Vibration and noise reduction of HVDC anode saturable reactor by polyurethane damping elastomer

Abstract

The vibration and noise produced by the anode saturable reactor (ASR) in the HVDC transmission converter valve are very serious, and the long-term vibration can accelerate the aging of the equipment and damage the friendly environment. In this paper, a core with race-track shape from the ASR in ±800 kV/4750 A project is used as the research object. An excitation winding is wounded on the core, and the vibrations and noises are measured when the winding is excited respectively by sine wave and rectangular waves at different frequencies. In order to reduce the noise, the polyurethane damping elastomer is filled into the box of core, and the vibrations and noises of core with polyurethane damping elastomer under different excitations are measured. The results show that the polyurethane damping elastomer can efficiently reduce the vibrations and noises of the anode saturated reactor core, especially under non-sinusoidal excitation. This research is of significant reference value for the vibration and noise reduction of ASR and other high frequency equipment.

Keywords

Anode saturable reactor vibration noise damping elastomer

1 Introduction

High voltage direct current (HVDC) transmission can effectively alleviate the problem of uneven distribution of energy and load in China [1,2]. Therefore, the proportion of HVDC transmission projects has increased a lot in China’s power grid development plan. The ASR is important equipment used to protect thyristor in converter valve, and the design and manufacture of ASR is also one of the key technologies of converter valve system. However, the problem of the vibration and noise of the converter valve is very prominent, and the main vibration source is the ASR. The long term vibration of the ASR will accelerate its aging and reduce its service life, which will cause the failure of the whole converter valve system. So it is of great engineering significance to study the vibration and noise of the core of ASR for the performance improvement of the converter valve and even the direct current transmission system.

The conversion of the ASR core between the magnetic unsaturated and saturation states is usually completed within a period of time from a number of μs to dozens of μs. Therefore, there are a lot of harmonics in the working current of the ASR, and the harmonic current will aggravate the vibration of the ASR. At the same time, the high frequency current causes the more sharp noise, which seriously affects the life of the equipment and the environment around.

There are extensive studies about the vibration and noise of electrical machines [3–5], the magnetostriction properties of silicon steel material [6–9], and the vibration and noise of power transformers operating at line frequency [10–13]. On the aspect of noise reduction, the noise reduction methods related to Maxwell force and magnetostrictive force is put forward in [14,15]. The changes of magnetostriction rate under different conditions have been studied in [16]. The vibrations and noises by using different type lamination iron core are analyzed in [17]. The usage of the sound insulation material and the clamping force of the core are studied in [18], and some measurements to effectively reduce the noise of the transformer are put forward. A noise reduction experiment on a 100 kVA transformer in an anechoic chamber is done in [19], and the influence of external environment changes on the active noise reduction system has studied in [20]. The vibration and noise reduction of converter valve should be solved not only from the improvement of the structure of the ASR, but also from the related auxiliary vibration reduction measurements.

In this paper, the ASR used in Jinping-Sunan ±800 kV/4750 A HVDC transmission project is studied. A core taken from ASR is wounded by 22 turns coil, and the winding is excited by programmable power supply. The voltage excitation with different frequency and amplitude is applied to the winding, and the vibration and noise generated by the core are measured. At the same time, in order to effectively reduce the noise of the core, the polyurethane elastomer is applied to the core, and the contrast test of reducing vibration and noise reduction is carried out.

2 Theoretical analysis

2.1 Vibration mechanism of iron core

There is a leakage magnetic field around the seam in laminated core of ASR, which results in the electromagnetic force between the laminations. But with the improvement of manufacturing technology and the superposition way of core, the electromagnetic force produced by leakage magnetic flux between silicon steel sheets is far less than magnetostrictive force. Therefore, it is considered that the magnetostrictive effect is the main factor that causes the vibration of the core [21].

The magnetostrictive calculation model is shown in Eq. (1), and the magnetostrictive model fully considers the change of the internal magnetic domain in the magnetization process [22], where 𝜆_m is the saturated magnetostriction, ϵ_c is the magnetostrictive strain, M is the magnetization intensity, θ is a step function which is related to the rotating stage of magnetic domain, and M _s is the saturated wall moving magnetization intensity. When the magnetization of the silicon steel laminated material is less than the magnetization of the saturated wall, the magnetostrictive strain is proportional to the square term of the flux density in the core. When the magnetization of silicon steel sheet is greater than M _s, the magnetostriction strain is related to both the square and the four power term of magnetization [23]. $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\varepsilon}_{c}=\frac{{\lambda}_{m}}{M_{s}^{2}}M^{2}+{\theta}\frac{{\lambda}_{m}}{M_{s}^{4}}(M-M_{s})^{4}\end{eqnarray}$ (1) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\theta}=\left\{\begin{array}{@{}ll@{}}0 & 0\lt M\lt M_{s}\\ -2 & M>M_{s}.\end{array}\right.\end{eqnarray}$ (2)

2.2 Magnetic flux density calculation under the excitation of rectangular wave

Rectangular wave is a typical voltage waveform in the converter valve, and the relation between the voltage and the change rate of magnetic flux density is as follows: $\begin{eqnarray}\displaystyle u(t)=\frac{d{\psi}(t)}{dt}=nS\frac{dB(t)}{dt} & & \displaystyle\end{eqnarray}$ (3) where 𝜓 is the magnetic flux, u is the voltage, B is the magnetic flux density, t is the time, n is the number of turns of the winding, S is the effective area of the magnetic circuit. The following Eq. (4) can be derived from Eq. (3). $\begin{eqnarray}\displaystyle \int _{0}^{T}\left|\frac{dB(t)}{dt}\right|^{k}dt=\frac{1}{(nS)^{k}}\int _{0}^{T}|u(t)|^{k}dt & & \displaystyle\end{eqnarray}$ (4) where k is constant, T is the period. The function expression of the rectangular wave within one period is as follows: $\begin{eqnarray}\displaystyle u(t)=U_{m}\left\{\begin{array}{@{}ll@{}}0 & 0<t<T(1-D)/2\\ 1 & T(1-D)/2<t<T/2\\ 0 & T/2<t<T(2-D)/2\\ -1 & T(2-D)/2<t<T\end{array}\right. & & \displaystyle\end{eqnarray}$ (5) where U _m is the voltage amplitude, and D is the duty cycle. It also can be expressed as the following form for the rectangular wave. $\begin{eqnarray}\displaystyle U_{m}=4fnB_{m}S & & \displaystyle\end{eqnarray}$ (6) where f is the frequency of the excitation, B _m is the amplitude of the magnetic flux density.

For the rectangular wave, the relation between voltage and magnetic flux density is shown in Fig. 1, where the voltage can be positive, negative, or zero. The corresponding magnetic flux density waveform in one switching period can be deduced by integration of voltage and divide it by winding turns and effective core cross section. Therefore, the magnetic flux density waveform has a linear behavior, and it can be accurately represented by a piecewise linear function as follows. $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle B(t)=B_{m}\left\{\begin{array}{@{}ll@{}}-1 & 0<∼t<T(1-D)/2\\ -1+\displaystyle \frac{4}{TD}\left[t-\displaystyle \frac{T(1-D)}{2}\right] & T(1-D)/2<t<T/2\\ 1 & T/2<t<T(2-D)/2\\ 1-\displaystyle \frac{4}{TD}\left[t-\displaystyle \frac{T(2-D)}{2}\right] & T(2-D)/2<t<T\end{array}\right.\end{eqnarray}$ (7) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle B_{m}=\displaystyle \frac{U_{m}D}{4NA_{e}f}\end{eqnarray}$ (8) where B _m is the peak magnetic flux density, U _m is the amplitude of output voltage, N is the number of winding turns, A _e is the effective cross section of the magnetic core, A _e = A ⋅ k _c, k _c is the packing factor, A is the cross section of the magnetic core, D is the duty cycle of the rectangular voltage, D = (T _on + T _off)∕T, T is the period of magnetic flux density waveform, and T _on and T _off are illustrated in Fig. 1.

2.3 Polyurethane damping elastomer

Polyurethane damping material is also known as viscoelastic damping materials, and has higher loss factor and better bonding properties. The strong vibration does not cause the damping material to fall off and aging, the polyurethane damping material has large internal loss and friction and it can tolerate the high temperature, high humidity, oil pollution. The polyurethane damping material can be used to reduce the vibration amplitude of ASR since a part of the vibration can be consumed by the elastomer before the high resonance amplitude is produced. The basic performance indexes of the polyurethane damping elastomer used in this paper are shown in Table 1.

When the polyurethane damping elastomer is subjected to external force at a certain temperature, the molecular chain inside it will distort and elongate, while the relative torsion and slip between molecular segments will occur. When the external force is disappearing, the molecular chain of elongated deformation is recovered. A part of the mechanical vibration energy is dissipated in the form of heat energy, and the other part is stored and released. The ratio of the modulus of loss to the stored modulus in a vibration period is called the loss factor (tanδ) [24].

In general, the damping and internal heat of the material is more significant with the increase of the loss factor (tanδ). The tanδ is not only related to the structure of the material itself, but also to the temperature. The tanδ of polyurethane damping elastomer used in this paper varies with temperature is shown in Fig. 2. It can be seen from Fig. 2 that the damping temperature in the range of tanδ > 0.2 is very wide. The tanδ of the polyurethane damping elastomer is still up to 0.17 at the temperature of 75°C, this indicates that the polyurethane damping elastomer has a good damping effect [25].

3 Experiment set-up

3.1 Measurement of core vibration of ASR

The working current of ASR contains a large number of harmonic components. In unstable working state, the harmonic current will increase significantly, and its normal working noise is very large and sharp. In this paper, the vibration under high frequency harmonic excitation, such as 400 Hz, 500 Hz, 1000 Hz, 2000 Hz and 2500 Hz, is tested and analyzed.

The anode saturation reactor used in Jinping-Sunan ±800 kV/4750 A HVDC power transmission project contains 9 race-track type cores. A core is taken as the experimental research object. The 22 turns winding is wounded on one side and connected to the programmable power supply (CSW5550). Different type excitations are applied to the winding. A-weight noise spectrum tester (HS5617B) is placed around the core to measure the noise produced by the vibration of core. The experiment set-up is shown in Fig. 3.

The polyurethane damping elastomer is used to reduce the vibration and noise of the core of the ASR. We put an iron cores into a special steel mold, and fill the special steel mold with the polyurethane damping elastomer, then raising the temperature and solidify the polyurethane damping elastomer. The test object of adding the polyurethane damping elastomer is shown in Fig. 4(a). The structure of the iron core and the measuring point’s distribution diagram are shown in Fig. 4(b). The vibration acceleration as well as the noise at point 1, 2 and 3 is measured respectively.

The sensitivity and range of piezoelectric vibration acceleration sensor used in experiment are 100 mV/g and ±50 g respectively. The data acquisition system can get real-time signal through analog and digital anti-aliasing filter, then the results as digital signals are displayed and stored by the computer. The piezoelectric acceleration sensor applied in the experiment can be firmly absorbed in the core by a magnetic base. Using cable and magnetic base with high insulation and shielding quality makes measurements more accurate without interference of the leakage flux. The sampling frequency is 32 kHz.

3.2 Background noise measurement

The background noise of the surrounding environment needs to be tested before the experiment of the core noise of the ASR. In order to prevent the electromagnetic field from interfering with the noise tester and make the measurement results as accurate as possible, the sound level measurement point is set at 0.3 m away from the outer surface of the ASR core, and the wall around is at least 3 m away from the microphone. Under the condition of no voltage excitation, the background noise is measured by the location of the 6 measured points in the position of the specified contour around the core. After more than 3 times the average sound pressure level measurement, the background noise is 42 dB, and it is at least 8 dB less than the measured noise. Therefore the influence of background noise can be ignored, which satisfies the basic requirements of noise measurement.

4 Experiment results

4.1 Vibration and noise of iron core without polyurethane elastomer

The 400 Hz sinusoidal excitation of 60 V is applied to the winding by programmable power supply. The peak value of magnetic flux density in the core is 0.93 T. The iron core works in the linear region of the magnetization curve, which is in unsaturated state. When the 400 Hz excitation is adjusted to 105 V, the magnetic flux density of the core is 1.6 T, the core will work in a nonlinear region and close to the saturation state. The time domain waveform of the vibration acceleration of point 3 at the saturation and unsaturated state is shown in Fig. 5. It can be seen that the acceleration of point 3 shows a good periodicity under the unsaturation of the core, and the amplitude of the vibration is 4 m/s². When the core is saturated, the acceleration of point 3 is periodic but with serious distortion. The amplitude of the vibration is 8.7 m/s², this is due to the rotation of the inclined subdomain in the iron core causes the reduction of the density of the “lancet” subdomain [26–28].

The vibration acceleration of point 3 under saturation and unsaturated conditions of the iron core is decomposed by fast Fourier transform (FFT) method respectively. The data of acceleration amplitude corresponding to each frequency after decomposition are shown in Table 2. The results of FFT decomposition show that when the core is in unsaturated state, the vibration of point 3 of the core is mainly concentrated on the frequency of 800 Hz (2 times excitation). A small amount of vibration is concentrated on the frequency of 1600 Hz (4 times of excitation), and the vibration components of other frequencies are less. When the core is saturated, the vibration of point 3 of the core is mainly concentrated on 800 Hz and 1600 Hz, a small amount of vibration is concentrated on 1200 Hz, 2000 Hz, 2400 Hz, 3200 Hz and 4000 Hz, which is consistent with the theoretical analysis.

When the ASR core is excited by 400 Hz sinusoidal excitation and the magnetic flux density is 0.465 T, the time domain waveform of vibration acceleration of the 3 measuring points of the core is shown in Fig. 6. It can be seen that the amplitude of the vibration acceleration of the point 3 is maximum. The amplitude of the vibration acceleration of the measuring point 1 is the second, and the amplitude of the vibration acceleration of the measuring point 2 is the smallest. This is because the measurement point 3 is in the middle of the core, the mechanical strength is lower and the magnetostrictive stress reaches the maximum. Because the point 1 is in the position near the core gap, there is much larger vibration by both the large alternating electromagnetic force and magnetostrictive force. Because the steel band is tight to the iron core, and the vibration acceleration is smaller than the measurement point 3. The mechanical strength of the point 2 of the measuring point is relatively stable, so the vibration amplitude is the smallest.

When the magnetic flux density in the core is 0.465 T, the time domain waveform of vibration of point 3 under rectangular wave excitation with 1.0 duty ratio is shown in Fig. 7. It can be seen that the vibration distortion of point 3 is very obvious, and the amplitude of vibration acceleration reaches 22.3 m/s², which indicates that the core vibration under the excitation of rectangular waves is very serious. The vibration of point 3 is decomposed by FFT, and is shown in Fig. 8. It can be seen that vibration is mainly concentrated on 800 Hz, 2400 Hz, 3200 Hz, 4000 Hz and 4800 Hz, while the frequency of 4000 Hz and 4800 Hz have the largest vibration components.

The vibration acceleration and noise amplitudes of 3 measuring points corresponding to different magnetic flux density under the sinusoidal excitation of 400 Hz are shown in Fig. 9. It can be seen that the vibration and noise amplitude of the core increase with the increase of magnetic flux density. The vibration and noise of the three measuring points increase slowly when the magnetic flux density of the core is less than 1.086 T. But the vibration and noise increase rapidly when the magnetic flux density is greater than 1.086 T. It is worth noting that the vibration and noise of point 3 reaches 35 m/s² and 81 dB when the core reaches the saturation state of 1.55 T. Higher vibration has a great impact on the stability of the equipment, the degree of aging and the environment around the converter station. Therefore, it is necessary to apply effective vibration and noise reduction measures to the ASR.

When the magnetic flux density of the core of the ASR is 0.155 T, the vibration of each measuring point and the noise of point 3 under different frequency excitations are shown in Fig. 10. It can be seen that the amplitude of the vibration acceleration and the noise size of the core increase with the increase of the frequency. When the excitation frequency and magnetic flux density of the core are 2000 Hz and 0.155 T respectively, the maximum vibration acceleration and noise of point 3 of the iron core are as high as 23 m/s² and 69 dB. This shows that the vibration of the ASR core is more intense when the frequency of the excitation becomes higher.

4.2 Vibration and noise of iron core with polyurethane elastomer

The vibration acceleration and noise of the anodic ASR core are greatly decreased after adding polyurethane damping elastomer. The vibration and noise at point 3 of the core under different magnetic flux density of 400 Hz sinusoidal excitation is shown in Fig. 11, and the vibration acceleration and noise value and reduction rate excited by sinusoidal and rectangular waves are shown in Table 3. From the data in Fig. 11 and Table 3, it can be seen that the vibration and noise reduction effect is better with the increase of the magnetic flux density of the core. When the magnetic flux density of the core is 1.55 T, the core has reached saturation state and the vibration reduction rate of the polyurethane damping elastomer is 80%, which indicates that the damping elastomer has a significant effect on the vibration reduction of the ASR core. When the magnetic flux density is 0.62 T, the percentage of the noise reduction is the largest, reaching 18.96%. In generally, the polyurethane elastomer has better effect on vibration reduction and noise reduction under rectangular wave excitation.

When the magnetic flux density is 0.155 T, the vibration acceleration, noise and the reduction rate of vibration and noise under sine and rectangular wave excitations are shown in Table 4. It can be seen that the vibration and noise reduction effect of the polyurethane elastomer is better with the increase of the excitation frequency. When the excitation frequency reaches 2000 Hz, the vibration reduction rate reaches 93.48%; it is shown that the damping effect of the elastomer is significant to the core under high frequency excitation. Therefore, this kind of polyurethane elastomer can be used to reduce vibration and noise of electrical equipment working under high frequency excitation.

5 Conclusions

In this paper, the vibration and noise tests of a race-track type core of ASR under different excitations have been done. The vibration of each measuring point of the core shows a distinct periodic characteristic, and the vibration component is mainly concentrated on the doubling frequency of the excitation, which is consistent with the theoretical analysis. With the increasing of the saturation degree of the core, the distortion degree of the vibration acceleration waveform increases significantly when the excitation frequency keeps constant. The vibration amplitude of the core becomes large with the increase of excitation frequency when the magnetic flux density of the core keeps constant. The vibration distortion of the ASR core is more serious under the rectangular wave excitation, and the noise is much larger than the sinusoidal excitation. The effect of vibration and noise reduction by the polyurethane damping elastomer is very significant, especially for rectangular wave excitation. The polyurethane damping elastomer used in this paper has a positive reference to the vibration and noise reduction of the magnetic saturation equipment and the high frequency vibration electrical equipment.

Footnotes

Acknowledgements

National Key R&D Program of (2017YFB0903905); Project Supported by National Natural Science Foundation of China(NSFC)(51677064); Project Supported by the Fundamental Research Funds for the Central Universities (2017XS032).

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