Dimensioning passive filters

The spread sheet serves to adequately size a passive filter or a detuned static var compensator consisting of a combination of two acceptor circuits, which means two serial circuits made up of one capacitor and one reactor each and operating in parallel connection with each other.

In the input sheet you enter your data into the marked cells, which is:

• Your mains voltage and frequency and the data of the two filters, which include the capacitance, the reactance and the ohmic winding resistance of the reactor (required) and
• the levels of harmonic voltages you find on your system (optional).

All of the other cells are locked, but without password protection, so if desired, they can be modified. The initial values which you find entered from the start for the acceptor circuit '5', the one meant to be the one with the lower resonance frequency (although this need not be so), are those from a practically existing var compensator rated 67.4 kvar and detuned by 7%. The inductance and capacitance figures for circuit '7' are converted from these using a ratio of 5/7. But you enter your own data here.

The two filters are named '5' and '7', since in case they are meant to form a passive filter, the filter will usually be tuned to the 5th and 7th harmonic, but this need not necessarily be so. If the whole plant is designed to be a detuned var compensator, one will usually avoid to tune the resonance frequencies of the acceptor circuits to any harmonic, i. e. an integer multiple of the mains frequency. '5' and '7' are only names here.

In the output table your results are given, among these the voltage and current load of each single component for the fundamental of each single harmonic and in total, plus the total ohmic loss in the reactor winding. Other losses are not included in this consideration because those in a capacitor are comparatively low and iron losses are not linear and require a separate consideration. This table can only make a rough first assessment.

The calculation of the L and C loads caused by the harmonics is an absolute worst case scenario because it assumes that the harmonic voltage levels, measured before installing any filter, will remain the same afterwards. Of course this is not the case, otherwise it would make no sense at all to install the filter! But to calculate the reduction of harmonic voltage levels when the filter is turned on would require knowledge of the system’s inner impedance at each particular harmonic frequency, which is not given.

The output chart works independently of the voltage harmonic levels and represents the filters’ behaviour in principle. The blue lines are the impedances of each single serial filter and both of them operating together in parallel, and the red lines give the commensurate phase angles.

Now feel free to modify your input data and see the changes of behaviour and the maximum possible load on your components!