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changed float placement config
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wallscheid committed Aug 1, 2024
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6 changes: 3 additions & 3 deletions exercise/tex/exercise03.tex
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\begin{solutionblock}
As described in the task, the windings are perfectly connected, which means, that no leakage flux occurs. In addition, the winding resistances and the iron losses of the transformer are neglected. This results in the equivalent circuit diagram shown in \autoref{fig:ex_transformer_T_ECD_core_losses_no_load}.
\begin{solutionfigure}[h!]
\begin{solutionfigure}[ht!]
\centering
\includegraphics{ex03/ex_transformer_T_ECD_core_losses_no_load.pdf}
\caption{Equivalent circuit diagram without leakage flux and neglected winding and iron losses.}
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\begin{solutionblock}

The equivalent circuit diagram for the no-load operation with the iron loss resistance $R_{\mathrm{c}}$ is shown in \autoref{fig:ex_transformer_open_circuit_test}.
\begin{solutionfigure}[h!]
\begin{solutionfigure}[ht!]
\centering
\includegraphics{ex03/ex_Transformer_open_circuit_test.pdf}
\captionsetup{labelfont={color=blue},textfont={color=blue}}
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In \autoref{fig:current_transformer} the two calculated current trajectories are visualized. They result from the applied voltage with the additional angle $\alpha$.
In this example is the peak current value during the transient process approximately double than in the steady state, which can trigger the overcurrent protection. Therefore, the magnetization current should be kept low and the overcurrent protection must be able to handle the inrush current.
\begin{solutionfigure}[h!]
\begin{solutionfigure}[ht!]
\centering
\includegraphics{ex03/current_transformer.pdf}
\caption{Current of the transformer, when the voltage is applied at two different angles for $\alpha$.}
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24 changes: 12 additions & 12 deletions exercise/tex/exercise04.tex
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For the calculation up to the $19\textsuperscript{th}$ harmonic, a short Python script is written.
The results are visualized in \autoref{tab:windingFactors}.
\begin{solutiontable}[h]
\begin{solutiontable}[ht]
\caption{Distribution, pitch, and winding factors as well as relative harmonic flux density amplitudes.}
\centering
\begin{tabular}{rcrrr}\toprule
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\begin{solutionblock}
The calculation is performed with \eqref{eq:harmonicOrderFluxDensity} in a separate Python script. The resulting trajectories are shown in \autoref{fig:fundamentalAnd11thHarm}.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex04/FundamentalAnd11thHarmonic.pdf}
\caption{Visualization of the flux density of the fundamental wave and the $11\textsuperscript{th}$ harmonic of phase~a.}
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which fulfills the requirement too.
With the calculated phase shift and the knowledge of the coil width of three slots from the figure, the winding scheme is completed.
In \autoref{tab:solution_distributedWinding} the inputs and outputs of each winding are given.
\begin{solutiontable}[h]
\begin{solutiontable}[ht]
\caption{Solution of the distributed winding scheme.}
\centering
\begin{tabular}{c|C{1cm}|C{1cm}|C{1cm}|C{1cm}|C{1cm}|C{1cm}}\toprule
Expand All @@ -265,7 +265,7 @@
\end{solutiontable}

The sketch of the distributed winding scheme is visualized in \autoref{fig:solution_MMF_distributed}.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex04/solution_MMF_distributed.pdf}
\caption{Solution of the distributed winding.}
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\end{equation}
where $i$ represents the number of the stator slot.
Therefore, the mechanical angles are given in \autoref{tab:mechanicalAngles_distributedWinding}.
\begin{solutiontable}[h]
\begin{solutiontable}[ht]
\caption{Mechanical angles of the distributed winding from \autoref{fig:MMF_distributed}.}
\centering
\begin{tabular}{C{3cm}|C{3cm}}\toprule
Expand All @@ -323,7 +323,7 @@
\end{solutiontable}

To calculate the winding factors, the total number of turns of the respective phase $N_{\mathrm{a}}$ is determined for each stator slot. A negative sign indicates, that the winding turn is oriented towards the negative $z$-axis. When no conductor is in a slot, $N_{\mathrm{a,}i}$ = 0. The result is shown in \autoref{tab:WindingTurns_distributedWinding}.
\begin{solutiontable}[h]
\begin{solutiontable}[ht]
\caption{Winding turns of phase a of the distributed winding.}
\centering
\begin{tabular}{C{3cm}C{3cm}C{3cm}}\toprule
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\begin{solutionblock}
The Python script is separately available, therefore, only the solution is presented in Tab~\ref{tab:complexWindingFactor_python}.
\begin{solutiontable}[h]
\begin{solutiontable}[ht]
\caption{Complex winding factor $\underline{\xi}_{\mathrm{a,}k}$ up to the $12\textsuperscript{th}$ harmonic order.}
\centering
\begin{tabular}{R{5cm}R{5cm}R{5cm}}\toprule
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which fulfills the requirement too.

With the coil width of one slot, the resulting winding is determined. The solution of this winding scheme is shown in \autoref{tab:solution_concentratedWinding}.
\begin{solutiontable}[h]
\begin{solutiontable}[ht]
\caption{Solution of the winding scheme of a concentrated winding.}
\centering
\begin{tabular}{c|C{1cm}|C{1cm}|C{1cm}|C{1cm}|C{1cm}|C{1cm}}\toprule
Expand All @@ -649,7 +649,7 @@


The completed winding scheme is visualized in Fig.\ref{fig:solution_MMF_concentrated}.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex04/solution_MMF_concentrated.pdf}
\captionsetup{labelfont={color=blue},textfont={color=blue}}
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\end{equation}
where $i$ represents the number of the stator slot.
Therefore, the mechanical angles are given in \autoref{tab:mechanicalAngles_concentratedWinding}.
\begin{solutiontable}[h]
\begin{solutiontable}[ht]
\caption{Mechanical angles of the concentrated winding from \autoref{fig:MMF_concentrated}.}
\centering
\begin{tabular}{C{3cm}|C{3cm}}\toprule
Expand All @@ -706,7 +706,7 @@
\end{solutiontable}

To calculate the winding factors, the total number of turns of the respective phase $N_{\mathrm{a}}$ is determined for each stator slot. A negative sign indicates, that the winding turn is oriented towards the negative $z$-axis. When no conductor is in a slot, $N_{\mathrm{a,}i}$ = 0. The result is shown in \autoref{tab:WindingTurns_concentratedWinding}.
\begin{solutiontable}[h]
\begin{solutiontable}[ht]
\caption{Winding turns of phase a of the concentrated winding rom \autoref{fig:MMF_concentrated}.}
\centering
\begin{tabular}{C{3cm}C{3cm}C{3cm}}\toprule
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\begin{solutionblock}
The Python script is separately available, therefore, only the solution is presented in Tab~\ref{tab:complexWindingFactor_concentratedW_python}.
\begin{solutiontable}[h]
\begin{solutiontable}[ht]
\caption{Complex winding factors $\underline{\xi}_{\mathrm{a,}k}$ for the concentrated winding up to the $12\textsuperscript{th}$ harmonic order.}
\centering
\begin{tabular}{R{3cm}R{3cm}R{3cm}R{3cm}}\toprule
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36 changes: 18 additions & 18 deletions exercise/tex/exercise05.tex
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Expand Up @@ -194,15 +194,15 @@

\begin{solutionblock}
The current in the dq coordinate system is shown in \autoref{fig:i_dq_noLoad}. After the steady state is reached, the current values are constant, which could be expected in the rotor flux-oriented coordinate system.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/i_dq_noLoad.pdf}
\caption{Transient process of an IM in the dq coordinate system.}
\label{fig:i_dq_noLoad}
\end{solutionfigure}

In \autoref{fig:i_ab_noLoad} the current in the $\upalpha, \upbeta$ coordinate system is visualized. The transient process is also clearly visible in this coordinate system.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/i_alphaBeta_noLoad.pdf}
\caption{Transient process of an IM in the $\upalpha \upbeta$ coordinate system.}
Expand All @@ -212,45 +212,45 @@
\autoref{fig:i_abc_noLoad} shows the transient process of the current in the three-phase abc coordinate system.

Compared to the abc current plot, one can observe also a sinusoidal signalform with the same amplitude and frequency evolution, while the phase difference between the currents is 120° in abc and 90° in $\upalpha\upbeta$. This fits to the expectations resulting from the amplitude-invariant Clarke transformation.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/i_abc_noLoad.pdf}
\caption{Transient process of an IM in the abc coordinate system.}
\label{fig:i_abc_noLoad}
\end{solutionfigure}

The electrical angular frequency of the stator and the angular frequency of the rotor are shown in \autoref{fig:speed_noLoad}. Due to the no load operation (also no friction) of the IM, the angular frequency of the rotor is equal to the angular electrical stator frequency.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/speed_noLoad.pdf}
\caption{Electric angular frequency of the stator and angular frequency of the rotor during the transient process at no load.}
\label{fig:speed_noLoad}
\end{solutionfigure}

The produced torque is shown in \autoref{fig:torque_noLoad}. During the transient process, very high torque values are reached and an oscillation of the rotor is visible. In the steady state, the torque is equal to zero, due to the no-load operation.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/torque_noLoad.pdf}
\caption{Produced torque of an IM during the transient process at no load.}
\label{fig:torque_noLoad}
\end{solutionfigure}

In \autoref{fig:rotorFlux_noLoad} the rotor flux is shown, which also shows the transient process. The d-axis of the coordinate system is oriented on the rotor flux and, therefore, the flux aligned to the q-axis is zero. Thus, only the rotor flux aligned to the d-axis is visualized.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/psi_rd_noLoad.pdf}
\caption{Rotor flux in dq coordinate system during the transient process at no load.}
\label{fig:rotorFlux_noLoad}
\end{solutionfigure}

\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/psi_r_ab_noLoad.pdf}
\caption{Rotor flux in $\upalpha\upbeta$ coordinate system during the transient process at no load.}
\label{fig:rotorFlux_r_ab_noLoad}
\end{solutionfigure}

\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/psi_r_abc_noLoad.pdf}
\caption{Rotor flux in abc coordinate system during the transient process at no load.}
Expand All @@ -267,73 +267,73 @@

\begin{solutionblock}
In \autoref{fig:speed_friction} the speed of the stator and rotor field is visualized. For this simulation a load term representing the friction is added, thus this load is speed dependent. Hence, this results in a different speed of the rotor in the steady state in comparison to the stator field. This occurs due to the load of the machine, and is representing with the slip of the machine.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/speed_friction.pdf}
\caption{Electrical angular frequency of the stator and angular frequency of the rotor during the transient process with a speed dependent load.}
\label{fig:speed_friction}
\end{solutionfigure}

To highlight the difference between the stator and rotor field, in \autoref{fig:speed_zoom_friction} the boundaries of the vertical axis are limited. Hence, the speed difference in the steady state is clearly visible.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/speed_zoom_friction.pdf}
\caption{Zoom into the electrical angular frequency of the stator and angular frequency of the rotor to visualize the difference in the steady state.}
\label{fig:speed_zoom_friction}
\end{solutionfigure}

The produced torque during the transient process is shown in \autoref{fig:torque_friction}.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/torque_friction.pdf}
\caption{Produced torque of an IM during the transient process and in the steady-state operation with a speed-dependent load.}
\label{fig:torque_friction}
\end{solutionfigure}
\autoref{fig:torque_zoom_friction} shows a zoomed version of the produced torque to highlight the torque in the steady state.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/torque_zoom_friction.pdf}
\caption{Produced torque of an IM during the transient process and in the steady-state operation with a speed-dependent load.}
\label{fig:torque_zoom_friction}
\end{solutionfigure}

In \autoref{fig:i_dq_friction} the currents in the dq coordinate system are visualized. Due to the load and, thus, the generated torque, the current $i_{\mathrm{q}}$ is no longer zero in the steady state.
\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/i_dq_friction.pdf}
\caption{Currents in dq coordinate system of an IM during the transient process and in the steady-state operation with a speed-dependent load.}
\label{fig:i_dq_friction}
\end{solutionfigure}

\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/i_alphaBeta_friction.pdf}
\caption{Currents in $\upalpha \upbeta$ coordinate system of an IM during the transient process and in the steady-state operation with a speed-dependent load.}
\label{fig:i_ab_friction}
\end{solutionfigure}

\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/i_abc_friction.pdf}
\caption{Currents in abc coordinate system of an IM during the transient process and in the steady-state operation with a speed-dependent load.}
\label{fig:i_abc_friction}
\end{solutionfigure}

\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/psi_rd_friction.pdf}
\caption{Rotor flux linkage in dq coordinate system of an IM during the transient process and in the steady-state operation with a speed-dependent load.}
\label{fig:psi_rq_friction}
\end{solutionfigure}

\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/psi_r_ab_friction.pdf}
\caption{Rotor flux linkage in $\upalpha\upbeta$ coordinate system of an IM during the transient process and in the steady-state operation with a speed-dependent load.}
\label{fig:psi_r_ab_friction}
\end{solutionfigure}

\begin{solutionfigure}[h]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex05/psi_r_abc_friction.pdf}
\caption{Rotor flux linkage in abc coordinate system of an IM during the transient process and in the steady-state operation with a speed-dependent load.}
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