POLYPHASE CIRCUITS LEARNING GOALS Three Phase Circuits Advantages
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 V0 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 V0 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 Y Rab Ra Rb Y Rab R2 || ( R1 R3 ) REVIEWOF Y Transforma tions 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 2 1 pf 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 70036.9 S2 100060 kVA S3 80025.8 kVA 560 j 420 kVA 500 j866 kVA 720 j 349 kVA Stotal 1780 j1635 kVA 241742.57 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
Siddhartha Gautama was born a Hindu prince in 563 B.C.When Gautama became aware of human suffering, he left his home to search for answers. Eventually, he believed he understood the cause and cure for suffering.
1Dept. of Surgery, 2Dept. of Computer Science, 3Department of Psychiatry, 4Dept. of Radiology, and 5Department of Radiation Oncology, University of North Carolina, Chapel Hill, NC 27599, USA SUMMARY RESULTS We analyzed the regional morphology of blood vessels segmented from the...
The importance of strong family centre partnerships cannot be underestimated when it comes to developing an Emergent Curriculum approach, after all the family is the richest source of information about the individual child and a true learning community welcomes the...
The detrital spectrum of the Dadeville Complex yields Proterozoic and Paleozoic zircon populations atypically of those found along the Laurentian margin. Proterozoic grains were likely sourced from a Gondwana terrane, and were likely deposited in an environment that received only...
Corunna High School Class of 1917 1917 Corunna High School Class of 1917 McCurdy Park 1917 Editorial 1917 The End 1917 * 1917 Harol Beemer Deceased 1917 Oliver N. Bush Deceased 1917 Lawrence Seward Lucile Hofacker Deceased 1917 Arthur E....
Ready to download the document? Go ahead and hit continue!