A New Three-Phase Three-Winding Transformer Electromagnetic Transient Model

Abstract

This paper firstly points out a defect of the damping trapezoidal method in electromagnetic transient simulation algorithm. The backward Euler method is recommended to use. Then, a new three-phase three-winding transformer model which could consider ratio and connection group feature is put forward. Compared with PSCAD, it is obtained the proposed model is accurate and reliable. In view of the implicit trapezoidal method with considerable accuracy and good numerical stability, the electromagnetic transient program mostly uses this method. But when the grid topology changes, non- state variables abrupt at same time, the implicit trapezoidal method calculates the equivalent current source of the abrupt time which is based on the abrupt non-state variable's value; this will result in numerical oscillation (1, 2). Obviously this oscillation is unreasonable. There are always two ways to eliminate this numerical oscillation which are backward Euler method (3-5) and the damping trapezoidal method (6). The former is that the implicit trapezoidal method has been using when the network topology remains unchanged; and the backward Euler method is used when the network changes, then cut back to the implicit trapezoidal method. As this method avoids the abrupt non-state variable values, and only uses non-abrupt state variable's value, it could solve the problem of numerical oscillation, but its programming is slightly more complex. The damping trapezoidal method takes the numerical calculation by mixing the implicit trapezoidal method and backward Euler method together from start to end, which is regardless of the grid topology whether changed, so it is easy to program. As to three-phase three-winding transformer model, paper (2) considered the three-winding transformer magnetizing slip alone, so it can not consider the transformer connection group. The transformer model of paper (7) is based on the controlled current source model which could consider the connection group feature and the ratio. This paper presents a new kind three-phase three-winding transformer electromagnetic transient model which takes into account the ratio and connection group feature. The transformer is taken as a coupling circuit of multi-slip series resistance and inductance. The connection group feature is achieved by the relationship of transformer's winding connection, and the ratio is simulated by the matrix of relationship of winding voltage/current and terminal voltage/current. This paper firstly points out a serious defect of damping trapezoidal method in the electromagnetic transient simulation algorithm, and the backward Euler method is recommended. Then a new three-phase three-winding transformer model is proposed which could consider the ratio and connection group feature.