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Derive the relation between power in Delta and Star Systems

written 3.5 years ago by teamques10 ★ 68k

•   modified 3.5 years ago

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written 3.5 years ago by teamques10 ★ 68k

Step 1: Calculate power in a star system

Power per phase: $P_{ph}=V_{ph} I_{ph} \ \cos⁡ϕ$

Total power PT :

$PT =3P_{ph} \\[2ex] PT=3 V_{ph} I_{ph} \ cos⁡ϕ \\[2ex] PT=3\times\dfrac{V_L}{\sqrt{3}}\times\dfrac{V_L}{\sqrt3 Z}=\dfrac{(V_L^2)}Z cos⁡ϕ \ \ \ ...(1) $

Step 2: Total power in a delta circuit

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