NAME ____________________________ Department of Electrical and Computer Engineering University of Idaho Moscow, Idaho 1. This is Exam #1 for ECE 420 for the Spring 2016 semester. 2. This exam consists of four problem groups on four pages and a cover sheet. 3. You have 50 minutes to complete this exam. 4. The format is open book and open notes. You may use a calculator and a desktop or laptop personal computer if you wish. If you have any computer results for which you want credit, please send them to the professor hhess@uidaho.edu. Please place your name on each page and file for which you want credit. 5. Please answer the questions in the space provided. If you need more writing space, please use the back of the preceding sheet. If you want to present additional page(s) or computer files generated during the allotted exam period, clearly indicate in the original problem space that such additional material exists. Failure to make such a notation will normally cause the grader to ignore your additional work. 6. You may disassemble this exam if you wish. If you do so, please place your name on each separated page for which you want credit. Problem Maximum 1. _________ (20) AC Power 2. _________ (40) Three Phase Transformer 3. _________ (20) Three Phase AC Power Basics 4. _________ Total _________ (20) (100) AC Power Basics NAME ____________________________ 1. (20 points) AC Power. Consider the circuit shown below. It is an AC circuit, 60 Hertz, 120VAC rms single phase. Its output voltages are as shown. Impedances are given in Ohms. 0.18
j0.30
j0.24
0.18
j0.42
j0.30
+
j0.24 +
jXs
+
120 / 0° V
+
-
-
Find the current in Load 2, magnitude and phase. Load
115.2 /-2 V
1
o
117.6 /-3oV
Load
2
-
NAME ____________________________ 2. (40 points) Three Phase Transformer. We build a three phase transformer from a set of three identical single‐phase transformers. The resulting three phase transformer has 69kV line to line rms connected in Delta on the low voltage side and 230kV line to line rms connected in Y on the high voltage side. Assume ideal transformers. You may attach a zero degrees phase angle to the voltage or current of your choice on the input (low voltage) side of the transformer. a. (15 points) Find the turns ratio of one of the single phase transformers. b. (25 points) If the current in the 69kV winding is 10kA and the input power factor to this transformer is 0.95 lagging, find a line current and a line to line voltage, magnitude and phase, on the other side of transformer. NAME ____________________________ 3. (20 points) Three Phase AC Power Basics. At the end of a distribution line, there is a three phase load connected in delta and a three phase load connected in Y. The three phase delta‐
connected load has a real power of 50kW with an inductive reactive power of 20kVAr. The three phase Y‐connected load absorbs 70kVA at a power factor of 0.91 lagging. The three distribution lines each have a current of 150 Amps, arrayed in a balanced three phase positive sequence. Each of the three lines have an impedance that is a series combination of 0.080 Ohms resistance and 0.62 Ohms reactance. a. (10 points) Find the line’s losses. Losses are real power. b. (10 points) Find this small distribution system’s energy efficiency. The output is the combined loads; the input is the combined loads and the distribution. NAME ____________________________ 4. (20 points) AC Power Basics. A certain single phase electrical load absorbs 1.0kW and 0.350 kVAr (inductive). Its terminal voltage is 100V ac rms at a frequency of 50Hz (Period=20ms). Determine a current that would give this amount of real and reactive power consumption. Plot the voltage and current, labelling the peak value of each and the phase difference between them, if any.