## 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:

- Single 1,000 kvar capacitor bank
- Anti-harmonic reactor-connected capacitor equipment rated 1,000 kvar
- 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).

**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).

The solution with capacitors alone is therefore **unacceptable.**

### 2. Reactor-connected capacitor bank

This equipment is **arbitrarily tuned to 4.8 f _{1}**.

#### 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.

#### 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.

#### 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).

### 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).

#### 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.

#### 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.

- The spectra of the currents flowing in the reactors connected to the capacitors;
- The total voltage distortion at the capacitor terminals;
- Reactor manufacturing tolerances and means for adjustment if necessary;
- The spectra of the currents flowing in the resistors of the damped filters and their total rms value;
- 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.

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