Sending power, receiving power and loss, are calculated as follows for a multi-phase line. Although the formulation is shown for three-phases case, it can be used for 1-phase as well as 2-phase lines.
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V_{F r o m}=\left[ \begin{array}{c}{V_{F r o m 1}} \\ {V_{F r o m 2}} \\ {V_{F r o m 3}}\end{array}\right] ; V_{T o}=\left[ \begin{array}{c}{V_{T o 1}} \\ {V_{T o 2}} \\ {V_{T o 3}}\end{array}\right] |
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I_{\text {From}}=\left[ \begin{array}{l}{I_{F r o m 1}} \\ {I_{F r o m 2}} \\ {I_{F r o m 3}}\end{array}\right] ; I_{T o}=\left[ \begin{array}{l}{I_{T o 1}} \\ {I_{T o 2}} \\ {l_{T o 3}}\end{array}\right] |
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V=\left[ \begin{array}{c}{V_{F r o m}} \\ {V_{T o}}\end{array}\right] ; I=\left[ \begin{array}{c}{I_{F r o m}} \\ {I_{T o}}\end{array}\right] |
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Y_{\text {serie}}=(Z * \text {Length})^{-1} ; Y_{\text {parallel}}=(B * \text {Length}) / 2 |
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Y V=I ; Y=\left[ \begin{array}{cc}{Y_{\text { serie }}+Y_{\text {parallel}}} & {-Y_{\text {serie}}} \\ {-Y_{\text {serie}}} & {Y_{\text { serie }}+Y_{\text {parallel}}}\end{array}\right] |
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S=\left[ \begin{array}{c}{S_{\text {From}}} \\ {S_{T o}}\end{array}\right]=V I^{*}=V(Y V)^{*}=\left(V V^{*}\right) Y^{*} |
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S_{F r o m}=\left[ \begin{array}{c}{S_{F r o m 1}} \\ {S_{F r o m 2}} \\ {S_{F r o m 3}}\end{array}\right] \quad ; \quad S_{T o}=\left[ \begin{array}{l}{S_{T o 1}} \\ {S_{T o 2}} \\ {S_{T o 3}}\end{array}\right] |
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S_{T o}^{\text { parallel }}=V_{T o} *\left(Y_{\text {parallel}} V_{T o}\right)^{*}=\left(V_{T o} V_{T o}^{*}\right) Y_{\text {parallel}}^{*} |
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S_{\text {Loss}}=S_{\text {From}}+S_{T o}-\left(S_{\text {From}}^{\text {paraulel}}+S_{T o}^{\text {paraluel}}\right) |
