Novel field-circuit assisted FEA of 110 kV power transformer for noise control and vibration reduction

Abstract

The vibration and noise are serious problems for large oil-immersed power transformers, which directly affect the performance and stability of transformers. The no-load current, as the excitation source, is very important for accurate calculation of vibration and noise. This paper provides a novel approach based on the new field-circuit coupling model to calculate no-load current of large power transformers. For one 110 kV large oil-immersed power transformer, the multi-physics coupling problem including magnetic field, structural force field and acoustic field under alternating magnetic field is analyzed. Following the multi-physics coupling calculation, distributions of vibration and noise are obtained. To validate feasibility and applicability of the proposed method, the actual vibration and noise of transformer are measured experimentally. Finally, the simulation results are compared with experimental ones, which show better goodness of fit.

Keywords

Transformer new field-circuit coupling model multi-physics field vibration and noise

1. Introduction

In recent years, with the rapid development of power industry, the 110 kV oil-immersed power transformers play an important role in the transmission system. Due to the influence of DC current intrusion in high voltage DC transmission, the noise problem becomes more and more serious. The noise level of transformer has become an important measure of quality [1]. Researches revealed that vibration and noise of power transformer mainly comes from electromagnetic vibration behaviors including vibrations of core, winding, and structural components [2]. The core vibration mainly results from magnetostrictive effect of silicon steel sheets (SSS) under alternating magnetic field, which makes core vibrate periodically with variation of excitation frequency. Magnetostriction can cause deformation during magnetization process [3,4].

The transformer with large capacity and high voltage level has a large time constant from closing to stable under no-load condition. The closing current decays slowly and lasts for tens of seconds. Previous researches have focused on conventional field-circuit coupling model. By combining an electrical circuit with nonlinear finite element analysis model, the no-load current is solved [5]. The traditional models oversimplify magnetic interactions in core topologies and employ single-value functions for modeling core nonlinearities [6]. For calculation of non-sinusoidal no-load currents, a combination of time domain and frequency domain is used in [7]. Unfortunately, it does not provide enough accuracy. In addition, it is very difficult to solve stable no-load current and core magnetic field distribution directly by using the conventional field-circuit full coupling method [8]. On one hand, it occupies large computer memory; on the other hand, it takes a huge computing time.

To study the vibration of a single structural member of a transformer, the strain, displacement and audible noise of core are analyzed by simulation model [9,10]. The effect of vibration characteristics and vibration shape on transformer noise under three-phase excitation source is studied in [11]. By studying mechanical resonance caused by magnetostriction of SSS, the relationship between vibration and noise of grainoriented SSS and transformer core is analyzed [12,13]. The relationship between magnetostriction of SSS and no-load noise of transformer is studied in [14].

In this paper, a new field-circuit coupling method is proposed to calculate no-load current of a 110 kV oil-immersed power transformer. The coupling problems of magnetic field, structural force field and sound field of the power transformer are calculated by COMSOL software. The vibration and noise of transformer under different voltages are studied.

Fig. 1.

B-H curve of 30Q120.

2. Analysis method of vibration and noise based on the novel field-circuit coupling method

2.1. Calculation method of no-load current by new field-circuit coupling model

In this paper, the main idea of the proposed method is to calculate the 𝜙-I curve based on the new field-circuit coupling model. Firstly, the magnetic flux 𝜙 is obtained by using B-H curve and a series of current values in the static magnetic field. Secondly, a series of 𝜙 and I values are simulated to synthesize 𝜙-I curve. Finally, the no-load current of transformer is calculated by using 𝜙-I curve. In this paper, the core is made of grain oriented SSS (30Q120) and the magnetization curve is shown in Fig. 1. The 𝜙-I curve obtained by static magnetic field is shown in Fig. 2. According to transformer parameters and 𝜙-I curve, the non-linear model of transformer system is established, as shown in Fig. 3. The transformer no-load current from switching-on status to stable operation process is calculated.

Fig. 2.

𝜙-I curve of 30Q120.

Fig. 3.

Non-linear simulation model of transformer system.

2.2. Multiple physical fields FEA for vibration noise analysis

In order to simulate the actual working circuit of transformer accurately, the Y-Δ connection of high and low windings should be considered. The high-voltage side of the transformer is star connection and the low-voltage side is Δ connection. Under normal alternating magnetic field, the coil is replaced by resistance and inductor. Under no-load operation, the impedance Z is infinite; the secondary side is open circuit as shown in Fig. 4.

Fig. 4.

Transformer equivalent circuit diagram.

Fig. 5.

Single-valued curve of magnetostriction.

The no-load current is taken as excitation of magnetic field governing equation. In the magnetic field analysis, only the transformer core is analyzed. The boundary of solution region is set as magnetic insulation boundary condition, and the magnetic field governing equation is established: $\begin{eqnarray}\displaystyle {\sigma}\frac{\partial \mathbf{A}}{\partial t}+{\nabla}\times ({\mu}^{-1}{\nabla}\times \mathbf{A})=\mathbf{J} & & \displaystyle\end{eqnarray}$ (1) where J is external current density, μ is permeability, and σ is conductivity.

The transformer model including core and oil tank is solved in the structural force field. The magnetostrictive effect of SSS and influence of inter-stack Lorentz force are mainly considered. The realization method is to load single-valued magnetostrictive curve to characterize magnetostriction on core domain. The structural force field and magnetic field are coupled with each other by using calculation results obtained in magnetic field analysis. According to experimental butterfly curve family of 30Q120 material, a single-valued magnetostrictive characteristic curve is fitted as shown in Fig. 5.

In this study, bottom surface of the core is directly contacted with oil tank. The core vibration transmits to oil tank as its excitation source. The governing equation is established as: $\begin{eqnarray}\displaystyle \mathbf{m}\frac{d^{2}\mathbf{u}}{dt^{2}}+{\zeta}\frac{d\mathbf{u}}{dt}+\mathbf{k}\mathbf{u}=\mathbf{f}(t) & & \displaystyle\end{eqnarray}$ (2) where ζ is damping coefficient matrix, k is stiffness matrix, m is mass matrix, u is displacement, and f(t) is excitation force. After calculating displacement u on each nodal point, the strain normal acceleration of each node is obtained.

The normal acceleration is the source of acoustic field, and the corresponding governing equation is: $\begin{eqnarray}\displaystyle \frac{1}{{\rho}_{0}c^{2}}\frac{\partial ^{2}p}{\partial t^{2}}-\frac{1}{{\rho}_{0}}{\nabla}\cdot ({\nabla}p-\mathbf{q})=Q & & \displaystyle\end{eqnarray}$ (3) where 𝜌 is fluid density, q is dipole source and Q is monopole source. In the calculation of the acoustic field, the transient solution is generally used to obtain the distribution of sound pressure level (SPL) in the solution domain, and the noise can be calculated by a certain quantitative relationship.

3. Finite element simulation of vibration and noise of power transformer

3.1. Establishment of transformer simulation model

In this paper, a 100 MVA three-phase three-limb oil-immersed power transformer is studied. The rated voltage on the high-voltage side is 115 kV, the rated current is 502 A. In order to accurately simulate practical transformer, the model is composed of core, winding, oil tank, air and so on. The main parameters of transformer winding are shown in Table 1. The geometric model is shown in Fig. 6. The corresponding mesh distribution is shown in Fig. 7.

Table 1
Main parameters of transformer coil

Parameter High-voltage winding Low-voltage winding

Number of turns 402 224

Resistance/ Ω 0.243 0.068

Parameter	High-voltage winding	Low-voltage winding
Number of turns	402	224
Resistance/ Ω	0.243	0.068

Fig. 6.

Transformer geometry model.

Fig. 7.

Mesh distribution.

In this paper, COMSOL software is adopted for analysis of the multi-physical fields coupling problem. The mechanical parameter setting has great influence on calculation results of transformer vibration and noise. The modified material parameters of core and oil tank are shown in Table 2. Considering the suppression of eddy current during simulation, the conductivity of core is appropriately reduced. In the modeling of structural force field and acoustic field, since core vibration state is similar to the rigid body vibration, the oil tank is fixed on the ground. Thus the core is defined as body load, and fixed constraints are imposed on the bottom of oil tank. The solution region is set as a hemispherical shape, in order to consider that the ground has a reflective effect on sound; the hard sound field boundary condition is set on the bottom surface of the hemispherical solution domain. The transient problem is calculated. In this paper, the MUMPS solver is applied, and the maximum number of iterations is set 25.

Table 2

Mechanical parameters of core and tank

Mechanical parameters	Core	Oil tank
Elastic modulus (Pa)	2.1E+11	2.2E+11
Poisson ratio	0.30	0.29
Density (kg/m³)	7650	7800

Fig. 8.

No-load excitation currents of transformer under different rated voltages.

3.2. Finite element analysis of vibration and noise under alternating magnetic field

No-load current of transformer from switching-on to stable operation process is solved by the proposed field-circuit coupling calculation method. Figure 8(a)–(e) shows the three-phase no-load current waveforms when the rated voltage percentages are set 80%, 85%, 90%, 95% and 100%, respectively. Figure 8(f) is the magnitude spectrum diagram obtained by FFT of phase A with no-load current at rated voltage. The excitation current is a sharp roof wave, which indicates the transformer core has been operating in the saturation region. From the FFT analysis, the odd harmonics are generated due to saturation of magnetic flux density of transformer core. The excitation current is symmetrical in positive and negative half cycles, so there are no even harmonics.

The magnetic field distribution of transformer core under no-load operation is shown in Fig. 9. It can be seen the flux density distribution of core is symmetrical. With increase of voltage percentage, the magnetic flux density of core increases gradually.

Fig. 9.

Distributions of magnetic field of transformer core at different rated voltages.

The vibration calculation results are shown in Fig. 10. The core vibration is transmitted to the oil tank under action of electromagnetic force and magnetostrictive force, which cause deformation of the oil tank. With the increase of rated voltage percentage, the deformation displacement of the oil tank increases. Under the rated voltage, the displacement of oil tank reaches a maximum about 1.5 μm. The increase of oil tank vibration leads to noise enhancement. Furthermore, the shape deformation of the upper-half core is slightly larger than the lower-half part, which results from weight of transformer itself.

Fig. 10.

Displacement deformation under different rated voltage percentages.

In the simulation model, 12 sampling points are arranged symmetrically around the oil tank, and the distance from the outer surface of the oil tank is 1.8 m, which locates at 1/2 of the overall transformer height, as shown in Fig. 11. The experiment environment is shown in Fig. 12.

Fig. 11.

Location of measurement points.

Fig. 12.

Photo of noise measurement.

Figure 13 shows a longitudinal section of the SP across the space. The variation of SPL and noise are proportional to the rated voltage percentage. From the noise distribution of the whole model, the SPL level near the transformer oil tank is obviously higher and the outward SPL is gradually reduced. This reflects the process in which noise is gradually propagated from sound source and attenuated continuously. Furthermore, the noise signal generated by transformer vibration shows a relatively obvious symmetrical distribution trend, and the maximum noise SP appears on the oil tank surface.

Fig. 13.

External SP distribution under different rated voltage percentages.

4. Comparison of simulation and experiment results

In order to verify the accuracy of simulation results of 110 kV power transformer vibration and noise based on the new field-circuit coupling method, the physical experiments under no-load condition are carried out at 100%, 95%, 90%, 85% and 80% rated voltages, respectively.

Table 3 shows comparison between simulation and experimental results when the rated voltage percentage is 100%, 90% and 80%, respectively. The experimental and simulation data of each point are the average noise of five cycles of transformer operation. Using the noise value of 12 points, the average value AVE (L_p), of spatial SP can be calculated as (4), where L_pi is the average SPL of a single measurement point in five periods. $\begin{eqnarray}\displaystyle \mathit{AVE}(L_{p})=10\text{lg}\left(\frac{1}{12}\mathop{\sum }_{i=1}^{12}10^{0.1L_{pi}}\right). & & \displaystyle\end{eqnarray}$ (4)

Figure 14 shows comparison curves between simulation and experimental results. From Table 3, it can be seen when the rated voltage percentage is 100%, the average spatial SP of simulation and experiment results are 73.957 dB and 70.600 dB, respectively. The difference is around 3.400 dB. Figure 14 shows that with the increase of rated voltage percentage, the levels of vibration and noise are also increased. Furthermore, the distribution of noise at each point around the oil tank is highly consistent with distribution of experimental results under different voltage percentages. From the above analysis, the simulation results are in good agreement with experiment data. The simulation results of 110 kV power transformer vibrations and noises are accurate.

Table 3

Comparison between simulation and experimental results under different rated voltage percentages

Measuring point	80% rated voltage		90% rated voltage		100% rated voltage
	Simulation (dB)	Experiment (dB)	Simulation (dB)	Experiment (dB)	Simulation (dB)	Experiment (dB)
1#	73.184	74.362	75.188	74.571	74.433	74.843
2#	66.713	63.832	66.808	65.724	69.188	68.464
3#	71.031	75.398	71.284	75.617	74.227	75.830
4#	69.662	61.554	69.019	62.768	72.316	65.844
5#	69.680	65.060	74.986	66.858	73.635	68.229
6#	75.231	70.114	75.083	70.862	76.516	72.557
7#	70.395	58.768	70.152	60.415	72.279	64.592
8#	68.419	61.176	68.113	63.078	71.647	66.352
9#	71.455	65.287	70.997	66.469	72.614	68.573
10#	67.398	62.139	66.408	64.078	70.834	67.858
11#	73.174	65.938	71.217	66.688	73.574	67.653
12#	78.409	62.474	78.911	64.589	78.215	68.544
AVE (L_p)	72.584	68.849	73.150	69.438	73.957	70.600

Fig. 14.

Results comparison under different rated voltage percentages.

5. Conclusion

In this paper, vibration and noise multi-physical field coupling problem of the 110 kV power transformers is established and solved based on the novel field-circuit coupling method. By comparing the simulation and experimental results, simulation accuracy of the vibration noise is verified. Through the analysis of the calculation results, this will provide reliable research data for the subsequent vibration and noise reduction of the large oil-immersed power transformer.

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