# Efficient Zero-Sequence Impedance Measurement in Autotransformers Using Low-Voltage Excitation
## 1 Introduction  
Power transformers are power equipment for transmitting electrical energy in power systems. In ultra-high-voltage, high-capacity grids of 220 kV and above, the main transformers used include ordinary conventional transformers and autotransformers; the characteristics of both transformers are shown in Table 1[1, 2]. Autotransformers are widely used because of their small size, low cost, large-capacity, high operating efficiency and high short circuit resistance. In the design stage of power systems, there are generally no strict requirements for the size and deviation of the transformer's zero-sequence impedance, nor are there clear calculation formulas; furthermore, the estimation methods are currently used [3]. However, accurate transformer zero-sequence impedance is an important basis for power system analysis, short circuit current zero-sequence component calculation, quantification of transformer short circuit resistance, selection of relay protection devices and calculation of protection calibration values [4, 5]. Therefore, it is important to obtain accurate values of transformer zero-sequences from tests [6, 7]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Transformer Type** & **Size** & **Cost** & **Applicability** \\ \hline Conventional transformer & Larger & Higher & General load \\ Autotransformer & Smaller & Cheaper & Large-capacity load \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The comparison between a conventional transformer and an autotransformer. The information on the transformer parameters is tested by the transformer manufacturer in a series of factory tests before the product leaves the factory, and is recorded in the product's factory report. However, only the positive-sequence parameters of the transformer are included in these tests. The zero-sequence impedance measurement of three-phase transformers is a special test that is carried out by mutual agreement between the transformer manufacturer and the user department [3; 8]. The standard method for measuring the zero-sequence impedance of an autotransformer is given in IEEE Std C57.12.90 [9], which describes two short circuit tests and two open circuit tests with zero-sequence voltages applied to different ports; then, any three of these values are combined to solve for the zero-sequence impedance of the autotransformer [10; 11; 12]. The standard test method is able to measure the zero-sequence impedance of auto-transformers accurately. However, one set of short circuit tests needs to be carried out on the high-voltage side. This test requires special instrumentation and equipment, which is costly for field tests on transformers already in operation, and sometimes impossible due to site constraints [13]. Considering the shortcomings of the standard test method, the literature [14] proposes a method for low-voltage measurement of the zero-sequence equivalent circuit parameters of three-phase, three-winding YNynd-type transformers. However, the test current only measures 1-4% of the rate current because it uses a low-voltage test on the high-voltage side, and this phenomenon can lead to large measurement errors. The literature [15; 16] proposes a method for estimating the zero-sequence impedance of transformers using finite element modelling. However, the method requires knowledge of the specific transformer geometry, winding arrangement and the properties of the core material. To reduce the difficulty of the test, ensure the personal safety of the staff and facilitate field testing, a method for measuring the low-voltage side of the zero-sequence impedance of transformers was proposed in the literature [17]. The method replaces the high-voltage side open circuit test required in the standard test with a low-voltage side disconnection test, mainly for the zero-sequence impedance equivalent circuit of conventional isolation type transformers, and it does not analyze autotransformers, which are widely used in high-capacity grids.