The Modeling Study Of Three Phase Transformer Based On Electric Quantity Transformation Matrix Method

The modeling of three-phase transformer is the key to the three-phase power flow calculation of distribution network.The node admittance matrix can be obtained through transformer modeling.The symmetric component method and incidence matrix method can be used for derivation.The former is relatively simple,but it is not suitable when the transformer parameters are asymmetric.The incidence matrix method can solve this problem by representing the incidence matrix between the electricity quantities.Using the incidence matrix method,the voltage and current incidence matrices are obtained separately.In most cases,these two matrices are mutually transposed,and the derivation process is relatively easy.However,in the connection group with a star ungrounded connection,the potential at the reference point is not zero,and the two are not transposed.The incidence matrix of voltage and current needs to be obtained separately.Using the transformation matrix method based on the electrical quantity,the neutral point potential needs to be listed for the voltage-related matrix,and the matrix obtained at this time is 6 by 7 order.By reducing the neutral point potential,the matrix is reduced to a 6 by 6 order.The matrix expresses the voltage relationship by this transformation matrix and combines the current matrix to obtain the node admittance matrix of the transformer.The connection mode,winding polarity and phase sequence arrangement of the transformer primary and secondary windings may generate a variety of different node admittance matrices,and the node admittance matrix is gradually deduced,which is complicated and cumbersome and error-prone.Therefore,Matlab symbolic operations can be used to achieve the derivation of symbolic expressions,resulting in non-numeric result expressions,ie solutions in symbolic form.In the process of designing the program's algorithm,by studying the establishment of the incidence matrix,we can find the rules and use the rules to simplify the derivation of the node admittance matrix of different connection groups,and establish the incidence matrix or transformation matrix of the primary winding and the secondary winding respectively.Based on the electric quantity transformation matrix method to study the three-phase transformer unfolding modeling,it can be seen that the traditional incidence matrix method is suitable for transformer connection groups that do not contain a neutral point ungrounded,but when one side is not grounded,it is necessary to adopt a transformation matrix method.Although different connection methods of transformers lead to a large number of connections,by studying the changes of the primary(secondary)winding's incidence matrix,the establishment law of the transformer's incidence matrix or transformation matrix can be found to simplify calculation and programming.