University of Saskatchewan s2

Total Number of Pages: 3 - 1 - University of Saskatchewan Department of Electrical Engineering EE 868.3 Digital Techniques for Power System Measurements & Protection (Spring & Summer Term 1 & 2) Final Examination (Classroom, Open-Book Examination)

Examination Paper Hand-In Time: July 13, 2012 (9:00 am) Return Time: 2:00pm Instructor: Dr. Rama Gokaraju Total Marks: 50

Instructions:

1) Important: After the exam, return the question paper along with your answer booklets (including the unused ones). 2) This examination paper consists of 4 problems and 3 pages in total. 3) You are not permitted to discuss or take assistance of others to solve the examination problems. You would be severely penalized if your solutions point to the above. 4) Your solutions should be methodical. You would be penalized if your solutions are illegible. 5) Mark allotted for each problem is shown on the right margin.

Problem 1

An admittance relay (mho relay) is used protect a transmission line with the line impedance equal to (0.02+j0.2593) Ω’s. The base values are: 2,220 MVA, 24 kV. A fault was applied at the middle of the line.

The voltage and current samples at the relay location at the beginning of the line were recorded from PSCAD/EMTDC simulations (sampled at 720 Hz) and are tabulated below. The excel sheet corresponding to this table will be supplied electronically at the beginning of the examination. The signals consist of an ac component of 60 Hz frequency and were sampled at 720 Hz. The quantized values of its samples are listed below:

Sample Current Samples Number (kA) Voltage Samples (kV) 1 23.95996087 12.54551889 2 13.75937546 3.576988863 3 -0.127534042 -6.349868359 4 -13.98024356 -14.57549614 5 -24.08740016 -18.89612394 6 -27.74115054 -18.15419102 7 -23.96261415 -12.5484741 8 -13.76413611 -3.580831531 9 0.121940408 6.346167754 10 13.9753147 14.57292919 11 24.08445616 18.89537862 12 27.74098024 18.15546728 13 57.80176871 6.646675663 14 70.69002181 1.108431619 Total Number of Pages: 3 - 2 -

15 59.58127783 -4.874016289 16 27.3154443 -9.583875922 17 -17.01646931 -11.6074956 18 -60.69834469 -10.36383355 19 -91.3927399 -6.301521721 20 -100.8758198 -0.673990084 21 -87.10722055 4.942038235 22 -54.23316581 9.116785383 23 -11.04877784 10.86260791 24 31.29211576 9.769335597 25 61.8306704 6.07122196 26 72.40581899 0.66236782 27 59.94054673 -5.030168823 28 27.67410998 -9.397254141 29 -15.42209531 -11.15772221 30 -57.18456243 -9.809715919 31 -85.94666856 -5.795854928 32 -93.9790757 -0.310716909 33 -79.47415806 5.123470155 34 -46.64779883 9.099950655 35 -4.304976151 10.64310142 36 36.47769184 9.378731712 37 65.01806222 5.604128357 38 73.66103923 0.263903724 39 59.90666344 -5.223425047 40 27.3732515 -9.323988936 41 -14.9713939 -10.85692994 42 -55.31589679 -9.388851407 43 -82.48500696 -5.37214693 44 -89.16563532 0.029468057 45 -73.80867641 5.328002194 46 -40.77186599 9.135740213 47 1.066919834 10.49385827

a) Use the Discrete Fourier Transform technique to estimate the magnitude and phase angle of the voltage and current phasors. Show the calculation steps clearly for one sample number. Plot the magnitude and phase angle of the current and voltage phasors versus time. b) Also, find the find the values of the impedance and plot the trajectory in an R, X plane. Show the mho circle for zone I protection in the impedance diagram (protects 80% of the line). c) Discuss the suitability of the DFT transformation technique, i.e. effect of noise, decaying dc component and other frequency components on the performance of the estimator.

15 Marks Total Number of Pages: 3 - 3 - Problem 2

Suppose a current signal consists of a 60 Hz ac component and a decaying dc component. The fundamental frequency is 60 Hz. The signal is sampled at 720 Hz.

The quantized values of its samples are listed below:

Sample Quantized Sample Quantized Sample Quantized No Value No Value No Value 1 0 17 1370 33 998 2 0 18 1706 34 480 3 0 19 1811 35 -36 4 0 20 1649 36 -418 5 0 21 1256 37 -567 6 0 22 730 38 -448 7 0 23 205 39 -96 8 0 24 -185 40 390 9 0 25 -342 41 876 10 0 26 -231 42 1229 11 0 27 113 43 1351 12 0 28 592 44 1205 13 0 29 1072 45 827 14 100 30 1418 46 316 15 433 31 1538 47 -195 16 901 32 1381 48 -571

Design a least squares filter for estimating the fundamental frequency component of the signal and the dc component of the signal. Also, estimate the time period of the decaying dc component. Use a 7-sample data window.

Show how the [A] matrix will look like. Show the numerical steps clearly for one sample number. 15 Marks Problem 3

Design the differential protection for a three-phase, 60 Hz transformer with the following nameplate ratings: 250 MVA, 15.75 kV/400 kV, 60 Hz, delta-star transformer. 10 Marks Problem 4

For relays Rd and Rg at buses D and G in Figure 1, determine the settings for the three zones of their distance relays. You may assume that the positive sequence impedance of line AB is (3+j30) Ω. In addition, you may assume that nothing beyond bus G needs backup. Assume I2/I3 = 0.5. Total Number of Pages: 3 - 4 -

Figure 1: System for Problem 4.

10 Marks

======