Parameter identification of the transformer winding based on least-squares method

The principles of the equivalent circuit principle and the magnetic property theory are not affected by the inrush current and over-excitation, which enable protection to act rapidly and reliably and implement ideas different from differential protection. However, the leakage inductance and resistance of each winding are required as priori parameters. At present, there is no accurate measurement method for the transformer winding parameters. Therefore, it is very important for a method to accurately estimate the leakage inductance and resistance of the transformer. A new identification algorithm for transformer winding parameters is presented in this paper. Based on the electromagnetic relation between the primary and the secondary sides, the equation for transformer flux balance can be derived based on the transformer model. Through the elimination of the ratio of flux change with respect to time change from the equation, the discrete flux balance equations can be obtained through discrete process. Using the derivative of voltage and current as the input and output variables, the leakage inductances and resistances of every winding as the identification parameters, an identification model for transformer is built. Then parameters can be identified using this model. The least squares method based on the orthogonal decomposition is used to identify the winding parameters in this paper. A modified orthogonal method is adopted which is able to improve the numerical stability of classical Gram-Schmidt orthogonal method in the calculation. The requirement for the input signal is also discussed. The input signal should include sufficient number of frequencies with sufficient exciting time. If a system has n parameters to be identified, continuous excitation signal should contain at least n/2 different frequency components. Considering the actual operating conditions, this paper uses data from both sides of transformer when it is switched on with no-load and over-excitation to identify the parameters. The simulation results of electromagnetic transient program EMTP show that the parameters identified by the method proposed in this paper are very close to the true values with vary small errors. When data of transformer switching on with no-load is employed, the error of resistance is round about 1% and the error of inductance is less than 0.1%. When data of over-excitation is employed, the error of resistance is under 3% and the error of inductance is about 0.3 %. The characteristic of the multi-value and convergence of least squares method are greatly improved by the method proposed in this paper. In a certain range, more accurate identification parameters can be achieved by using the longer data length. The correctness of the identification results are also verified by simulation test. It has a great potential for the application to online identification.