A voltage regulating transformer changes its tap ratio to maintain a constant voltage magnitude at its regulation point. The normalized change in voltage (denoted by v) required to bring the regulation point to its designated value is just
k is the regulated vertex.
is the specified (desired) voltage at vertex k, the regulation point.
Vk is the actual voltage at vertex k.
Assuming that the normalized change in voltage at the regulation point is proportional to the normalized change in voltage at the transformer’s secondary, the secondary voltage must change as follows
where is the constant of proportionality.