Distribution system and power quality

Cal Poly Pomona ECE 5750 Distribution System and Power Quality – Instructor Dr. Ha Thu Le

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California State Polytechnic University Pomona

Department of Electrical and Computer Engineering

ECE 5750 Distribution system and power quality – Spring 2020

Final exam Exam policy:

1. The exam is open-book and take-home. Students can use any materials such as lecture PPT, books, and notes. Any computer program may be used.

2. Exam duration: From 9am May 15 to midnight May 17, 2020.

3. NO discussion with anyone is allowed during exam.

4. Submission: Submit a soft copy of the solution to the instructor via email. Also submit a code and/or Simulink file as specified in the exam question(s) to the instructor via email.

Problem 1

Consider the feeder in the following figure.

The substation transformer is connected to an infinite bus. The infinite bus voltages (i.e. the substation primary voltages) are balanced and being held at 138 kV for all power-flow problems. The substation transformer ratings are:

5000 kVA, 138 kV delta – 25 kV grounded Y, Z = 1.7 + j8.5 %

The phase impedance matrix for a four-wire wye line between Node 2-3 is

The four-wire wye feeder between Node 2-3 is 9.5 miles long. An unbalanced wye-connected load is located at Node 3 and has the following values:

Phase a: 700 kVA at 0.85 lagging power factor

Phase b: 600 kVA at 0.90 lagging power factor

Phase c: 1020 kVA at 0.95 lagging power factor

Cal Poly Pomona ECE 5750 Distribution System and Power Quality – Instructor Dr. Ha Thu Le

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Two single-phase loads are also located at Node 3 and have the following values:

Load 1: 120 kVA at 0.82 lagging power factor, connected to Phase a

Load 2: 100 kVA at 0.92 lagging power factor, connected to Phase c

Assuming that the regulators are in the neutral position:

1) Determine the forward and backward sweep matrices for the substation transformer and the line segment.

2) Use the modified ladder technique to determine the line-to-ground voltages at all nodes. Use a tolerance of 0.0001 per unit.

3) Calculate all node voltages in volts, in per unit, and on a 120-V base.

Problem 2

Consider the following system where a battery is connected to a load via a 3-phase converter. The system diagram is shown in Fig. 1 below and its Simulink file is provided via email.

Fig. 1 Battery and converter system generating harmonics

The battery DC power is converted to AC 60-Hz power by the 3-phase converter to supply a 240-V 3- phase AC resistive load. The converter generates a number of harmonics. Therefore, the load voltages and currents are severely distorted, as seen by the scopes (IC Load, VC Load, Converter, and Load).

Design a filter to reduce and/or eliminate the harmonic content of the converter output. Perform the following task:

1) Use a Fourier waveform analyzer (e.g. FFT function, a spectrum analyzer, or other waveform analyzing functions) to determine significant harmonic voltages and currents that the converter generates. Provide a list of the frequencies and magnitudes (as percentage of the fundamental) of the obtained voltage and current harmonics (up to harmonic order 55 or 3300Hz). Also include a graph of the frequency spectrum to show the voltage harmonics and a graph to show current harmonics.

Hint: Run the provided m-file (an example by Matlab) to see how to use FFT function to analyze a waveform and obtain its frequency spectrum.

Cal Poly Pomona ECE 5750 Distribution System and Power Quality – Instructor Dr. Ha Thu Le

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2) Based on the result in Part 1, design a filter to eliminate the most significant harmonic component(s). The design MUST include calculation of the filter parameters. If you design a single-tuned LC filter, calculate its capacitance and inductance values. NO need to evaluate the filter duty requirements.

Note: You can have more than one filter to reduce the harmonics. The filter must be 3-phase.

3) Connect the LC filter to the output terminals of the converter (as shown in Fig. 1) and verify by simulation that the filter does eliminate most of the harmonics. If this is true, the load voltages and currents must be SINUSOIDAL with little or no noises. Include a graph of the load IC and VC to show that the waveforms are clean and sinusoidal after the filter is connected.

4) Submit the *.slx file with the designed filter via email to the instructor to prove that your filter is actually effective. Make sure to replace the word “Student” in the *.slx file name with your last name before submission.

Problem 3

(Optional, Extra Credit of 15 points)

A current i(t) through a load is non-sinusoidal, as shown in the figure below.

Determine:

1) The Trigonometric Fourier series of i(t).

2) The RMS value of the fundamental component of the load current. Consider the first order harmonic component as the fundamental component for this circuit.

3) The RMS value of the harmonic load current (i.e. including all harmonics except the fundamental component)

4) The RMS value of the load current (i.e. including the DC, the fundamental, and all harmonics)

5) The THD of the load current.

Note: Include the first 5000 harmonics (zero and non-zero values) for calculating the RMS values in part 2 through 4.