The latching relay uses a permanent maget in each state to hold the contacts.
A coil with a magnetic force and pulsed current is capable of pulling the armature contacts away from the permanent magnet with much higher strength to accelerate with sufficient velocity that the transition time bewteen states to minimize contact chatter or perhaps the arc time for inductive currents.
en-g5rl_uk.pdf G5RL-K1A-E-DC12 Omron Electronics Inc-EMC Div | Relays | DigiKey
Drivers
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you have a choice between dual coils or single coil which requires dual low side drivers or a dual half bridge or full bridge.
The flux in the solenoid action must change direction. This can be a single coil with a center tap common to the V+ supply with either winding shunted to ground to force the momentary acceleration ( hopefully in the opposite direction of the current state. THese are usful for low side dual drivers using common emitters a.k.a. open collector or open drain switches to ground. ( or smart "low side switches" with thermal protection.
The switched current starts at zero for the inductive load then rises quickly with L/R time constant as it accelerates to the opposite state, where at maximum velocity counter EMF is produced and thus current is miniimum until it slams again the end stop and then current ramps up to the V+/DCR resistance of the coil again.
Since these types of relays have greater magnetic force needs, the resistance of the coil and thus current is a much higher percentage of the maximum contact thermal ( resistive ) current ratings.
It is common for DC relays to have 12V coils and 240V contact ratings with a coil current / contact current ratio of 1:2000 compared to a transistor this may seem like a pretty high current gain and it is, but not for a FET switch. However for Latching ratios, this RATIO is much lower due to the forces required and thus the time for the operation must follow the device specs but consider the size of the part , self heating applied/rated voltage ratio and applied/required time to complete the transition.
This transfer can be defined in terms of energy so that sufficient stored energy is kept with a AC charged storage cap to dump the energy to transfer the power to the relay coil.
I dont know the exact formula
but the basics are integrated RMS energy min. E= V(t)*I(t)*t vs stored inductive energy + losses Pd= 1/2LI^2 + I*DCR*t and similar for the Cap. Pc = 1/2C(Vi^2-Vf^2) + I(t)^2*ESR where final voltage results in no force against opposing permanent magnet.