POLYPHASE CIRCUITS LEARNING GOALS Three Phase Circuits Advantages of

POLYPHASE CIRCUITS LEARNING GOALS Three Phase Circuits Advantages of polyphase circuits Three Phase Connections Basic configurations for three phase circuits Source/Load Connections Delta-Y connections Power Relationships Study power delivered by three phase circuits Power Factor Correction Improving power factor for three phase circuits

THREE PHASE CIRCUITS V an 3 phase v o lta g e V bn V 0 120 cn 240 Instantane ousPhaseVoltages van (t ) Vm cos( t )(V ) vbn (t ) Vm cos( t 120 )(V ) vc (t ) Vm cos( t 240 )(V ) Vm 120 2

a a W y e C o n n e c te d S ource V 0 n V -2 4 0 c V -1 2 0 b b c

Delta Source a a D e lta S o urce b c b c Vab Vab 0 Vbc Vab -120 Vca Vab -240

Wye – Wye System a A Z l ZL n c N ZL b B Z l Z l ZL C

Delta – Delta System a A Z l c L ZL Z b B Z l Z l C ZL

Delta – Wye System a A Z ZL c l ZL b B Z l Z l ZL C

a a IaA A V 0 n V -2 4 0 IC Z Z IB V -1 2 0 IAB b b c C C B Z c A

V cn - V bn V ab 30 o V V bn V V an ab V ab 3 V an - V an bn 30o

Vab Van Vbn V p 0 V p 120 V p 1 (cos120 j sin 120) 1 3 V p V p j 2 2 3 V p 30 Vbc 3 V p 90 Vca 3 V p 210 VL 3 V p Line Voltage

IC 3 I A B -3 0 o IaA A IAB IaA IB C - IC A

INSTANTANEOUS POWER Instantane ousPhaseVoltages van (t ) Vm cos( t )(V ) BalancedPhaseCurrents ia (t ) I m cos( t ) vbn (t ) Vm cos( t 120 )(V ) ib ( t ) I m cos( t 120 ) vc (t ) Vm cos( t 240 )(V ) ic (t ) I m cos( t 240 ) Instantane ous power p(t ) van (t )ia (t ) vbn ( t ) ib ( t ) vcn ( t )ic (t ) Theorem For a balanced three phase circuit the instantaneous power is constant p(t ) 3 Vm I m cos (W ) 2

REVIEWOF Y Transforma tions Ra R1R2 R1 R2 R3 Rb R2 R3 R1 R2 R3 Rc R3 R1 R1 R2 R3 Y R1 Ra Rb Rb Rc Rc Ra Rb R2 Ra Rb Rb Rc Rc Ra Rc R3 Ra Rb Rb Rc Rc Ra Ra Y

REVIEWOF Rab R2 ( R1 R3 ) Y Transforma tions Y Rab Ra Rb Y Ra R1 Rb R1 Rb R2 Rb R1 R1R2 R R 3 2 Ra Rc R1 Rc R2 ( R1 R3 ) Ra R1 R2 R3 Rb R3 Ra Rb REPLACE IN THE THIRD AND SOLVE FOR R1 R1 R2 R3 R2 R3 Rb R1 R2 R3 Ra Rb Rb Rc Rc Ra R3 ( R1 R2 ) R 1 Rb Rc Rb R R 3 1 R1 R2 R3 Rc R1 R2 R3 R R Rb Rc Rc Ra R2 a b Rc Y R (R R ) Rc Ra 1 2 3 R1 R2 R3 SUBTRACT THE FIRST TWO THEN ADD TO THE THIRD TO GET Ra R3 Ra Rb Rb Rc Rc Ra Ra Y

POWER FACTOR CORRECTION Similar to single phase case. Use capacitors to increase the power factor Balanced load Low pf lagging Keep clear about total/phase power, line/phase voltages Q Qnew Qold ReactivePowerto be added To use capacitors this value should be negative pf cos f sin f 1 pf 2 tan pf f 1 pf 2 Q P tan f lagging Q 0

f 60 Hz , Vline 34.5kV rms. Required: pf 0.94 leading LEARNING EXAMPLE Pold 18.72 MW S P jQ P S cos f Q S sin f pf cos f Q P tan f tan f pf 1 pf 2 lagging Qold 0 pf cos f sin f 1 pf 2 0.626 Qold 15.02 MVA Pold 18.72 MW Qnew 6.8 MVA pf new 0.94 leading Q 6.8 15.02 21.82 MVA Qper capacitor 7.273MVA 34.5 Y connection Vcapacitor kV rms 3 34.5 103 6 7.273 10 2 60 C 3 C 48.6 F 2

LEARNING BY DESIGN Proposed new store #4ACSRwireratedat 170A rms S1 700 36.9 S2 1000 60 kVA S3 800 25.8 kVA 560 j 420 kVA 500 j866 kVA 720 j 349 kVA Stotal 1780 j1635 kVA 2417 42.57 kVA S total 2.417 106 I line 101.1A rms 3 3 Vline 3 13.8 10 Wire is OK Pold Qnew P tan f ( new ) 758.28kVA pf new Q Qnew Qold 876.72kVA Q per capacitor CV 2 876.72 10 / 3 C 2 60 13.8 10 3 3 2 12.2 F /3