3상 1회선 1선당 작용 인덕턴스⁕

\[L=L_e+L’_e(\dot{I_b}에 의한 것)+L’_e(\dot{I_c}에의한것)\] \[\cdot\cdot\cdot a상기준\] \[L=0.05+0.4605\log_{10}\frac{D}{r}[mH/㎞]\] \[\cdot\cdot\cdot이론식\]

\[내부자속(\dot{\Phi}_{a-in})=\frac{\mu_0\dot{I}_a}{8\pi}[Wb/m]\] \[외부자속(\dot{\Phi}_{a-ext})=\frac{\mu_0\dot{I}_a}{2\pi}ln\frac{S}{r}[Wb/m]\]

\[\Phi_{ba}=\frac{\mu_0\dot{I}_b}{2\pi}ln\frac{S}{D}[Wb/m]\] \[\Phi_{ca}=\frac{\mu_0\dot{I}_c}{2\pi}ln\frac{S}{D}[Wb/m]\]

\[\dot{\Phi}=\dot{\Phi}_{a-in}+\dot{\Phi}_{a-est}+\dot{\Phi}_{ba}+\dot{\Phi}_{ca}\] \[=\frac{\mu_0\dot{I}_a}{8\pi}+\frac{\mu_0}{2\pi}(\dot{I}_a ln\frac{S}{r}+\dot{I}_b ln\frac{S}{D}+\dot{I}_c in\frac{S}{D})\]

\[=\frac{\mu_0\dot{I}_a}{8\pi}+\frac{\mu_0}{2\pi}(\dot{I}_a ln\frac{1}{r}+\dot{I}_abln\frac{1}{r}+\dot{I}_c ln\frac{1}{r}+ln S(\dot{I}_a+\dot{I}_b+\dot{I}_c))\]

\[\dot{I}_a+\dot{I}_b+\dot{I}_c=0,\dot{I}_b+\dot{I}_c=-\dot{I}_a\]

\[\Phi=\frac{\mu_0\dot{I}_a}{8\pi}+\frac{\mu_0}{2\pi}(\dot{I}_a ln\frac{1}{r}-\dot{I}_a ln\frac{1}{D})\] \[=\frac{\mu_0\dot{I}_a}{8\pi}+\frac{\mu_0\dot{I}_a}{2\pi}ln\frac{D}{r}[Wb/m]\]

\[L=\frac{\Phi}{I_a}=\frac{\mu_0}{8\pi}+\frac{\mu_0}{2\pi}ln\frac{D}{r}[H/m]\]\[\to L=0.05+0.4605 log\frac{D}{r}[mH/㎞]\]