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classDescription.txt

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+EEET-242-04
+Electrical Machines and Transformers
+Professor: Shola Olabisi
+Semester: 2195 (2020 Spring)
+Time Slot: Unknown
+
+Professor Olabisi is a wonderful guy. Happy to help, very trusting, very calm. He is extremely well versed in this topic, and this seems to be his true passion. He is very willing to help, and is also willing to accept students mistakes, such as missing a deadline by an hour, or accidentally copying a value incorrectly.
+Lab tools are all provided, but lab reports are quite lengthy. If you have taken Chem, you are familiar with the length that is required.
+As with EEET-221/2, we highly recommend QUCS as a circuit simulator, for diagrams.

lab1.md

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+### 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
+
+![wiringDiagramPart1](lab1.assets/part1WiringDiagram.png)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+## Part 2
+
+![wiringDiagramPart2](lab1.assets/part2WiringDiagram.png)
+
+## Part 3
+
+![wiringDiagramPart3](lab1.assets/part3WiringDiagram.png)
+
+
+
+
+
+
+
+# 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 $84.6VA \ at \ 0.80pf$.

lab2/lab2.md

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+# Objective
+
+The objective of this lab was to measure power in a 3-phase circuit using wattmeters and to determine the phase sequence of a 3-phase line.
+
+# Procedure
+
+For part 1, we connected the power source to a wye resistive, inductive, and capacitive load through a wattmeter, with a voltmeter measuring the line voltage and an ammeter measuring one of the line currents. 
+
+For part 2, we connected the power source to a singular capacitor, by way of a synchronizing switch, as shown in figure 2. 
+
+
+
+# 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 $138.5VA \ at\ pf\approx1$ for the resistive load, $78VA\ at\ pf\approx0.02$ for the capacitive load, and $76VA\ at\ pf\approx0.28$. For part 2,  
+
+# Questions
+
+1. Could 1 wattmeter be used to measure the total 3-phase power on a balanced 3-phase, 4-wire system?
+
+One wattmeter system (consisting of 2 individual wattmeters) would be enough to measure the total power of a 3-phase, 4-wire system.
+
+2. Can a Wattmeter that has I through and V across it indicate $0W$? Explain.
+
+The wattmeter cannot indicate $0W$. Although they are standard wattmeters, they are still used to calculate the complex power output, which means that one of them will register the power if there is any current and voltage through and across them.
+
+3. Could a 3-phase induction motor be used to establish the phase sequence of a 3 phase line?
+
+Yes. The direction of spin of the induction motor will show you where the phases are in reference to each other.
+
+4. Line voltages are $120^\circ$ out of phase with each other. Are the phase voltages also $120^\circ$ out of phase with each other? Explain.
+
+Yes, they are. 
+
+
+
+# Wiring Diagrams
+
+## Part 1
+
+![resistiveWye](lab2.assets/resistiveWye.png)
+
+***Figure 1: Resistive circuit***
+
+![capacitiveWye](lab2.assets/capacitiveWye.png)
+
+***Figure 2: Capacitive Circuit***
+
+![inductiveWye](lab2.assets/inductiveWye.png)
+
+***Figure 3: Inductive Circuit***
+
+![syncCap](lab2.assets/syncCap.png)
+
+***Figure 4: Capacitive Circuit***
+
+![syncInductor](lab2.assets/syncInductor.png)
+
+***Figure 5: Inductive Circuit***
+
+# Experimental Data
+
+## Part 1
+
+| Type            | Current (A) | Power  $(W_1) $ | Power $(W_2)$ | $S_{3\phi}$(VA) | $P_{3\phi}$(W) | $Q_{3\phi}$(VAR) | $pf_{3\phi}$ |
+| --------------- | ----------- | --------------- | ------------- | --------------- | -------------- | ---------------- | ------------ |
+| $\Omega_{meas}$ | 0.46        | $+68.5$         | $+70$         | $138.5$         | $138.5$        | $-1.5$           | $\approx1$   |
+| $X_{C_{meas}}$  | 0.42        | $-40$           | $+38$         | $78$            | $-2$           | $-78$            | $0.02$       |
+| $X_{L_{meas}}$  | 0.46        | $+47$           | $-26$         | $76$            | $21$           | $73$             | $0.28$       |
+
+$$
+P_{3\phi}=W_1+W_2=68.5W+70W\\
+\underline{\overline{|P_{3\phi}=138.5W|}}\\[12pt]
+Q_{3\phi}=W_1-W_2=68.5VAR-70VAR\\
+\underline{\overline{|Q_{3\phi}\approx-1.5VAR|}}\\[12pt]
+S=\sqrt{P^2+Q^2}\\
+S=\sqrt{(138.5W)^2+(-1.5VAR)^2}\\
+\underline{\overline{|S_{3\phi}\approx 138.5VA|}}\\[12pt]
+pf={P\over S}={138.5W \over 138.5VA}\\
+\underline{\overline{|pf_{3\phi}\approx1|}}\\
+$$
+
+
+
+## Part 2
+
+Upon reading the synchronization unit.
+
+
+
+The voltage phasor system rotates $45^\circ$ clockwise from expected, due to the cap. When you swap the lines, it swaps the lamp locations. the voltage phasor system rotates $90^\circ$ counterclockwise from the cap’s location. When you swap lines, it swaps the lamp locations.

lab3-4/lab3-4.md

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+# Objective
+
+The objective of this lab was to study the relationship between primary and secondary values in a single phase transformer.
+
+# Procedure
+
+For lab 3, for each part, connect the power supply to the transformer according to the respective figure below. Then, connect the load to the opposite side of the transformer. Then measure the voltage, current, and power, using the wattmeter.  
+
+# Results and Conclusions
+
+At the end of lab 3, we showed that changing the turns ratios of the transformers changes the power out to the load, and that the load being partially reactive does pass over to the primary side of the transformer. 
+
+At the end of lab 4, we were able to calculate the internal losses of the transformer. We found the internal resistance for the core to be $R_m=5760\Omega$ and $X_m=5559\Omega$. We then found the internal resistances of the transformer to be $R_f=23\Omega$ and $X_f=25.3\Omega$.  We also found that the efficiency of a transformer goes down as the load resistance goes up. 
+
+# Wiring Diagrams
+
+## Lab 3
+
+### Figure 1: Resistive Circuit 1
+
+![](lab3-4.assets/resistiveCircuit1.png)
+
+### Figure 2: Resistive Circuit 2
+
+![](lab3-4.assets/resistiveCircuit2.png)
+
+### Figure 3: Resistive and Inductive Circuit 1
+
+![](lab3-4.assets/inductiveCircuit1.png)
+
+### Figure 4: Resistive and inductive Circuit 2
+
+![](lab3-4.assets/inductiveCircuit2.png)
+
+## Lab 4
+
+### Figure 5: Short Circuit Test
+
+![](lab3-4.assets/shortCircuitTest.png)
+
+### Figure 6: Open Circuit Test
+
+![](lab3-4.assets/openCircuitTest.png)
+
+### Load Test
+
+![](lab3-4.assets/loadTest.png)
+
+# Experimental Data
+
+## Lab 3
+
+### Resistive Circuit 1
+
+| Measurement | Value          |
+| ----------- | -------------- |
+| $V_p$       | $120.17V$      |
+| $V_s$       | $58.7V$        |
+| $I_p$       | $0.0962A$      |
+| $I_s$       | $0.1425A$      |
+| $P_p$       | $11.30W$       |
+| $P_s$       | $8.48W$        |
+| $S_p$       | $11.56VA$      |
+| $S_s$       | $8.36VA$       |
+| $a$         | $\approx2.047$ |
+
+$$
+V_p,V_s,I_p,I_s,P_p,P_s\ measured\\
+S_p=V_p\times I_p=120.17V\times0.0962A=11.56VA\\
+S_s=V_s\times I_s=58.7V\times0.1425A=8.36VA\\
+a=\frac{V_p}{V_s}=\frac{120.17V}{58.7V}\approx2.047
+$$
+
+
+
+### Resistive Circuit 2
+
+
+| Measurement | Value          |
+| ----------- | -------------- |
+| $V_p$       | $120.54V$      |
+| $V_s$       | $99.03V$       |
+| $I_p$       | $0.234A$       |
+| $I_s$       | $0.2414A$      |
+| $P_p$       | $28.21W$       |
+| $P_s$       | $24.25W$       |
+| $S_p$       | $28.206VA$     |
+| $S_s$       | $23.906VA$     |
+| $a$         | $\approx1.217$ |
+
+$$
+V_p,V_s,I_p,I_s,P_p,P_s\ measured\\
+S_p=V_p\times I_p=120.54V\times0.234A=28.206VA\\
+S_s=V_s\times I_s=99.03V\times0.2414A=23.906VA\\
+a=\frac{V_p}{V_s}=\frac{120.54V}{99.03V}\approx1.217
+$$
+
+### Resistive and Inductive Circuit 1
+
+| Measurement | Value          |
+| ----------- | -------------- |
+| $V_p$       | $119.95V$      |
+| $V_s$       | $58.41V$       |
+| $I_p$       | $0.0831A$      |
+| $I_s$       | $0.1066A$      |
+| $P_p$       | $7.95W$        |
+| $P_s$       | $5.19W$        |
+| $S_p$       | $9.97VA$       |
+| $S_s$       | $6.23VA$       |
+| $a$         | $\approx2.054$ |
+
+$$
+V_p,V_s,I_p,I_s,P_p,P_s\ measured\\
+S_p=V_p\times I_p=119.95V\times0.0831A=9.97VA\\
+S_s=V_s\times I_s=58.41V\times0.1066A=6.23VA\\
+a=\frac{V_p}{V_s}=\frac{119.95V}{58.41V}\approx2.054
+$$
+
+
+
+### Resistive and Inductive Circuit 2
+
+| Measurement | Value         |
+| ----------- | ------------- |
+| $V_p$       | $119.93V$     |
+| $V_s$       | $221.8V$      |
+| $I_p$       | $1.138A$      |
+| $I_s$       | $0.417A$      |
+| $P_p$       | $97.9W$       |
+| $P_s$       | $77.3W$       |
+| $S_p$       | $136.48VA$    |
+| $S_s$       | $92.49VA$     |
+| $a$         | $\approx0.54$ |
+
+$$
+V_p,V_s,I_p,I_s,P_p,P_s\ measured\\
+S_p=V_p\times I_p=119.93V\times1.138A=136.48VA\\
+S_s=V_s\times I_s=221.8V\times0.417A=92.49VA\\
+a=\frac{V_p}{V_s}=\frac{119.93V}{221.8V}\approx0.54
+$$
+
+
+
+## Lab 4
+
+### Short Circuit Test
+
+| %     | $I_H\ (A)$ | $V_H\ (V)$ | $P_H\ (W)$ |
+| ----- | ---------- | ---------- | ---------- |
+| $25$  | $0.125$    | $4.26$     | $0.362$    |
+| $50$  | $0.25$     | $8.59$     | $1.463$    |
+| $75$  | $0.375$    | $12.73$    | $3.17$     |
+| $90$  | $0.45$     | $15.25$    | $4.63$     |
+| $100$ | $0.5$      | $17.09$    | $5.75$     |
+
+All values measured
+$$
+R_f={P\over I^2}={5.75W\over0.5A^2}\\R_f=23\Omega\\
+X_f=\sqrt{({V\over I})^2- ({P\over I^2})^2}= \sqrt{({17.09V\over 0.5A})^2- ({5.75W\over0.5A^2})^2}\\
+X_f=25.3\Omega
+$$
+
+
+### Open Circuit Test
+
+| %     | $V_L\ (V)$ | $I_L\ (A)$ | $P_L\ (W)$ |
+| ----- | ---------- | ---------- | ---------- |
+| $25$  | $15$       | $0.0227$   | $0.248$    |
+| $50$  | $30$       | $0.0339$   | $0.771$    |
+| $75$  | $45$       | $0.0458$   | $1.576$    |
+| $100$ | $60$       | $0.0600$   | $2.50$     |
+| $125$ | $75$       | $0.0829$   | $3.92$     |
+
+All values measured
+$$
+R_m=a^2{V_s^2\over P}= 4({60V^2\over2.5W})\\R_m=5760\Omega\\
+X_m={V^2\over\sqrt{(VI)^2-P^2}}={60V^2\over\sqrt{(60V\times0.06A)^2-2.5W^2}}\\
+X_m=5559\Omega
+$$
+
+
+### Load Test
+
+| $R_L$  | $I_H(A)$ | $V_H(V)$ | $P_H(W)$ | $I_L(A)$ | $V_{L_{NL}}(V)$ | $V_{L_{FL}}(V)$ | $P_L(W)$ | Eff      | % Reg  |
+| ------ | -------- | -------- | -------- | -------- | --------------- | --------------- | -------- | -------- | ------ |
+| $1200$ | $0.0517$ | $120$    | $5.49$   | $0.0492$ | $59.3$          | $59.6$          | $2.8$    | $51.0\%$ | $0.50$ |
+| $600$  | $0.0719$ | $120$    | $8.31$   | $0.0951$ | $59.1$          | $59.6$          | $5.67$   | $68.2\%$ | $0.84$ |
+| $400$  | $0.0954$ | $120$    | $11.20$  | $0.1428$ | $58.7$          | $59.6$          | $8.48$   | $75.7\%$ | $1.51$ |
+| $300$  | $0.1234$ | $120$    | $14.62$  | $0.1996$ | $58.6$          | $59.6$          | $11.79$  | $80.6\%$ | $1.68$ |
+| $240$  | $0.1470$ | $120$    | $17.43$  | $0.2463$ | $58.3$          | $59.6$          | $14.50$  | $83.2\%$ | $2.18$ |
+| $200$  | $0.1688$ | $120$    | $20.04$  | $0.2903$ | $57.9$          | $59.6$          | $16.98$  | $84.7\%$ | $2.85$ |
+
+$$
+eff(\%)=\frac{P_L}{P_H}=\frac{2.8}{5.49}\approx51.0\%\\
+\%\ reg = \frac{V_{L_{NL}-V_{L_{FL}}}}{V_{L_{FL}}}=\frac{59.3-59.6}{59.6}=0.50\%
+$$
+

lab5/lab5.md

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+# Objective
+
+The objective of this lab was to experimentally look at the polarity of the wiring of a single phase autotransformer.
+
+# Procedure
+
+First, we connected up a simple transformer circuit, with an open. This allowed us to find the transformers polarity, and understand how to set up all future circuits. We then set up a definite step-up transformer and a step-down transformer, using two different coils, one at a time. Finally, we set up a multi-coil autotransformer, in both step up and step-down configurations.
+
+# Results and Conclusions
+
+In this lab we learned the polarity of the transformers used in lab. All of these circuits are correct, and the numbers we got are fairly reasonable. 
+
+# Wiring Diagrams
+
+![Figure 1: Polarity Test](lab5.assets/polarityTest.png)
+
+*Figure 1: Polarity Test Diagram*
+
+![](lab5.assets/singleCoilStepUp.png)[^1]
+
+*Figure 2: Single Coil Autotransformer (Step Up)*
+
+![](lab5.assets/singleCoilStepDown.png)[^1]
+
+*Figure 3: Single Coil Autotransformer (Step Down)*
+
+![](lab5.assets/multiCoilStepUp.png)[^2]
+
+*Figure 4: Multi-Coil Autotransformer (Step Up)*
+
+![](lab5.assets/multiCoilStepDown.png)[^2]
+
+*Figure 5: Multi-Coil Autotransformer (Step Down)*
+
+![](lab5.assets/transformerGuide.png)
+
+*Figure 6: Transformer Guide*
+
+[^1]:In these tests, the $V_{in}$ was actually 60V.
+[^2]: In these diagrams, the numbers are typed due to QUCS not accepting numbers in the annotations as the first character. Annotations with two numbers represent nodes in the transformer depicted in Figure 6 that were connected for the lab.
+
+# Experimental Data
+
+## Polarity Tests
+
+These are set up according to the Figure 1 in the wiring diagrams. The numbers refer to the transformer boxes used in lab, which is shown in Figure 6. 
+
+| Setup                            | $V_s$ (V) | Polarity    |
+| -------------------------------- | --------- | ----------- |
+| $H_1=2;\ H_2=1;\ X_1= 9;\ X_2=5$ | $59.5$    | Step Down   |
+| $H_1=2;\ H_2=1;\ X_1= 5;\ X_2=9$ | $178$     | Step Up     |
+| $H_1=2;\ H_2=1;\ X_1= 2;\ X_2=7$ | $16$      | Step Down   |
+| $H_1=2;\ H_2=1;\ X_1= 7;\ X_2=2$ | $100.8$   | Step Up[^3] |
+
+[^3]:don’t completely understand why this happened. While this is configured as a step up transformer, the voltage is still low. I don’t completely understand why this happened.
+
+## Single Coil Autotransformer (Step Up)
+
+These are set up according to the Figure 2 in the wiring diagrams. The numbers refer to the transformer boxes used in lab, which is shown in Figure 6. 
+
+| Setup                     | $V_L$ (V) | $I_{p_{in}}$(A) | $I_{p_{out}}$(A) | $I_L$(A) |
+| ------------------------- | --------- | --------------- | ---------------- | -------- |
+| $H_1= 3;\ H_2= 7;\ X_2=8$ | $100$     | $0.297$         | $0.297$          | $0.161$  |
+| $H_1= 5;\ H_2= 9;\ X_2=6$ | $117.6$   | $0.417$         | $0.417$          | $0.189$  |
+
+
+
+## Single Coil Autotransformer (Step Down)
+
+These are set up according to the Figure 3 in the wiring diagrams. The numbers refer to the transformer boxes used in lab, which is shown in Figure 6. 
+
+| Setup                     | $V_L$ (V) | $I_{p_{in}}$(A) | $I_{p_{out}}$(A) | $I_L$(A) |
+| ------------------------- | --------- | --------------- | ---------------- | -------- |
+| $H_1= 3;\ H_2= 7;\ X_2=8$ | $34.3$    | $0.0552$        | $0.0552$         | $0.0387$ |
+| $H_1= 5;\ H_2= 9;\ X_2=6$ | $29.7$    | $0.0381$        | $0.0381$         | $0.0479$ |
+
+## Multi-Coil Autotransformer (Step Up)
+
+These are set up according to the Figure 4 in the wiring diagrams. The numbers refer to the transformer boxes used in lab, which is shown in Figure 6. 
+
+| $V_{15}$ (V) | $V_{19}$(V) | $I_{p_{in}}$(A) | $I_{p_{out}}$(A) | $I_L$(A) |
+| ------------ | ----------- | --------------- | ---------------- | -------- |
+| $34.3$       | $176.3$     | $0.0427$        | $0.0427$         | $0.0285$ |
+
+## Multi-Coil Autotransformer (Step Down)
+
+These are set up according to the Figure 5 in the wiring diagrams. The numbers refer to the transformer boxes used in lab, which is shown in Figure 6. 
+
+| $V_{12}$(V) | $V_{15}$(V) | $V_{19}$(V) |
+| ----------- | ----------- | ----------- |
+| $59.72$     | $59.72$     | $88.8$      |
+

lab6/lab6.md

@@ -0,0 +1,247 @@
+# Objective
+
+The objective of this lab was to experimentally look at the wiring and measurement of values in three-phase transformer circuits.
+
+# Procedure
+
+First, we connected the power supply to the load through a Delta-Wye transformer. We then collected measurements, and changed the transformer to be a Delta-Delta transformer. After collecting the same measurements, we then 
+
+# Results and Conclusions
+
+
+
+# Wiring Diagrams
+
+![](lab6.assets/deltaWye.png)[^1]
+
+*Figure 1: Delta-Wye Transformer Diagram*
+
+![](lab6.assets/deltaDelta.png)
+
+*Figure 2: Delta-Delta Transformer Diagram*
+
+![](lab6.assets/splitPhase.png)
+
+*Figure 3: Delta-Delta Split Phase Transformer Diagram*
+
+![](lab6.assets/unbalancedLoad.png)[^2]
+
+*Figure 3: Delta-Delta Split Phase Transformer* ***unbalanced*** *Diagram*
+
+![](lab6.assets/transformerGuide.png)
+
+*Figure 6: Single Transformer Guide*
+
+[^1]:The source side of this circuit is used in all other configurations in this lab. This will not be repeated in future configurations, to save space.
+[^2]:Boxes over gaps denote removed resistors
+
+# Experimental Data
+
+## Delta-Wye Transformer
+
+### Voltage (V)
+
+<<<<<<< HEAD
+| Location    | Line   | Phase | Line (ideal) | Phase (ideal) |
+| ----------- | ------ | ----- | ------------ | ------------- |
+| Primary 1   | 206.63 | 119.3 | 120          | 120           |
+| Primary 2   | 201.26 | 116.2 | 120          | 120           |
+| Primary 3   | 203.34 | 117.4 | 120          | 120           |
+| Secondary 1 | 101.70 | 58.72 | 103.92       | 60            |
+| Secondary 2 | 101.62 | 58.67 | 103.92       | 60            |
+| Secondary 3 | 101.50 | 58.60 | 103.92       | 60            |
+=======
+| Location            | Measured | Ideal | Error |
+| ------------------- | -------- | ----- | ----- |
+| Primary 1 (phase)   | 119.3    | 120   |       |
+| Primary 1 (line)    |          |       |       |
+| Primary 2 (phase)   | 116.2    | 120   |       |
+| Primary 2 (line)    |          |       |       |
+| Primary 3 (phase)   | 117.4    | 120   |       |
+| Primary 3 (line)    |          |       |       |
+| Secondary 1 (phase) | 58.72    | 60    |       |
+| Secondary 1 (line)  |          |       |       |
+| Secondary 2 (phase) | 58.67    | 60    |       |
+| Secondary 2 (line)  |          |       |       |
+| Secondary 3 (phase) | 58.60    | 60    |       |
+| Secondary 3 (line)  |          |       |       |
+>>>>>>> acba6896f2a9a9eee4514aef623a2127202e38f0
+
+$$
+In\ \Delta,V_L=\sqrt3V_\phi=\sqrt3(119.3V)=206.63\\In\ Y,V_L=V_\phi
+$$
+
+### Current (A)
+
+<<<<<<< HEAD
+| Location    | Line  | Phase | Line (ideal) | Phase (ideal) |
+| ----------- | ----- | ----- | ------------ | ------------- |
+| Primary 1   | 0.117 |       | 0.050        | 0.050         |
+| Primary 2   | 0.118 |       | 0.050        | 0.050         |
+| Primary 3   | 0.117 |       | 0.050        | 0.050         |
+| Secondary 1 | 0.097 | 0.097 | 0.100        | 0.100         |
+| Secondary 2 | 0.097 | 0.097 | 0.100        | 0.100         |
+| Secondary 3 | 0.097 | 0.097 | 0.100        | 0.100         |
+=======
+| Location            | Measured | Ideal | Error |
+| ------------------- | -------- | ----- | ----- |
+| Primary 1 (phase)   |          | 0.028 |       |
+| Primary 1 (line)    | 0.117    | 0.050 |       |
+| Primary 2 (phase)   |          | 0.028 |       |
+| Primary 2 (line)    | 0.118    | 0.050 |       |
+| Primary 3 (phase)   |          | 0.028 |       |
+| Primary 3 (line)    | 0.117    | 0.050 |       |
+| Secondary 1 (phase) |          | 0.100 |       |
+| Secondary 1 (line)  | 0.097    | 0.100 |       |
+| Secondary 2 (phase) |          | 0.100 |       |
+| Secondary 2 (line)  | 0.097    | 0.100 |       |
+| Secondary 3 (phase) |          | 0.100 |       |
+| Secondary 3 (line)  | 0.097    | 0.100 |       |
+>>>>>>> acba6896f2a9a9eee4514aef623a2127202e38f0
+
+$$
+In\ Y, I_L=I_\phi\\In\ \Delta, I_L=\sqrt3I_\phi
+$$
+
+### Miscellaneous
+
+| Measurement              | Value  | Ideal Value |
+| ------------------------ | ------ | ----------- |
+| $R_{1_{calc}}\ (\Omega)$ | 605    | 600         |
+| $R_{2_{calc}}\ (\Omega)$ | 604    | 600         |
+| $R_{3_{calc}}\ (\Omega)$ | 604    | 600         |
+| $a_a$                    | 2.0316 | 2.0         |
+| $a_b$                    | 1.9806 | 2.0         |
+| $a_c$                    | 2.0034 | 2.0         |
+| $P_{\phi a_p}\ (W)$      | 9.602  |             |
+| $P_{\phi b_p}\ (W)$      | 9.548  |             |
+| $P_{\phi c_p}\ (W)$      | 9.546  |             |
+| $P_{\phi a_s}\ (W)$      | 5.577  | 6.0         |
+| $P_{\phi b_s}\ (W)$      | 5.567  | 6.0         |
+| $P_{\phi c_s}\ (W)$      | 5.534  | 6.0         |
+| $P_{3\phi_p}\ (W)$       | 28.696 |             |
+| $P_{3\phi_s}\ (W)$       | 16.678 | 18.0        |
+
+## Delta-Delta Transformer
+
+### Voltage (V)
+
+| Location    | Line | Phase | Line (ideal) | Phase (ideal) |
+| ----------- | ---- | ----- | ------------ | ------------- |
+| Primary 1   |      |       |              |               |
+| Primary 2   |      |       |              |               |
+| Primary 3   |      |       |              |               |
+| Secondary 1 |      |       |              |               |
+| Secondary 2 |      |       |              |               |
+| Secondary 3 |      |       |              |               |
+
+### Current (A)
+
+| Location    | Line | Phase | Line (ideal) | Phase (ideal) |
+| ----------- | ---- | ----- | ------------ | ------------- |
+| Primary 1   |      |       |              |               |
+| Primary 2   |      |       |              |               |
+| Primary 3   |      |       |              |               |
+| Secondary 1 |      |       |              |               |
+| Secondary 2 |      |       |              |               |
+| Secondary 3 |      |       |              |               |
+
+### Miscellaneous
+
+| Measurement              | Value | Ideal Value |
+| ------------------------ | ----- | ----------- |
+| $R_{1_{calc}}\ (\Omega)$ |       | 600         |
+| $R_{2_{calc}}\ (\Omega)$ |       | 600         |
+| $R_{3_{calc}}\ (\Omega)$ |       | 600         |
+| $a_a$                    |       |             |
+| $a_b$                    |       |             |
+| $a_c$                    |       |             |
+| $P_{3\phi_p}\ (W)$       |       |             |
+| $P_{3\phi_s}\ (W)$       |       |             |
+
+
+
+## Delta-Delta With Split Phase Transformer
+
+### Voltage (V)
+
+| Location  | Line | Phase | Line (ideal) | Phase (ideal) |
+| --------- | ---- | ----- | ------------ | ------------- |
+| Primary 1 |      |       |              |               |
+| Primary 2 |      |       |              |               |
+| Primary 3 |      |       |              |               |
+| $R_1$     |      |       |              |               |
+| $R_2$     |      |       |              |               |
+| $R_3$     |      |       |              |               |
+| $R_4$     |      |       |              |               |
+| $R_5$     |      |       |              |               |
+
+### Current (A)
+
+| Location  | Line | Phase | Line (ideal) | Phase (ideal) |
+| --------- | ---- | ----- | ------------ | ------------- |
+| Primary 1 |      |       |              |               |
+| Primary 2 |      |       |              |               |
+| Primary 3 |      |       |              |               |
+| $R_1$     |      |       |              |               |
+| $R_2$     |      |       |              |               |
+| $R_3$     |      |       |              |               |
+| $R_4$     |      |       |              |               |
+| $R_5$     |      |       |              |               |
+
+### Miscellaneous
+
+| Measurement              | Value | Ideal Value |
+| ------------------------ | ----- | ----------- |
+| $R_{1_{calc}}\ (\Omega)$ |       |             |
+| $R_{2_{calc}}\ (\Omega)$ |       |             |
+| $R_{3_{calc}}\ (\Omega)$ |       |             |
+| $a_a$                    |       |             |
+| $a_b$                    |       |             |
+| $a_c$                    |       |             |
+| $P_{3\phi_p}\ (W)$       |       |             |
+| $P_{3\phi_s}\ (W)$       |       |             |
+
+
+
+## Delta-Delta With Split Phase Transformer - Unbalanced Load
+
+### Voltage (V)
+
+| Location  | Line | Phase | Line (ideal) | Phase (ideal) |
+| --------- | ---- | ----- | ------------ | ------------- |
+| Primary 1 |      |       |              |               |
+| Primary 2 |      |       |              |               |
+| Primary 3 |      |       |              |               |
+| $R_1$     |      |       |              |               |
+| $R_2$     |      |       |              |               |
+| $R_3$     |      |       |              |               |
+| $R_4$     |      |       |              |               |
+| $R_5$     |      |       |              |               |
+
+### Current (A)
+
+| Location  | Line | Phase | Line (ideal) | Phase (ideal) |
+| --------- | ---- | ----- | ------------ | ------------- |
+| Primary 1 |      |       |              |               |
+| Primary 2 |      |       |              |               |
+| Primary 3 |      |       |              |               |
+| $R_1$     |      |       |              |               |
+| $R_2$     |      |       |              |               |
+| $R_3$     |      |       |              |               |
+| $R_4$     |      |       |              |               |
+| $R_5$     |      |       |              |               |
+
+### Miscellaneous
+
+| Measurement              | Value | Ideal Value |
+| ------------------------ | ----- | ----------- |
+| $R_{1_{calc}}\ (\Omega)$ |       |             |
+| $R_{2_{calc}}\ (\Omega)$ |       |             |
+| $R_{3_{calc}}\ (\Omega)$ |       |             |
+| $a_a$                    |       |             |
+| $a_b$                    |       |             |
+| $a_c$                    |       |             |
+| $P_{3\phi_p}\ (W)$       |       |             |
+| $P_{3\phi_s}\ (W)$       |       |             |
+

lab6/lab6Data.md

@@ -0,0 +1,170 @@
+# Experimental Data
+
+## Delta-Wye Transformer
+
+### Voltage (V)
+
+| Location    | Line   | Phase | Line (ideal) | Phase (ideal) |
+| ----------- | ------ | ----- | ------------ | ------------- |
+| Primary 1   | 206.63 | 119.3 | 207.85       | 120           |
+| Primary 2   | 206.63 | 119.3 | 207.85       | 120           |
+| Primary 3   | 203.34 | 117.4 | 207.85       | 120           |
+| Secondary 1 | 101.84 | 58.8  | 103.92       | 60            |
+| Secondary 2 | 98.21  | 56.7  | 103.92       | 60            |
+| Secondary 3 | 98.03  | 56.6  | 103.92       | 60            |
+
+$$
+V_L=\sqrt3V_\phi=\sqrt3(119.3V)=206.63
+$$
+
+
+
+### Current (A)
+
+| Location    | Line   | Phase  | Line (ideal) | Phase (ideal) |
+| ----------- | ------ | ------ | ------------ | ------------- |
+| Primary 1   | 0.1175 | 0.1175 |              |               |
+| Primary 2   | 0.1170 | 0.1170 |              |               |
+| Primary 3   | 0.2779 | 0.2779 |              |               |
+| Secondary 1 | 0.0100 | 0.0100 |              |               |
+| Secondary 2 | 0.367  | 0.367  |              |               |
+| Secondary 3 | 0.367  | 0.367  |              |               |
+
+### Miscellaneous
+
+| Measurement              | Value | Ideal Value |
+| ------------------------ | ----- | ----------- |
+| $R_{1_{calc}}\ (\Omega)$ |       | 600         |
+| $R_{2_{calc}}\ (\Omega)$ |       | 600         |
+| $R_{3_{calc}}\ (\Omega)$ |       | 600         |
+| $a_a$                    |       | 0.5         |
+| $a_b$                    |       | 0.5         |
+| $a_c$                    |       | 0.5         |
+| $P_{3\phi_p}\ (W)$       |       |             |
+| $P_{3\phi_s}\ (W)$       |       |             |
+
+
+
+## Delta-Delta Transformer
+
+### Voltage (V)
+
+| Location    | Line  | Phase | Line (ideal) | Phase (ideal) |
+| ----------- | ----- | ----- | ------------ | ------------- |
+| Primary 1   | 118.0 | 118.0 | 120          | 120           |
+| Primary 2   | 121.0 | 121.0 | 120          | 120           |
+| Primary 3   | 117.0 | 117.0 | 120          | 120           |
+| Secondary 1 | 59.4  | 59.4  | 60           | 60            |
+| Secondary 2 | 59.7  | 59.7  | 60           | 60            |
+| Secondary 3 | 59.9  | 59.9  | 60           | 60            |
+
+### Current (A)
+
+| Location    | Line   | Phase | Line (ideal) | Phase (ideal) |
+| ----------- | ------ | ----- | ------------ | ------------- |
+| Primary 1   | 0.1244 |       |              |               |
+| Primary 2   | 0.1230 |       |              |               |
+| Primary 3   | 0.1253 |       |              |               |
+| Secondary 1 | 0.1735 |       |              |               |
+| Secondary 2 | 0.1711 |       |              |               |
+| Secondary 3 | 0.1695 |       |              |               |
+
+### Miscellaneous
+
+| Measurement              | Value | Ideal Value |
+| ------------------------ | ----- | ----------- |
+| $R_{1_{calc}}\ (\Omega)$ |       | 600         |
+| $R_{2_{calc}}\ (\Omega)$ |       | 600         |
+| $R_{3_{calc}}\ (\Omega)$ |       | 600         |
+| $a_a$                    |       |             |
+| $a_b$                    |       |             |
+| $a_c$                    |       |             |
+| $P_{3\phi_p}\ (W)$       |       |             |
+| $P_{3\phi_s}\ (W)$       |       |             |
+
+
+
+## Delta-Delta With Split Phase Transformer
+
+### Voltage (V)
+
+| Location  | Line  | Phase | Line (ideal) | Phase (ideal) |
+| --------- | ----- | ----- | ------------ | ------------- |
+| Primary 1 | 120.2 | 120.2 | 120          | 120           |
+| Primary 2 | 118.5 | 118.5 | 120          | 120           |
+| Primary 3 | 119.1 | 119.1 | 120          | 120           |
+| $R_1$     | 114.3 | 114.3 | 120          | 120           |
+| $R_2$     | 113.7 | 113.7 | 120          | 120           |
+| $R_3$     | 116.0 | 116.0 | 120          | 120           |
+| $R_4$     | 55.9  | 55.9  | 60           | 60            |
+| $R_5$     | 57.1  | 57.1  | 60           | 60            |
+
+### Current (A)
+
+| Location  | Line   | Phase | Line (ideal) | Phase (ideal) |
+| --------- | ------ | ----- | ------------ | ------------- |
+| Primary 1 | 1.2    |       |              |               |
+| Primary 2 | 1.2    |       |              |               |
+| Primary 3 | 1.2    |       |              |               |
+| $R_1$     | 1.48   |       |              |               |
+| $R_2$     | 1.21   |       |              |               |
+| $R_3$     | 1.19   |       |              |               |
+| $R_4$     | 0.1941 |       |              |               |
+| $R_5$     | 0.1484 |       |              |               |
+
+### Miscellaneous
+
+| Measurement              | Value |
+| ------------------------ | ----- |
+| $R_{1_{calc}}\ (\Omega)$ |       |
+| $R_{2_{calc}}\ (\Omega)$ |       |
+| $R_{3_{calc}}\ (\Omega)$ |       |
+| $a_a$                    |       |
+| $a_b$                    |       |
+| $a_c$                    |       |
+| $P_{3\phi_p}\ (W)$       |       |
+| $P_{3\phi_s}\ (W)$       |       |
+
+
+
+## Delta-Delta With Split Phase Transformer - Unbalanced Load
+
+### Voltage (V)
+
+| Location  | Line | Phase |
+| --------- | ---- | ----- |
+| Primary 1 |      | 120.9 |
+| Primary 2 |      | 118.9 |
+| Primary 3 |      | 2.4   |
+| $R_1$     |      | 3.5   |
+| $R_2$     |      | 4.2   |
+| $R_3$     |      | 115.1 |
+| $R_4$     |      | 56.9  |
+| $R_5$     |      | 60.6  |
+
+### Current (A)
+
+| Location  | Line   | Phase |
+| --------- | ------ | ----- |
+| Primary 1 | 1.34   |       |
+| Primary 2 | 0.0513 |       |
+| Primary 3 | 1.46   |       |
+| $R_1$     | 0.78   |       |
+| $R_2$     | 1.26   |       |
+| $R_3$     | 0      |       |
+| $R_4$     | 1.28   |       |
+| $R_5$     | 0      |       |
+
+### Miscellaneous
+
+| Measurement              | Value |
+| ------------------------ | ----- |
+| $R_{1_{calc}}\ (\Omega)$ |       |
+| $R_{2_{calc}}\ (\Omega)$ |       |
+| $R_{3_{calc}}\ (\Omega)$ |       |
+| $a_a$                    |       |
+| $a_b$                    |       |
+| $a_c$                    |       |
+| $P_{3\phi_p}\ (W)$       |       |
+| $P_{3\phi_s}\ (W)$       |       |
+

lab6/simulationAttempt.dat

@@ -0,0 +1,31 @@
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+<indep V1.I 1>
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+<indep _net0.V 1>
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lab6/simulationAttempt.sch

@@ -0,0 +1,62 @@
+<Qucs Schematic 0.0.19>
+<Properties>
+  <View=0,0,800,800,1,0,0>
+  <Grid=10,10,1>
+  <DataSet=simulationAttempt.dat>
+  <DataDisplay=simulationAttempt.dpl>
+  <OpenDisplay=1>
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+  <FrameText2=Date:>
+  <FrameText3=Revision:>
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