ELECTRIC CIRCUITS THEORY 1 These lecture slides have been compiled by Mohammed LECTURE 10 Cont… SalahUdDin Ayubi. Three Phase Power Systems
7. Three Phase Power Systems • 7.1 Single phase supply
v(t ) =Vm ⋅cos(ωt +θ)
Vm 2
θ
• European Supply 230V rms at 50 Hz S ingle P hase V oltage S upply
3 2 5 .2 6 94 0 0 320 240
Voltage in volts
160 v t
80 n
0 80 160 240
320 3 2 5 .2 6 9 400 0
0
0 .0 0 5
0 .0 1
0 .0 1 5
0 .0 2 t
0 .0 2 5
n T im e in seco n d s
0 .0 3
0 .0 3 5
0 .0 4 0 .0 4
7.2 Three Phase Industrial Supplies R v R (t ) = Vm ⋅ cos( ωt )
Vm
2 ⋅π v S (t ) = Vm ⋅ cos ωt − 3
2
0
Vm
N
-120
2
4 ⋅π vT (t ) = Vm ⋅ cos ωt − 3
T
Angles on the diagram are in degrees. They could Have been in radians
Vm 2
S -240
Balanced, three-phase voltage supply • Magnitude of three voltages is exactly the same • Phase angle between adjacent voltages is 120 degrees exactly • European labelling Three terminals are R, S and T. Common point is neutral N (R, Y, B – red, yellow, blue or A, B, C alternatives) ( N Neutral is wired in black normally)
Time Representation of Three Voltages Three Phase Line to Neutral Voltages
325.269 400 320 240
Voltage in volts
160 vR vS vT
n n n
80 0 80 160 240 320
− 325.269 400
0
0.005
0.01
0
θ := −30⋅
π 180
0.015
0.02 tn Time in second
0.025
0.03
0.035
0.04 0.04
Phasor diagram of supply vTN
+j
120 degrees 120 degrees
vRN N
120 degrees VSN
real
7.3 Three Phase Loads Star and Delta il
R
ip Z
vp
R
il
vll vll
N
Z
Z Z
T
vp
ip Z
T Z
S S
Star Connection
Delta Connection
Where il is the rms line current ip is the rms phase current vll is rms the line to line voltage vp is rms the phase voltage
Power Supply and Load R Vm 2
0
R Z
Vm
N
iR
2
N
T Vm 2
VRN
-120
Z
S -240
iT T iS S
Z
Phasor Diagram of Three Phase System vT
+j iT φ vR φ
iS
real
φ iR
vS
7.4 Balanced Loads Need no Neutral Conductor • Consider the phasor sum of the three phase currents for a balanced, star-connected load. They add to zero. iT
real
iS
iR
7.5 Instantaneous Power for Single phase • Instantaneous single phase power always pulsates as it must go to zero when v is zero and when i is zero. Instantaneous Single Phase Power
4500 4500 4000 3500
Power in Watts
3000 P
n
2500
o n
2000 1500 1000 500 0 500 500
0
0.005
0.01
0
• v = 230V i = 10 / -30
0.015
0.02 t
n Time in Seconds
0.025
0.03
0.035
0.04 0.04
7.6 Instantaneous Power in Three Phase Systems • Three phase instantaneous power remains constant in balance systems Power Per Phase and Total
65006500 6000 5500 PR
Power in Watts
PS PT
5000
n
4500 4000
n
3500 n
3000
P R + P S + P T 2500 n
on
n
n
2000 1500 1000 500
− 500
0 500
0 0
0.005
0.01
0.015
0.02 tn Time in Seconds
0.025
0.03
0.035
0.04 0.04
• Balance voltages at 230V to neutral and balanced currents of 10A lagging 30 degrees on the voltage
Power in the three phase load • The instantaneous power is constant • Thus the instantaneous power is the same as the average power per cycle evaluated by the phasor approach
P = 3 ⋅ v rms ⋅ i rms ⋅ cos (φ ) Where vrms and irms are the phase quantities
7.7 The Voltage in Three-Phase Systems is Always Quoted in Terms of Line to Line Voltage 230 V 60 230 V
vSN
v RS = 2 ⋅ v RN ⋅ sin(60) v RS = 230 ⋅ 3 v RS = 400
vRN vRS
real
3
The line to line voltage in 3 phase systems is always root 3 times the Line to neutral voltage
7.8 Advantages of Three Phase Power Systems • Most importantly, the instantaneous power is always constant (balanced conditions) • There is a reduction in the volume of conductor required to transmit a given power (no neutral conductor)- transmission lines and cables • Very efficient use of magnetic steel and copper conductors in transformers and motors. (next semester)