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Injecting a harmonics with 6-pulse rectifier

The diagram in figure 1 represents a simplified network comprising a 2,000 kVA six-pulse rectifier, injecting a harmonic current spectrum, and the following equipment which will be considered consecutively in three different calculations:

Figure 1 - Example of the analysis of a simplified network - Installation with disturbing equipment, capacitors and filters
Figure 1 - Example of the analysis of a simplified network - Installation with disturbing equipment, capacitors and filters
  1. Single 1,000 kvar capacitor bank
  2. Anti-harmonic reactor-connected capacitor equipment rated 1,000 kvar
  3. Set of two filters
    (comprising a resonant shunt tuned to the 5th harmonic and a 2nd order damped filter tuned to the 7th harmonic)

Note that:

  • The 1,000 kvar compensation power is required to bring the power factor to a conventional value;
  • The harmonic voltages already present on the 20 kV distribution network have been neglected for the sake of simplicity.


This example will be used to compare the performance of the three solutions. However the results can obviously not be applied directly to other cases.


1. Capacitor bank alone

The network harmonic impedance curve (see fig. 2), seen from the node where the harmonic currents are injected, exhibits a maximum (anti-resonance) in the vicinity of the 7th current harmonic.

This results in an unacceptable individual harmonic voltage distortion of 11% for the 7th harmonic (see fig. 3).

Harmonic impedance seen from the node where the harmonic currents are injected in a network equipped with a capacitor bank alone
Figure 2 – Harmonic impedance seen from the node where the harmonic currents are injected in a network equipped with a capacitor bank alone

Harmonic voltage spectrum of a 5.5 kV network equipped with a capacitor bank alone
Figure 3 – Harmonic voltage spectrum of a 5.5 kV network equipped with a capacitor bank alone

The following characteristics are also unacceptable:

  • A total harmonic voltage distortion of 12.8% for the 5.5 kV network, compared to the maximum permissible value of 5% (without considering the requirements of special equipment);
  • A total capacitor load of 1.34 times the rms current rating, exceeding the permissible maximum of 1.3 (see fig. 4).
Spectrum of the harmonic currents flowing in the capacitors for a network equipped with a capacitor bank alone
Figure 4 – Spectrum of the harmonic currents flowing in the capacitors for a network equipped with a capacitor bank alone



The solution with capacitors alone is therefore unacceptable.

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2. Reactor-connected capacitor bank

This equipment is arbitrarily tuned to 4.8 f1.

Harmonic impedance

The network harmonic impedance curve, seen from the node where the harmonic currents are injected, exhibits a maximum of 16 ohms (anti-resonance) in the vicinity of harmonic order 4.25. The low impedance, of an inductive character, of the 5th harmonic favours the filtering of the 5th harmonic quantities.

Harmonic impedance seen from the node where the harmonic currents are injected in a network equipped with reactor-connected capacitors
Figure 5 – Harmonic impedance seen from the node where the harmonic currents are injected in a network equipped with reactor-connected capacitors


Voltage distorsion

For the 5.5 kV network, the individual harmonic voltage ratios of 1.58% (7th harmonic), 1.5% (11th harmonic) and 1.4% (13th harmonic) may be too high for certain sensitive loads. However in many cases the total harmonic voltage distortion of 2.63% is acceptable.

For the 20 kV network, the total harmonic distortion is only 0.35%, an acceptable value for the distribution utility.

Harmonic voltage spectrum of a 5.5 kV network equipped with reactor-connected capacitors
Figure 6 – Harmonic voltage spectrum of a 5.5 kV network equipped with reactor-connected capacitors

Capacitor current load

The total rms current load of the capacitors, including the harmonic currents, is 1.06 times the current rating, i.e. less than the maximum of 1.3. This is the major advantage of reactor-connected capacitors compared to the first solution (capacitors alone).

Spectrum of the harmonic currents flowing in the capacitors for a network equipped with reactor-connected capacitors
Figure 7 – Spectrum of the harmonic currents flowing in the capacitors for a network equipped with reactor-connected capacitors

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3. Resonant shunt filter tuned to the 5th harmonic and a damped filter tuned to the 7th harmonic

In this example, the distribution of the reactive power between the two filters is such that the filtered 5th and 7th voltage harmonics have roughly the same value. In reality, this is not required.


Harmonic impedance

The network harmonic impedance curve, seen from the node where the harmonic currents are injected, exhibits a maximum of 9.5 ohms (anti- resonance) in the vicinity of harmonic 4.7.

  • For the 5th harmonic, this impedance is reduced to the reactor resistance, favouring the filtering of the 5th harmonic quantities.
  • For the 7th harmonic, the low, purely resistive impedance of the damped filter also reduces the individual harmonic voltage.
  • For harmonics higher than the tuning frequency, the damped filter impedance curve reduces the corresponding harmonic voltages.

This equipment therefore offers an improvement over the second solution (reactor-connected capacitors).

Harmonic impedance seen from the node where the harmonic currents are injected in a network equipped with a resonant shunt filter tuned to the 5th harmonic and a damped filter tuned to the 7th harmonic
Figure 8 – Harmonic impedance seen from the node where the harmonic currents are injected in a network equipped with a resonant shunt filter tuned to the 5th harmonic and a damped filter tuned to the 7th harmonic

Voltage distorsion (see fig. 34 )

For the 5.5 kV network, the individual harmonic voltage ratios of 0.96%, 0.91%, 1.05% and 1% for the 5th, 7th, 11th and 13th harmonics respectively are acceptable for most sensitive loads. The total harmonic voltage distortion
is 1.96%.

For the 20 kV network, the total harmonic distortion (THD) is only 0.26%, an acceptable value for the distribution utility.

Harmonic voltage spectrum of a 5.5 kV network equipped with a resonant shunt filter tuned to the 5th harmonic and a damped filter tuned to the 7th harmonic
Figure 9 – Harmonic voltage spectrum of a 5.5 kV network equipped with a resonant shunt filter tuned to the 5th harmonic and a damped filter tuned to the 7th harmonic

Capacitor current load

The capacitor rating must be adequately chosen considering the overvoltage at fundamental frequency, the harmonic voltages and currents. This example demonstrates an initial approach to the problem.

However in practice, over and above the calculations relative to the circuit elements (L, r, C and R), other calculations are required before proceeding with the implementation of any solution:

  1. The spectra of the currents flowing in the reactors connected to the capacitors;
  2. The total voltage distortion at the capacitor terminals;
  3. Reactor manufacturing tolerances and means for adjustment if necessary;
  4. The spectra of the currents flowing in the resistors of the damped filters and their total rms value;
  5. Voltage and energy transients affecting the filter elements during energization.

These more difficult calculations, requiring a solid understanding of both the network and the equipment, are used to determine all the electro- technical information required for the filter manufacturing specifications.

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Reference // Harmonic disturbances in networks, and their treatment by C. Collombet, J.M. Lupin and J. Schonek (Schneider Electric)

About Author //

author-pic

Edvard Csanyi

Edvard - Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV high power busbar trunking (<6300A) in power substations, buildings and industry fascilities. Designing of LV/MV switchgears.Professional in AutoCAD programming and web-design.Present on

2 Comments


  1. Mark
    Apr 21, 2017

    Hi ,
    I have a question. I am a solar electrician and at work the boss has installed two Feronius inverters to a 30 Kw solar system on a commercial premises. They are are kitchen manufacturer with three cnc machines with there own inverters. The company is now having electrical problems with there machines. Could this be a harmonic problem between the solar inverters and the machines own inverters.?

    Regards
    Mark


  2. Nitin
    Apr 21, 2017

    This is direction ..eep..great stuff

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