三相纯电阻负载功率电压电流计算
三相纯电阻负载是最基本的三相电路形式，功率因数 $\cos\varphi = 1$。掌握星形和三角形两种接法的计算是电气工程的基础。
一、星形接法（Y）
线电压与相电压：$U_L = \sqrt{3} \cdot U_P$文章源自公式库网-https://www.gongshiku.com/html/201910/sanxiangchundianzufuzaisanjiaoxing-xingxingfuzaigongshuaidianyadianliuzaixianjisuanqi.html
线电流与相电流：$I_L = I_P$文章源自公式库网-https://www.gongshiku.com/html/201910/sanxiangchundianzufuzaisanjiaoxing-xingxingfuzaigongshuaidianyadianliuzaixianjisuanqi.html
三相总功率：$P = 3 \cdot U_P \cdot I_P = \sqrt{3} \cdot U_L \cdot I_L$文章源自公式库网-https://www.gongshiku.com/html/201910/sanxiangchundianzufuzaisanjiaoxing-xingxingfuzaigongshuaidianyadianliuzaixianjisuanqi.html
二、三角形接法（$\Delta$）
线电压与相电压：$U_L = U_P$文章源自公式库网-https://www.gongshiku.com/html/201910/sanxiangchundianzufuzaisanjiaoxing-xingxingfuzaigongshuaidianyadianliuzaixianjisuanqi.html
线电流与相电流：$I_L = \sqrt{3} \cdot I_P$文章源自公式库网-https://www.gongshiku.com/html/201910/sanxiangchundianzufuzaisanjiaoxing-xingxingfuzaigongshuaidianyadianliuzaixianjisuanqi.html
三相总功率：$P = 3 \cdot U_P \cdot I_P = \sqrt{3} \cdot U_L \cdot I_L$文章源自公式库网-https://www.gongshiku.com/html/201910/sanxiangchundianzufuzaisanjiaoxing-xingxingfuzaigongshuaidianyadianliuzaixianjisuanqi.html
三、纯电阻负载特点
- $\cos\varphi = 1$（电压电流同相位）
- 无功功率 $Q = 0$
- 视在功率 $S = P$
- 两种接法下 $P = \sqrt{3}U_L I_L$ 恒成立
四、计算示例
三相对称纯电阻负载，星形接法，线电压380V，每相电阻 $R=10\Omega$：文章源自公式库网-https://www.gongshiku.com/html/201910/sanxiangchundianzufuzaisanjiaoxing-xingxingfuzaigongshuaidianyadianliuzaixianjisuanqi.html
$U_P = \dfrac{380}{\sqrt{3}} = 220\text{V}$，$I_P = \dfrac{220}{10} = 22\text{A} = I_L$文章源自公式库网-https://www.gongshiku.com/html/201910/sanxiangchundianzufuzaisanjiaoxing-xingxingfuzaigongshuaidianyadianliuzaixianjisuanqi.html
$P = \sqrt{3} \times 380 \times 22 \approx 14476\text{W} \approx 14.5\text{kW}$文章源自公式库网-https://www.gongshiku.com/html/201910/sanxiangchundianzufuzaisanjiaoxing-xingxingfuzaigongshuaidianyadianliuzaixianjisuanqi.html 文章源自公式库网-https://www.gongshiku.com/html/201910/sanxiangchundianzufuzaisanjiaoxing-xingxingfuzaigongshuaidianyadianliuzaixianjisuanqi.html
