Sorry for the tardy reply.
The selection of a detuning frequency is 1) defined by the objective and 2) customary and usual practices within a country or region of geography or 3) philosophy of the designer.
The 189 Hz tuning represents a detuning to protect the PF capacitors used for power factor correction from 5th harmonic currents (for a 50 Hz electrical system). This tuning actually permits small amounts of 5th harmonic current to flow in the capacitors. The 5th harmonic frequency is at 250 Hz.
The detuning frequnecy defines the amount of 5th harmonic (in this case) current that will be permitted to enter the capacitors. Tuning at the 5th harmonic will result in resonance. So, tuning below the 5th harmonic is done to limit the 5th harmonic current flow and prevent resonance.
189 Hz tuning is at the 3.78th harmonic. This indicates that the resonant point for this PF cap bank is at this frequency. Since this frequency is not suppose to be present it is a safe frequency to prevent excessive 5th harmonic current flow into the capacitors and prevent resonance from occurring. This tuning permits the capacitors to provide power factor correction at the banks rating and survive in a 5th harmonic rich environment
By tuning closer to the 5th harmonic, more 5th harmonic current will flow into the capacitors and provide more 5th harmonic filtering. The capacitors must be increased in current capacity to handle the total higher current as 5th harmonic current flows into the capacitors.
The capacitor bank is considered a 5th harmonic filter when the tuning frequency is above the 4.7th harmonic order. At 4.8, about 80% of the 5th harmonic current is removed from the source system. At 4.9, about 90% of the 5th harmonic current is removed from the source system.
Simulations must be made to review the resonant frequencies that may occur due to adding capacitance into the electrical system. Source characteristics, transformer and cabling impedances, the type of loads installed – both linear and nonlinear – must be included in the simulation. Omission of any data could result in an undefined resonance frequency.
Our engineers typically use SKM Tools to model the system. I assume Matlab can do the job as well.
Something to keep in mind, as capacitors age the farad rating changes. This results in the frequency rating of the detuned circuit increasing. Thus a detuned capacity bank for some frequency below the 5th harmonic will actually over time ‘walk’ to the 5th harmonic frequency and resonate. So, regular maintenace must be performed to insure the capacitors are healthy and are not in danger of causing resonance.
Also, if any of the simulation variables (electrical system, transformers and cable impedance, loads, etc) change the simulation must be reviewed. It is possible to add one load and cause resonance.
Finally, different companies that provide detuned capacitor systems tune to different frequencies. Some of this is based upon their capacitor designs and some is based upon local customs or company philosophy. It is typical to see detuing for PF correction to levels between 3.8 and 4.3. 5th harmonic filters are typically tuned to 4.8 to 4.9. But any tuning can be achieved based upon the needs.
Obviously, tuning to perform 5th harmonic cancellation for the source system costs more than tuning at 3.8th order. The capacitors and inductors must be rated for the higher currents permitted at the higher tuning points.
Hope this helps,