Linear Models of Power Transformers—Derivation of Equivalent Models and Comparison of Results From a Case Study of Circuit Analysis When Used as a Terminal Device

ABSTRACT

Power system analysis has always been a nonlinear task—both in terms of characteristics of components as well in the formulation of the problem. The practices followed in power system protection, operation, and control have been based on the nonlinear analysis of power system. However a linear analysis can clarify many issues related to power system. A linear model for a single‐phase transformer is the focus of this study—given its ubiquitous presence in power systems. However not much work appears to have been done towards a systematic approach for the development of its model and obtaining equivalents. On the one side there is a model obtained from open‐circuit measurements on two ports and on the other side there is a referred model obtained from short‐circuit test on one side. Both models incorporate a shunt branch to account for the no load losses and the no load current. It is intended to study these models and their derivatives, compare the performances, and find out reasons for the deviations. The process of obtaining the equivalents is neatly laid‐out with all its features. A T‐equivalent (M3) and the generally used simplified equivalent circuits (M4) are derived from a true and base model. The parameters are obtained for a laboratory grade 2 kVA, 230 V/230 V, 50 Hz, single‐phase power transformer. The parameters for the equivalents are computed and presented, highlighting their dependency on frequency. Steady‐state and dynamic analysis of all the models are discussed, highlighting their features, by considering the case of a transformer used as a terminal device—connected at the end of a power system network supplying a load.