# Analysis And Measurements For Three Phase Circuits Lab Report Rewriting lab report that already has been written but needs to write again and changes words

Analysis And Measurements For Three Phase Circuits Lab Report Rewriting lab report that already has been written but needs to write again and changes words and paraphrase all the pages Analysis and Measurements for Three Phase Circuits

Abstract

In a world surrounded by electric power, the power systems are three phase systems, and

can be connected in two ways. Y-Y connected system is one of these two ways of connections,

and Y-∆ connected system is the other. Y-Y system means that the sources are connected in wye

connection as well as the loads. However, in a Y-∆ system, the sources are still connected in wye,

but the loads are now connected in delta connection. The objective for this experiment was to

connect the Y-Y load as well as line-line. Furthermore, the phasor voltages were measured

separately along with the currents. Along with the Y-Y loads, the Y-∆ load was as connected and

all phasor and line-line. The measurement of voltages and currents was also conducted. Once the

loads were successfully connected, the next step was to determine the power factor as well as

reactive and real power using two-wattmeter technique.

Introduction

This lab introduced the overall idea of three phase systems, and provided all needed

concepts as well as methods of computing and preforming three phase circuits in phasor and time

domain. In order to have a better understanding of three phase circuits, it was very critical to

perform prelab calculations and match them to the MATLAB results. This helped verify both

results before performing the hands on experiment. The phasor and line to line voltages and

currents were measured in the Y-Y and Y-∆ connected circuits. These pre-lab stages also helped

with the two-wattmeter technique as well as the power balance.

Procedure

For this lab two systems were observed and analyzed, then implemented. A three phase

Y-Y system and a Y-∆ system. In the Y-Y coennected system the phase voltage across each load

is the line to nutrual voltage, and the line current is the phase current flowing through the loads.

However, in the Y-∆ systems the phase voltage across each load is the line-line voltage, and the

line current is bigger than the phsae current by a factor of √3. Please see below Figure 1 for Y-Y

system and Figure 2 for Y-∆ system.

Figure1. Y-Y System

Figure2. Y-∆ System

A. Pre-Lab Hand Calculations

In this part of the lab, the phasor voltages, currents and the real, reactive and complex power

for the Y-Y and Y-∆ connected loads systems were calculated. The purpose of doing the hand

calculations was to expect each system’s behavior. For both the Y-Y and Y-∆ connected loads

systems, the phasor and line voltages and currents were calculated. In addition, all real and

apparent powers for single and three phase were computed as well as the power factor for both

systems. The phasor diagrams were drawn as well in order to use geometry to visualize the

behavior of each voltage and current with respect to the line to natural voltage Van. Once the phasor

voltage and current were known, the complex power was calculated using equation 1 shown below.

All basic calculation methods such as KVL, KCL, ohm’s law and power equations as well as the

complex power equation 1 shown below were used to get the final results. The detailed hand

calculations can be found labeled in the appendix section of this assignment.

= = √ = +

(1)

B. Matlab Calculations

The next part of the lab was to compute all the system parameters for both Y-Y and Y-∆

connected loads systems which were hand calculated using MATLAB. To achieve this, a function

was created to receive circuit element values, and source voltage as well as the radian frequency,

and produce all phasor voltages and currents including In and the power factor of the source as

well as all real, reactive, and complex powers for each phase and for the total three phase when

the system is connected in Y-Y. Likewise, a similar function was created for the Y-∆ connected

system. The Matlab code that contain all functions for both the Y-Y and Y-∆ systems can be found

labeled in appendix section of this lab.

C. Circuit Measurements

After the circuits were simulated using Matlab, the lab instruments were set up to construct and

measure the relevant system parameters. However, all connected systems were not powered up

unless a confirmation of either the professor or the teaching assistance (TA) obtained. First, the YY connected system was constructed, and all required system parameters were measured and

compared to the hand and MATLAB results. The loads in both systems were parallel RLC circuits.

In both systems, same values were used for the inductors, capacitors, and resistors for all three

load. The RLC circuit element’s values can be seen in table 1 shown below.

R(Ω)

L( )

C ( F )

490

0.7

2.5

Table 1. RLC Circuit Components Values

➢ Y-Y Connected System

The Y-Y system was set up by simply connecting each voltage source in a serial connection

with its load as can be seen in Figure 1 above. There was a single ammeter connecting in series at

the start of the system measuring the line current, and a voltmeter was connected in parallel across

each system load to measure the line voltage which in Y-Y connection was the line to neutral

voltage. The software was then setup to display the measurements recorded by the DMM’s. Using

the tools in the software provided the capability of measuring phase angles, real and apparent

power, and also the wave forms of the phase and line currents and voltages. After getting and

saving all the desired readings for the system parameters, and before moving to the next part, the

system was powered down.

➢ Y-∆ Connected System

The Y-∆ system was set up by connecting the sources and loads same way as can be seen

in Figure 2 above. There was a single ammeter connecting in series at the start of the system

measuring the line current, and a voltmeter was connected in parallel across each system load to

measure the line voltage which in Y-∆ connection was found to be the phase voltage. Also, the

phase currents were simply measured by connecting an ammeter in series with each load. The

software was then setup to display the measurements recorded by the DMM’s. Using the tools in

the software provided the capability of measuring phase angles, real and apparent power, and also

the wave forms of the phase and line currents and voltages. After getting and saving all the desired

readings for the system parameters the system was powered down.

D. Two wattmeter technique

The two wattmeter technique was used to determine the three phase real power. Both

wattmeters measure real power of the system. In this lab, this technique was used mathematically

and physically. There were some calculations and derivations that were made in order to achieve

the correct expression for real and reactive power as functions of W1 and W2. Once this relationship

was obtained mathematically, then this technique was physically used. In order to implement this

technique, two ammeters were used to measure ia and ic, and two voltmeters were used to measure

Vab and Vcb. After doing all the calculations and derivations, the final formulas obtained can be

seen in the following equations. Equation 2 and 3 represent the final derivation for the first and the

second wattmeters, respectively. The sum of the two wattmeters was found to be equal to the real

three phase power which can be seen in equation 4 below. Equation 5 shows the formula

representing the reactive power of the three phase system.

= | | | | – | | | |

(2)

= | | | | + | | | |

(3)

= + = √ | | | |

(4)

= √ ( − ) = √ | | | |

(5)

E. Power Factor Correction

In this part, first step was to do hand calculations in order to design a compensator to

improve the overall power factor for the three phase Y-Y and Y-∆ systems to 0.9 lagging. The

overall power factor was corrected to 0.9 by adding a capacitance in parallel with each load. The

load was first simulated on the circuit panels using the values of the circuit elements shown in

table 1 above. The compensating capacitor value was then calculated using equation 6. Finding

the compensating reactive power using equation 7 below was the best way to determine a value of

approximately 2.505 μF for the compensating capacitor for both systems.

=

( )

| |

= −

(6)

(7)

Measurements and Experimental Results

This part of the report represents all the actual results of the experiments in organized

subsections that also contain all graphs and tables of both experiments the Y-Y and Y-∆ systems.

The hand calculations and MATLAB results were fairly close to the experimental data obtained.

However, when doing the hand calculations and MATLAB, all system components were assumed

idea, whereas in real life applications they are not. This was one of the reasons behind the slight

differences between the experimental and calculated results. The experimental readings are

included in the same table that contain the hand and MATLAB results. This helps in making the

report more organized.

A. Y-Y System

The results for Y-Y system calculations and experimental data can be seen in tables 2 below.

Table 2 contains hand calculated the voltages and currents of the phase and line quantities. Table

3 contains measured voltages and currents of the phase and line quantities. The calculated real,

reactive, and power factor for each phase can be seen in table 4. The measured real, reactive, and

power factor for each phase can be seen in table 5. Table 6 represent magnitude and angle. It can

be seen from all the three tables that there are small differences between the theoretical and

experimental results. Table 7 shows the power factor correction obtained by experimenting. These

insignificant differences were due to the internal resistance of the load’s

Y-Y

Y-Y

Van

Vbn

Vcn

CALCULATED

Voltage (V)

60

60

60

Angle

0

-120

120

Van

Vbn

Vcn

MEASURED

Voltage (V)

61

61

60

Angle

0

-120.7

117.7

Vab

Vbc

Vca

Voltage (V)

103.92

103.92

103.92

Angle

30.3

-90

150

Vab

Vbc

Vca

Voltage (V)

105

104

103

Angle

30.3

-91.2

150.6

Ia

Ib

Ic

Current (A)

0.21

0.210

0.210

Angle

-54.36

-174.36

65.64

Ia

Ib

Ic

Current (A)

0.191

0.196

0.197

Angle

-41.2

-160.3

77.8

Ir

Il

Ic

In

Current (A)

0.12246

0.22734

0.0566

0

Angle

0

-90

90

0

Ir

Il

Ic

In

Current (A)

0.126

0.179

0.057

0.013

Angle

-1.3

-82.6

86

2.6

Table 2. Line/Phase voltages and currents

Table 3. Line /Phase voltages and currents

By observing table 2 and table 3 we can see that both hand calculated and measured values are

very close. If there hanppens to be a slight difference in both datas, this would be because the

system elements have toaleerance which makes diffrences as well as the reason that the software

is not as accurate as it suppose to be.

Y_Y Calculated

Apparent Power (VA)

12.6 < 54.36
12.6 < 54.36
12.6 < 54.36
Power (W)
7.342
7.342
7.342
22.026
A
B
C
Total
Power Factor
0.583
0.583
0.583
Table 4. Real Power, Apparent Power, Power Factor
Y_Y Measured
Apparent Power (VA)
11.4
11.8
11.7
Power (W)
8.6
9.1
9
26.7
A
B
C
Total
Power Factor
0.751
0.77
0.771
Table 5. Real Power, Apparent Power, Power Factor
Vab
Ia
Vcb
Ic
pf
W1
W2
S1
S2
P3
Y-Y
Magntude
103
0.186
104
0.192
6.1
19.8
19.8
20.2
26.1
Angle
-71.9
-10.8
25.9
Table 6. Magnitude and Angle
Ia
Ib
Ic
Power
Apparent
Power
pf
Y-Y Power Factor Correction
Magnitude
0.161
0.165
0.165
26.9
29.9
0.898
Table 7. Power factor correction
B. Y-∆ System
The results for Y-∆ system calculations and experimental data can be seen in tables 8 below.
Table 8 contains hand calculated the voltages and currents of the phase and line quantities. Table
9 contains measured voltages and currents of the phase and line quantities. The calculated real,
reactive, and power factor for each phase can be seen in table 10. The measured real, reactive, and
power factor for each phase can be seen in table 11. The measured Table 12 represent magnitude
and angle. It can be seen from all the three tables that there are small differences between the
theoretical and experimental results. Table 13 shows the power factor correction obtained by
experimenting. These insignificant differences were due to the internal resistance of the load’s
components which were ignored in the calculations performed.
Y-∆
Y-∆
Angle
0
-113
116
MEASURED
Voltage (V)
Van
Vbn
Vcn
CALCULATED
Voltage (V)
60
60
60
Vab
Vbc
Vca
Voltage (V)
106
106
106
Angle
25
-89
143
Ia
Ib
Ic
Current (A)
0.630
0.630
0.630
Angle
-54.4
-174.4
65.62
Iab
Ibc
Ica
In
Current (A)
0.364
0.364
0.364
0
Angle
-24.36
-144.4
95.64
0
Table 8. Line/Phase voltages and currents
Van
Vbn
Vcn
Vab
Vbc
Vca
Ia
Ib
Ic
Iab
Ibc
Ica
In
Angle
60
60
60
0
-120
117.8
Voltage (V)
Angle
107
106
104
30.6
-91.1
150.6
Current (A)
Angle
0.598
0.608
0.621
-41.9
-160.5
78.6
Current (A)
Angle
0.342
0.348
0.359
0
-12.6
-133.5
105.9
0
Table 9. Line/Phase voltages and currents
By observing table 8 and table 9 we can see that both hand calculated and measured values are
very close. If there hanppens to be a slight difference in both datas, this would be because the
system elements have toaleerance which makes diffrences as well as the reason that the software
is not as accurate as it suppose to be.
Pab
Pbc
Pca
Total
Power (W)
Y-∆ Calculated
Apparent Power (VA)
Power Factor
22
22
22
37.8
37.8
37.8
0.582
0.582
0.582
66
113.4
Table 10. Real Power, Apparent Power, Power Factor
Pab
Pbc
Pca
Total
Power (W)
Y-∆ Measured
Apparent Power (VA)
25.4
27.3
26.2
78.9
35.5
38.3
35.8
109.6
Power Factor
0.731
0.738
0.73
Table 11. Real Power, Apparent Power, Power Factor
Y-∆
Magntude
Vab
Ia
Vcb
Ic
W1
W2
S1
S2
P3
S3
Angle
104
0.59
103
0.607
18.9
61.1
62
62.6
82
107
-72.4
-9.6
80
124.6
Table 12. Magnitude and Angle
Y-∆ Power Factor Correction
Magnitude
Ia
Ib
Ic
Power
0.496
0.5
0.517
81
Apparent
Power
pf
91
0.886
Table 13. Power factor correction
Analysis and Discussion
As we can see that the results for both experiments the Y-Y and Y-∆ systems were as
expected. However, as can be observed from the data obtained shown in the tables above, there
were slight differences in the experimental results compared to the hand and MATLAB results.
These differences were most likely due to internal tolerance of the circuit elements and the scopes.
Inductors were the major effect causing these small differences because they were the reasons
behind the changes in the line current phase. The difference in the line current phase affected the
power factor as can be seen in the tables above. Thus, the theoretical results were very close to the
empirical results, and the insignificant differences were within the accepted range.
Furthermore, the vectors in the phasor diagrams of either system show that the voltage and
current vectors sum up to the source voltage and current, respectively. In other words, by
performing KVL and KCL, the voltages and currents will sum up to zero, respectively. Detailed
hand calculations including the verification of KVL and KCL as well as the phasor diagrams can
be found labeled in the appendix section of this assignment. The following equations represent the
voltages and currents in Y-Y and Y-∆ systems.
➢ Y-Y system:
Van = Vrms∠0° = Ia(Zline+ ZY )
(8)
Vbn = Vrms∠−120° = Ib(Zline+ ZY )
(9)
Vcn = Vrms∠120° = Ic(Zline+ ZY )
Ia = | | ∠−
Ib = | | ∠− °−
Ic = | | ∠ °−
➢
(10)
(11)
(12)
(13)
Y-∆ system:
Ia = Iab – Ica
(14)
Ib = Ibc – Iab
(15)
Ic = Ica – Ibc
(16)
Ia = Irms ∠
(17)
Ib = Irms ∠−
(18)
Ic = Irms ∠
(19)
Conclusion
The objectives for this lab were successfully met. By performing there lab experiments, it
helped better understand the analysis three phase circuits using phasor and time domain
techniques. Also, one of the important concepts and methods that was learned in this lab was the
two-wattmeter technique as an efficient way to calculate the overall power of three phase systems.
Overall, the meter readings were relatively close to the hand and MATLAB calculations. If there
may be any large errors, this could be because of the non-ideal inductors.
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