From 2c1e3d91d89c4be904146a55eec3f6dea272e8c5 Mon Sep 17 00:00:00 2001 From: Peter Date: Thu, 27 Oct 2022 21:05:17 +0800 Subject: [PATCH] synchronous machine --- 2022-10-27-15-31-49.png | Bin 0 -> 44702 bytes 2022-10-27-15-32-07.png | Bin 0 -> 41378 bytes 2022-10-27-20-15-13.png | Bin 0 -> 38270 bytes 2022-10-27-20-15-19.png | Bin 0 -> 36214 bytes 2022-10-27-20-19-47.png | Bin 0 -> 39013 bytes README.md | 60 +++++++++++++++++++++++++++++++++++++++- 6 files changed, 59 insertions(+), 1 deletion(-) create mode 100644 2022-10-27-15-31-49.png create mode 100644 2022-10-27-15-32-07.png create mode 100644 2022-10-27-20-15-13.png create mode 100644 2022-10-27-20-15-19.png create mode 100644 2022-10-27-20-19-47.png diff --git a/2022-10-27-15-31-49.png b/2022-10-27-15-31-49.png new file mode 100644 index 0000000000000000000000000000000000000000..1061809b1d7ae6ede751809d3fa01e9c4165e8ed GIT binary patch literal 44702 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Multiplications and divisions by $\sqrt{3}$ or $3$ where necessary must be checked! Try annotating everything that does not have an associated phase. +- Check conjugate in current. $\bar{S}=\bar{V}\bar{I}^*$ + +#### Y-$\Delta$ transformation (Balanced case) + +$Z_\Delta=3Z_Y$ + ### Types of power factors (From `ENSC2003`) Where $\bar{S}=|\bar{S}|\angle\varphi$: @@ -17,7 +28,7 @@ $$ \varphi = \arctan\left(\frac{Q}{P}\right) = \theta_v-\theta_i$$ | PF [Load] | $[0,1)$ | $[0,1)$ | $1$ | | PF [Source] | $[0,-1)$ | $[0,-1)$ | $-1$ | -## Power types in motor +## Power types in induction motor | Type | Description | Equivalent terms | | ------------------ | ---------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------- | @@ -142,3 +153,50 @@ Ignore magnetizing path #### Diagram ![](2022-10-26-21-47-49.png) + +## Synchronous machine + +### Etc + +$$E_A=V_{1\phi}-I_A(R_A+j X_s)$$ +$$I_A=\text{CONJUGATE}\left(\frac{|S_{3\phi}|\angle\arccos(x)}{3V_{1\phi}}\right), \begin{cases}x=+\text{PF} && \text{lagging} \\ x=-\text{PF} && \text{leading}\end{cases}$$ + +### Voltage regulation + +$$\text{VR}=\frac{|V_\text{NL}|-|V_\text{FL}|}{|V_\text{FL}|}=\frac{|E_A|-|V_{1\phi,\text{rated}}|}{|V_{1\phi,\text{rated}}|}$$ + +- $V_\text{FL}$ is the full-load voltage which is the full-load/maximum rated voltage at the output terminal. +- Calculate $E_A$ at full load by calculating the current as shown above. +- $V_\text{NL}$ is the no-load voltage, which in the no-load case will be $E_A$. + +| No-load | Full-load | +| ---------------------------- | ---------------------------- | +| ![](2022-10-27-20-15-13.png) | ![](2022-10-27-20-19-47.png) | + +| Power factor | Voltage regulation | +| ------------ | ------------------ | +| Lagging | Positive | +| Unity | Near 0 | +| Leading | Negative | + +### Open and short circuit test + +#### **Note** - double-check if the axis refers to per-phase or line voltage/current. + +| Open-circuit test | Short-circuit test | +| ---------------------------- | ---------------------------- | +| ![](2022-10-27-15-31-49.png) | ![](2022-10-27-15-32-07.png) | + +### Power flow + +$P_\text{out}$ is the rated power +$$P_\text{out}=S_\text{rated}\times \text{PF}$$ + +$$ +\begin{align} +P_\text{in}&=P_\text{copper}+P_\text{core}+P_\text{F\\\&W}+P_\text{misc}+P_\text{out}\\ +P_\text{mech}&=P_\text{F\\\&W}+P_\text{misc}+P_\text{out} +\end{align} +$$ + +---