Terminal Measurements-Based Series Capacitance Estimation of Power Transformer Windings Using Frequency-Domain Subspace Identification

Estimating the series capacitance (
$C_{s}$
) of power transformers is challenging due to the lack of direct measurement methods and the impracticality of traditional approaches such as analytical formulas or finite-element simulations without design specifications. Furthermore, iterative optimization-based evolutionary algorithms do not yield a unique and physically feasible solution. In this article, we propose an indirect method for estimating
$C_{s}$
of an
$N$
-section ladder network of a transformer based on the frequency response input impedance
$Z(s)$
and effective shunt capacitance (
$C_{g,\text {eff}}$
) measured at the winding terminals. The proposed method involves estimating a continuous-time state–space model from
$Z(s)$
, converting it to pole-zero-gain (
$p-z-K$
) form, and solving a matrix equation using estimated values of
$K$
and
$C_{g}$
(calculated using
$C_{g,\text {eff}}/N$
). The accuracy of the proposed method is validated through simulations and experiments on various types of windings. This method provides precise results and is particularly valuable for older transformers where detailed information about the winding geometry is unavailable.