AC Power and Power Factor Correction ECE 2100 Circuit Analysis updated 8 January 2008 Pre-Laboratory Assignment Consider the circuit of Figure 1. The “load” consists of all circuit elements connected to V1. 1. This lab uses potentially lethal voltages. REVIEW SAFE LABORATORY PROCEDURES. Remember that capacitors must be handled carefully even when not connected as they store energy! 2. For C1 = 0uF (no capacitor present), find the equivalent impedance of the load (consisting of R1 and L1) at the indicated frequency of 60 Hz. Express your result in rectangular and polar coordinates. 3. Calculate the complex power S of the load (consisting of R1 and L1), the power dissipated by the resistor, and the inductor reactive power. As always, use proper units for all results. 4. Calculate the load (consisting of R1 and L) power factor. Indicate whether the power factor is leading or lagging. Figure 1. Power Factor Correction Circuit 15. Calculate the value of C1 needed to provide a unity load (now consisting of R1, L, and C1) power factor. 6. Using your SPICE engine, demonstrate that the value of C1 computed in pre-laboratory step 5 does indeed correct the power factor to 1. Do this by comparing the relative phase of the source voltage V and source current I. Note that in LTspice/SwitcherCAD III you can simply click on a node to plot the voltage or click on a voltage source to plot the current through the voltage source (you will need to multiply the current trace by a -1 as the current through the source is in the opposite direction of the indicated current). An example plot for C1 = 0uF is provided in Figure 2.TM 7. Bring an electronic copy of your simulation files to lab. Figure 2. Example Plot for the Circuit of Figure 1 Procedures Part One 1. TURN OFF POWER TO THE BENCH POWER SUPPLY UNIT. Insure that the AC voltage source is set to the zero position. Do not turn on power until instructed to do so. 2. Verify that the provided variable resistor is set to 50Ω using your DMM. 3. BEFORE PROCEEDING DISCHARGE ALL POSSIBLE CAPACITOR SUBSTITUTION BOX COMBINATIONS THROUGH R1. 4. Verify that the provided capacitor substitution box is set to “no capacitance.” 5. DO NOT TURN ON THE BENCH POWER SUPPLY. Build the circuit of Figure 1. 6. DO NOT TURN ON THE BENCH POWER SUPPLY. Connect a DMM to measure the source voltage V (AC RMS of course) and another DMM to measure the inductor voltage (AC RMS of course). 7. HAVE THE INSTRUCTOR CHECK YOUR CIRCUIT. 28. Turn on the bench power supply. Slowly rotate the dial until the source voltage is at 40V RMS as indicated by the voltage-measuring DMM. DO NOT EXCEED 40V. 9. Record the DMM voltages. TURN OFF POWER AND RETURN THE DIAL TO 0V RMS. 10. Use your measurements of laboratory procedure step 9 to compute the value of the inductor. Update your pre-laboratory computations using the measured value of L1. 11. DO NOT TURN ON THE BENCH POWER SUPPLY. Connect a DMM to measure the source voltage V (AC RMS of course) and another DMM to measure the source current I (AC RMS of course). Following directions from you instructor, setup a wattmeter to measure the real power of the load. 12. HAVE THE INSTRUCTOR CHECK YOUR CIRCUIT. 13. Turn on the bench power supply. Slowly rotate the dial until the source voltage is at 40V RMS as indicated by the voltage-measuring DMM. DO NOT EXCEED 40V. 14. Measure the voltage V and current I provided by the source. Use these measurements to compute the magnitude of the complex power S. 15. Measure the real power delivered to the load using the wattmeter. 16. Calculate the power factor of the load. 17. TURN OFF POWER AND RETURN THE DIAL TO 0V RMS. 18. Compare results from laboratory procedures steps 14-16 to hand analysis (USING YOUR MEASURED VALUE of L1) and simulation results. Use a table. Include error percentages (as usual). Part Two 19. Turn on the bench power supply. Slowly rotate the dial until the source voltage is at 40V RMS as indicated by the voltage-measuring DMM. DO NOT EXCEED 40V. 20. Set the capacitor substitution box to the value needed to achieve a unity power factor. Using appropriate experimental measurements verify that the load power factor is unity. 21. Now vary the capacitance between 0 and 100uF. For at least 7 capacitor values in this range, determine the load current I, the load voltage V, the magnitude of the complex power delivered to the load, the power dissipated in the resistor, and the load power factor. Use a table to organize your data and computations. 22. TURN OFF POWER AND RETURN THE DIAL TO 0V RMS. DISCHARGE ALL POSSIBLE CAPACITOR SUBSTITUTION BOX COMBINATIONS THROUGH R1. Analysis 1. Use the data from laboratory procedure 21 above to plot the load real power P vs. the 3capacitance C1 and the load current I vs. C1. Use a single piece of graph paper and a common horizontal axis for C1. What value of C1 results in the most efficient circuit in terms of power transfer from source to load? Justify. 2. Provide a phasor diagram (showing the load complex power, the capacitor, inductor, and resistor complex powers, the resistor voltage, and the voltage source voltage and current vectors) for two cases: a. C1=0, and b. C1 corresponding to the unity power factor case. 3. Provide a general conclusion on lessons learned from this experiment. Credits and Copyright Adapted from material developed by current and former ECE faculty, including Professor Joseph Kelemen. © 2008 Damon A. Miller. All rights reserved.