The distortions of the voltage and current waveforms are generated from non-linear loads (inverter, saturated transformers, rectifier, etc.) and produce the following problems:
- On the A.C. motors we find mechanical vibration that can reduce the life. The increase of the losses creates overheating with consequent damaging of the insulating materials;
- In transformers they increase the copper and iron losses with possible damaging of the windings. The eventual presence of continuous components of voltage or current could cause the saturation of the nucleus with consequent increasing of the magnetising current;
- The capacitors suffer from the overheating and the increasing of the voltage that reduce the life.
The wave form of the current (or voltage) generated from a non-linear load (fig. 3), being periodical, could be represented by the sum of more sinusoidal waves (a 50Hz component called fundamental and other components with multiple frequency of the fundamental components, called HARMONICS):
It is not advisable to install the power factor correction without considering the harmonic content of a system.
This is because, even if we could manufacture capacitors that can withstand high overloads, capacitors produce an increase of harmonic content, with the negative effects just seen. We speak about resonance phenomena when an inductive reactance is equal to the capacitive one
The resonance is divided in two different typologies: series or parallel. The electric circuit could be represented with the equivalent circuit below:
Ideal current generator represents motor as harmonic current components generator, these are independent from circuit inductance, while Lcc is obtainable by capacitor upstream short circuit power (in general it is equal to transformer short-circuit inductance).
Scc= Short-circuit power of the network (MVA);
Q = Output of power factor correction bank (kvar);
A = Rated power transformer (kVA);
vcc%= Short-circuit voltage %;
N = harmonic order.
In parallel resonance conditions the current and the voltage of the circuit LCC - C are hardly amplified like the harmonics. Hereinafter an example.
A = 630kVA (rated power transformer);
vcc% = 6 (shot-circuit voltage %);
Q = 300kvar (output of power factor correction bank).
The result shows that in these conditions the system transformer- capacitor bank has the parallel resonance frequency of 300Hz (N*50Hz). The most convenient solution is the detuned filter, formed introducing a filter reactor in series with the capacitors, making this a more complex resonant circuit but with the desired feature of having a resonance frequency below the first existing harmonic.
It is easy verify that with this typology of solution the parallel resonance frequency is modified from
Normally the resonance frequency between the capacitor and the series reactance is under than 250Hz and it is generally between 135Hz and 210Hz. The lower values correspond to higher harmonic loads. The installation of a reactance in series with the capacitor bank produces a series resonance frequency:
If a harmonic Ih with the same frequency of the resonance in series exists, this one will be totally absorbed by the system capacitors – reactors without any interest on the network. The realisation of a tuned filter is based on this simple principle. This application is required when we want the reduction of the total distortion in current (THD) on the system:
I1= Component at the fundamental frequency (50Hz) of the total harmonic current;
I3, I5…= Harmonic components at the multiple frequency of the fundamental (150Hz, 250Hz, 350Hz, ...).
The dimensioning of these equipments is linked to the circuit parameter:
- impedance of the network (filtrable effect less as the short-circuit power on the network increases: in some cases could be useful to add in series with the network a reactance to increase the filtering effect);
- presence of possible and further loads that generate harmonics linked to other nodes on the network;
- capacitor types.
About this third point we must remark. As we know the polypropylene metallic capacitors (standard capacitors) lose capacitance during time of operation; for example it could happen that after 2-3 years the capacitance decreases by 5% or more (this phenomena is caused typically by voltage and temperatures rise). Decreasing the capacitance automatically varies the series resonance frequency
and this inconveniently could be very dangerous because the system could have parallel resonance. In this case not only does the filter does not absorb any more of the harmonics but it amplifies them. To have the guarantee of a constant capacitance during the time it is necessary use another type of capacitor in bi-metallic paper and with polypropylene totally impregnated (3In type).
Besides the tuned filter made of capacitors and inductance (passive filter) it is possible, to remove the harmonics in the network, to use another type of construction of tuned filter: the Active Filter. The working is based on the injection in the network of the same current harmonics created by the non-linear loads but with angle phase.