Recently, arc suppression coils are often completed by active systems connected to the secondary winding such as ground fault neutralizers, active earthing and fault localization systems, or systems for current injection. These systems often operate with quantities related to the primary winding. However, direct measurement on the high-voltage side is often not possible. This paper deals with a frequency-independent mathematical modeling of arc suppression coils (Petersen coils) which would enable to simply recalculate quantities from the secondary to the primary side of the coil. Unlike traditional transformers, mathematical modeling is more complicated due to significant difference between high-voltage primary and low-voltage secondary side, high leakage flux, variable coil inductance and variable magnetic circuit topology caused by tunable air gap.