Z-Transform Models for the Analysis of Electromagnetic Transients in Transformers and Rotating Machines Windings

Z-Transform Models for the Analysis of Electromagnetic Transients in Transformers and Rotating Machines Windings

Charles Su (Charling Technology, Australia)
DOI: 10.4018/978-1-4666-1921-0.ch008


High voltage power equipment with winding structures such as transformers, HV motors, and generators are important for the analysis of high frequency electromagnetic transients in electrical power systems. Conventional models of such equipment, for example the leakage inductance model, are only suitable for low frequency transients. A Z-transform model has been developed to simulate transformer, HV motor, and generator stator windings at higher frequencies. The new model covers a wide frequency range, which is more accurate and meaningful. It has many applications such as lightning protection and insulation coordination of substations and the circuit design of impulse voltage generator for transformer tests. The model can easily be implemented in EMTP programs.
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Conventional Transformer And Rotating Machine Models For Terminal Transient Analysis

Transformers, HV motors and generators have complicated winding structure. Under surge voltages at the terminal, their responses are very complicated and are dependent on the frequency of transient. At low frequencies, they can be simulated by their inductances and loss resistances. As shown in Figure 1, a two-winding transformer is represented by its leakage and magnetizing inductances (L1, L2 & Lm), winding and core losses (R1, R2 & Rc) and an ideal transformer with the turn ratio of N1 and N2. In order to consider the stray capacitances, Baccigalupi (1993) added three capacitances to the transformer equivalent circuit, as shown in Figure 2. However, it was found that these simple models could not accurately simulate the transient at transformer and rotating machine terminals.

Figure 1.

The general equivalent circuit for a two-winding transformer at low frequencies

Figure 2.

The general equivalent circuit for a two-winding transformer with stray capacitances

Much work has been done on the models in which the distributed characteristics of the transformer and rotating machine windings are considered. In the early 1950’s, Abetti (1953) introduced the electromagnetic model of the transformer core and windings to represent all of the self and mutual inductances, supplemented by an equivalent circuit of capacitances connected in the circuit at a multiplicity of points. The R, L and C ladder networks were also analysed by other researchers such as Lewis (1954). Based on the uniformed or almost uniformed equivalent circuit, detailed mathematic derivations were done and complicated close-form equations were derived. These equations are useful for the theoretical analysis of voltage distributions and electromagnetic transients in the winding. However, they are too complicated for the calculation of terminal transients.

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