Author: Angelo Baggini and Zbigniew Hanzelka
Source: Handbook of Power Quality Edited by Angelo Baggin, John Wiley & Sons, Ltd
1.0 SELECTION AND RATING OF TRANSFORMERS FOR A SIX-PULSE CONVERTER 
When the harmonic spectrum is known, or at least can be measured with a certain reliability or predicted, the additional losses can be easily calculated.
The process of calculation should be made through the following steps:
- Determination of all the coponents of additional losses due to the presence of harmonics.
- Determination of the harmonic spectrum, either by measurement or by estimation, taking into account all harmonic generating equipment, in particular electronic converters.
- Calculation of the contribution of each harmonic component and determination of total additional losses.
In practice, it is important to use the real harmonic current magnitudes rather than theoretical values.
Table 1 shows the calculated additional losses, for harmonic currents up to order 25, for two transformers at normal environmental temperature, assuming the current harmonic spectrum illustrated in Figure 1.
The results demonstrate that the transformer characteristics play an important role in determining the losses with harmonic loads.
The transformers in this example were measured at slightly different temperatures (21.5°C for the first and 22.8°C for the second); this will not change the reliability of results.
1.1 Calculation of the K Factor
Table 2 shows the calculation of the K factor for the harmonic spectrum of Figure 1 on a per unit basis.
The first step is the calculation of the r.m.s. value of total current I, 1.0410 in this case, after which the squares of the proportionate values of each harmonic current can be calculated, leading to the value of K. For such a load, a transformer with a K rating of 9 would be appropriate for a six-pulse converter.
1.2 Calculation of the Factor K
The first step in establishing factor K (Table 2) is to discover the value of e, the ratio of eddy current loss to total load loss at fundamental frequency. The transformer manufacturer should be able to provide this, otherwise it is likely to lie in the range of 0.05 to 0.1. The exponent q depends critically on the construction of the transformer and should also be available from the manufacturer. It is likely to lie in the range 1.5 to 1.7. As before, the calculations are based on the theoretical values from Figure 1. In practice, the transformer would need to be derated to 84.75 % (1/1.18) of nominal power rating when supplying a six-pulse converter.
2.0 DERATING CABLES
As described in Section 6.2, the current amplitude in the neutral due to the third harmonic could exceed in amplitude the phase current at the fundamental frequency. In this case the neutral current should be considered with regard to the sizing of the circuit cables. This example is related to an office building where four different harmonics spectra have been used to evaluate the cable size to be installed.
The system is a three-phase circuit with a 32 A rated load to be installed using a four-core EPR insulated cable laid directly onto the wall.
These are as follows:
- Absence of harmonics. For this current it is common practice to use a copper conductor cable with a 4 mm2 cross-section with a capacity of 35 A  .
- A value of 22 % of the third-order harmonic (Figure 2). For this spectrum the neutral current will be IN = 32·0,22·3 = 21,1A, IN <IF, so the value is selected on the basis of the line current. Applying a 0.86 reduction factor (Table 12), the equivalent load current is 32/0,86 =37,2 A. For this value the cable section hasa6mm2 cross-section with a capacity of 44 A .
For a value of 42 % of the third-order harmonic (Figure 3), IN = 32·0,42·3=40.3A, IN >IF, so the value is selected on the basis of the neutral current. Applying a 0.86 reduction factor, the equivalent load current is 40,3/0,86=46,9 A. For this value the cable section has a 10 mm2 cross-section with a capacity of 60A .
Figure C7.4 Current waveform and its spectrum
3. Third-order, harmonic-rich environment, as in Figure 4. The neutral current will be In= 32·1.31·3 = 125.76A, In>If, so the value is selected on the basis of the neutral current. Applying a reduction factor equal to 1, the equivalent load current is 125.76/1 = 125,67 A. For this value the cable section has a 35 mm2 cross-section with a capacity of 128 A .
3.0 HARMONIC SOURCE LOCATION
In the event of significant distortion of the supply network voltage at the PCC between the electricity supplier and customer, the source of disturbance should be located. This becomes of particular significance when formulating contracts for electric power supply or charging for worsening the quality of supply.Inmanycasesalsoaquantitative determination of the supplier and customer(s) contribution to the total voltage distortion at the PCC is required.
The most common practical method for locating harmonic sources is based on determining the direction of active power flow for given harmonics, though many authors indicate its limitations and propose others methods (investigation of the direction of reactive power flow and the ‘critical impedance’, interharmonic injection, determining voltage and current relative values, etc. ,). In most cases these methods, apart from their technical complexity, require precise information on values of equivalent parameters of the analyzed system, which are difficult to access, or can only be obtained as a result of costly measurements.
According to the direction of active power flow method, the dominant source of a given harmonic (of order n) can be located by determining the direction of this harmonic active power flow at various points of the system (Figure 5). A non-zero value of P(n) =U(n)I(n) cos(Φiu(n)−Φii(n))is the effect of the interaction of voltage and current with the same frequency. A linear load supplied with distorted voltage draws active power for each harmonic: P(n) ≥ 0. If non-linear elements exist at the customer side, the active power for someharmonicscan besuppliedtothenetwork: P(n)<0. Thesignof P(n) canbedetermined by means of measuring the phase angles of the voltage and current of the same order: Φiu(n)and Φi(n).
The principle of this method is explained in the example of a single-phase circuit, shown in Table 4 (the supply voltage source is US, LS), where the nonlinear load is the thyristor power controller (TYR1, TYR2, resistance RONL, inductance LONL), which is the source of harmonic currents of order n = 2k ± 1 = 3, 5, 7, 9, 11, 13, 15, (for k = 1,2,3,…). There cases, distinguished by location of the voltage distortion source, are discussed for the power controller located: (i) upstream of the PCC, (ii) downstream of the PCC, and (iii) harmonic sources at both sides of the PCC
BIBLIOGRAPHY Arrillaga J., Watson N. R., Chen S., Power system quality assessment, John Wiley & Sons, Ltd, Chichester, 2000.  Arsenau R., Filipski P. S., Zelle J., A VA-meter-error analyzer. IEEE Transactions on Power Delivery, vol. 6, no. 4, 1991.  Baggini A., Zanoli F., Progetto di trasformatori per l’alimentazione di azionamenti e carichi non lineari. VIII Seminario Interattivo su Azionamenti elettrici innovazioni tecnologiche e problematiche emergenti, Bressanone (BZ), 10–12 marzo 1997.  CEI 14-4/1983, Trasformatori di potenza.  CEIUNEL35024/1, Cavi elettrici isolati con materiale elastomerico o termoplastico per tensioni nominali non superiori a 1000 V in corrente alternata e 1500 V in corrente continua. Portate di corrente in regime permanente per posa in aria, 1997.  Chapman D., Harmonics – causes and effects. Leonardo Power Quality Application Guide – Part 3.1, 2001.  Correggiari F., Costruzione di macchine elettriche, Cisalpino Goliardica, Milan.  Datta S. K., Nafsi A., Distribution relay performance under harmonics conditions. PQA’92, Atlanta, Georgia, USA, 1992.  Desmet J., Baggini A., Harmonics – neutral sizing in harmonic rich installations. Leonardo Power Quality Application Guide – Part 3.5.1, 2003.  DesmetJ.,DelaereG.,Harmonics –selectionandratingoftransformers.Leonardo Power Quality Application Guide – Part 3.5.2, 2005.  Elmore W. A., Kramer C. A., Zocholl E., Effect of waveform distortion on protective relays. IEEE Transactions on Industry Applications, vol. 29, no. 2, 1993.  EN 50160, Voltage characteristics of electricity supplied by public distribution systems.  Fassbinder S., Harmonics – passive filters. Leonardo Power Quality Application Guide – Part 3.3.1, 2003.  Girgis A. A., Nims J. W., Jacomino J., Dalton J. G., Bishop A., Effect of voltage harmonics on the operation of solid-state relays in industrial applications. IEEE Transactions on Industry Applications, vol. 28, vol. 5, 1992.  Gruzs T. M., A survey of neutral currents in three-phase computer power systems. IEEE Transaction on Industry Applications, vol. 26, no. 4, 1990.  HanzelkaZ.,BienA.,Harmonics –interharmonics. Leonardo Power Quality Application Guide – Part 3.3.1, 2004.  IEC 60364–5-523, Electrical installations of buildings – Part 5-52: Selection and election of electrical equipment – Wiring systems.  IEC 61000-1-4, Historical rationale for the limitation of power-frequency conducted harmonic current emissions from equipment in the frequency range up to 9 kHz, Technical Report.  IEC 61000-2-1, Electromagnetic compatibility (EMC) Part 2-1: Environment – Description of the environment: Electromagnetic environment for low-frequency conducted disturbances and signalling in public power supply systems, 1990.  IEC 61000-2-2, Electromagnetic Compatibility (EMC) – Part 2-2: Environment – Compatibility levels for low frequency conducted disturbances and signalling in public low-voltage power supply systems.  IEC 61000-3-2, Limits for harmonic current emissions (equipment input current ≤ 16 A per phase).  IEC 61000-4-7, Electromagnetic compatibility (EMC) Part 4: Testing and measurement techniques Section 7: General guide on harmonics and interharmonics measurements and instrumentation for power supply systems and equipment connected thereto.  IEC TC 64 WG 2, Current-carrying capacity and related overcurrent protection, Revision of section 523″, September 1996.  IEEE 519-92, IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems, 1992.  IEEE 1159, Recommended practice for monitoring electric power quality.  Karve S., Harmonics – active harmonic conditioners. Leonardo Power Quality Application Guide – Part 3.3.3, 2001.  Norma CEI 64-8/5, Impianti elettrici utilizzatori a tensione nominale non superiore a 1000 V in corrente alternata e a 1500 V in corrente continua. Parte 5: Scelta ed installazione dei componenti elettrici, 1992.  Power System Harmonics, Power Technologies, Inc., 1989.  Purkayastha I., Savoce P. J., Effect of harmonics on power measurement. IEEE Transactions on Industry Applications, vol. 26, no. 5, 1990.  Shepherd W., Zakikhani P., Energy flow and power factor in non-sinusoidal circuits, Cambridge University Press, New York.  Stade D., Shau H., Influence of voltage harmonics on single-phase earth fault currents. PQA’91.  Tsukamoto M., Kouda I. N., Minowa Y., Nishimura S., Advanced method to identify harmonics characteristic between utility grid and harmonic current sources. 8th International Conference on Harmonics and Quality of Power, Athens, Greece, 14–16 October, 1998.  West K., Harmonics – true RMS – the only true measurement. Leonardo Power Quality Application Guide – Part 3.2.2, 2001.  Xu Wilsun, Liu Yilu, A method for determining customer and utility harmonic contributions at the point of common coupling. IEEE Transactions on Power Delivery, vol.15, no.2, 2000.  Xu Wilsun, Liu Xian, Liu Yilu, An investigation on the validity of power-direction method for harmonic source determination. IEEE Transactions on Power Delivery, vol. 18, no. 1, 2003.  Yacamini R., Chang S. C., Noise and vibration from induction machines fed from harmonic sources. Proceedings of IEEE ICHPS VI, Bologna, 21–23 September, 1994.  ˙zelenko I. W., Harmonics in power system supplying industrial loads, Elektroatomizdat, Ze˙Moscow, 1994 (in Russian).