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@wallscheid
wallscheid committed Jan 22, 2025
2 parents ec7d16a + a938f54 commit ea4a55c
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10 changes: 5 additions & 5 deletions exercise/fig/ex06/Solution_subtask_6_1_2.tex
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Expand Up @@ -11,16 +11,16 @@
\begin{axis}[
% x/y range adjustment
xmin=0, xmax=180,
ymin=0, ymax=1,
ymin=-1, ymax=1,
samples=500,
axis y line=center,
axis x line=bottom,
axis x line=middle,
extra y ticks=0,
% Label text
xlabel={$\alpha / \text{rad}$},
ylabel={$\frac{ U_\mathrm{2}(\alpha)}{U_\mathrm{2}(\alpha=0)}$},
% Label adjustment
x label style={at={(axis description cs:1,-0.1)},anchor=south west},
x label style={at={(axis description cs:1,0.4)},anchor=south west},
y label style={at={(axis description cs:-.05,.97)},anchor=south,yshift=0.2cm},
width=0.6\textwidth,
height=0.3\textwidth,
Expand All @@ -29,8 +29,8 @@
xticklabels={0,0.871,$\frac{\pi}{2}$,$\pi$},
xticklabel style = {anchor=north},
% y-Ticks
ytick={0,0.5,0.644,1},
yticklabels={0,0.5,0.644,1},
ytick={-1,-0.5,0,0.5,0.644,1},
yticklabels={-1,,0,,0.644,1},
yticklabel style = {anchor=east},
% Grid layout
grid,
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141 changes: 84 additions & 57 deletions exercise/fig/ex07/Fig_ThreePhaseInverter_6StepMode.tex
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Expand Up @@ -4,64 +4,91 @@
\begin{figure}[htb]
\begin{center}
\begin{circuitikz}
\def\vd{1.5cm} % vertical distance AC sources
\def\hd{1.5cm} % horizontal distance diode bridge
\def\h1d{5.0cm} % horizontal position first diode string
% Base point for voltage supplies
\coordinate (orig) at (0,0);
% Voltage sources and neutral connection
\draw
% draw the neutral connection
(0,0) to [short, -*] ++(0,-1.5) to [short] ++(0,-1.5)
% draw first phase ua
(0,0) to [sinusoidal voltage source, v^<=$u_{1\mathrm{a}}(t)$] ++(1.5, 0) to [short, i=$i_{1\mathrm{a}}(t)$]++(0.75,0) -- ++(0.25,0) coordinate (A)
% draw second phase ub
(0,-1*\vd) to [sinusoidal voltage source, v^<=$u_{1\mathrm{b}}(t)$] ++(1.5, 0) to [short, i=$i_{1\mathrm{b}}(t)$]++(0.75,0) -- ++(0.25,0) coordinate (B)
% draw third phase uc
(0,-2*\vd) to [sinusoidal voltage source, v^<=$u_{1\mathrm{c}}(t)$] ++(1.5,0) to [short, i=$i_{1\mathrm{c}}(t)$]++(0.75,0) -- ++(0.25,0) coordinate (C)
%thyristor bridge
% Add thyristor T1
(\h1d,0) to [thyristor, l=$T_1$, name=D1] ++(0,1.25) coordinate (D1top)
% Add thyristor T2
(\h1d,-4.25) coordinate (D2bot) to [thyristor, l=$T_2$, name=D2] ++(0,1.25) to [short] (\h1d, 0)
% Add connection to junction A
(\h1d, 0) to [short, *-] (A)
% Add thyristor T3
(\h1d+\hd,0) to [thyristor, l=$T_3$, name=D3] ++(0,1.25) coordinate (D3top)
% Add thyristor T4
(\h1d+\hd,-4.25) coordinate (D4bot) to [thyristor, l=$T_4$, name=D4] ++(0,1.25) to [short] (\h1d+\hd, 0)
% Add thyristor T5
(\h1d+2*\hd,0) to [thyristor, l=$T_5$, name=D5] ++(0,1.25) coordinate (D5top)
% Add thyristor T6
(\h1d+2*\hd,-4.25) coordinate (D6bot) to [thyristor, l=$T_6$, name=D6] ++(0,1.25) to [short] (\h1d+2*\hd, 0)
% Add connection to junction B
(B -| D3) to [crossing, *-, mirror] ++(-2*\hd,0) -- (B)
% Add connection to junction C
(C -| D5) to [short, *-] ++(-\hd/2,0) to [crossing, mirror] ++(-\hd,0) to [crossing, mirror] ++(-\hd,0) -- (C)
% Add wire T1-T3-T5
(D1top) to [short, -*] (D3top) to [short, -*] (D5top) to [short, -] ++(0.5,0) coordinate (jL1)
% Add inductor L and motor current
(jL1) to [L, l=$L$, name = L] ++(2,0) to [short,i=$\overline{i}_\mathrm{mot}$] ++(0.5,0) coordinate (jL2)
% Add DC-motor and motor voltage
(jL2) ++ (0,-3) node[elmech](motor){M}
(jL2) to (motor.north)
(motor.bottom) to (D6bot -| \tikztostart) to (D6bot)
% (jL2) to [R, l=$R$, name = R, v_>=$\overline{u}_\mathrm{mot}$, voltage = straight] (D6bot -| \tikztostart) to (D6bot)
% Add voltage U1p
\draw (0,0) coordinate (U1p) to [open, o-o, v = $U_1p\hspace{0.5cm}$, voltage = straight] ++(0,-2.5) coordinate (Gnd)
(Gnd) to [short,o-o] ++(1,0)
(Gnd) to [open, -o, v = $U_1m\hspace{0.5cm}$, voltage = straight] ++(0,-2.5) coordinate (U1m)
% Add current
(U1p) to [short, o-, i=$i_1(t)$] ++(2,0) coordinate (jT1c)
% Add T1
(jT1c) to [Tnpn, n=T1, invert, bodydiode] ++(0,-2) coordinate (jT1e)
% Add connection to u2a
(jT1e) to [short, *-] ++(1,0) to [crossing] ++(2,0) to [crossing] ++(2,0) to [short,-] ++(1,0) coordinate (ju2a)
% Add junction to T2
(jT1e) to [short] ++(0,-1) coordinate (jT2c)
% Add T2
(jT2c) to [Tnpn, n=T2, invert, bodydiode] ++(0,-2) coordinate (jT2e)
% Add connection to T3
(jT1c) to [short, *-] ++(2,0) coordinate (jT3c)
% Add T3
(jT3c) to [Tnpn, n=T3, invert, bodydiode] ++(0,-2) coordinate (jT3e)
% Add junction to ju2b
(jT3e) to [short] ++(0,-0.5) coordinate (jmu2b)
% Add connection to u1b
(jmu2b) to [short,*-] ++(1,0) to [crossing] ++(2,0) to [short,-] ++(1,0) coordinate (ju2b)
% Add junction to T4
(jmu2b) to [short] ++(0,-0.5) coordinate (jT4c)
% Add T4
(jT4c) to [Tnpn, n=T4, invert, bodydiode] ++(0,-2) coordinate (jT4e)
% Add connection to T5
(jT3c) to [short, *-] ++(2,0) coordinate (jT5c)
% Add T5
(jT5c) to [Tnpn, n=T5, invert, bodydiode] ++(0,-2) coordinate (jT5e)
% Add junction to T6
(jT5e) to [short] ++(0,-1) coordinate (jT6c)
% Add T6
(jT6c) to [Tnpn, n=T6, invert, bodydiode] ++(0,-2) coordinate (jT6e)
% Add connection to T4
(jT6e) to [short, -*] (jT4e)
% Add connection to T2
(jT4e) to [short, -*] (jT2e)
% Add connection to U1m
(jT2e) to [short, -] (U1m)
% Add connection to u1c
(jT6c) to [short,*-] ++(2,0) coordinate (ju2c)
% Add connection to u2a inductor
(ju2a) to [short,-] ++(0,2) coordinate (ju2ax)
% Add u2a inductor
(ju2ax) to [L, l=$L$, name = L] ++(2,0) coordinate (ju2ae)
% Add u2ae
(ju2ae) to [sV=$u_\mathrm{1ae}$] ++(1.5,0) coordinate (ju2an)
% Add u2b inductor
(ju2b) to [L, l=$L$, name = L] ++(2,0) coordinate (ju2be)
% Add u2be
(ju2be) to [sV=$u_\mathrm{1be}$] ++(1.5,0) coordinate (ju2bn)
% Add connection to u2c inductor
(ju2c) to [short,-] ++(0,-2) coordinate (ju2cx)
% Add u2a inductor
(ju2cx) to [L, l=$L$, name = L] ++(2,0) coordinate (ju2ce)
% Add u2ce
(ju2ce) to [sV=$u_\mathrm{1ce}$] ++(1.5,0) coordinate (ju2cn)
% Add connection of u2in
(ju2an) to [short,-*] (ju2bn) to [short,-] (ju2cn);


% Add component name of transistors
\draw let \p1 = (T1.B) in node[anchor=east] at (\x1,\y1) {$T_1$};
\draw let \p1 = (T2.B) in node[anchor=east] at (\x1,\y1) {$T_2$};
\draw let \p1 = (T3.B) in node[anchor=east] at (\x1,\y1) {$T_3$};
\draw let \p1 = (T4.B) in node[anchor=east] at (\x1,\y1) {$T_4$};
\draw let \p1 = (T5.B) in node[anchor=east] at (\x1,\y1) {$T_5$};
\draw let \p1 = (T6.B) in node[anchor=east] at (\x1,\y1) {$T_6$};
% Add current arrows i2a, i2b and i2c
\draw (jT1e) ++(1,0) node[currarrow](i2a){}
(i2a) node[anchor=north,color=black]{$i_\mathrm{2a}(t)$}
(jmu2b) ++(1,0) node[currarrow](i2b){}
(i2b) node[anchor=north,color=black]{$i_\mathrm{2b}(t)$}
(jT6c) ++(1,0) node[currarrow](i2c){}
(i2c) node[anchor=north,color=black]{$i_\mathrm{2c}(t)$}
% Add voltage arrows u2an, u2bn and u2cn
(ju2ax) ++(0,-0.8) to [open,v^=$u_\mathrm{2a}(t)$,voltage = straight] ++(3.8,0)
(ju2b) ++(0,-0.8) to [open,v^=$u_\mathrm{2b}(t)$,voltage = straight] ++(3.8,0)
(ju2cx) ++(0,-0.8) to [open,v^=$u_\mathrm{2c}(t)$,voltage = straight] ++(3.8,0)
% Add voltage arrows u2ab and u2bc
(ju2ax) ++(0.2,0) to [open,v^=$u_\mathrm{2ab}(t)$,voltage = straight] ++(0,-2.5)
(ju2b) ++(0.2,0) to [open,v^=$u_\mathrm{2bc}(t)$,voltage = straight] ++(0,-2.5);


% Add wire T2-T3-T6
(D2bot) to [short, -*] (D4bot) to [short, -*] (D6bot)
% Add voltage arrow u2(t) between Dtop and Dbot
(jL1) to [open, v^>=$\hspace{0.5cm}u_2(t)$, voltage = straight] (D6bot-|jL1)
% Add voltage arrow u2+n(t) between Dtop and neutral
(D1top) ++(-0.2,0) to [open, v_>=$u_\mathrm{2,p}(t)$, voltage = straight] ++(-5.5,0)
% Add voltage arrow u2-n(t) between Dbot and neutral
(D2bot) ++(-0.2,0) to [open, v_>=$u_\mathrm{2,m}(t)$, voltage = straight] ++(-5.5,0)
% Add voltage arrow between AC source a and b
(A) to [open, v^>=$\hspace{0.75cm}u_{1\mathrm{ab}}(t)$, voltage = straight] (B)
% Add voltage arrow between AC source b and c
(B) to [open, v^>=$\hspace{0.75cm}u_{1\mathrm{bc}}(t)$, voltage = straight] (C)
% Add voltage arrow between AC source a and c
(-0.5,-2*\vd) to [open, v^>=$u_{1\mathrm{ca}}(t)\hspace{0.75cm}$, voltage = straight] (-0.5,0);
\end{circuitikz}
\end{center}
\caption{Three-phase inverter in six-step mode.}
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178 changes: 86 additions & 92 deletions exercise/fig/ex07/Fig_graphic_solutions_cos_terms.tex
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Expand Up @@ -4,103 +4,97 @@

\begin{figure}[htb]
\centering
\begin{tikzpicture}
\begin{axis}[
axis lines=middle, % Achsen wie im Koordinatensystem
xlabel={$\cos(\varphi)$},
ylabel={$\sin(\varphi)$},
width=7cm, height=7cm,
grid=both,
major grid style={line width=.2pt,draw=gray!50},
minor grid style={line width=.1pt,draw=gray!20},
xmin=-1.5, xmax=1.5,
ymin=-1.5, ymax=1.5,
% xtick={-1, -0.5, 0, 0.5, 1},
% ytick={-1, -0.5, 0, 0.5, 1},
]
\draw[thick, ->] (0,0) -- ({cos(40)}, {sin(40)}) node[above right] {};
\node at ({0.5*cos(40)}, {0.5*sin(40)}) [below] {$\varphi$};

\addplot[
domain=0:360, % 360° für den ganzen Kreis
samples=200, % Anzahl der Punkte
thick,
color=blue,
]
({cos(x)}, {sin(x)}); % Kreisparameter (cos, sin)

\end{axis}
\end{tikzpicture}

\hspace{1cm} % Abstand zwischen den beiden Diagrammen

\begin{tikzpicture}
% Achsen
\draw[->, thick] (-2,0) -- (2,0) node[right] {$(x)$};
\draw[->, thick] (0,-2) -- (0,2) node[above] {$(y)$};
\begin{minipage}[t]{0.45\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
xlabel={$\cos(\varphi)$},
ylabel={$\sin(\varphi)$},
width=7cm, height=7cm,
major grid style={line width=.2pt,draw=gray!50},
minor grid style={line width=.1pt,draw=gray!20},
xmin=-1.5, xmax=1.5,
ymin=-1.5, ymax=1.5,
]

\draw[thick, ->] (0,0) -- ({cos(40)}, {sin(40)}) node[above right] {};
\node at ({0.5*cos(40)}, {0.5*sin(40)}) [below] {$\varphi$};

% Punkte auf den Achsen
\foreach \x in {-2,2} {
\draw[thick] (\x,0) node[below] {\x} -- (\x,0.2);
}
\foreach \y in {-1,1} {
\draw[thick] (0,\y) -- (0.2,\y) node[right] {\y};
}

% Werte cos(k*pi/2)
\node at (1.5,1.5) {$\cos\left(k \frac{\pi}{2}\right)$};
\node[below right] at (0.1,0) {1,5,9,...};
\end{tikzpicture}
\caption{Switch-on behavior and switch-off behavior of $i_{\mathrm{C}}(t)$.}
\label{fig:Switch-on behavior and switch-off behavior of}
\addplot[
domain=0:360,
samples=200,
thick,
color=blue,
]
({cos(x)}, {sin(x)});
\end{axis}
\end{tikzpicture}
\end{minipage}
\hspace{0.5cm}
\begin{minipage}[t]{0.45\textwidth}
\centering
\begin{tikzpicture}
\draw[->] (-2,0) -- (2,0) node[right] {};
\draw[->] (0,-2) -- (0,2) node[above] {};
\node at (-1.5,1.5) {$\cos\left(k \frac{\pi}{2}\right)$};
\node at (-2,0) [left] {$2,6,\ldots$};
\node at (2,0) [right] {$0,4,\ldots$};
\node at (0,2) [above] {$1,5,9,13,\ldots$};
\node at (0,-2) [below] {$3,7,11,15,\ldots$};

% Kreuz bei jedem markierten Punkt
\foreach \x/\y in {-1.5/0, 1.5/0, 0/1.5, 0/-1.5} {
\draw[thick]
(\x,\y) +(-0.1,0.1) -- +(0.1,-0.1) % Diagonale des Kreuzes
+(-0.1,-0.1) -- +(0.1,0.1); % Andere Diagonale des Kreuzes
}
\end{tikzpicture}
\end{minipage}

\begin{tikzpicture}
\begin{axis}[
width=7cm, height=4.5cm,
grid=both,
major grid style={line width=.2pt,draw=gray!50},
minor grid style={line width=.1pt,draw=gray!20},
xlabel={$t$ / ns},
ylabel={$u_{\mathrm{CE}}(t)$ / V},
xmin=0, xmax=150,
ymin=0, ymax=800,
xtick={0, 50, 100, 150},
ytick={0,200, 400, 600, 800},
]
% Einschaltverhalten graph
\addplot[
thick,
mark=none,
color=black,
] coordinates {
(0,600) (100, 600) (100, 0)
};
\end{axis}
\draw[->] (-2,0) -- (2,0) node[right] {};
\draw[->] (0,-2) -- (0,2) node[above] {};
\node at (-1.5,1.5) {$\cos\left(k \frac{\pi}{3}\right)$};
\node at (-2,0) [left] {$2,6,\ldots$};
\node at (2,0) [right] {$0,4,\ldots$};
\node at (0,2) [above] {$1,5,9,13,\ldots$};
\node at (0,-2) [below] {$3,7,11,15,\ldots$};

% Kreuz bei jedem markierten Punkt
\foreach \x/\y in {-1.5/0, 1.5/0, 0/1.5, 0/-1.5} {
\draw[thick]
(\x,\y) +(-0.1,0.1) -- +(0.1,-0.1) % Diagonale des Kreuzes
+(-0.1,-0.1) -- +(0.1,0.1); % Andere Diagonale des Kreuzes
}
\end{tikzpicture}
\hspace{1cm} % Abstand zwischen den beiden Diagrammen
\begin{tikzpicture}
\begin{axis}[
width=7cm, height=4.5cm,
grid=both,
major grid style={line width=.2pt,draw=gray!50},
minor grid style={line width=.1pt,draw=gray!20},
xlabel={$t$ / ns},
ylabel={$u_{\mathrm{CE}}(t)$ / V},
xmin=0, xmax=600,
ymin=0, ymax=1000,
xtick={0,200, 400, 600},
ytick={0,200, 400, 600,800, 1000},
]
% Ausschaltverhalten graph
\addplot[
thick,
mark=none,
color=black,
] coordinates {
(50,0) (200, 900) (250, 600) (600, 600)
};
\end{axis}
% Koordinatensystem zeichnen
\draw[->] (-2,0) -- (2,0) node[right] {};
\draw[->] (0,-2) -- (0,2) node[above] {};
\node at (-1.5,1.5) {$\cos\left(k \frac{\pi}{3}\right)+1$};

% Beschriftungen an der x-Achse
\foreach \x in {0, 1, 1.5} {
\node at (\x, 0) [below] {\x};
}

% Beschriftungen an spezifischen Punkten
\node at (1.5,1.1) [above] {$1,7,13,19,\ldots$};
\node at (1.5,-1.1) [below] {$5,11,17,23,\ldots$};

% Kreuz bei jedem markierten Punkt
\foreach \x/\y in {0/0, 1.5/1, 1.5/-1} {
\draw[thick]
(\x,\y) +(-0.1,0.1) -- +(0.1,-0.1) % Diagonale des Kreuzes
+(-0.1,-0.1) -- +(0.1,0.1); % Andere Diagonale des Kreuzes
}

% Verbindungslinien zwischen den Punkten
\draw[thick, color=blue!70!black]
(0,0) -- (1.5,1) -- (1.5,-1) -- cycle;
\end{tikzpicture}
\caption{Switch-on behavior and switch-off behavior of $u_{\mathrm{CE}}(t)$.}
\label{fig:Switch-on behavior and switch-off behavior of voltage}
\caption{Graphical solution of the cos terms.}
\label{fig:Graphical solution of the cos terms}
\end{figure}
6 changes: 3 additions & 3 deletions exercise/tex/exercise06.tex
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Expand Up @@ -34,7 +34,7 @@
\end{equation}
where
\begin{equation}
\hat{u}_\mathrm{1} = \sqrt{2}U_\mathrm{1} = \sqrt{2} \cdot 230 \approx \SI{325.27}{\volt}.
\hat{u}_\mathrm{1} = \sqrt{2}U_\mathrm{1} = \sqrt{2} \cdot \SI{230}{\volt} \approx \SI{325.27}{\volt}.
\label{sub6.1.1:eq:voltage_amplitude}
\end{equation}
Hence,
Expand Down Expand Up @@ -76,7 +76,7 @@
period is equal to $\frac{2\pi}{3}$. Thus, $a_1$ ($\hat{i}^\mathrm{(1)}_\mathrm{1a}$) can be calculated as:

\begin{equation}
a_1 = \hat{i}^\mathrm{(1)}_\mathrm{1a} = \frac{2}{\pi}\int_{0}^{\frac{\pi}{3}}I_\mathrm{2}\cos(\omega t) d\omega t = \left[\frac{2}{\pi} \sin(\omega t)\right]^{\frac{\pi}{3}}_{0} = \frac{1}{\pi}I_\mathrm{2}\sqrt{3}.
a_1 = \hat{i}^\mathrm{(1)}_\mathrm{1a} = \frac{2}{\pi}\int_{0}^{\frac{\pi}{3}}I_\mathrm{2}\cos(\omega t) \mathrm{d}\omega t = \left[\frac{2}{\pi} \sin(\omega t)\right]^{\frac{\pi}{3}}_{0} = \frac{1}{\pi}I_\mathrm{2}\sqrt{3}.
\label{sub6.1.4:eq:calculate_a1}
\end{equation}

Expand All @@ -101,7 +101,7 @@
\begin{solutionblock}
The fundamental reactive power drawn for one full period $(2\pi)$ can be calculated using
\begin{equation}
Q^\mathrm{(1)} = 3 U_1 I^\mathrm{(1)}_1 \sin(\alpha) = 3 \cdot 230 \cdot 13.5 \cdot \sin(0.871) \approx \SI{7.12}{\kilo \volt \ampere}.
Q^\mathrm{(1)} = 3 U_1 I^\mathrm{(1)}_1 \sin(\alpha) = 3 \cdot \SI{230}{\volt} \cdot \SI{13.5}{\ampere} \cdot \sin(0.871) \approx \SI{7.12}{\kilo \volt \ampere}.
\end{equation}
\end{solutionblock}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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