time area of $\SI{17.8}{\milli \volt \second}$. The starting point is marked with \textbf{x}.\\
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46-
Hint: The current harmonics $i^\mathrm{(n)}_\mathrm{2}(t)$ have no mean values.}
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Hint: The current harmonics $i^{(k)}_\mathrm{2}(t)$ are free of any bias.}
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% Subtask4
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\subtask{Draw the inverter's output current $i_\mathrm{2}(t)$, its fundamental wave $i^\mathrm{(1)}_\mathrm{2}(t)$
50-
and its harmonics $i^\mathrm{(n)}_\mathrm{2}(t)$ in Fig. \ref{sfig:ex07_sub1.4_current_and_components}.}
50+
and its harmonics $i^{(k)}_\mathrm{2}(t)$ in Fig. \ref{sfig:ex07_sub1.4_current_and_components}.}
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% Subtask5
53-
\subtask{Mark the input current $i_\mathrm{i}(t)$ of the DC voltage inverter in the same figure of subtask 2.1.4.}
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\subtask{Mark the input current $i_\mathrm{i}(t)$ of the DC voltage inverter in the same figure of subtask 7.1.4.}
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\input{fig/ex07/Fig_subtask1.1_modulation.tex}
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\input{fig/ex07/Fig_subtask1.2.tex}
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\input{fig/ex07/Fig_subtask1.3.tex}

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