joan271273 is on the right track - the Petersen coil is tuned to the system distributed capacitance; the tuned circuit comes into play when there is a ground fault, minimizing the current in the fault. The reactive current flowing in the coil balances the capacitive charging current in the two unfaulted phases - if properly tuned, transient faults are self-extinguishing.
This grounding system has been used mainly in Europe, but also some areas in the US. As I recall, there was a good IEEE (or AIEE) paper on the topic published sometime around the late 60's.
All system equipment and insulation (PTs, line insulator strings, transformers, surge arrestors etc.) has to be rated for full line-line voltage to ground. Weak insulation anywhere in the metallically connected system is vulnerable to breakdown when a ground fault occurs - this can lead to "cross country" faults on other phases, which can result in unexpected relay operations at widely different geographical locations.
The coil works to clear transient faults. If a permanent ground fault occurs, there is a need to close a bypass switch (or breaker) across the coil to solidly ground the system - this allows regular ground relaying to operate & selectively clear the faulted circuit. The switching is initiated by a definite time neutral displacement voltage relay & needs to be coordinated at all grounding points.
In addition to the manufacturers mentioned in the previous posts, I have worked in the 70's with a coil made by Toshiba.