|
25 | 25 | \end{figure}
|
26 | 26 |
|
27 | 27 |
|
28 |
| -\subtask{Determine the operating mode of the machine characterized by Fig.~\ref{fig:phasor_SM}.}{2} |
29 |
| -\subtaskGerman{Bestimmen Sie die Betriebsart der Maschine auf Basis von Abb.~\ref{fig:phasor_SM}.} |
| 28 | +\subtask{Determine the operating mode of the machine characterized by \autoref{fig:phasor_SM}.}{2} |
| 29 | +\subtaskGerman{Bestimmen Sie die Betriebsart der Maschine auf Basis von \autoref{fig:phasor_SM}.} |
30 | 30 |
|
31 | 31 | \begin{solutionblock}
|
32 | 32 | The machine is operating as an overexcited generator, since the excitation voltage $\underline{U}_\mathrm{i}$ is leading the stator voltage $\underline{U}_\mathrm{s}$ by an angle $\theta$ and the induced voltage amplitude is larger than the stator voltage amplitude.
|
|
39 | 39 | \begin{solutionblock}
|
40 | 40 | The short-circuit current $\underline{I}_\mathrm{s,sc}$ is orthogonal to $\underline{U}_\mathrm{i}$ and lagging behind by $\SI{90}{\degree}$, that is, pointing towards the real axis with a length of \SI{1.33}{\cm}. The synchronous reactance is then
|
41 | 41 | $$X_\mathrm{s} = \frac{\underline{U}_\mathrm{i}}{\underline{I}_\mathrm{s,sc}} = \frac{\SI{3}{\kilo\volt}}{\SI{1.33}{\kilo\ampere}} = \SI{2.26}{\ohm}.$$
|
42 |
| - Here, the induced voltage $\underline{U}_\mathrm{i}$ has been obtained from optical measurement of the phasor diagram and also represents the open-circuit voltage. |
| 42 | + Here, the induced voltage $\underline{U}_\mathrm{i}$ has been obtained from optical measurement of the phasor diagram and also represents the open-circuit voltage. The completed phasor diagram is shown in \autoref{fig:phasor_SM_final}. |
43 | 43 | \end{solutionblock}
|
44 | 44 |
|
45 | 45 |
|
|
54 | 54 | The angle $\varphi$ is then
|
55 | 55 | $$\varphi = -\arccos(0.96) = \SI{-16.25}{\degree}.$$
|
56 | 56 | The power factor angle is negative as the generator operates in an over-excited mode, i.e., its reactive power is negative. The resulting complex stator current is then $$\underline{I}_\mathrm{s} = \SI{0.62}{\kilo\ampere} \cdot e^{\mathrm{j}(\SI{16.25}{\degree} + \SI{63.5}{\degree})} = \SI{0.11}{\kilo\ampere} + \mathrm{j} \SI{0.61}{\kilo\ampere}.$$
|
57 |
| - Here, the angle $\SI{63.5}{\degree}$ is the stator voltage angle counted from the real axis. |
58 |
| -\end{solutionblock} |
59 |
| - |
60 |
| -\begin{solutionblock} |
61 |
| - \begin{figure}[h!] |
| 57 | + Here, the angle $\SI{63.5}{\degree}$ is the stator voltage angle counted from the real axis. The final solution phasor diagram is shown in \autoref{fig:phasor_SM_final}. |
| 58 | + \begin{solutionfigure}[ht] |
62 | 59 | \centering
|
63 | 60 | \begin{tikzpicture}
|
64 | 61 | \coordinate (b) at (0,0);
|
|
77 | 74 | \pic[draw, <-, angle eccentricity=1.7, angle radius=1.25cm]{angle = a--b--d};
|
78 | 75 | \node at (0.45,1.5) {$\varphi$};
|
79 | 76 | \end{tikzpicture}
|
80 |
| - \end{figure} |
| 77 | + \caption{Final phasor diagram} |
| 78 | + \label{fig:phasor_SM_final} |
| 79 | + \end{solutionfigure} |
81 | 80 | \end{solutionblock}
|
| 81 | + |
| 82 | + |
82 | 83 |
|
83 | 84 | \subtask{Determine the apparent power $S$ and the reactive power $Q$.}{2}
|
84 | 85 | \subtaskGerman{Bestimmen Sie die Scheinleistung $S$ und die Blindleistung $Q$.}
|
|
0 commit comments