Test Systems for Harmonics Modeling and Simulation

*Task force members and contributors are: R. Abu-hashim, R. Burch, G. Chang, M. Grady, E. Gunther, M. Halpin, C. Hatziadoniu, Y. Liu, M. Marz, T. Ortmeyer, V. Rajagopalan, S. Ranade, P. Ribeiro (vice chair), T. Sims, W. Xu (chair, editor).

Abstract - This paper presents three harmonic simulation test systems. The purpose is to demonstrate guidelines for the preparation and analysis of harmonic problems through case studies and simulation examples. The systems can also be used as benchmark systems for the development of new harmonic simulation methods and for the evaluation of existing harmonic analysis software.

10.1 Introduction

Harmonic studies have become an important aspect of power system analysis and design in recent years. Harmonic simulations are used to quantify the distortion in voltage and current waveforms in a power system and to determine the existence and mitigation of resonant conditions. Many digital computer programs are available for harmonic analysis. New analysis techniques are being developed. With a wide variety of solution methods and modeling assumptions implemented in many different programs, there is a need for benchmark test systems so that the features and results of the programs can be evaluated and compared.

* Editors' Note: It is not guaranteed that the web page will always be available. Therefore, the test systems are given in the Appendix Section B.

10.2 Test System No.1: A 14-Bus Balanced Transmission System

This test system contains two harmonic sources. One is a twelve-pulse HVDC terminal at bus 3 and the other is a SVC at bus 8 (Figure 10.1 and Figure 10.2). Because the system has balanced bus loads and the transmission lines are transposed, a balanced harmonic analysis is generally sufficient for determining harmonic distortion levels in this case. Main harmonic analysis issues to be demonstrated by this test system are:

1. The need to solve fundamental frequency load flows for harmonic analysis. The load flow results affect the magnitudes and phase angles of the harmonic current injected from harmonic sources. Correct representation of the phase angles are important for systems with multiple harmonic sources [1]. The harmonic filters can have a large impact on the load flow results.
2. The harmonic cancellation effects due to Y-Y and Y-Delta transformer connections (at the HVDC terminal) and the impact of other harmonic sources (the SVC). For this purpose, the HVDC terminal is modeled as two six-pulse harmonic sources.
3. The effects of using different line models such as the distributed-parameter model and the lumped pi-circuit model in harmonic resonance assessment.

f1

Complete data for this system are shown in Tables 10.1 to 10.4. Key modeling and simulation features for this case are:

1. All transmission lines are modeled using a distributed-parameter line model. Long line effects are included in the model. Figure 10.3 shows the effects of using different line models. The curves are the frequency scan results seen at the HVDC bus (bus 3). The results suggest that the long-line effects should be included for long distance transmission lines.
2. The generators are modeled as either slack or PV buses for the fundamental frequency load flow solutions and as sub-transient reactance for the harmonic analysis. The sub-transient reactances are 0.25 per-unit.
3. Transformers are modeled using short-circuit impedances. The winding connections are represented in the model so that the phase-shifting effects on harmonic currents are included. If harmonics from transformer saturation are of interest, the magnetizing branches with saturation characteristics should be modeled. The off-nominal tap ratios of all transformers are 1.0 per-unit in this particular case.
4. The loads are modeled as constant power loads for load flow solutions and as impedances for harmonic solutions. The harmonic impedances are determined according to the 3^rd model recommended in reference [2].
5. Harmonic filters are modeled as shunt harmonic impedances. All filters are the single-tuned type.
6. The HVDC terminal is modeled as two six-pulse bridge rectifiers according to the model of reference [3]. Because voltage distortion at the HVDC terminal is small, sensitivity studies showed that the terminal can be modeled as two harmonic current sources. The source spectra is provided in Table 10.4. It must be noted that the magnitudes and phase angles should be scaled and shifted according to the load flow results [1]. The HVDC terminal is modeled as a constant power load in the load flow solution.
7. The SVC consists of harmonic filters and a delta-connected TCR. The TCR was modeled using the model of reference [1]. The firing angle is about 120 degrees. To facilitate the solution of the case using programs without a TCR model, the equivalent load and harmonic spectra of the TCR are listed in this paper. With this information, the TCR can be represented as a constant reactive power load in load flow solution and a harmonic current source in harmonic analysis. Because the SVC is relatively small as compared to the HVDC, its impact on overall system harmonic distortion is not significant.
8. The harmonic distortion results were obtained using the harmonic iteration method described in reference [1]. Because the results showed that the voltage distortions at the harmonic source buses are small and the equivalent harmonic current injections from the HVDC and SVC are made available in this paper, a non-iterative harmonic solution method which models harmonic sources as harmonic current injections should give the same solution results.

10.3 Test System No.2: A 13-Bus Unbalanced Utility Distribution System

This system is based on the IEEE 13 bus radial distribution test feeder [4]. The system is unbalanced and serves as a benchmark system for unbalanced harmonic propagation studies. The system was used in [1] for illustrative purposes and, with additional modifications, is proposed here as a harmonics test system.

* Editors Note: Click here to link to the data for Test System II.

As demonstrated in [1], relatively moderate variations in the models can have a significant impact on results. The test system is specified in a way that highlights all of these issues. The Alternative Transients Program was used to calculate harmonic propagation in the system [5,6]. Partial results are shown in Table 10.5 and Figure 10.5.

f4

Figure 10.4. Test System 2 - Unbalanced Distribution System

Table 10.5. Voltage THD (Fundamental Frequency Component)

f5

Modeling and simulation features for this case are:

1. Conventional loads were modeled as constant RL impedances obtained from the given kVA at 60Hz.
2. Harmonic producing loads were modeled as current sources with the specified spectra using the ‘Models’ capability of the ATP. Magnitudes were scaled based on the fundamental component of load current and phase angles were adjusted based on the phase angle of the voltage across the load obtained from the fundamental frequency solution.
3. The motor and the capacitor at node 34 were assumed out of service. For harmonic frequencies, the motor should be modeled using its sub-transient impedance (or locked rotor impedance).
4. The voltage regulator was not modeled. Rather, the substation transformer secondary taps on the three-phases were set at +15,+10 and +13, respectively.
5. Lines were modeled as mutually coupled p branches.

For the case studied, the voltage distortion levels are low. This is because several loads are connected phase-phase and harmonic phase angles are modeled. As described in reference [1], significantly different results are obtained depending on the choice of load models and harmonic current source models. It is noted that in the examples in [1], all loads were assumed to be connected phase-ground, the motor and capacitor at node 34 are in service and harmonic source spectra were different from the ones used here.

nbsp;

10.4 Test System No.3: A 13-Bus Balanced Industrial Distribution System

This test case consists of 13 buses and is representative of a medium-sized industrial plant. The system is extracted from a common system that is being used in many of the calculations and examples in the IEEE Color Book series [7]. The plant is fed from a utility supply at 69 kV and the local plant distribution system operates at 13.8 kV. The system is shown in Figure 10.6 and described by the data in Tables 10.6-10.9. Due to the balanced nature of this example, only positive sequence data is provided. Capacitance of the short overhead line and all cables are neglected.

f6

Additional data used to conduct a harmonic analysis of the example industrial system include the following:

1. System equivalent impedance. For this study, the system impedance was determined from the fault MVA and X/R ratio at the utility connection point. These values are 1000 MVA and 22.2, respectively. Driving point impedance (as a function of frequency) at the connection point was not available, but should be used whenever possible.
2. The local (in-plant) generator was represented as a simple Thevenin equivalent. The internal voltage, determined from the converged power flow solution, is 13.98/-1.52° kV. The equivalent impedance is the sub-transient impedance which is 0.0366+j1.3651W.
3. The plant power factor correction capacitors are rated at 6000 kvar. As is typically done, leakage and series resistance of the bank are neglected in this study.
4. The displacement power factor for the drive load is 0.97 lagging. This high power factor is typical of drives operated at or near full load.

Table 10.6. Per-Unit Line and Cable Impedance Data (base values: 13.8 kV, 10,000 kVA)

Specific issues related to modeling for harmonic analysis must also be considered if the results presented here are to be obtained using different analysis programs. Modeling considerations applicable to this example include:

The results of a harmonic analysis of the system of Figure 10.6 are given in Table 10.10. Fundamental, fifth, and seventh voltage harmonic amplitudes and THD_V are given for each of the system buses. These results, along with those obtained from a fundamental frequency power flow study (shown in Table 10.8), give an accurate description of the voltage profiles in the plant.

10.5 Conclusions

Complete data for three harmonic test systems has been presented in this chapter. The systems can be used as benchmark systems for the development of new harmonic analysis methods and for the evaluation of existing harmonic software. Researchers, developers and users of harmonic analysis programs are encouraged to use these systems to test their programs and report their comments to the IEEE PES Harmonics Modeling and Simulation Task Force.

Table 10.10: Plant Harmonic Voltage Distortion Summary.

10.6 Acknowledgment

The Task Force would like to acknowledge the support of the IEEE PES Harmonics Working Group chaired by Mr. T. Gentile. Case 1 was prepared by W. Xu, Case 2 by S.J. Ranade, and Case 3 by M. Halpin. Results were verified by R. Burch, M. Halpin, C.J. Hatziadoniu, and T.H. Ortmeyer.

10.7 References

1. IEEE Task Force on Harmonics Modeling and Simulation, "Modeling and Simulation of the Propagation of Harmonics in Electric Power Networks, Part 1 & 2", IEEE Trans. on Power Delivery, Vol. 11, No.1 January 1996, pp. 452-474.
2. CIGRE Working Group 36-05, "Harmonics, Characteristic Parameters, Methods of Study, Estimates of Existing Values in the Network", Electra, no. 77, July 1981, pp.35-54.
3. W. Xu, J.E. Drakos, Y. Mansour, A. Chang, "A Three-Phase Converter Model for Harmonic Analysis of HVDC Systems", IEEE Trans. on Power Delivery, Vol. 9, No.3, July 1994, pp.1724-1731.
4. IEEE Distribution Planning Working Group Report," Radial Distribution Test System," IEEE Trans. on Power Systems, Vol. 6, No.3, Aug.1991, pp.975-985.
5. Canadian/American EMTP User's Group "Alternative Transients Program(ATP) Rule Book" , Portland, OR, 1995.
6. H.W. Dommel, "Electromagnetic Transients Program Reference Manual (EMTP Theory Book)", Prepared for Bonneville Power Administration, Dept. of Electrical Engineering, University of British Columbia, Aug. 1986.
7. IEEE Standard 399-1990, "IEEE Recommended Practice for Industrial and Commercial Power System Analysis", IEEE, New York, 1990.

Go to Contents of Chapters