  This paper presents a new method to determine the susceptances of a reduced
transmission network representation by using nonlinear optimization. We use
Power Transfer Distribution Factors (PTDFs) to convert the original grid into a
reduced version, from which we determine the susceptances. From our case
studies we find that considering a reduced injection-independent evaluated PTDF
matrix is the best approximation and is by far better than an
injection-dependent evaluated PTDF matrix over a given set of
arbitrarily-chosen power injection scenarios. We also compare our nonlinear
approach with existing methods from literature in terms of the approximation
error and computation time. On average, we find that our approach reduces the
mean error of the power flow deviations between the original power system and
its reduced version, while achieving higher but reasonable computation times.
