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:موقع ويب

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Gulf StandardGSO IEC 61642:2014

GSO IEC 61642:2014Gulf Standard

Gulf Foreword

GCC Standardization Organization (GSO) is a regional organization which consists of the national standardization bodies of GCC member states. One of GSO main functions is to issue gulf standards and technical regulations through specialized technical committees.

GSO Technical Council in its meeting number (34) held on 03/03/1436 H, which corresponds to 25/12/2014, has approved Gulf Standard GSO IEC 61642:2014 titled "Industrial a.c. networks affected by harmonics - Application of filters and shunt capacitors" in English language which was studied and adopted by endorsement from International Electrotechnical Commission Standard IEC 61642:1997 through fast track .

تقديم خليجي

هيئة التقييس لدول مجلس التعاون لدول الخليج العربية هيئة إقليمية تضم في عضويتها أجهزة التقييس الوطنية في الدول الأعضاء ، ومن مهام الهيئة إعداد المواصفات القياسية واللوائح الفنية الخليجية بواسطة لجان فنية متخصصة.

قرر المجلس الفني لهيئة التقييس لدول مجلس التعاون لدول الخليج العربية في الاجتماع الـ (34) بتاريخ 1436/03/03 هـ ،الموافق 2014/12/25م اعتماد المواصفة القياسية الخليجية رقم GSO IEC 61642:2014 وعنوانها "شبكات التيار المتردد الصناعية المتأثرة بالتوافقيات -تطبيق المرشحات ومواسعات التوازي" باللغة الانجليزية التي تم دراستها وتبنيها بالمصادقة عبر المسار السريع عن اللجنة الدولية الكهروتقنية رقم IEC 61642:1997 .

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IEC 61642:1997 ED1 © IEC 1997

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IEC 61642:1997 ED1 © IEC 1997

Gulf StandardGSO IEC 61642:2014

GSO IEC 61642:2014Gulf Standard

IEC 61642

	INTERNATIONAL STANDARD	Edition 1.0 1997-09


	Industrial a.c. networks affected by harmonics – Application of filters and shunt capacitors

IEC 61642:1997 ED1

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Gulf StandardGSO IEC 61642:2014

GSO IEC 61642:2014Gulf Standard

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IEC 61642:1997 ED1 © IEC 1997

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IEC 61642:1997 ED1 © IEC 1997

Gulf StandardGSO IEC 61642:2014

GSO IEC 61642:2014Gulf Standard

IEC 61642

	INTERNATIONAL STANDARD	Edition 1.0 1997-09


	Industrial a.c. networks affected by harmonics – Application of filters and shunt capacitors

INTERNATIONAL

ELECTROTECHNCIAL

COMMISSION

ICS 29.120.99, 29.240.99, 31.060.70ISBN 2831839890Warning! Make sure that you obtained this publication from an authorized distributor.© Registered trademark of the International Electrotechnical Commission

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IEC 61642:1997 ED1 © IEC 1997

Gulf StandardGSO IEC 61642:2014

GSO IEC 61642:2014Gulf Standard

CONTENTS

FOREWORD

1 General

1.1 Scope and object

1.2 Normative references

1.3 Definitions

1.4 General considerations

1.4.1 AC harmonics

1.4.2 Reactive power

2 Resonance problems and solutions

2.1 Introduction

2.2 Supply impedance view, load-busbar impedance view

2.3 Example of a series resonance

2.4 Example of parallel resonance

2.5 Solutions to avoid resonances

2.5.1 Capacitor-reactor connection: series resonance

2.5.2 Capacitor-reactor connection: parallel resonance

3 Shunt capacitors and filters for networks having a voltage up to and including 1 000 V

3.1 Introduction

3.2 Shunt capacitors

3.3 Detuned filter

3.4 Tuned filter

3.5 Components selection

3.5.1 Capacitors

3.5.2 Reactors

3.5.3 Contactors and/or circuit-breakers

3.5.4 Short-circuit protection (fuses)

3.6 Disturbance of ripple control installations by shunt capacitors and filters

3.6.1 Shunt capacitors

3.6.2 Detuned filter

3.6.3 Tuned filter

4 Shunt capacitors and filters for networks having a voltage above 1 000 V

4.1 Introduction

4.2 Specific requirements

4.3 Choice of power factor correction installation

4.4 Type of filters

4.5 Filter components selection

4.5.1 Circuit-breaker

4.5.2 Capacitors

4.5.3 Reactors

4.5.4 Resistors

4.5.5 Relay protection

4.6 Disturbance of ripple control installations by shunt capacitors and filters

Annex A Bibliography

Figure 1 – Simplified network and one-line diagram

Figure 2a – Supply impedance view of a network and one-line diagram

Figure 2b – Load-busbar impedance view of a network and one-line diagram

Figure 3a – One-line diagram of a series resonance circuit

Figure 3b – Impedance in ohms versus harmonic order of the circuit shown in figure 3a

Figure 4a – One-line diagram of a parallel resonance circuit

Figure 4b – Impedance in ohms versus harmonic order of the circuit shown in figure 4a

Figure 5a – One-line diagram of a series resonance circuit with capacitor-reactor connection

Figure 5b – Impedance in ohms versus harmonic order h of the circuit shown in figure 5a

Figure 6a – One-line diagram of a parallel resonance circuit with capacitor-reactor connection

Figure 6b – Impedance in ohms versus harmonic order of the circuit shown in figure 6a

Table 1 – Numerical results of impedances, voltages and currents at characteristic harmonic orders of a series resonance circuit in a network with a distorted supply voltage

Table 2 – Numerical results of impedances, voltages and currents at characteristic harmonic orders of a parallel resonance circuit in the presence of a harmonic current source.

Table 3 – Numerical results of impedances, voltages and currents at characteristic harmonic orders of a series resonance circuit with a capacitor-reactor-connection in a network with distorted supply voltage

Table 4 – Numerical results of impedances, voltages and currents at characteristic harmonic orders of a parallel resonance circuit with a capacitor-reactor connection in the presence of a harmonic current source

INTERNATIONAL ELECTROTECHNICAL COMMISSION

International StandardIEC 61642:1997 ED1

Industrial a.c. networks affected by harmonics - Application of filters and shunt capacitors

FOREWORD

The IEC (International Electrotechnical Commission) is a worldwide organization for standardization comprising all national electrotechnical committees (IEC National Committees). The object of the IEC is to promote international co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and in addition to other activities, the IEC publishes International Standards. Their preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with may participate in this preparatory work. International, governmental and non-governmental organizations liaising with the IEC also participate in this preparation. The IEC collaborates closely with the International Organization for Standardization (ISO) in accordance with conditions determined by agreement between the two organizations.

The formal decisions or agreements of the IEC on technical matters express, as nearly as possible, an international consensus of opinion on the relevant subjects since each technical committee has representation from all interested National Committees.

The documents produced have the form of recommendations for international use and are published in the form of standards, technical reports or guides and they are accepted by the National Committees in that sense.

In order to promote international unification, IEC National Committees undertake to apply IEC International Standards transparently to the maximum extent possible in their national and regional standards. Any divergence between the IEC Standard and the corresponding national or regional standard shall be clearly indicated in the latter.

The IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any equipment declared to be in conformity with one of its standards.

Attention is drawn to the possibility that some of the elements of this International Standard may be the subject of patent rights. The IEC shall not be held responsible for identifying any or all such patent rights.

International Standard IEC 61642 has been prepared by IEC technical committee 33: Power capacitors.

The text of this standard is based on the following documents:

FDIS	Report on voting
33/255/FDIS	33/274/RVD

Full information on the voting for the approval of this standard can be found in the report on voting indicated in the above table.

Annex A is for information only.

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GSO IEC 61642:2014Gulf Standard

International StandardIEC 61642:1997 ED1

Industrial a.c. networks affected by harmonics - Application of filters and shunt capacitors

1General

1.1Scope and object

This International Standard gives guidance for the use of passive a.c. harmonic filters and shunt capacitors for the limitation of harmonics and power factor correction intended to be used in industrial applications, at low and high voltages. The measures proposed in this standard are applicable to harmonic orders greater than 1 and up to and including 25.

The following capacitors are excluded from this standard:

–

capacitors for inductive heat generating plants, operating at frequencies between 40 Hz and 24 000 Hz (see IEC 60110 [1]*);

–

series capacitors for power systems (see IEC 60143 [2]);

–

coupling capacitors and capacitor dividers (see IEC 60358 [3]);

–

power electronic capacitors (see IEC 61071 [4]);

–

AC motor capacitors (see IEC 60252 [5]);

–

capacitors for use in tubular fluorescent and other discharge lamp circuits (see IEC 61048 [6] and IEC 61049 [7]);

–

capacitors for the suppression of radio interference;

–

capacitors intended to be used in various types of electric equipment and thus considered as components;

–

capacitors intended for use with d.c. voltage superimposed on a.c. voltage;

–

capacitors intended for use with arc furnaces.

The object of this standard is to identify problems and give recommendations for general applications of capacitors and a.c. harmonic filters in a.c. power systems affected by the presence of harmonic voltages and currents.

1.2Normative references

The following normative documents contain provisions which, through reference in this text, constitute provisions of this International Standard. At the time of publication, the editions indicated were valid. All normative documents are subjected to revision, and parties to agreements based on this International Standard are encouraged to investigate the possibility of applying the most recent editions of the normative documents indicated below. Members of IEC and ISO maintain registers of currently valid International Standards.

IEC 60050(131):1978, International Electrotechnical Vocabulary (IEV) – Chapter 131: Electric and magnetic circuits

IEC 60050(161):1990, International Electrotechnical Vocabulary (IEV) – Chapter 161: Electro-magnetic compatibility

1.3Definitions

For the purpose of this International Standard, the following definitions apply.

1.3.1

harmonic

The component of the Fourier-series decomposition of a voltage or current periodic wave.

[SOURCE: IEV 161‑02‑18 modified]

1.3.2

harmonic order, h

The ratio of the frequency of a harmonic (fh) to the fundamental (rated) network frequency (f1).

[SOURCE: IEV 161‑02‑19 modified]

1.3.3

characteristic harmonics

Those harmonics produced by static converters in the course of theoretically ideal operation. The characteristic-harmonic order of static a.c./d.c. converters is given by h = mp ± 1, where p is the pulse number of the converter and m is any integer. For example, the six-pulse converter circuit has characteristic harmonics with order numbers h = 5, 7, 11, 13, 17, 19....

1.3.4

non-characteristic harmonics

Those harmonics which are produced as a result of imbalance in the a.c. power system or asymmetrical delay of firing angle of the converter. They are also produced by other non-linear, time-varying devices, for example frequency changers, fluorescent lamps, arc furnaces, electric welding machines, etc.

1.3.5

power factor

The ratio of the active power to the apparent power.

[SOURCE: IEV 131‑03‑20]

1.3.6

displacement factor

The ratio of the active power of the fundamental wave to the apparent power of the fundamental wave.

[SOURCE: IEV 131‑03‑21 modified]

1.3.7

distortion factor

The ratio of the root-mean-square value of the harmonic content to the root-mean-square value of the fundamental quantity, expressed as a percentage of the fundamental.

[SOURCE: IEV 131‑03‑04 modified]

DF = \frac{{(sum of the squares of r . m . s values of the harmonics)}^{1 / 2}}{r . m . s value of the fundamental} 100 %

1.3.8

filter

An equipment generally constituted of reactors, capacitors and resistors if required, tuned to present a known impedance over a given frequency range.

1.3.9

tuning frequency

The frequency for which the filter impedance, calculated from the rated values, has a minimum or maximum value.

1.3.10

tuned filter

A filter with a tuning frequency which differs by no more than 10 % from the frequency which is to be filtered.

1.3.11

detuned filter

A filter with a tuning frequency more than 10% below the lowest harmonic frequency with considerable current/voltage amplitude.

1.3.12

damped filter

A filter with low, predominantly resistive, impedance over a wide band of frequencies.

1.3.13

ripple control installation

An installation to inject audio-frequency signals into the high voltage (HV) network in order to control receivers on the low voltage (LV) network.

1.3.14

reference voltage

The voltage to which the impedance calculations are referred.

1.4General considerations

1.4.1AC harmonics

Harmonic currents in power networks are produced, in general, when the loads are non-linear or time-varying. One of the main sources of harmonics in industrial networks are static converters.

There are two groups of converter a.c. current harmonics: characteristic and non-characteristic. The characteristic harmonics correlate strongly with the converter circuit and have a constant frequency spectrum. Their magnitude is approximately in inverse proportion to the harmonic number.

The main sources of non-characteristic harmonics are frequency changers, although small amounts of non-characteristic harmonics can result from system imbalances (voltage and impedance) and imbalance in the converter firing angle.

The rectifiers for d.c. drives produce mostly characteristic harmonics.

The effect of non-linear and time-varying loads can be amplified under certain conditions of the electrical supply-network, for example by resonances. Depending on the network conditions and on the amplification effect of the resonances, the supply voltage can be distorted even in electrical installations where non-linear and time-varying loads are absent or represent a small part of the total utility power.

Harmonics increase the losses in power networks and may affect the correct operation of various equipments, in particular electronic circuits.

To keep the harmonic disturbances to an acceptable level, local requirements and national and international standards may specify limits for the harmonic distortion. For the reduction of harmonic distortion, filters can be used.

1.4.2Reactive power

In general, the reactive power flowing in networks is caused by inductive loads and static converters.

In a network the power factor is determined by the most economical use of the distribution system or is imposed by the utility. Penalties may be imposed through the tariff structure for poor power factor. It is therefore advisable to compensate the inductive reactive power by fitting suitable compensating equipments.

For power factor correction shunt capacitors are normally used. If there are harmonics in the network, unwanted overvoltages and/or overcurrents can appear. In addition, ripple control installations may be disturbed. In these cases, filters can be used in place of shunt capacitors alone.

2Resonance problems and solutions

2.1Introduction

In electrical networks, different components are connected together, for example generators, power lines, cables, transformers, capacitors and loads.

The impedance at any point of the network is dependent on the frequency, on the components and on the configuration.

The series connection of an inductance and a capacitance will result in a very low impedance in a certain frequency range, close to the resonance frequency. This effect is called series resonance.

The parallel connection of an inductance and a capacitance will result in a very high impedance in a certain frequency range, close to the resonance frequency. This effect is called parallel resonance.

Series resonance and parallel resonance may occur in the same network over a wide range of frequencies.

If harmonic voltage– or current-sources excite such resonance circuits, an amplification of voltages and currents may occur which can disturb, overload or even destroy network components.

An example of a simplified network and its one-line diagram is shown in figure 1.

Figure 1 — Simplified network and one-line diagram

This example consists of the supply network, a supply-busbar (on the high-voltage side), a transformer, a load-busbar (on the low-voltage side) and a capacitor. The source of harmonic currents may be a drive which is controlled by a six-pulse rectifier. Harmonic voltages may be present in the network itself due to other harmonic current sources.

2.2Supply impedance view, load-busbar impedance view

To analyze the behaviour of a network with respect to harmonics, it is useful to look, at least, at two impedances:

–

the supply impedance takes the view from the supply network (see figure 1).

This view is useful for the analysis of the capacitor and reactor load in the presence of harmonic voltages and currents on the supply-busbar, for the calculation of the branch impedance at ripple control-frequencies and for the evaluation of the resulting harmonic voltages (quality of the voltage) on the load-busbar;

–

the load-busbar impedance takes the view from the load-busbar (see figure 1).

This view is useful for the analysis of the capacitor and reactor load in the presence of harmonic current sources on the load-busbar and for the calculation of the resulting harmonic voltages (quality of the voltage) on the load-busbar.

Figure 2a — Supply impedance view of a network and one-line diagram

Figure 2b — Load-busbar impedance view of a network and one-line diagram

2.3Example of a series resonance

In the following calculation example, the series connection of a transformer (inductance XT and resistance RT) and a capacitor is analyzed. Figure 3a shows the one-line diagram and figure 3b shows the impedance versus harmonic order. It shows a series resonance close to the 11th harmonic. Typical numerical results of impedances, voltages and currents at characteristic harmonic frequencies in the network shown in figure 1 with a distorted supply voltage are shown in table 1 [8].

Figure 3a — One-line diagram of a series resonance circuit

Figure 3b — Impedance in ohms versus harmonic order of the circuit shown in figure 3a

Explanation of the symbols and values used in figures 3a, 3b and table 1.

UN	reference voltage (example: 3-phase 400 V)
$h = f_{h} / f_{1}$	harmonic order, f1 fundamental frequency, fh harmonic frequency
$X_{T} = X_{T 1} \cdot h$	short-circuit reactance of a transformer of 1 000 kVA having an impedance voltage of 6 %
QT = 8	transformer quality factor
$X_{C} = X_{C 1} / h$	reactance of a capacitor of 160 kvar
Z	equivalent impedance (see figure 3a)
UA	voltage on the supply-busbar. The values are taken from a CIGRE report about harmonics and multiplied by 60 % [8].
$U_{A} (%) = (U_{A} / U_{N}) \cdot 100$
IC	capacitor current
ICN	rated capacitor current
UB	resulting voltage on the load-busbar
$U_{B} (%) = (U_{B} / U_{N}) \cdot 100$

Table 1 — Numerical results of impedances, voltages and currents at characteristic harmonic orders of a series resonance circuit in a network with a distorted supply voltage

h	XT Ω	XC Ω	Z Ω	UA V	UA(%) %	IC A	UB V	UB(%) %
1	0,010	−1,000	0,990	400,0	100,0	233	404	101,0
5	0,048	−0,200	0,152	12,0	3,0	46	16	3,9
7	0,067	−0,143	0,076	9,6	2,4	73	18	4,5
11	0,106	−0,091	0,020	6,0	1,5	175	28	6,9
13	0,125	−0,077	0,050	4,8	1,2	55	7	1,8
17	0,163	−0,059	0,106	2,4	0,6	13	1	0,3
19	0,182	−0,053	0,132	1,9	0,5	8	1	0,2
				$DF (A) % = 4,4$			$DF (B) % = 9,3$
$R_{T} = X_{T} / Q_{T} = X_{T} / 8$ (simplified)					IC.eff = 313 A
					$I_{C} / I_{CN} = 1,35$

The following can be concluded from table 1:

–

a relatively low voltage on the supply-busbar can cause a high current, if the frequency is close to the series resonance frequency.

The example at h = 11 results in a capacitor current of 175 A which is about 75 % of the fundamental capacitor current;

–

the high current causes a high voltage drop on the load-busbar, which leads to a distortion of the sinusoidal voltage.

The example at h = 11 results in 6,9 % voltage distortion factor although the voltage was only 1,5 % on the supply-busbar;

–

the r.m.s. current through the capacitor is 1,35 times the rated capacitor current. This is an overload condition because the normal limit is 1,3 times the rated capacitor current.

It is possible to design a capacitor which is able to withstand such a current. But this is not a solution to the problem because the voltage distortion on the load-busbar is about 7 % for a single harmonic frequency (h = 11) which is much higher than normal compatibility levels.

Additionally, it can be seen that magnification is not only obtained when the frequency equals the resonance frequency, but also when the frequency is close to the resonance frequency. The resonance frequency where the resulting impedance has a minimum is approximately

f_{res} = f_{1} \sqrt{∣ \frac{X_{C 1}}{X_{T 1}} ∣}

2.4Example of parallel resonance

In the following calculation example, the parallel connection of a transformer (inductance XT and resistance RT) and a capacitance is analyzed. Figure 4a shows the one-line diagram and figure 4b shows the impedance versus harmonic order. Typical numerical results of impedances, voltages and currents at characteristic harmonic frequencies are shown in table 2.

Figure 4a — One-line diagram of a parallel resonance circuit

Figure 4b — Impedance in ohms versus harmonic order of the circuit shown in figure 4a

Explanation of the symbols and values used in figures 4a, 4b and table 2.

UN	reference voltage (example: 3-phase 400 V)
$h = f_{h} / f_{1}$	harmonic order, f1 fundamental frequency, fh harmonic frequency
$X_{T} = X_{T 1} \cdot h$	short-circuit reactance of a transformer of 1 000 kVA having an impedance voltage of 6 %
QT = 8	transformer quality-factor
$X_{C} = X_{C 1} / h$	reactance of a capacitor of 160 kvar
Z	equivalent impedance (see figure 4a)
I, I(%)	current on the load-busbar. The values are the theoretical values of a 300 kVA drive
UB	resulting voltage on the load-busbar
$U_{B} (%) = (U_{B} / U_{N}) \cdot 100$
IC	capacitor current
ICN	rated capacitor current

Table 2 — Numerical results of impedances, voltages and currents at characteristic harmonic orders of a parallel resonance circuit in the presence of a harmonic current source.

h	XT Ω	XC Ω	Z Ω	I A	I (%) %	UB V	UB (%) %	IC A
1	0,010	−,000	0,010	433	100,0	---	---	231
5	0,048	−0,200	0,064	87	20,0	10	2,4	28
7	0,067	−0,143	0,127	62	14,3	14	3,4	55
11	0,106	−0,091	0,490	39	9,1	33	8,3	212
13	0,125	−0,077	0,192	33	7,7	11	2,8	83
17	0,163	−0,059	0,091	25	5,9	4	1,0	39
19	0,182	−0,053	0,073	23	5,3	3	0,7	32
						$DF (B) % = 9,8$
$R_{T} = X_{T} / Q_{T} = X_{T} / 8$ (simplified)								IC eff. = 334 A
								$I_{C} / I_{CN} = 1,45$

The following can be concluded from table 2:

–

a relatively low current on the load-busbar can cause a high capacitor current, if the frequency is close to the parallel resonance frequency.

The example at h = 11 results in a capacitor current of 212 A which is more than 90 % of the fundamental capacitor current, although the harmonic current was only 39 A on the load-busbar;

–

the high current causes a high voltage drop on the load-busbar, which leads to a distortion of the sinusoidal voltage.

The example at h = 11 results in 8,3 % voltage distortion factor;

–

the r.m.s. current through the capacitor is 1,45 times the rated capacitor current. This is an overload condition because the normal limit is 1,3 times the rated capacitor current.

It is possible to design a capacitor which is able to withstand such a current. But this is not a solution to the problem because the voltage distortion on the load-busbar is about 8 % for a single harmonic frequency which is much higher than normal compatibility levels.

f_{res} = f_{1} \sqrt{∣ \frac{X_{C 1}}{X_{T 1}} ∣}

NOTEIn practice, the network impedance is connected in series to the transformer impedance. This will affect the resonance frequency and the voltage and current amplitudes to a certain extent.

2.5Solutions to avoid resonances

The principal method used to avoid resonance problems is to keep the resonance frequency as far away as possible from the harmonic frequencies which have considerable amplitudes.

This can be done by changing the inductance or the capacitance of the network components. However, there is little latitude, if a particular network configuration is defined by the power supply and reactive power compensation. In particular when an automatic capacitor bank is to be used, many resonance conditions have to be considered.

The most common solution to avoid resonance problems is to connect a reactor in series with the capacitor, tuned to a series resonance frequency which is below the lowest frequency of the harmonic voltages and currents in the network. Below the tuning frequency, the impedance of the capacitor-reactor-connection is capacitive, above the tuning frequency, it is inductive. The interaction of the network inductance and the (inductive) impedance of the capacitor-reactor-connection can no longer create a resonance condition, neither a series or a parallel resonance, at the frequencies of the harmonic voltages and currents in the network. The reactor may be specified by its relative impedance:

p = ∣ \frac{X_{L 1}}{X_{C 1}} ∣

The tuning order is:

\frac{f_{LC}}{f_{1}} = \sqrt{\frac{1}{p}}

In most networks, the 5th harmonic is the lowest frequency with a considerable amplitude. For such networks, it is useful to choose a capacitor-reactor-connection with a tuning frequency below 5 ·f1, i.e. p > 4 %.

If the network is loaded with strong 3rd harmonic voltages between phases as occurs for example with single phase rectifiers and overexcited transformers, the tuning frequency shall be below 3 ·f1, i.e. p > 11 %.

In the following examples of figures 5a, 5b, 6a, 6b and tables 3 and 4 the same values are used as before, but with a capacitor-reactor-connection tuned to 3,78 ·f1 with a p = 7 % reactor and compensation power at power frequency as before.

2.5.1Capacitor-reactor connection: series resonance

Figure 5a — One-line diagram of a series resonance circuit with capacitor-reactor connection

Figure 5b — Impedance in ohms versus harmonic order h of the circuit shown in figure 5a

Explanation of the symbols and values used in figures 5a, 5b and table 3.

UN	reference voltage (example: 3-phase 400 V)
$h = f_{h} / f_{1}$	harmonic order, f1 fundamental frequency, fh harmonic frequency
$X_{T} = X_{T 1} \cdot h$	short-circuit reactance of a transformer of 1 000 kVA having an impedance voltage of 6 %
QT = 8	transformer quality factor
XL + XC	reactance of a capacitor with a p = 7 % reactor for 160 kvar compensation power
QL = 30	reactor quality factor
Z	equivalent impedance (see figure 5a)
UA	voltage on the supply-busbar. The values are taken from a CIGRE report about harmonics and multiplied by 60 % [8]
$U_{A} (%) = (U_{A} / U_{N}) \cdot 100$
IC	capacitor current
ICN	rated capacitor current
UB	resulting voltage on the load-busbar
$U_{B} (%) = (U_{B} / U_{N}) \cdot 100$

Table 3 — Numerical results of impedances, voltages and currents at characteristic harmonic orders of a series resonance circuit with a capacitor-reactor-connection in a network with distorted supply voltage

h	XT Ω	XC + XL Ω	Z Ω	UA V	UA (%) %	IC A	UB V	UB (%) %
1	0,010	−1,000	0,990	400,0	100,0	233	404	101,0
5	0,048	0,161	0,212	12,0	3,0	33	9	2,3
7	0,067	0,373	0,443	9,6	2,4	13	8	2,0
11	0,106	0,730	0,840	6,0	1,5	4	5	1,3
13	0,125	0,896	1,026	4,8	1,2	3	4	1,0
17	0,163	1,216	1,386	2,4	0,6	1	2	0,5
19	0,182	1,374	1,563	1,9	0,5	1	2	0,4
				$DF (A) % = 4,4$			$DF (B) % = 3,5$
$R_{T} = X_{T} / Q_{T} = X_{T} / 8$ (simplified)						IC eff. = 236 A
$R_{L} = X_{L} / Q_{L} = X_{L} / 30$ (simplified)						$I_{C} / I_{CN} = 1,02$

The following can be concluded from table 3:

–

a resonance-problem with an amplification of voltages and currents is avoided with the capacitor-reactor connection;

–

the voltage distortion factor on the load-busbar is 3,5 % while that in the example of table 1 is 9,3 %. The power quality is improved in this respect.

2.5.2Capacitor-reactor connection: parallel resonance

Figure 6a — One-line diagram of a parallel resonance circuit with capacitor-reactor connection

Figure 6b — Impedance in ohms versus harmonic order of the circuit shown in figure 6a

Explanation of the symbols and values used in figures 6a, 6b and table 4.

UN	reference voltage (example: 3-phase 400 V)
$h = f_{h} / f_{1}$	harmonic order, f1 fundamental frequency, fh harmonic frequency
$X_{T} = X_{T 1} \cdot h$	short-circuit reactance of a transformer of 1 000 kVA having an impedance voltage of 6 %
QT = 8	transformer quality-factor
XL + XC	reactance of a capacitor with a p = 7 % reactor for 160 kvar compensation power
QL = 30	reactor quality-factor
Z	equivalent impedance (see figure 6a)
I, I(%)	current on the load-busbar. The values are the theoretical values of a 300 kVA drive.
UB	resulting voltage on the load-busbar
$U_{B} (%) = (U_{B} / U_{N}) \cdot 100$
IC	capacitor current
ICN	rated capacitor current

Table 4 — Numerical results of impedances, voltages and currents at characteristic harmonic orders of a parallel resonance circuit with a capacitor-reactor connection in the presence of a harmonic current source

h	XT Ω	XL + XC Ω	Z Ω	IA	I (%)%	UB V	UB(%) %	IC A
1	0,010	−1,000	0,010	433	100,0	–	–	231
5	0,048	0,161	0,037	87	20,0	6	1,4	20
7	0,067	0,373	0,057	62	14,3	6	1,5	10
11	0,106	0,730	0,093	39	9,1	6	1,6	5
13	0,125	0,896	0,110	33	7,7	6	1,6	4
17	0,163	1,216	0,145	25	5,9	6	1,6	3
19	0,182	1,374	0,162	23	5,3	6	1,6	3
						$DF (B) % = 3,8$
$R_{T} = X_{T} / Q_{T} = X_{T} / 8$ (simplified)								IC eff. = 232 A
$R_{L} = X_{L} / Q_{L} = X_{L} / 30$ (simplified)								$I_{C} / I_{CN} = 1,01$

The following can be concluded from table 4:

–

a resonance problem with an amplification of voltages and currents is avoided with the capacitor-reactor connection;

–

the voltage distortion factor on the load-busbar is 3,8 % while that in the example of table 2 is 9,8 %. The power quality is improved in this respect.

NOTEIn practice, the network impedance is connected in series to the transformer impedance. This will affect the resonance frequency and the voltage and current amplitudes to a certain extent.

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*Figures in square brackets refer to the bibliography given in annex A.