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Power in Balanced 3 phase Loads - h1011v3_85
Power in Balanced 3 phase Loads - h1011v3_87

Electrical Science Volume 3 of 4
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THREE-PHASE CIRCUITS Basic AC Power In a balanced delta load, the line voltage (VL) is equal to the phase voltage (Vf), and the line current (IL) is equal to the square root of three times the phase current ( ).   Equation (9-5) 3 If is a mathematical representation of VL in a balanced delta load.  Equation (9-6) is a mathematical representation of IL  in a balanced delta load. VL  = Vf (9-5) (9-6) IL 3 If In  a  balanced  wye  load,  the  line  voltage  (VL)  is  equal  to  the  square  root  of  three  times  phase voltage  ( ),  and  line  current  (IL)  is  equal  to  the  phase  current  (If).    Equation  (9-7)  is  a 3 Vf mathematical  representation  of  VL  in  a  balanced  wye  load.    Equation  (9-8)  is  a  mathematical representation of IL  in a balanced wye load. (9-7) VL 3 Vf (9-8) IL If Because the impedance of each phase of a balanced delta or wye load has equal current, phase power  is  one  third  of  the  total  power.   Equation  (9-10)  is  the  mathematical  representation  for phase power (Pf) in a balanced delta or wye load. Pf  = Vf  If  cosq (9-10) Total  power  (PT)  is  equal  to  three  times  the  single-phase  power.     Equation  (9-11)  is  the mathematical representation for total power in a balanced delta or wye load. PT  = 3Vf  If  cosq (9-11) In a delta-connected load, VL  = Vf  and so: If 3 IL 3 PT 3 VL IL cos q In a wye-connected load, IL  = If  and so: Vf 3 VL 3 PT 3 VL IL cos q ES-09 Page 20 Rev. 0







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