178 lines
No EOL
5.2 KiB
Markdown
178 lines
No EOL
5.2 KiB
Markdown
### Objective
|
||
|
||
The objective of this lab was to study the relationship between voltage and current in wye and delta 3-phase circuits, as well as to determine the real, apparent, and reactive power in said circuits.
|
||
|
||
# Wiring Diagram
|
||
|
||
## Part 1
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
## Part 2
|
||
|
||
|
||
|
||
## Part 3
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
# Procedure
|
||
|
||
## Part 1
|
||
|
||
1. Connect the above wye circuit using the resistance and meter modules. **DO NOT** connect to the neutral.
|
||
2. Set each resistance to $400\Omega$ per phase. Use ohmmeter to measure the phase resistance (including the connecting cables).
|
||
3. Turn on the power supply and adjust for $208V_{AC}$ line voltage.
|
||
4. Measure and record the voltages across the current through the 3 load resistors.
|
||
5. Calculate the total power delivered to the three loads.
|
||
|
||
## Part 2
|
||
|
||
1. Connect the delta circuit shown above.
|
||
2. Set each resistance to $400\Omega$. Before turning on the power suppluy, call the instructor or the TA to inspect your connections.
|
||
3. Turn on the power supply and adjust for $120V _{AC}$ line voltage.
|
||
4. Measure and record the line voltages.
|
||
5. Calculate, using measured data, the total 3-phase power.
|
||
|
||
## Part 3
|
||
|
||
1. Connect the above wye circuit shown below. **DO NOT** connect the neutral.
|
||
2. Set each resistance to $400\Omega$ and each inductance to $0.8H$.
|
||
3. Turn the power supply on and adjust for $208V_{AC}$.
|
||
4. Measure and record the line currents and the voltages across each inductive load.
|
||
5. Measure and record the voltages across each resistor.
|
||
6. Using measured date, calculate the real power on each load.
|
||
7. Calculate the total 3-phase real power, the reactive power in each load, the total 3-phase reactive power, the total 3-phase apparent power and the power factor.
|
||
|
||
# Experimental Data
|
||
|
||
## Part 1
|
||
|
||
| Phase | Measured Resistance ($\Omega$) | Line Currents ($A$) | Load Voltage ($V$) | Per $\phi$ Power ($W$) |
|
||
| ----- | ------------------------------ | -------------------- | ------------------ | ---------------------- |
|
||
| 1 | 415 | 0.34 | 120 | 40.8 |
|
||
| 2 | 413 | 0.35 | 120 | 42.0 |
|
||
| 3 | 414 | 0.34 | 120 | 40.8 |
|
||
|
||
**Total Three-phase power**: $123.6W$
|
||
|
||
|
||
|
||
|
||
|
||
## Part 2
|
||
|
||
| Phase | Resistance ($\Omega$) | Currents ($A$) | Per $\phi$ Power ($W$) |
|
||
| ----- | --------------------- | -------------- | ---------------------- |
|
||
| 1 | 400 | 0.5 | 100 |
|
||
| 2 | 400 | 0.6 | 144 |
|
||
| 3 | 400 | 0.55 | 121 |
|
||
|
||
**Total three-phase power**: $365W$
|
||
|
||
## Part 3
|
||
|
||
| Phase | Measured Current($A$) | Inductive Voltage($V$) | Resistive Voltage($V$) |
|
||
| ----- | --------------------- | ---------------------- | ---------------------- |
|
||
| 1 | 0.25 | 67.5 | 89 |
|
||
| 2 | 0.26 | 67.5 | 89 |
|
||
| 3 | 0.25 | 67.5 | 89 |
|
||
|
||
| Phase | Real Power ($W$) | Reactive Power ($VAR$) | Apparent Power($VA$) | Power Factor |
|
||
| ----- | ---------------- | ---------------------- | -------------------- | ------------ |
|
||
| 1 | 22.25 | 16.875 | 27.9 | 0.80 |
|
||
| 2 | 23.14 | 17.550 | 29.0 | 0.80 |
|
||
| 3 | 22.00 | 16.875 | 27.7 | 0.79 |
|
||
|
||
**Three Phase Real Power**: $67.39W$
|
||
|
||
**Three Phase Reactive Power**:$51.625VAR$
|
||
|
||
**Three Phase Apparent Power**:$84.6VA$
|
||
|
||
**Power Factor**: $0.80$
|
||
|
||
# Calculations and Analysis
|
||
|
||
## Power Calculation: Part 1
|
||
|
||
$$
|
||
R_{theory}=400\Omega; I_{in}=0.34\overline3A\\
|
||
P=I^2R=(0.34\overline3A)^2(400\Omega)\\
|
||
P=47W\\
|
||
P_{total}=141W
|
||
$$
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
## Power Calculation: Part 2
|
||
|
||
$$
|
||
P=I^2R; R=400\Omega; I=0.5A;\\
|
||
P=(0.5A)^2\times 400\Omega\\
|
||
P=100W\\
|
||
$$
|
||
|
||
## Power Calculation: Part 3
|
||
|
||
$$
|
||
P=IV;\hspace{2mm}Q=IV_{reactive} I=0.25A;\hspace{2mm} V_1=67.5V\angle90^\circ; \hspace{2mm} V_2=89V\angle0^\circ\\
|
||
Q_1=0.25A\times 67.5V_{reactive}; P_1=0.25A\times89V\\
|
||
Q_1=16.875VAR; P_1=22.25W\\
|
||
S=\sqrt{P^2+Q^2}\\
|
||
S=\sqrt{(22.25W)^2+(16.875VAR)^2}\\
|
||
S\approx27.9VA\\
|
||
pf={P\over S}={22.25W\over 27.9VA}\\
|
||
pf=0.80
|
||
$$
|
||
|
||
|
||
|
||
# Questions
|
||
|
||
1. Redo the calculations in part 1 with the ideal resistances of $400\Omega$. How do these results compare to the actual? If the values are different, explain the differences.
|
||
|
||
---
|
||
|
||
$$
|
||
R_{avg_{meas}}=414\Omega\\
|
||
I_{avg_{meas}}=0.34\overline{3}A\\
|
||
P_{avg_{meas}}=44.8W\\
|
||
P_{total_{meas}}=146W
|
||
$$
|
||
|
||
These numbers are within error of the measured values.
|
||
|
||
# Results and Conclusions
|
||
|
||
All of our results were within error. They weren’t exactly the same, because of tolerances and impurities.
|
||
|
||
For part 1 of the lab, we had a three phase power of $123.6W$. For part 2 of the lab, we had a three phase power of $365W$. For part 3 of the lab, we had $84.6VA \ at \ 0.80pf$. |