Simple case:
Normal voltage phase to neutral;- 11kV x 1.73 = 6351 Volts.
With the loss of one phase, the other two phases become a series circuit across 11kV.
If the burdens are balanced, each winding will see 1/2 voltage or 5.5kV. The secondary voltages will be 110V x (5500/6351)= 95.3 Volts (86.6%).
For minor burden unbalances the secondaries will share 11kV in inverse proportion to the burdens.
For greater burden unbalances saturation will limit the maximum voltage of the burden with the higher voltage.
The lost phase will show zero volts.
Grounding is important for safety. Grounding does not affect the voltages. A neutral connection is important. A ground connection may also connect the neutral, but not always, depending on the circuit details.
This assumes equal X:R ratios of the burdens. If the power factors or X:R ratios of the burdens is not equal the solution becomes more complicated.
With one phase lost the circuit becomes a single phase circuit and both energized secondaries will be at the same phase angle, (or at 180 degrees if you prefer).
With a three legged core, if the primary neutral is connected to the primary neutral the loss of one phase will result in a blown fuse in the primary or a destroyed transformer due to the effect of the phantom neutral.
Even if the 11kV system source does not have a grounded neutral point, system capacitance to ground will usually form an artificial neutral with sufficient capacity to destroy a metering transformer, so a primary ground connection may be considered as a primary neutral connection.
Quick check: If the system charging current is much above the rated primary current of the metering transformer a primary neutral connection may destroy the transformer.
Bill
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"Why not the best?"
Jimmy Carter