18 kV to 13.8 kV, 4.16 kV sounds like a power plant auxiliary transformer fed from the 18 kV generator bus to supply in-plant generator loads.
The three winding transformer saves money and space with only one foundation, one HV input, one HV circuit breaker or tap.
Disadvantages: Since it is custom, it is hard to find a replacement if it fails. The voltage taps cannot be changed individually for the 13,8 and 4.16 kV. Any trip on one system trips the other.
Three winding transformers can also provide some benefits for short circuit issues by selecting different impedances for the H-X, H-Y and X-Y windings. For example, if there is a generator on the 13.8 kV winding and utility at 18 kV, the 18-13.8 kV impedance could be low for good MVAR capability and voltage control with the 13.8 kV-4.16 kV impedance high to limit 4.16 kV SC levels.
Biggest savings is when the high voltage connection is on a bus with high short circuit levels (>100kA) or high voltage (>69kV) and we can save the $1M cost of a second breaker.