𝑉𝑝 = 𝑉𝑎𝑛 = 𝑉𝑏𝑛 = 𝑉𝑐𝑛
𝑉𝑝 = 𝑉1𝑛 = 𝑉2𝑛 = 𝑉3𝑛
𝑉𝑎𝑛 = 𝑉𝑎𝑛 ∠0° = 𝑉𝑃 ∠0°
𝑉𝑏𝑛 = 𝑉𝑏𝑛 ∠ − 120° = 𝑉𝑃 ∠ − 120°
𝑉𝑐𝑛 = 𝑉𝑐𝑛 ∠ + 120° = 𝑉𝑃 ∠ + 120°
𝑉𝑎𝑛 = 𝑉𝑎𝑛 ∠0° = 𝑉𝑃 ∠0°
𝑉𝑏𝑛 = 𝑉𝑏𝑛 ∠ − 120° = 𝑉𝑃 ∠ − 120°
𝑉𝑐𝑛 = 𝑉𝑐𝑛 ∠ + 120° = 𝑉𝑃 ∠ + 120°
𝑉𝑎𝑛 = 𝑉𝑎𝑛 ∠𝜃𝑎𝑛 = 𝑉𝑃 ∠𝜃𝑎𝑛
𝑉𝑏𝑛 = 𝑉𝑎𝑛 ∠𝜃𝑎𝑛 − 120° = 𝑉𝑃 ∠(𝜃𝑎𝑛 − 120°)
𝑉𝑐𝑛 = 𝑉𝑎𝑛 ∠𝜃𝑎𝑛 + 120° = 𝑉𝑃 ∠(𝜃𝑎𝑛 + 120°)
𝑉𝑎𝑏 = 𝑉𝑎𝑛 ∠𝜃 + (−𝑉𝑏𝑛 ∠ − 120°)
𝑉𝑏𝑐 = 𝑉𝑏𝑛 ∠ − 120° + (−𝑉𝑐𝑛 ∠ + 120°)
𝑉𝑐𝑎 = 𝑉𝑐𝑛 ∠ + 120° + (−𝑉𝑎𝑛 ∠0°)
𝑉𝑎𝑏 = 𝑉𝑎𝑛 ∠𝜃 + (−𝑉𝑏𝑛 ∠ − 120°)
𝑉𝑏𝑐 = 𝑉𝑏𝑛 ∠ − 120° + (−𝑉𝑐𝑛 ∠ + 120°)
𝑉𝑐𝑎 = 𝑉𝑐𝑛 ∠ + 120° + (−𝑉𝑎𝑛 ∠0°)
𝑉𝑎𝑏 = √3 𝑉𝑃 ∠30°
𝑉𝑏𝑐 = √3 𝑉𝑃 ∠ − 90°
𝑉𝑐𝑎 = √3 𝑉𝑃 ∠ − 210°
𝐼𝐿1 = 𝑉𝑎𝑏
𝐼𝐿2 = 𝑉𝑏𝑐
𝐼𝐿3 = 𝑉𝑐𝑎
𝐼𝐿1 = 𝐼𝐿1 ∠0° = 𝐼𝐿 ∠0°
𝐼𝐿2 = 𝐼𝐿2 ∠ − 120° = 𝐼𝐿 ∠ − 120°
𝐼𝐿3 = 𝐼𝐿3 ∠ + 120° = 𝐼𝐿 ∠ + 120
𝐼𝐿1 = 𝐼𝐿1 ∠0° = 𝐼𝐿 ∠0°
𝐼𝐿2 = 𝐼𝐿2 ∠ − 120° = 𝐼𝐿 ∠ − 120°
𝐼𝐿3 = 𝐼𝐿3 ∠ + 120° = 𝐼𝐿 ∠ + 120
𝐼𝐿1 = 𝐼𝐿1 ∠𝜃𝑎𝑛 = 𝐼𝐿 ∠𝜃𝑎𝑛
𝐼𝐿2 = 𝐼𝐿1 ∠𝜃𝑎𝑛 − 120° = 𝐼𝐿 ∠(𝜃𝑎𝑛 − 120°)
𝐼𝐿3 = 𝐼𝐿1 ∠𝜃𝑎𝑛 + 120° = 𝐼𝐿 ∠(𝜃𝑎𝑛 + 120°)
𝐼𝐿1 = 𝐼𝑃1
𝐼𝐿2 = 𝐼𝑃2
𝐼𝐿3 = 𝐼𝑃3
𝑍𝑌 = 𝑍𝑆 + 𝑍𝐿 + 𝑍𝑙
𝑍𝑌 = Total load impedance per phase
𝑍𝑆 = Source impedance
𝑍𝐿 = Load impedance
𝑍𝑙 = Line impedance
𝑉𝑎𝑛 𝑜𝑟 𝑉1𝑛
𝑉𝑏𝑛 𝑜𝑟 𝑉2𝑛
𝑉𝑐𝑛 𝑜𝑟 𝑉3𝑛
𝑉𝑎𝑏 𝑜𝑟 𝑉12
𝑉𝑏𝑐 𝑜𝑟 𝑉23
𝑉𝑐𝑎 𝑜𝑟 𝑉31
𝑉𝐿 = 𝑉𝑎𝑏 = 𝑉𝑏𝑐 = 𝑉𝑐𝑎
𝑉𝑎𝑏 = 𝑉𝑎𝑛 ∠0° + (−𝑉𝑏𝑛 ∠ − 120°)
𝑉𝑏𝑐 = 𝑉𝑏𝑛 ∠ − 120° + (−𝑉𝑐𝑛 ∠ + 120°)
𝑉𝑐𝑎 = 𝑉𝑐𝑛 ∠ + 120° + (−𝑉𝑎𝑛 ∠0°)
𝑉𝑎𝑛 = 𝑉𝑎𝑏
𝑉𝑏𝑛 = 𝑉𝑏𝑐
𝑉𝑐𝑛 = 𝑉𝑐𝑎
𝑉𝐿 = √3 𝑉𝑃
𝑉𝐿 = 𝑉𝑃
𝐼𝐿1 = 𝑉𝑎𝑏
𝐼𝐿2 = 𝑉𝑏𝑐
𝐼𝐿3 = 𝑉𝑐𝑎
𝐼𝐿1 = 𝑉𝑎𝑏
𝐼𝐿2 = 𝑉𝑏𝑐
𝐼𝐿3 = 𝑉𝑐𝑎
𝐼𝑃1 = 𝑉𝑎𝑏
𝐼𝑃2 = 𝑉𝑏𝑐
𝐼𝑃3 = 𝑉𝑐𝑎
𝐼𝑃 = 𝐼𝑃1 = 𝐼𝑃2 = 𝐼𝑃3
𝐼𝐿1 = 𝐼𝐿2 = 𝐼𝐿3 = 𝐼𝑃
𝐼𝐿1 + 𝐼𝐿2 + 𝐼𝐿3 = 0
𝐼𝑛 = −(𝐼𝐿1 + 𝐼𝐿2 + 𝐼𝐿3 ) = 0
𝑉𝑃 = 𝑉𝑎𝑛 = 𝑉𝑏𝑛 = 𝑉𝑐𝑛
𝐼𝐿1 =
𝑉𝑎𝑛
𝑉𝑏𝑛
𝑉𝑐𝑛
, 𝐼𝐿2 =
, 𝐼𝐿3 =
𝑍𝑌
𝑍𝑌
𝑍𝑌
𝑍𝑌 =
𝑍∆
3
𝐼𝐿1 = 𝐼𝑃1 − 𝐼𝑃3
𝐼𝐿2 = 𝐼𝑃2 − 𝐼𝑃1
𝐼𝐿3 = 𝐼𝑃3 − 𝐼𝑃2
𝑉𝑎𝑛 = 𝑉𝑎𝑛 ∠0°
𝑉𝑏𝑛 = 𝑉𝑏𝑛 ∠ − 120°
𝑉𝑐𝑛 = 𝑉𝑐𝑛 ∠ + 120°
𝑉𝐿 = √3 𝑉𝑃
𝐼𝐿1 = √3 𝐼𝑃1
𝐼𝐿2 = √3 𝐼𝑃2
𝐼𝐿3 = √3 𝐼𝑃3
𝑍𝑃 = 𝐼𝑃1
𝐼𝑃 =
𝑉𝑃
𝑍𝑃
𝐼𝐿 = 𝐼𝑃
𝑉𝐿 = √3 𝑉𝑃
𝐼𝐿
= √3
𝐼𝑃