Name: Jevon Reid
Student ID#: 816024880
Course: ECNG 1007
Course Lecturer: Andrew Balgobin
Lab #3: Three Phase Circuits
Due Date: 6th April, 2021
Date Submitted: 4th April, 2021
Three Phase Circuits Lab Report
Results:
Star Connection Results:
Vrn
Ir
Pr
Vry
In
126.4
1.264
159.9
219.1
2.913e-06
126.5
1.265
160
219
Vyn
Iy
Py
Vyb
Vbn
Ib
Pb
Vbr
126.4
1.264
159.8
218.9
Unbalanced Conditions Results:
128.9
0.6446
1.02
Vrn
Ir
In
124.8
1.665
Vyn
Iy
124.9
1.665
Vbn
Ib
Power Factor Determination Results:
Vrn
Ir
Pr
Vry
In
127.5
1.259
119
220.8
0
127.4
1.259
118.8
220.7
Vyn
Iy
Py
Vyb
Vbn
Ib
Pb
Vbr
Delta Connection Results:
Vry
Ir
P1
I1
224.7
1.948
378.7
1.123
Vyb
Iy
P2
I2
224.7
1.948
378.4
1.123
Vbr
Ib
P3
I3
224.7
1.948
378.8
1.124
127.4
1.259
118.8
220.8
Questions and Calculations:
5.2.1
a) The phase and line currents at the load are equal.
b) The line voltage is equal to root-three multiplied by the phase voltage and is 30° ahead of the
phase voltage.
c) -In = Ir + Iy + Ib = 1.2640°+ 1.265-120°+ 1.264120°
= 1.264 -0.6325 - j1.095522136 -0.632 + j1.09465611
= -5×10-4 – j8.66026×10-4 = -1×10-3
In = 1×10-3
d)
e) Pphase = Vphase × Iphase × cos
cos = 1 since the load is solely resistive.
Prc = 126.4×1.264=159.77W
Pyc = 126.5×1.265= 160.02W
Pbc = 126.4×1.264 = 159.77W
The reason for the difference between the calculated and measured phase power is the
resistance in the connecting wires.
Ptotal = √3 |Vline| |Iline| cos
cos = 1 since load is solely resistive.
Prc = √3×219.1×1.264=479.68W
Pyc = √3×219×1.265= 479.84W
Pbc = √3×218.9×1.264 = 479.24W
5.2.2
a) -In = Ir + Iy + Ib = 0.64460° + 1.665-120° + 1.665120°
= 0.6446 -0.8325 -j1.442 -0.8325 + j1.442
= -1.02A
In = 1.02A
b)
c) Pphase = Vphase × Iphase × cos
cos = 1 since the load is solely resistive.
Prc =128.9 × 0.6446 = 83.09W
Pyc = 124.8 × 1.665 = 207.79W
Pbc = 124.9 × 1.665 = 207.96W
5.2.3
a) Pphase = Vphase × Iphase × cos
119 = 127.5 × 1.259 × cos
119
cos = 127.5 ×
1.259
= 0.74
b) -In = Ir + Iy + Ib = 1.2590° + 1.259-120° + 1.259120°
=1.259 -0.6295 -j1.09 -0.6295 +j1.09 = 0
In = 0
c)
d) Real power = √3 × Vline × Iline × cos
Real Pr = √3 × 220.8 × 1.259 × 0.74 = 356.30 Watts
Real Py = √3 × 220.7 × 1.259 × 0.74 = 356.14 Watts
Real Pb = √3 × 220.8 × 1.259 × 0.74 = 356.30 Watts
Reactive power = √3 × Vline × Iline × sin
= cos-1(0.74)= 42.27°
sin(42.27) = 0.67
Reactive Pr = = √3 × 220.8 × 1.259 × 0.67 = 322.60 VAR
Reactive Py = √3 × 220.7 × 1.259 × 0.67 = 322.45 VAR
Reactive Pb = √3 × 220.8 × 1.259 × 0.67 = 322.60 VAR
e)
5.2.4
a) For the delta connection, the line current is equal to root-three multiplied by the phase current
and 30 degrees behind of the phase current.
b) For a delta connection, the phase voltage is equal to the line voltage at the load.
c)
d) Pphase = Vphase × Iphase × cos
cos = 1 since the load is solely resistive
Prc = 224.7 × 1.123 × 1 = 252.34W
Pyc = 224.7 × 1.123 × 1 =252.34W
Pbc = 224.7 × 1.124 × 1 = 252.56W
The reason for the difference between the calculated and measured powers is that the
measured powers are the respective line powers of each phase.
Ptotal = 3 × Vphase × Iphase × cos
cos = 1 since the load is solely resistive.
Prc = 3 × 224.7 × 1.123 = 757.0143 Watts
Pyc = 3 × 224.7 × 1.123 = 757.0143 Watts
Pbc = 3 × 224.7 × 1.124 = 757.6884 Watts