The proportionality constant (referenced in Equation 45 and Equation 42) represents the sensitivity of the controlled voltage to tap changes at the regulating transformer. It commonly assumed that is one (the controlled voltage is perfectly sensitive to tap changes). An alternate assumption is that
is a row vector with 1 in the kth position.
N is a column vector with -bpst in position p and bpst in position s.
Carrying out these matrix operations yields
bij is an element from the nodal susceptance matrix Bbus.
is an element from the inverse of as defined by Stott and Alsac (2).
t is magnitude of the transformer’s tap ratio.