## 1 Introduction  
Due to the geomagnetically induced current (GIC) caused by periodic solar storms, monopole operation of the large-scale construction of high voltage direct current (HVDC) transmission and harmonics caused by the increasing nonlinear loads in the power grid, the direct current (DC) flows through the earthed neutrals of the transformer and cause a DC bias to the magnetizing current of the transformer [1; 2; 3; 4; 5]. This results in the asymmetric magnetic core saturation during a sinusoidal half-period, the serious distortion of excitation current, increased reactive power absorption, partial overheating and increase of vibration and noise [6; 7; 8; 9; 10; 11; 12]. Because of depletion of fossil fuel reserves and increasing demand for energy consumption, the ultra-high voltage UHV transmission projects have been put into service for solving the energy crisis. The (UHV) autotransformer is the key equipment of the UHV transmission systems, mostly with self-couplingstructure, which has less tolerance to the DC bias [13]. Thus, precise and in-depth analysis of DC bias for UHV autotransformers is necessary for the safe operation of equipment and transmission systems. Much in-depth research and analysis have been carried out on the transformer DC bias problem by simulation and experiment. The finite element method (FEM) is widely used in the precise analysis of simulations for its ability to obtain the excitation current waveform, the local flux and losses distribution under DC bias [14; 15; 16; 17; 18; 19; 20]. Nevertheless, the results obtained only through simulation are not convincing enough. Some no-load experiments of large capacity transformer have been carried out to verify their FEM and discuss the excitation current, reactive power absorption, vibration and noise characteristics under DC bias [21; 22; 23]. However, the no-load experimental data do not reflect the actual operation condition of UHV autotransformer, and the research about the winding current distortion of UHV transformer with load under DC bias is significant and urgent, which is rare in the literature. The UHV autotransformer is very expensive and it is difficult to carry out an in-depth investigation on the practical equipment and the DC bias effects on the UHV autotransformer with rated load is impossible to carry out due to the insufficient capacity of the generator, the unaffordable economic cost and the damage to UHV autotransformer. Therefore, the reduced-scale model is a significant method to implement the experiment which cannot be carried out in the practical condition. In [24; 25] some reduced-scale models (RSMs) are proposed to equivalent the practical situation based on the similarity theory and structure characteristics. A reduced-scale model of UHV autotransformer is built and the no-load experiment is carried out based on the magnetic circuit method [26]. However, this reduced-scale model has a very restricted limits of identical core structure, steel sheet material type and the flux density, which is not suitable for general transformer and other operation. For the purpose of discussing the DC bias characteristics of UHV autotransformer with load condition, the RSM has its own unique design theory, based on the theory of identical saturation degree, rather than a simple size reduction ratio is proposed. Its core structure, connection mode and relationship of turns and capacity among each side are consistent with the UHV autotransformer. This paper proposes a new RSM technique, which overcomes the aforementioned difficulties. Firstly, the saturation degree is characterized by the ratio of the second harmonic to the fundamental of the excitation current, which are calculated by a field-circuit coupling FEM. Afterwards, the DC bias current equivalent relationship between the UHV transformer and the reduced-scale model is established by means of the identical saturation degree. Finally, the experiment of the reduced-scale model is conducted with and without DC bias current.