My experience is from the distribution perspective.
I understand that while the same principles apply, there are significant differences between transmission and distribution due to protection schemes and because loss of one phase is much less likely on a transmission circuit.
I spent about 15 years in an area where grounded wye/delta transformer banks were common, let me tell you about the possible issues.
How does a delta winding stabilize voltages?
First lets look at the difference between EMF and terminal voltage.
The terminal voltage is the EMF minus the internal voltage drop.
Second, lets look at the delta as represented by an equilateral triangle.
The with a balanced supply, the equilateral triangle may represent the delta EMFs, the delta or the delta terminal voltages.
The angles of the sides of the triangle are locked by the phase angles pf the grounded wye primary circuit.
What happens when the voltage is low on one phase?
If you draw the vector diagram, the triangle will not close on itself.
Let's state a 10% difference.
But how can we close the delta (closed physically by the delta connection) if the angles are locked at 120 degrees but the voltages are different?
The answer is by circulating currents.
The circulating current is limited by three times the transformer impedance.
Thus a 10% voltage unbalance on a 3% imp transformer will cause a current of 10%/9% = 111% of full load current to flow in the delta.
This current is in a direction to cause a voltage rise on the low voltage phase and a voltage drop on the full voltage phases.
So while the EMFs may differ from phase to phase, the terminal voltages will be equal due to the combination of internal voltage drops and rises.
I am skipping over the effects of voltage drops in the supply conductors and possible phase angle errors due to a voltage drop in the primary neutral conductor.
An unloaded grounded wye/delta transformer bank may be overloaded by a voltage %unbalance over 3 times the %imp of the transformer.
Let's hope that the tertiary impedance is higher than the working impedance, although the higher the tertiary impedance the less effective it is in balancing the voltages.
Without a tertiary, the plant motors try to act as the balance mechanism.
A effect related to the impedance of the motor interacting with the impedance of the supply conductors and the impedance of the supply transformer determine how effective the motor is at balancing the umbalace, but as more motors go online, they share the correction duties and the voltage unbalance at each motor is less.
A tertiary delta will reduce the unbalance and extra heating at the motors and replace it with extra heating of the transformer.
What is the downside of a grounded wye/delta connection?
Worst case example, your plant is on a shared distribution circuit.
One supply phase is lost to your plant and other customers.
Now the two healthy phases act as an open delta and back-feed the winding with the missing primary.
The transformer back-feeds to the primary circuit and now the failed phase of the distribution circuit is energized at both sides of the open circuit.
That back-feed will supply the missing phase to the other shared services on the primary circuit.
Your wye/delta transformer may be badly overloaded.
A grounded primary conductor may have the effect of 1/3 of a short circuit on the wye/delta transformer.
When considering a tertiary winding you may want to consider the following questions:
How likely is a loss of phase?
What is the impedance of the tertiary winding?
Will we have phase loss protection on the system?
Are other other loads on the distribution circuit that may be fed by the wye/delta in the event of a phase loss?
On the other hand, a lot of large motors may develop a similar back-feed until differential protection or overload protection takes them offline.
Oh, and by the way, with the loss of two primary phases, the two lost phases will be back-fed by approximately 50% of rated voltage.
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Ohm's law
Not just a good idea;
It's the LAW!