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
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.
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.
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.
= = √ = +
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.
C ( F )
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.
= | | | | – | | | |
= | | | | + | | | |
= + = √ | | | |
= √ ( − ) = √ | | | |
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.
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
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.
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. Purchase answer to see full attachment