Starting task5

exercise/fig/ex05/Fig_BoostConverter_with_Rectifiers.tex

@@ -0,0 +1,34 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ % Boost converter with single-phase diode bridge Schematic
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+    \begin{figure}[htb]
+        \begin{center}
+            \begin{circuitikz}[european currents,european resistors,american inductors]
+            \draw (0,0) to [open, o-o, v = $u_1(t)\hspace{0.5cm}$, voltage = straight] ++(0,-2) coordinate (A)
+            (0,0) to [short, i=$i_1(t)$, -*] ++(2,0)
+            to [diode, l=$D_1$]  ++(0,1.5)
+            to [short, -*] ++(2,0) coordinate (C)
+            to [diode, l=$D_3$, invert]  ++(0,-1.5)
+            to [short] ++(0, -2) coordinate (B)
+            to [diode, l=$D_2$, invert, -*]  ++(0, -1.5) coordinate (D)
+            to [short] ++(-2,0)
+            to [diode, l=$D_4$]  ++(0, 1.5)
+            to [short] ++(0, 2)
+            (B) to [crossing, *-, mirror] ++(-4,0)
+            to [short] (A)
+            (C) to [short, i=$i_2(t)$] ++(2,0) coordinate (E)
+            to [short] ++(0,-1.5)
+            to [C, v= $u_2(t)$, voltage = straight, l=$C$, i=${i_\mathrm{C}(t)}$] ++(0,-2)
+            to [short] ++(0,-1.5) coordinate (F)
+            to [short] (D)
+            (E) to [short, *-] ++(2,0)
+            to [short] ++(0,-1.5)
+            to [isource, l=$I_0$] ++(0,-2)
+            to [short] ++(0,-1.5)
+            to [short, -*] (F);
+        \end{circuitikz}
+    \end{center}
+        \caption{PFC rectifier.}
+        \label{fig:Boost converter with single-phase diode bridge_topology}
+    \end{figure}
+

exercise/main.tex

@@ -1,11 +1,12 @@
 \documentclass[solution]{../course_template/exerciseClass}
 \title{Power Electronics}
 
-\includeonly{tex/exercise04}
+\includeonly{tex/exercise05}
 
 \begin{document}
     \include{tex/exercise01}
     \include{tex/exercise02}
     \include{tex/exercise03}
     \include{tex/exercise04}
+    \include{tex/exercise05}
 \end{document}

exercise/tex/exercise05.tex

@@ -0,0 +1,64 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Begin exercise %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\ex{Rectifiers}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Task 1: B2U topology with capactive filtering %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Task 2: PFC rectifier %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\task{Current control with constant clock frequency}
+Due to the constantly increasing load on the grid with harmonics as a result of the use of power converters, the regulations regarding the permissible harmonic content of the current consumption of electrical consumers are being tightened. It is therefore necessary, e.g. for the rectification of single-phase AC mains voltage, for example, it is necessary to design power converters with a high power factor or a largely sinusoidal input current. The system consists of a diode bridge $(D_{\mathrm{1}} \, \dots \, D_{\mathrm{4}})$, an inductor $L$, a power transistor $T_\mathrm{H}$ (usually a power MOSFET), a freewheeling diode $D_\mathrm{H}$ and an output capacitor $C_\mathrm{d}$. The prerequisite for the use of the boost converter is: $u_\mathrm{d} = U_\mathrm{d}>U_\mathrm{1}$. The boost converter is operated with a modified current control method ('Average Current Mode Control') for which the switching frequency $f_\mathrm{T}$ has a constant value $f_\mathrm{T} = \SI{20}{\kilo\hertz}$. This is realized
+by comparing the current controller output variable with a triangular oscillation with switching frequency $f_\mathrm{T} = \SI{20}{\kilo\hertz}$ and suitable amplitude is compared.
+Let $L = \SI{570}{\micro\henry}$ and the inductance carry a continuous current.
+Definition: Transmission ratio: $M = \frac{ U_\mathrm{d}}{\hat U_\mathrm{1}}$
+\input{fig/ex05/Fig_BoostConverter_with_Rectifiers.tex}
+
+\begin{table}[ht]
+    \centering  % Zentriert die Tabelle
+    \begin{tabular}{llll}
+        \toprule
+
+        Input voltage: &  $u_{\mathrm{1}} = \hat U_{\mathrm{1}} \sin(\omega t) = \sqrt{2} \cdot \SI{230}{\volt} \sin(\omega t)$ & Output voltage: & $U_{\mathrm{d}} = \SI{400}{\volt}$ \\ 
+        Output power: & $P_d = \SI{4}{\kilo\watt}$  & Circular frequency: & $\omega = 2 \pi \SI{50}{\hertz}$ \\ 
+        Inductance: & $L = \SI{570}{\micro\henry}$
+         &Power factor: & $k = 0.08$ \\ 
+         switching frequency: & $f_\mathrm{T} = \SI{20}{\kilo\hertz}$\\
+        \bottomrule
+    \end{tabular}
+    \caption{Parameters of the PFC rectifier.}  
+    \label{table:ex05_Parameters of the circuit}
+\end{table}
+
+\subtask{Specify the voltage transformation ratio $m(t)= \frac{U_\mathrm{d}}{u'(t)}$ as a function of the duty cycle $d(t)$ is specified.}
+\begin{solutionblock}
+
+\end{solutionblock}
+
+\subtask{Specify the conduction time of the transistor and the diode as a function of the transformation ratio $M$ and the time $t$.} %\label{subtask:TEST}
+
+\subtask{Calculate the maximum amplitude of the switching frequency fluctuation of the mains current $i_\mathrm{1}$ for the specified operating point.
+Note: Consider the conductive state of $T_\mathrm{H}$ and set the voltage across the inductance as a function of the phase angle $(\omega t)$and the conduction time of the transistor according} %\subtaskref{subtask:TEST}.}
+
+\subtask{Complete the current curve for one switching frequency $f_\mathrm{T2} = \SI{2}{\kilo\hertz}$ and one inductance $L = \SI{5}{\milli\henry}$ in......
+Note: At the time $t =0$ is $i'=0$. The switch-on and switch-off times are determined by the control signal of the transistor $T_\mathrm{H}$ and are summarized for the first 4 switching times in the following table...............}
+
+\subtask{Approximately sketch the envelope of the current ripple in Fig. 2.
+of the voltage across the inductor in Supplement 3, Fig. 3 and enter the local mean value of the voltage as an approximation. How would the switch-on/switch-off ratio of the transistor have to be changed before and after the
+current peak in order to bring the mean actual current value closer to the current setpoint?}
+
+\subtask{Calculate the losses in the diode $D_\mathrm{H}$.}
+
+\subtask{Dimension the output capacitance $C_\mathrm{d}$ in a way that the amplitude of the output voltage ripple is at twice the mains frequency $\Delta u_{\mathrm{d}}<0.05U_{\mathrm{1}}$.
+Note: Take the approach using the instantaneous input power $p_{\mathrm{d}(t)}$ and assume that this power is fed directly to the output.}
+
+\subtask{Calculate the RMS value of the current through the capacitor $I_{\mathrm{C_{\mathrm{d}}}}$.
+Note: The mean value of the current through the capacitor is $\overline i_{\mathrm{C_{\mathrm{d}}}}=0$!}
+
+\subtask{The current carrying capacity of the capacitor is $\frac{\SI{10}{\ampere}}{\SI{1}{\milli\farad}}$. How large must its capacitance be selected? Is the permissible output voltage fluctuation from ..... or is it the current carrying capacity that determines the capacitance?}
+
+\subtask{What is the current load (effective and average value) of the mains diodes?}