# 三相 (电学)

## 定义

${\displaystyle V_{L1-N}=\sin \left(\theta \right)*V_{P}\,\!}$
${\displaystyle V_{L2-N}=\sin \left(\theta -{\frac {2}{3}}\pi \right)*V_{P}=\sin \left(\theta +{\frac {4}{3}}\pi \right)*V_{P}}$
${\displaystyle V_{L3-N}=\sin \left(\theta -{\frac {4}{3}}\pi \right)*V_{P}=\sin \left(\theta +{\frac {2}{3}}\pi \right)*V_{P}}$

${\displaystyle V_{P}}$代表最大电压,
${\displaystyle \theta =2\pi ft\,\!}$代表相位角
${\displaystyle t}$代表时间，单位为
${\displaystyle f}$代表頻率，单位为转/秒
${\displaystyle V_{L1-N}}$${\displaystyle V_{L2-N}}$${\displaystyle V_{L3-N}}$则分别代表L1到中性点（N）、L2到中性点和L3到中性点的电压。

## 電壓和電流

${\displaystyle V_{L}={\sqrt {3}}V_{ph}}$
${\displaystyle I_{L}=I_{ph}}$

${\displaystyle V_{L}=V_{ph}}$
${\displaystyle I_{L}={\sqrt {3}}I_{ph}}$

### 功率

${\displaystyle P=3P_{ph}=3V_{ph}I_{ph}\cos \phi ={\sqrt {3}}V_{L}I_{L}\cos \phi }$

${\displaystyle P_{\Delta }=3\times P_{Y}}$

${\displaystyle S=2\ VI}$

${\displaystyle S={\sqrt {3}}\ VI}$

## 稳定输出

### 恒定功率转化

${\displaystyle P_{Li}={\frac {V_{Li}^{2}}{R}}}$
${\displaystyle P_{TOT}=\sum _{i}P_{Li}}$

${\displaystyle p=\sin ^{2}\theta +\sin ^{2}\left(\theta -{\frac {2}{3}}\pi \right)+\sin ^{2}\left(\theta -{\frac {4}{3}}\pi \right)={\frac {3}{2}}}$

${\displaystyle P_{TOT}={\frac {3V_{P}^{2}}{2R}}}$

${\displaystyle Z=|Z|e^{j\varphi }}$

${\displaystyle I_{P}={\frac {V_{P}}{|Z|}}}$

${\displaystyle I_{L1}=I_{P}\sin \left(\theta -\varphi \right)}$
${\displaystyle I_{L2}=I_{P}\sin \left(\theta -{\frac {2}{3}}\pi -\varphi \right)}$
${\displaystyle I_{L3}=I_{P}\sin \left(\theta -{\frac {4}{3}}\pi -\varphi \right)}$

${\displaystyle P_{L1}=V_{L1}I_{L1}=V_{P}I_{P}\sin \left(\theta \right)\sin \left(\theta -\varphi \right)}$
${\displaystyle P_{L2}=V_{L2}I_{L2}=V_{P}I_{P}\sin \left(\theta -{\frac {2}{3}}\pi \right)\sin \left(\theta -{\frac {2}{3}}\pi -\varphi \right)}$
${\displaystyle P_{L3}=V_{L3}I_{L3}=V_{P}I_{P}\sin \left(\theta -{\frac {4}{3}}\pi \right)\sin \left(\theta -{\frac {4}{3}}\pi -\varphi \right)}$

${\displaystyle P_{L1}={\frac {V_{P}I_{P}}{2}}\left[\cos \varphi -\cos \left(2\theta -\varphi \right)\right]}$
${\displaystyle P_{L2}={\frac {V_{P}I_{P}}{2}}\left[\cos \varphi -\cos \left(2\theta -{\frac {4}{3}}\pi -\varphi \right)\right]}$
${\displaystyle P_{L3}={\frac {V_{P}I_{P}}{2}}\left[\cos \varphi -\cos \left(2\theta -{\frac {8}{3}}\pi -\varphi \right)\right]}$

${\displaystyle P_{TOT}={\frac {V_{P}I_{P}}{2}}\left\{3\cos \varphi -\left[\cos \left(2\theta -\varphi \right)+\cos \left(2\theta -{\frac {4}{3}}\pi -\varphi \right)+\cos \left(2\theta -{\frac {8}{3}}\pi -\varphi \right)\right]\right\}}$

${\displaystyle P_{TOT}={\frac {3V_{P}I_{P}}{2}}\cos \varphi }$

${\displaystyle P_{TOT}={\frac {3V_{P}^{2}}{2|Z|}}\cos \varphi }$

### 中線電流

{\displaystyle {\begin{aligned}I_{L1}&={\frac {V_{L1-N}}{R}},\;I_{L2}={\frac {V_{L2-N}}{R}},\;I_{L3}={\frac {V_{L3-N}}{R}}\\0&=I_{L1}+I_{L2}+I_{L3}+I_{N}\end{aligned}}}

{\displaystyle {\begin{aligned}i&=\sin \theta +\sin(\theta -{\frac {2\pi }{3}})+\sin(\theta +{\frac {2\pi }{3}})\\&=\sin \theta +2\sin \theta \cos {\frac {2\pi }{3}}\\&=\sin \theta -\sin \theta \\&=0\end{aligned}}}

## 不稳定输出

${\displaystyle I_{L1}+I_{L2}*\cos {\frac {2}{3}}\pi +j*I_{L2}*\sin {\frac {2}{3}}\pi +I_{L3}*\cos {\frac {4}{3}}\pi +j*I_{L3}*\sin {\frac {4}{3}}\pi }$
${\displaystyle I_{L1}-I_{L2}*0.5-I_{L3}*0.5+j*{\frac {\sqrt {3}}{2}}*\left(I_{L2}-I_{L3}\right)}$

${\displaystyle {\sqrt {I_{L1}^{2}+I_{L2}^{2}+I_{L3}^{2}-I_{L1}*I_{L2}-I_{L1}*I_{L3}-I_{L2}*I_{L3}}}}$[2]

## 旋转磁场

### 励磁磁动势

${\displaystyle F_{0}={\frac {m_{1}}{2}}{\frac {4}{\pi }}{\frac {\sqrt {2}}{2}}{\frac {N_{1}k_{dp1}}{p}}I_{0}}$

## 参考资料

1. ^
2. ^ Keljik, Jeffrey. Electricity 3: Power Generation and Delivery. Clifton Park, NY: Cengage Learning/Delmar. 2008: 49. ISBN 1435400291.
3. ^ Lowenstein, Michael. The 3rd Harmonic Blocking Filter: A Well Established Approach to Harmonic Current Mitigation. IAEI Magazine. [24 November 2012]. （原始内容存档于2011年3月27日）.
4. ^ Enjeti, Prasad. Harmonics in Low Voltage Three-Phase Four-Wire Electric Distribution Systems and Filtering Solutions (PDF). Texas A&M University Power Electronics and Power Quality Laboratory. [24 November 2012]. （原始内容存档 (PDF)于2010-06-13）.
5. ^ 三相电机改为单相运行. [2013-07-15]. （原始内容存档于2021-03-24）.
6. ^ Measurement of three-phase power with the 2-wattmeter method. (PDF). [2013-07-15]. （原始内容 (PDF)存档于2020-07-03）.
7. ^ THE TWO-METER WATTMETER METHOD (PDF). [2013-07-15]. （原始内容 (PDF)存档于2013-03-19）.