The transformer is an important piece of transmission and distribution equipment in the power system, and there is a significant amount of loss. Transformer losses account for approximately 8% of total power generation capacity in China’s power grids. Dry type distribution transformer losses account for 60% to 80% of total distribution network losses [
1,
2,
3]. The efficiency of the transformer is directly related to the efficiency of the grid’s power conversion and is an important economic indicator for electrical energy transmission. The power characteristics of distributed power generation and the diversity of loads in the new type of distribution network can cause power quality pollution in the distribution network, such as harmonics, three-phase voltage imbalance, voltage fluctuations, and flicker. Distributed power generation degrades distribution network power quality and increases distribution network losses [
4]. As a result, an in-depth examination of transformer loss calculation under power quality disturbance is extremely useful in reducing network losses and optimizing distribution network structure. The abbreviations involved in this paper are shown in
Table 1.
The equivalent model method, the parametric method, and the harmonic factor method are the three main analytical methods for calculating transformer harmonic losses. This paper [
5] compares six commonly used transformer harmonic equivalent models and validates the applicability of the currently used transformer harmonic simplification models. In the literature [
6], a transformer harmonic loss model based on circuit theory was developed to derive a formula for calculating transformer harmonic loss. However, the harmonic winding resistance model
in this model has errors at high frequency harmonics. In the IEEE Std C57.110 standard [
7] the correction method for eddy current losses and additional losses in transformer windings under harmonics is proposed. In this standard the concept of harmonic lead-in is introduced, but harmonic winding ohmic losses are not corrected. In the literature [
8], the concept of AC resistance factor
is proposed for improving the harmonic winding AC resistance formula, the accuracy of which is yet to be verified.
Numerical models are frequently used to solve such problems in order to obtain an accurate model for calculating transformer losses under harmonic conditions. In terms of the means and accuracy with which the problem can be solved, the numerical method outperforms the analytical method. Because of its high computational accuracy and ability to adapt to various complex shapes, the finite element method has become a proven analytical tool in engineering. Several researchers used the finite element method of field-path coupling to model the two-dimensional structure of the transformers used. In the literature [
9,
10], researchers have analysed the leakage field distribution and the influence of harmonic currents on harmonic losses. The Finite element analysis software ANSYS was used to build a simplified two-dimensional simulation model of the leakage field of the transformer, but the two-dimensional model simulation is subject to some errors with respect to the actual operating conditions [
11]. A 3D simulation model of the transformer electric-magnetic-structural force field was established in [
12], which basically matched the simulation results with the test data to verify the effectiveness of the 3 D finite element method. The Steinmetz model was used in [
13] to investigate the magnetic loss characteristics of transformers. The effect of harmonic characteristic quantities on the core loss characteristics was investigated using the generalised Steinmeth model, and the simulation results demonstrated that the method has a high degree of computational accuracy. Furthermore, using the field-circuit coupling method and a finite element model, the loss characteristics of a high-voltage DC converter transformer, a filter transformer, a harmonic filter distribution transformer, and a high-speed permanent magnet generator were simulated. The method’s validity was established [
14,
15,
16,
17,
18,
19,
20]. Kamran Dawood et al. [
21] proposed a method for determining the leakage impedance in the tap winding using finite elements. For all cases, the difference between the finite element models and the experimental short-circuit test was less than 1%. A design method for economical, low harmonic loss distribution transformers is presented in the paper [
22]. Yazdani-Asrami et al. [
23] used the finite element method (FEM) to simulate and analyze the effect of non-sinusoidal voltages on distribution transformer no-load losses. The simulation results show that increasing the THD of distorted voltage will significantly increase the transformer’s no-load loss. In literature [
24], an analytical algorithm for calculating the hysteresis losses of three-phase HTS transformer windings in the presence of harmonic loads is presented and the results show that this algorithm is highly accurate. Susnjic et al. [
25] used 3D FE analysis to calculate eddy current losses in power transformers generated in yoke ply-wood and unshielded tank walls. A numerical study of copper losses in three-phase transformers with different geometrical designs was carried out using the finite element method by Chiu et al. [
26]. The results show that the eddy currents in the windings cause additional losses. The non-sinusoidal AC losses of coils have been studied using the finite element method by M. Yazdani–Asrami et al. [
27]. The results of the study have important implications for the design of HTS transformers and HTS power cables.
The effect of harmonic voltage and harmonic current on the iron and copper losses of transformers is investigated in this paper. An analytical calculation model for transformer iron and copper losses under harmonic action is developed. A three-phase 10 kV transformer model is created using a field-circuit coupled model and a finite element simulation model to calculate transformer core and winding losses, and the effects of harmonic voltages and currents are quantified.