 # HBFEM Model of HVDC Transformer

Consider a three-phase HVDC transformer model with a three-phase voltage-driven source connected to the magnetic system, which is always coupled to the external Figure 3.10 HVDC power transmission system Figure 3.11 B-H curve with hysteresis characteristics and a DC biased condition. (a) DC-biased hysteresis loop; (b) Magnetizing current Figure 3.12 The block diagram of the three phase HVDC transformer including neutral points

circuits [10-13]. The current in the input circuits will be unknown, but saturation of the current waveform occurs because of the nonlinear characteristic of the magnetic core. For a three-phase transformer connected in wye-wye, as shown in Figure 3.12, a computer simulation model with a neutral NN and external circuits for both primary and secondary windings is obtained using the HBFEM technique.

According to the Galerkin procedure, system matrix equations of HBFEM for the HVDC three phase Y/Y connection transformer can be obtained through Faraday’s and Kirchhoff’s laws for the external circuit, as described below : where [Gk] is obtained from a single element - that is, [Ge] = Де/3. [Zin], [Zout] and Sin, Sout are external circuit impedances and cross-sectional areas of windings respectively, [T] is unit matrix, VNN is the voltage of primary or secondary neutral points when it is not grounded, [Cin] and [Cout] are geometric coefficients related to transformer windings, and current density J can be presented as: [H] is the single-element matrix, and the detailed definitions can be expressed from: where matrix D and N are: In the DC-biased case, the D matrix is different from a normal D matrix, due to the DC component v0 being involved in magnetizing, as shown in equation (3-98): The N matrix is also different from the normal N matrix; an additional harmonic 0 is considered in the N matrix as presented below: The system matrix equations of the HBFEM model in a compact form can be obtained as: where the input and output voltages can be defined as: and 