At first, if you are using passive filters, your system always have a parallel resonance because there are always a source and transformer impedance. To avoid parallel resonance you should use Active Power Filters (APF).

You should consider 2 cases.

The first case is that the load does not behave as a harmonic source. Since load current does not contain any (significant) harmonics, the harmonics produced by TCR is seem to be low as compared to load fundamental current. Then you may use one or two passive filter(s) for the most dominant harmonics that are exceeding allowable limits (suggested in standards). You should consider the parallel resonance with source and transformer impedance. You should tune your parallel resonance frequency to a non characteristic frequency of TCR current or any possible frequencies in the power system so that you may not cause any over currents. Also never exactly tune your passive filters to a frequency, make them detuned a little bit.

The second case is  that the load ,itself, is a harmonic source. For this case, the load may contain characteristic integer multiplication harmonics or any inter-harmonics regarding the type of the load. Then, if you use passive filters to compensate harmonics, it is possible to increase some frequency components because most of the times more than 3 shunt passive filters are needed, especially if your load is in metal melting industry. For a general rule, you should compute an AC Analysis with a correct model of load and source, try to keep parallel resonances away from current harmonics. For some loads, especially containing low frequency currents, it is not always possible to avoid parallel resonances, that time you should keep the parallel resonance gain at a reasonable values so that the resonance currents may not cause any damage.

My solution and the certain solution that would not cause any parallel resonance is Active Power Filters. Also you can provide reactive power compensation, voltage regulation and possibly flicker mitigation using active power filters. I have designed and succesfully operate 2 active power filters, having installed capacity 2.5 MVA, if you have any questions regarding APF's I can try to help.  

Your question is not clear. Current harmonics produced by TCR are taken care of by adding a shunt connected series tuned LC filter across the lines. If the tuning is at 5th harmonic, then the series LC network, which is connected across the lines,  behaves as near-zero impedance for the 5th harmonic of current, hence providing a low impedance shunt path instead of the higher impedance path back to the source.

The same LC network will behave as a capacitor at fundamental frequency and you might consider this effective capacitor to resonate with the TCR. Even that will happen only at one value of firing angle. However, since this is in parallel with other capacitor banks (TSC) in a static VAR application, where the TCR is used only to smoothen the steps created by the TSC, what is vital is smooth variation of VAR with reduced current harmonics.

Hi,

Below paper is useful:  

Asiminoaei, L.; Blaabjerg, F.; Hansen, S., "Detection is key - Harmonic detection methods for active power filter applications," Industry Applications Magazine, IEEE , vol.13, no.4, pp.22,33, July-Aug. 2007

doi: 10.1109/MIA.2007.4283506

This article gives a survey of the commonly used methods for harmonic detection in active power filters (APFs). The work proposes a simulation setup that decouples the harmonic detection method from the active filter model and its controllers. In this way, the selected methods can be equally analyzed and compared with respect to their performance, which helps in anticipating possible implementation issues. A comparison is given that may be used to decide the future hardware setup implementation. The comparison shows that the choice of numerical filtering is a key factor for obtaining a good accuracy and dynamic performance of an active power filter.

Go for active power filters to avoid resonance problem. Also they provide efficient harmonic mitigation.

Thyristor-Controlled Reactors (TCRs) are commonly used for reactive power compensation in power systems. However, TCRs can generate significant levels of harmonic distortion, which can cause problems in the power system. There are several methods for compensating the harmonics produced by TCRs, including passive filtering, active filtering, and series resonance compensation. Here are some common methods for 5th harmonic mitigation:

In summary, passive filtering, active filtering, and series resonance compensation are all effective methods for compensating the harmonics produced by TCRs. For 5th harmonic mitigation, a passive or active filter can be designed to specifically target the 5th harmonic component, while series resonance compensation can also be used to attenuate the 5th harmonic component. The choice of method depends on the specific application and system requirements.

Rana Hamza Shakil

I am curious about the methodology of:

"capacitor/inductor is sized to resonate at the 5th harmonic

while the inductor/capacitor is sized to provide the required inductance/capacitance"

Is not the resonance dependent on both the L and the C together ?

I am not clear how a specific inductance or capacitance would be

selected to resonate at a particular frequency....

and then a C or L selected after that.

Perhaps that takes into account the "parasitic" characteristics

of the circuit either calculated or measured ?

I can provide you with the mathematical formulas commonly used for designing the values of inductors and capacitors in resonance compensation circuits. The formulas depend on the specific circuit configuration and requirements. I'll outline two common cases: series LC resonance and parallel LC resonance.

To design the values of L and C for a desired resonance frequency (fr), the formula can be rearranged as: L = (1 / (4 * π^2 * f_r^2 * C)), C = (1 / (4 * π^2 * f_r^2 * L)). Where: fr = Resonance frequency L = Inductance C = Capacitance π = Pi (approximately 3.14159)

2. Parallel LC Resonance: In a parallel LC resonance circuit, the inductor (L) and capacitor (C) are connected in parallel. The resonance frequency (fr) is given by: fr = 1 / (2 * π * √(L * C)). To design the values of L and C for a desired resonance frequency (fr), the formula can be rearranged as: L = (1 / (4 * π^2 * f_r^2 * C)); C = (1 / (4 * π^2 * f_r^2 * L))

The same formulas are used as in the series LC resonance, but the interpretation of L and C changes since they are in parallel. These formulas provide a starting point for selecting the values of inductors and capacitors for resonance compensation circuits. It's important to note that practical considerations, such as component tolerances, parasitic elements, and system requirements, may require adjustments and iterative refinement in the design process. Simulation tools and experimental validation are often employed to optimize the values and achieve the desired performance.

Rana Hamza Shakil

Thank you.

I see that with these equations one must at some point

make a semi-arbitrary experience-based choice for L or C

and then use the equation to select the associated C or L

and then recursively tweak L and/or C to compensate for parasitics

to optimize the resonance / 5th harmonic reduction.

For filtering of different harmonise, it is advised to use either passive LC filters for the even and odd harmonics or use tunable active filters.