How a filter do in the power system?

The application of a filter to a power system requires that, first, you know how much capacitive vars are necessary to accomplish the power factor correction you seek. Then, the process involves measurement of system loads at the secondary of each transformer. The measurement must provide the harmonic content of the current. This is determined by harmonic magnitude and phase angel for each harmonic at each location. Armed with this data, you must also develop the short circuit model, load flow model, and utility fault contribution on a software package capable of running the digital harmonic study. ETAP, SKM, etc.

Once the model is properly created, the filter can be designed. In a typical three phase system the filter would be designed for the 4.7th harmonic. This is typically selected because 6 pulse drive systems will produce approximately 17% 5th harmonic current. That's 17% of the max drive current rating. Using higher order filters will result in the need for lower order filters, thus we start at the lowest possible harmonic.

Then this filter design is inserted into the model. Then calculations will show if the capacitor ratings are exceeded for voltage, KVA, and amperes. Then, it is recommended that small changes to the model be tested, such as the loss of a single capacitor can. This will determine if any change in system tuning will occur. It is very critical to be absolutely sure resonance is never possible.

While this sounds simple, it is quite time consuming and I strongly recommend that you utilize the services of an engineer having a lot of experience in this area.

Now, if your concerns are in the order of triplen harmonics, that is a very different approach. It involves trapping the triplens in the delta winding of a transformer. Simple, but must be approached carefully because of overheating.

I will respond with reference to a mains-connected passive filter. These may be designed to be effective at one frequency (or rather a band of frequencies) but due to the upstream (or downstream) network impedance, i.e. inductance, they may be unintentionally tuned to another frequency. The significance of the network frequency depends on whether there are there harmonics present at a significantly high level. For example, consider the world is full of non-linear loads that generate triplen harmonics (3rd, 9th, 15th etc). If the mains-connected filter is unintentionally tuned to (or close to) the 9th harmonic then it could cause resonance with the harmonic generating loads, resulting in problems related to the resulting potential difference, such as that voltage could exceed insulation levels or have adverse effects on electromagnetically induced circuits.