University Lab Report: 55-501319 Electrical Power and Machines

This electrical engineering lab report details experiments on three-phase circuits, power transmission, and transformer characteristics. The report includes measurements of line and phase voltages and currents in wye and delta configurations, analysis of unloaded and loaded transmission lines, an...Read More

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Electrical Power and Machines
Author
Course
Date

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Table of Contents
Introduction...........................................................................................................................................2
Results and discussion...........................................................................................................................3
PART-1 Phase and line measurement in the power supply...............................................................3
Part-2 Transmission Lines..................................................................................................................6
Task 1: measurement of unloaded lines........................................................................................6
Task 2: Transformation Ratios.......................................................................................................8
Task 3: Measurement of loaded lines: resistive, & inductive reactive load.................................11
Part-3 3-Phase Power Measurements and Calculations..................................................................15
Part-4 Voltage, current and power measurements in a delta-connected circuit.............................17
Conclusion...........................................................................................................................................21
References...........................................................................................................................................23
Introduction
Three phase circuits are the basis of every electrical power transmission network
(Zhang, Rehtanz and Pal 2012). Power is usually generated using three phase alternators and
transmitted to the load centers using three phase transmission lines. Long distance
transmission can not be realized using the generated voltages hence transformers are used
throughout the system to increase or decrease the voltage magnitudes (Kalaga and Yenumula
2016). The effective and economic operation of the entire system requires an understanding
of three phase circuits under different configurations. This laboratory exercise was carried out
with the general aim to familiarize with the operation and characteristics of transformers,
transmission lines, and different three phase circuit configurations.
One of the specific objectives of this exercise was to determine the relationship
between phase and line voltages for both wye and delta three phase circuits. It was
established through measurement that for a wye connection, the phase voltage is equivalent to
the line voltage. However, the line current is √3 times the phase current. For a wye
connection, the phase current was shown to be equal to the line current. However, the line
voltage was √3 times the phase voltage. Measurements real, reactive and apparent power in

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the three phase circuits were also performed. It was established that for a balanced three
phase circuit, the total power in the circuit is the sum of the powers in the independent
phases. Disconnecting one of the lines introduces an imbalance into the system and some
current flows through the neutral conductor.
The second objective was to investigate the current and voltage relationships on
unloaded and loaded transmission lines. The transmission line investigated was the nominal π
model for medium transmission lines. For the unloaded line, there was no current at the
receiving end due to the absence of a load. The line voltage at the receiving end was almost
equal to the phase voltage while a small current was registered at the sending end due to the
capacitance. For the loaded line, a small drop in the currents and voltages in the three phases
was observed.
The third objective was to investigate transformer characteristics by performing the
open circuit test and determining the transformation ratio. The ratio was determined by
measuring the primary and secondary voltages of an unloaded transformer. For capacitively-
loaded transformer, it was observed that the secondary voltage was significantly greater than
the primary voltage compared to when an inductive load was used.
Results and discussion
PART-1 Phase and line measurement in the power supply
The objective of this exercise was to measure the line-to-neutral (phase) and line to line (line)
voltages of a three phase ac power supply.

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Phase voltages of the three phase supply
V 1−N V 2−N V 3− N Average value
193 194 193 111.33
Line voltages of the three phase supply
V 1−2 V 2−3 V 1−3 Average value
110 112 112 193.33

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Average line voltage
Average p h ase voltage = 193.3
111.33 =1.7363 ≈ √3
Q5
The individually measured phase voltages are approximately equal
Q6
The individual measured line voltages are approximately equal
Q7
The individual measured line currents are approximately equal
Q8
The ratio of the average line voltage to the average phase voltage is 1.7363 which is
approximately equal to √3 .
Q9
The current flowing through the neutral line is approximately equal to zero.
Q11
Since no current flows through the neutral line, disconnecting the neutral line has no effect on
the measured quantities.
Q12
P1=V 1− N × I 1 × PF1 3.27
P1=V 2− N × I 2 × PF2 3.3

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P1=V 3− N × I 3 × PF3 3.3
PT =P1+P2+ P3 9.87
PT =3 ×V p h ase × I p h ase × PF 9.887
PT = √ 3× IL ×V L × PF 9.89
Part-2 Transmission Lines
Task 1: measurement of unloaded lines
The aim of this task was to measure the variables for the unloaded lines
The settings for the various parameters were,
Resistance at per phase transmission line R=3.6Ω
Inductance at per phase transmission line L=115 mH
Half of the earth capacitance CE
2 =3 ×0.55 μ F

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Half of the line capacitance CL
2 =3 ×150 nF
The measurements from the meters are,
At sending End At receiving end
Line voltage (V 12) 241 142
Line voltage (V 23 ) 241 141
Line voltage (V 31) 242 141
Phase voltage (V A ) 140 141
Phase voltage (V B) 139 141
Phase voltage (V C ) 139 141
Line current (I A ) 0.09 0
Line current (I B ) 0.09 0
Line current (I C) 0.09 0
Power at phase (PA ) 0 0
Power at phase (PB ) 0 0
Power at phase (PC ) 0 0

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Task 2: Transformation Ratios
V 1
V 2
= N1
N2
= I2
I1
=n
Primary voltage ¿ 226.8 V
Secondary voltgae = 233.9 V
The primary number of turns = 1311
Secondary number of turns = 682 ×2=1364
Therefore, n= N1
N2
= 1311
1364 =0.96
Inductive load

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Capacitive load
Load Primary Secondary
U Prim I Prim PPrim QPrim PFPrim U Sec I Sec PSec QSec PFSec
Resistive
load
223 0.13 26.3 11.4 0.919 221 0.14 22 8.8 0.935
Inductive
load
227 0.1 5.3 21.6 0.235 226 0.07 1.9 16.6 0.114
Capacitive
load
225 0.07 3.3 -16.6 -0.19 241.7 0.04 0 20.6 1.00

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The open circuit test
The aim of this exercise was to determine the value of Rc and X m for the no-load setup.
Experimental measurements
U Prim=226
IPrim=0.05
PPrim=2.8
SPrim=11.6
Calculation
PFPrim=cos φ0 = PPrim
SPrim
=0.25
φ0=76.11
Rc= V 1 oc
2
P1oc
=18 k Ω
X m= 1
√ ( I1 oc
V 1oc )2
− 1
Rc
2
=4.6 k Ω
Experimental measurements
U Prim=17.22
I Prim=0.14
Pprim=1.5

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PFPrim=cosφ=0.628
Calculation
φ=cos−1 ( PFPrim ) =cos−1 0.628=51.09
Re= P1 sc
I 1 sc
2 =16.53 Ω
X e= √ (V 1 sc
I1 sc )2
− ( Re ) 2=96.3 Ω
X2
' = Xe
2 =48.14
Task 3: Measurement of loaded lines : resistive, & inductive reactive load
The aim of this exercise was to measure the parameters of the transmission lines loaded with
resistive and inductive loads.
At Sending end At receiving end
Line voltage (V 12) 239 239
Line voltage (V 23 ) 238 240
Line voltage (V 31) 239 240

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Phase voltage (V A ) 138 138
Phase voltage (V B) 138 138
Phase voltage (V C ) 138 138
Line current (I A ) 0.21 0.19
Line current (I B ) 0.20 0.19
Line current (I C) 0.21 0.19
Power at phase A (PA ) 27 27
Power at phase B (PB ) 26 26
Power at phase C (PC ) 26 26
Power factor at phase A
(PFA )
0.93 1
Power factor at phase B
(PFB )
0.93 1
Power factor at phase C
(PFC )
0.93 1
At sending End At receiving end
Line voltage (V 12) 238 229
Line voltage (V 23 ) 238 230
Line voltage (V 31) 239 230
Phase voltage (V A ) 138 133
Phase voltage (V B) 137 132

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Phase voltage (V C ) 138 132
Line current (I A ) 0.20 0.24
Line current (I B ) 0.20 0.23
Line current (I C) 0.20 0.23
Power at phase A (PA ) 27 26
Power at phase B (PB ) 26 26
Power at phase C (PC ) 26 26
Power factor at phase A
(PFA)
0.96 0.84
Power factor at phase B
(PFB)
0.96 0.83
Power factor at phase C
(PFC)
0.96 0.83
Task 4: Analysis based on task 3
Sending end voltage per phase ( V S )=138 V
Receiving end voltage per phase ( V R )=133V
Current per phase at sending end ( IS ) =0.20 A
Current per phase at Receiving end ( I R )=0.24 A
Power factor per phase at sending end ( PFS=0.96)
Power factor per phase at receiving end (PF R=0.86)

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Calculation
Reactance of L,
X L=2 πfL=ωL
¿ ( 2 π ) ( 115
1000 )=1004.8 Ω
Operational capacitance C
2
C
2 =1 μ F
Reactance of C
2 ,
XC = 1
2 πfC = 1
ωC
The phase angle between V R and I R,
ΦR =cos−1 ( PFR ) =cos−1=32.85⃗
V R=V R + j 0
Load current,⃗
I R =I R ¿⃗ I R =0.24 ( cos 32.86− jsin 32.86 ) =0.2016− j 0.1302=0.24 ∠−32.86⃗
I C 1= jω ( C
2 )⃗ V R= jπfC⃗ V R
¿ j ( 2 π ×50 ) ( 1 ×10−6 ) ( 133 )=0.042 A
Line current,

15⃗
I L=⃗ I R +⃗ IC 1
¿ 0.042+0.2016− j 0.1302=0.2436− j 0.1302=0.2762∠−28.12
Sending end voltage,⃗
V s =⃗ V R +⃗ I L Z=V R +⃗ I L (R+ j X L)⃗
V s =133+(0.2762∠−28.12) Z
Charging current, ⃗
I C 2= jω ( C
2 )⃗ V R= jπfC⃗ V R
¿ j ( 2 π ×50 ) ( 1 ×10−6 ) ( 138 )=0.043 A⃗
I s=⃗ IC 2+⃗ I L=0.043+0.2436− j 0.1302=0.2866− j 0.1302
¿ 0.3148 ∠−24.43
Part-3 3-Phase Power Measurements and Calculations

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Voltages, currents, and power in the circuit above
V P h ase
(average)
V Line
(average)
I (average) PF
(measure
d)
PT
(measure
d)
QT
(measured)
ST
(measured )
Neutr
al
curre
nt I N
109 188.3 0.2 0.71 46 W 46 VR 65 VA 0
Calculation of the power components
PT =3 VIcos θ=3 ( 109 ) (0.2)( 0.71)
QT =3 VIsinθ=3(109)(0.2)sin (cos ¿¿−10.71) ¿
ST =3 VI =3 ( 109 ) ( 0.2 ) =65.4
Calculated Values PT QT ST
46.434 46.05 65.4

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Part-4 Voltage, current and power measurements in a delta-connected circuit
Voltages and currents in the circuit
V 1−2 V 2−3 V 1−3 Average line voltage
185 187 185 186.5
I 1 I 1 I 1 Average line current
0.59 0.6 0.6 0.596
PF−1 PF−2 PF−3 Average power
factor
0.71 0.71 0.71 0.71
P1 P2 P3 PT
45 46 46 137
Q1 Q2 Q3 QT
45 46 46 136
S1 S2 S3 ST
64 65 65 194
Voltages, currents, and power in the loaded circuit

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V 1−N V 2−N V 3− N Average phase
voltage
109 110 110 109.66
V 1−2 V 2−3 V 1−3 Average line voltage
190 191 190 190.33
I 1 I 2 I3 Average line current
0.03 A 0.03 A 0.03 A 0.03 A
Neutral Current
I N
0
P1 P2 P3
34 35 35
Q1 Q2 Q3
0 0 0
S1 S2 S3
34 35 35
PF1 PF2 PF3
1.00 1.00 1.00

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Neutral Current I N
0.31 A
In many parts of the world, electrical power is generated and transmitted in the form of three-
phase ac circuits. A three phase system is mainly made of three-phase generators,
transmission lines and the loads connected to the system. A three-phase circuit may be either
delta or wye connected depending on the application. Transmission is usually done using
delta circuits while distribution is implemented using wye circuits. A delta connected circuit
consists of three line conductors while a wye circuit has 3 line conductors and a neutral
conductor. For a balanced three phase system, no current flows through the neutral
conductor. Such a system has equal impedances in the three line conductors. The
relationships between the voltages in the lines and the voltages in the phases for a wye
connection are given by,
V L= √ 3 V p
Where V p is the voltage between any of the line conductors and the neutral conductor which
is the phase voltage. The line current is given by (Fleckenstein 2017),
I L= √ 3 I p

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The relationship between the line and phase voltages in a delta connected load is given by
(Fleckenstein 2017),
V L=V p
The relationship between the line and phase currents is,
I L= √ 3 I p
The calculation of power in three phase circuits requires the knowledge of several circuit
parameters such as the voltages, currents and the power factor angle (Wildi, 2014). The
power factor angle is the angle between the voltage and the current. If the current lags behind
the voltage, it is known as a lagging power factor while for a current that leads the voltage, it
is known as a leading power factor (Gonen 2015).
From the results presented in this section, we were able to verify the relationships
between line and phase parameters for three phase delta and wye connected circuits. It was
observed that there was a small difference between the voltages in the three phases. This
could be due to the fact that it is impossible to have perfectly matched impedances in all the
conductors in the three phases. Generally, the values for the measured and calculated
quantities were not the same. Small differences were observed. The small difference between
the measured and calculated values can be attributed to the fact that the accuracy of the
measuring instruments is limited by the number of decimal places that can be obtained. To
calculate the values, these measured quantities are multiplied introducing precision errors and
rounding off errors into the final result.
Any conductor offers some impedance to the flow of current. Transmission lines normally
have a combination of three impedances distributed along the length of the lines (Northcote-
Green and Wilson 2017). This means that there is always a voltage drop along the

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transmission lines hence the voltage, current and phase angles at the receiving end are always
different from the quantities at the sending end. Specifically, the voltage at the receiving end
is always less than the voltage at the sending end (Wang, Song and Irving 2010). The length
of the transmission line determines the model used to represent the line to simplify
calculations (Dorf and Svoboda 2010). There are short, medium and long transmission lines.
A short transmission line is modeled using only the series resistance and inductance of the
lines (Weedy et al. 2012). For a medium transmission line, shunt admittance is also included
to model the charging current between the transmission lines. As expected, the voltages at the
receiving end were less compared to the voltages at the sending end.
The power in three phase circuits depends on whether the three phases are balanced or
not. A balanced circuit has symmetrical quantities (Bouchekara, 2010). This means that the
parameters such as voltage, current, and the lead/lag angle are equivalent in all the phases
hence one phase can be used to analyze the circuit. For the delta connected circuit, it was
observed that the quantities in the three phases were similar. The power factor for the circuit
was the same in all the three phases indicating that the angle between the voltage and current
was the same in all the phases. This is expected for a balanced three phase load. For the wye
connected circuit, it was observed that disconnecting one phase introduced imbalance into the
system, with current flowing through the neutral line.
Conclusion
The overall aim of this laboratory exercise was to investigate the relationships
between the electrical quantities in three phase circuits. A resistive load has a very little
impact on the power factor of the transmission line. This is because ideally, the current
drawn by a resistive load should be in phase with the voltage thus the power factor should be
unity. However, in this exercise the power factor was slightly less than unity since in practice,

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a load can never be purely resistive. For inductively loaded circuits, the power factor was
very low, in the order of 0.114. this is not acceptable in many applications as it places a
burden on the power supply and increases the cost of operation. The power factor for the
capacitively-loaded circuit was unity which is the ideal value. The experimental results
obtained for the various circuit configurations were shown to be in agreement with theoretical
predictions for the various quantities including currents and voltages. The small differences
between the measured and calculated values can be considered negligible for this exercise.

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References
Bouchekara, H.R.E.H., 2010. Transmission and Distribution of Electrical Power. Kingdom
Of Saudi Arabia, Ministry Of High Education, Umm Al-Qura University, College of
Engineering & Islamic Architecture, Department Of Electrical Engineering.
Dorf, R. C., & Svoboda, J. A. (2010). Introduction to electric circuits. John Wiley & Sons.
Fleckenstein, J. E. (2017). Calculating currents in three-phase circuits. Three-Phase
Electrical Power, 109-160. doi:10.1201/9781315214146-4
Fleckenstein, J. E. (2017). Generation, transmission, and distribution. Three-Phase Electrical
Power, 57-93. doi:10.1201/9781315214146-2
Gonen, T. (2015). Electrical power transmission system engineering: Analysis and
design (3rd ed.). CRC Press.
Kalaga, S. and Yenumula, P., 2016. Design of electrical transmission lines: structures and
foundations. CRC Press.
Northcote-Green, J. and Wilson, R.G., 2017. Control and automation of electrical power
distribution systems (Vol. 28). CRC press.
Wang, X.F., Song, Y. and Irving, M., 2010. Modern power systems analysis. Springer
Science & Business Media.
Weedy, B.M., Cory, B.J., Jenkins, N., Ekanayake, J.B. and Strbac, G., 2012. Electric power
systems. John Wiley & Sons.
Wildi, T., 2014. Electrical machines, drives, and power systems.
Zhang, X., Rehtanz, C., & Pal, B. (2012). Flexible AC transmission systems: Modelling and
control. Springer Science & Business Media.