Chapter 1:

    1. Define the term Power System Harmonics
    2. Can any type of voltage/current distortion be modeled using harmonics?
    3. What is the purpose of a harmonic propagation study?
    4. What type of data do I need to conduct a harmonics study?

Chapter 2:

    1. Define (a) characteristic harmonics, (b) non-characteristic harmonics, (c) interharmonics, and (d) sub-harmonics.
    2. What are (a) total harmonic distortion, (b) telephone influence factor, and (c) transformer K-factor?
    3. What is the resonance in a power system? Please give some factors that contribute series and parallel resonance?
    4. Write down the solutions to power system harmonics that you know.

Chapter 3:

    1. Give four power-electronic type harmonic sources.
    2. Describe the advantages and disadvantages of the current injection model for static power converter used in harmonic simulation.
    3. In harmonic simulation, why we need more advanced static power converter models other than the current injection model?

Chapter 4:

    1. What causes magnetic core saturation?
    2. How to model magnetic core saturation?
    3. What happens to three-phase transformers in unbalanced operation condition?
    4. What is the major impact of Geomagnetic Disturbance (GMD) to power transformers?


Chapter 5:

Design problem taken from the paper "Distribution System Harmonic Filter Planning"

by T. H. Ortmeyer and T. Hiyama


Table A1. Per cent impedances for source and line segments, to a 1MVA, 13.2 KV base.

Line segment %R %X Line segment %R %X
Source 0.033 0.532 1-4 0.129 0.278
1-2 0.079 0.174 4-10 0.040 0.096
2-12 0.103 0.246 4-11 0.072 0.171
1-3 0.045 0.107 11-14 0.019 0.045
3-5 0.519 1.209 14-15 0.069 0.164
3-6 1.191 2.968 14-16 0.105 0.251
3-7 0.074 0.160 16-17 0.171 0.354
5-8 1.046 2.282 17-18 0.056 0.134
5-9 0.145 0.127      

Capacitor sizes--


Load Data (series model, primary connected):

Node P(MW) Q(MVAR)
2 0.224 0.038
7 1.911 0.837
9 0.657 0.283
15 1.110 0.422
17 1.395 0.521
6 1.515 0.677
8 0.200 0.086
10 1.692 0.655
13 0.539 0.090
16 0.773 0.292
18 3.89 1.438
Total loading    



    1. Model the system and do a frequency scan with 1 amp injected at node 8, for both no load and full load cases. All capacitor banks should be in service.
    2. This distribution system has been determined to have significant harmonic levels at the fifth and seventh harmonics. Furthermore, it has been determined that harmonic voltages are highest at peak load conditions. Therefore, the harmonic models of steps 3 and 4 have been developed.
    3. Model the background fifth harmonic current level with 300 hertz current sources at each load site. The magnitude of each of these sources should be 2.8% of the 60 hertz load current at that site. Assume all harmonic sources are in phase.
    4. Model the background seventh harmonic current level in the same fashion, with 420 hertz current sources of 2.8% of the 60 hertz load current.
    5. Using the results of steps 2 and 3, use the technique described in the paper "Distribution System Harmonic Filter Planning", Section 3, to select capacitor locations which are candidates for harmonic filtering. Investigate these options by replacing the capacitors at the candidate sites with a series tuned filter. For a series tuned filter, select a tuning coil using the formula:
    6. where n= tuned frequency, in per unit, Xc is the 60 hertz capacitive impedance of the bank, and XL is the 60 hertz inductive impedance of the tuning coil. A typical tuning frequency is 4.9 per unit-- just under the 5th harmonic. Note that capacitors in a series tuned filter experience a higher voltage rating than line voltage, and the tuning coils consume vars. Therefore, for a given Xc, the tuned filters deliver less vars than a capacitor bank. You will therefore need to adjust the value of Xc for the filter in order to get a similar level of vars as the capacitor bank it replaces.

    7. Continue replacing capacitor banks with series tuned filters until voltage objectives at both the fifth and seventh harmonics are reached. Use the procedures of "Distribution System Harmonic Filter Planning".
    8. Develop a capacitor switching strategy according to Section 5 of the paper. Assume that 50% of the system capacitors will be on time clocks.

Transmission Network Exercises

This exercise involves the transmission test system, Test System 1 from Chapter 10.

    1. At the fifth or seventh harmonic frequency, calculate the component sensitivities using the adjoint method as discussed in Chapter 5 and the reference listed below. Identify components of low sensitivity- replace .series elements with short circuits and shunt elements with open circuits. Run a frequency scan on the resulting reduced system, and compare with the original frequency scan given in Chapter 10.
    2. Using the sensitivity results of Step 1,
      a. Identify high sensitivity components. One by one, remove these from the system model and verify that their absence causes significant changes in the frequency scan at frequencies near the study frequency.
      b. Identify low sensitivity components. Remove several of these one at a time and verify that their absence has relatively little effect on the frequency scan in the vicinity of the study frequency.
    3. Use the bilinear theorem to analyze the sensitivity of the results to the system equivalent of node 1.

Reference. "An Improved Harmonic Modeling Technique for Transmission Networks", by M. Fayyaz Akram, Thomas Ortmeyer, and James Svoboda, IEEE Transactions on Power Delivery, Vol. 9, No. 3 (July, 1994). Pp. 1510-1516.


Chapter 6:

    1. What is the difference between current source and voltage source "frequency scans?" What types of harmonic situations do you investigate with each method?
    2. What are the analytical step required to conduct a harmonic study using the "current source" method? What common freatures do these steps share with the "current source" frequency scan?
    3. Under what conditions should you consider using a more detailed harmonic analysis algorithm, for example time-domain simulation, instead of the more common "current source" method?


Chapter 7:

    1. Explain what harmonic phenomena are better studied with time domain analysis.
    2. Can you find two examples from your own professional applications that would require time domain analysis?
    3. Which basic concept of system modeling does the frequency domain analysis use? Which one does the time domain analysis use? Compare and contrast these concepts.
    4. Why nonlinear devices, such as the transformer, cannot be directly represented in the frequency domain studies?
    5. What is achieved by dynamic network reduction?
    6. Provide an example from your own applications where dynamic network reduction is effective and another example where it is not necessary.
    7. If you consider the utility system that interconnects to your facility, what kind of information would you need to effectively represent it in a harmonic study?
    8. Under what conditions can you represent a converter as a rigid harmonic current-source?
    9. What information do you gain when you use a detailed converter model?
    10. Which loop(s) of the converter control should we represent in a time simulation and which are not critical?
    11. Describe the switching function and the associated relations between ac and dc quantities of a square wave forced-commutated voltage-sourced inverter, such as one used in motor drive systems.
    12. Why is it important to let the simulation run for a few periods before we apply FFT?

Chapter 8:

    1. Why is three-phase harmonic analysis needed for an adequate telephone interference assessment?
    2. Is third harmonic always in zero sequence?
    3. Can a three-phase variable speed drive produce zero sequence harmonics?
    4. Why DC current is harmful to transformers and their connected power systems?
    5. What are the zero and positive sequence harmonic impedances of a zero sequence harmonic trap?
    6. Why are there 2nd harmonics in the harmonic spectra plot (Figure 8.11) for case 3?

Chapter 9:

    1. What is the basic philosophical difference between IEEE and IEC regarding limiting harmonics in power systems?
    2. Explain the difference between demand current and fundamental current?
    3. Explain the difference between THD and TDD?
    4. Considering the philosophy of IEEE-519, for what corrective actions is the end-user responsible? For which corrective actions is the supplying utility responsible?
    5. Under what conditions (in terms of end-user harmonic production) is a detailed study not required? When is a detailed study required?
    6. How are the available fault MVA and maximum average end-user demand used in assessing compliance with the limits given in IEEE-519?
    7. Given a system with a Ssc of 36MVA, determine if a load consisting of 2kVA of florescent lighting and 4kVA of 12-pulse converters would meet the automatic acceptance criteria.
    8. Given the above system, operating at 13.8kV, determine the appropriate voltage and current harmonic distortion limit tables based on a demand of 7kVA.

Chapter 10:

    1. What are the basic parameters for representing linear loads and transmission lines in harmonic penetration studies?
    2. How should the phase angles of the harmonic current sources be adjusted?
    3. How should induction motors be represented in harmonic studies?
    4. Why is the frequency dependence of resistances normally neglected in harmonic studies?




  1. In general a considerable number of electric loads are located close together and supplied from a main distribution point. How should they be differentiated according to their electric characteristics?
  2. In frequency domain harmonic studies, the nonlinear part of the electric loads should be always represented by an ideal harmonic current or eliminated, but never represented by a passive component. Why? Discuss.
  3. When modeling linear loads in harmonics studies can the real power (P) and reactive power (Q) values be directly converted into resistances and inductances? Explain.
  4. Is there a simple / unified linear load model that can be used in any study? Why not?
  5. Can power factor correction capacitors be neglected in harmonic studies?
  6. How important is the representation of the skin effect on harmonic studies?
  7. Can the linear loads modeling affect compliance with harmonic voltage distortion standards?
  8. When dealing studying existing systems how should the background distortion be represented?
  9. Using a harmonic analysis tool, set up the above problem and calculate the harmonic voltage and current distortions. For simplicity, assume that the system impedance has no resistance and that there is no transformation. Also, assume that both non-linear loads have a current spectrum based on the "text book" method of the reciprocal of the harmonics for (nh +/- 1), where h represents the 12-pulse drive and n in the integer multiple.