2016 3rd International Conference on Engineering Technology and Application (ICETA 2016) ISBN: 978-1-60595-383-0

1 INTRODUCTION

With continuous improvement in urban construction, quantity of 110kV substation is in rapid increase. Thus, there’s a contradictory relation between urban land use and substation quantity. Therefore, ful-ly-sealed substation with high integration level has become the mainstream scheme for 110kV power distribution network. This thesis mainly studies the noise problem of prefabricated distribution substation. Many predecessors have made great contribution to solve substation noise problem, among which:

In 2014, Yang Gao made deep analysis of the low frequency characteristics and propagation laws of substation equipment noise in theory and proposed noise management plan in his Predictive Research on Sound Field Features and Noise Distribution of Sub-station, providing technical support for future substa-tion optimization design [1].

In 2014, Xueyun Ruan established acoustic model to predict transformer noise based on outdoor half- open spatial coherence virtual source in his Prediction Theo-ry of Coherent Acoustic Field Noise and Research on its Application in High-voltage DC Transmission System, containing great significance in improving the noise prediction of DC exchange station [2].

In 2010, Haozheng Wei studied the formation me- chanism of the main noise source equipment noise inside high-voltage DC convertor station and made

separation amendment on superimposed noise of complex sound field in his Research on Audible Noise Prediction System in High-Voltage DC Transmission System, providing important reference proof for the noise prediction calculation of high-voltage DC con-vertor station [3].

In 2014, Liang Huang did digital exchange of “dis-placement-superposition” according to several sample data from the same discharge source in his Research on the Semidefinite Relaxation Successive Approxima-tion Positioning Methods of Substation Partial Dis-charge Sources. He used fourth-order cumulant to obtain time difference and effectively restrained noise while improving SNR [4].

Based on predecessors’ research, this paper firstly introduces the computational formula of noise attenu-ation. Then, it combines the propagation theory of sound in media to establish the substation noise atten-uation computing model based on geometric diver-gence. Lastly, it calculates the noise propagation of point sound source, plane sound source, and global sound source of substation respectively; and obtains the attenuation relation between noise and distance in different sound sources, aiming to contribute to solv-ing the noise interference problem existing in ful-ly-sealed compact substation.

Substation Noise Research Based on Geometric Divergence

Rui Liu, Yun Fu, Chundong Li, Zhe Shi, Shishen Guan & Jun Zhao State Grid Liaoning Electric Power Company, Shenyang, Liaoning, China

ABSTRACT: with increasingly strained urban land resources, fully sealed substation with high integration level has become the mainstream scheme for 110kV power distribution network. Therefore, this thesis mainly studies the noise problem of prefabricated distribution substation, aiming to solve the noise interference of fully sealed compact substation. This thesis introduces the computational formulas of noise attenuation firstly. Then, it establishes the computing model of substation attenuation based on geometric divergence in combination of the theory for sound propagation in media. At last, it offers computation to the noise propagation of point sound source, plane sound source, and global sound source of substation respectively; and concludes the attenuation relationships between noise and distance in different sound sources.

Keywords: noise; prefabricated distribution substation; geometric divergence; plane sound source

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2 NOISE ATTENUATION CALCULATION

In combination of the propagation characteristics of sound, it can be known that vibration of sound source can cause vibration of surrounding media molecules. Then, the vibration can cause vibration of other media molecules. Thus, vibration of sound source can be propagated outwards in form of wave beam. During the propagation process, scattering, refraction, and diffraction can occur due to shielding. As a result, energy will be gradually attenuated during propaga-tion. With increase in distance, sound will be reduced. According to actual situation, the energy attenuation of sound during propagation can be mainly divided into the following parts: geometric divergence, ground absorption, atmospheric absorption, shielding acoustic absorption, and many other attenuation factors. Therefore, in the entry noise calculation of substation, the method to calculate the sound pressure level at prediction point r away from sound source after vari-ous attenuation is shown in Formula (1) given below:

)()()(0 misxgrbaratmdivpp AAAAArLrL (1)

In formula (1), Lp0(r) refers to the weighting A sound pressure level at r away from sound source, dB.

Adiv refers to the noise attenuation caused by geo-metric divergence, dB.

Aatm refers to the noise attenuation caused by at-mospheric absorption, dB.

Abar refers to the noise attenuation caused by acous-tic shielding, dB.

Agr refers to the noise attenuation caused by ground effect, dB.

Amisx refers to the noise attenuation caused by other factors, dB.

In Formula (1), there’s interrelation between the at-tenuation caused by atmospheric absorption Aatm and frequency of sound wave, gas molecule density, and degree of activity. Related research have manifested

the formula to calculate the attenuation at the point r away from sound source caused atmospheric absorp-tion as shown in Formula (2) given below:

1000

)( 0rraAatm

(2)

Among which, r refers to the propagation distance (m) from sound source to prediction point; r0 refers to the propagation distance (m) from sound source to reference point; and a refers to temperature, humidity, and wave frequency function.

Atmospheric attenuation coefficients can be ob-tained in Outdoor Acoustic Attenuation. See Table 1 shown as below for common reference data.

2.1 Shielding diffraction attenuation process

Shielding noise attenuation Abar refers to the obvious acoustic wave energy attenuation caused by reflection, projection, and diffraction that sound makes in propa-gation while encountering materials with high density, such as walls or boards. See Figure 1 given below for the propagation path after acoustic wave encounters shielding.

Figure 1. Propagation path of acoustic wave after encountering shield.

See Formula (3) given below for the method to cal-culate the noise attenuation caused by finite-long shielding:

Table 1. Attenuation coefficient table of absolute music absorbed in atmosphere.

Temperature ( ) Relative humidity

Attenuation coefficient of atmospheric absorption dB/km

Mid-frequency of octave band Hz

63 125 250 500 1000 2000 4000 8000

0 20 0.225 0.614 1.85 6.16 12.9 34.6 47 58.1

10 20 0.271 0.579 1.2 3.27 11 36.2 91.5 154

20 20 0.26 0.712 1.39 2.6 6.53 21.5 74.1 215

30 20 0.212 0.725 1.87 3.41 6.00 14.5 47.1 165

0 50 0.181 0.411 0.821 2.08 6.83 23.8 71 147

10 50 0.161 0.486 1.05 1.9 4.26 13.2 46.7 155

20 50 0.123 0.445 1.32 2.73 4.66 9.86 29.4 104

30 50 0.0907 0.351 1.25 3.57 7.03 11.7 24.5 73.1

520

321 203

1

203

1

203

1lg10

NNNAbar

(3)

In Formula (3), N1, N2 and N3 refer to Fresnel num-bers of which the computational methods are related to the lengths of three propagation paths. The three propagation paths are the shortest distances between sound source and prediction points as shown in Figure 2 given below:

Figure 2. Diffraction paths while acoustic wave going through shielding.

Computational formula of Fresnel number:

/2 iiN (4)

Among which, i refers to No. i path difference:

iiii SRORSO (5)

λ refers to wave length. λ = c / f and c refers to sound velocity. Under normal conditions, the propaga-tion velocity of sound in air c = 340m/s is selected in which f refers to acoustic wave frequency.

Figure 3. Diffraction path of acoustic wave while encountering multiple shielding.

According to the multiple shielding as shown in Figure 3, Formula (6) shall be applied to calculate diffraction path difference.

dded ORSO (6)

In Formula (6), dSO refers to the diffraction distance of sound source to the first shield. dOR refers to the

diffraction distance of prediction point to the las shield. e refers to the diffraction distances of multiple shield-ing between boundaries. d refers to the distance from sound source to prediction point.

When sound propagates along the ground, due to the influence from complex ground-surface conditions, the following computational formula is generally ap-plied to calculate the noise attenuation caused by ground effect:

rr

hA m

gr

30017

28.4 (7)

Among which, r refers to the distance between sound source and prediction point; hm refers to average ground clearance; and hm= (hs+hr)/2. If it is calculated that Agr is negative, the calculation shall take Agr =0.

3 ESTABLISHMENT OF GEOMETRIC DIVER-GENCE NOISE ATTENUATION MODEL

Geometric noise attenuation is mainly caused by in-crease of propagation distance. There are three main types of sound source: point sound source, line sound source, and plane sound source. When sound source vibrates, elastic objects surround the sound source will also vibrate and the surrounding air molecules will also vibrate. Thus, sound source is propagated in form of acoustic wave. The wave equation of plane acoustic wave is as follows:

2

2

22

2

2

2

2

2 1

t

p

cz

p

y

p

x

p

(8)

In Formula (8), c refers to sound velocity and is taken as 340m/s; t refers to time (unit: s); and p refers to sound pressure (unit: pa).

From Formula (8), it can be seen that sound pres-sure is the function of space (x, y, z) and time t and is described as p(x, y, z), meaning the change law of sound pressure at some location. According to some pulsation spherical sound wave with even surface, the sound radiation pressure at location r away from cen-ter of sphere is as follows:

)cos(4

)cos(),(2

0 krtQr

ckkrt

r

ptrp

(9)

Among which, Q refers to strength of sound source and Q=4πa2u0; ω refers to angular frequency and ω=2πf; k refers to wave number and k=ω/c; and ρ refers to air density with unit of kg/m3.

As the range of sound pressure is wide, the loga-rithm of the specific value between effective sound pressure and standard sound pressure is generally applied to calculate sound pressure. See Formula (10) given below for the method to calculate sound pres-sure:

521

020

2

lg20lg10p

p

p

pLP (10)

Among which, p refers to effective value of tested sound pressure; and p0 refers to standard sound pres-sure. According to geometric divergence attenuation of omnidirectional sound source, the calculation method is given in Formula (11) as follows:

)/lg(10 0rrAdiv (11)

In Formula (11), r refers to the distance from pre-diction point to sound source while r0 refers to the distance from reference point to sound source.

According to the cube structures of transformer and high-voltage reactor inside substation, the propagation space of noise is a half free field. Except the base, all the other five surfaces are noise radiant surfaces. This thesis abstracts cubic equipment such as transformer into cuboid mathematical model as shown in Figure 4 given below:

Figure 4. Schematic diagram of sound radiation of transformer.

According to the plane sound source structure of Figure 4, energy superposition principle can be used to obtain the acoustic level. See Formula (12) given be-low for the sound energy density at p:

S S

dsr

Wds

r

wD

22

1

44 (13)

Therefore, the acoustic level of point p is

S

Wp ds

r

LL

2

1lg10

5 (14)

8 frequency band sound pressure values are gener-ally used to describe information about sound source inside substation. See Table 2 for the corresponding wave lengths under barometric pressure.

Table 2. Acoustic wave lengths corresponding to each frequency under standard atmospheric pressure.

Frequency (Hz)

63 125 250 500 1000 2000 4000 8000

Wave length (m)

5.40 2.72 1.36 0.68 0.34 0.17 0.09 0.04

In combination of Table 2, it can be known that wave length of low frequency band is close to trans-

former dimension. After acoustic wave exceeds 250Hz, its wave length is much less than transformer dimen-sion. Therefore, this thesis concludes attenuation of plane sound source as attenuation of acoustic wave diffraction. Assume a plane sound source is dimension of a×b, the method to calculate the sound field formed on prediction point r on the other side surface of the machine according to the differential ds on plane sound source is shown in Formula (15) given below:

S

dskrDGVkr

j

kr

jscujkrP )()()1(1

2

)()( 0

(15)

Among which, u(s) refers to vibration velocity of micro-facet element, m/s.

3.1 Numerical integration of computing model

In combination of the fact that there is integral com-putation in both Formula (14) and Formula (15), this thesis takes numerical integration in form of numerical value. In definite integral of function, Newton-Vortex formula is mainly used to calculate the isometry of node distribution, including trapezoid formula and Simpson formula. This thesis takes trapezoid formula for integral solution. Set the coordinates of cubic cen-ter as (x, y, z), cubic dimension as a×b×c, and the coordinates of spatial midpoint as (x0, y0, z0); then, Formula (14) can be turned into

2

2

2

2

2

22

02

02

01

1

1

1

1

1

1 )()()(

1lg10

5

ax

ax

by

by

cz

cz

W dxdydzzzyyxx

LL

(15)

In combination of compound trapezoid formula, respectively divide integral sections

1 1 1 1 1 1, ,2 2 2 2 2 2

a a b b c cx ,x y , y z ,z

into m, n and p equal parts. Thus, the step size of each section is:

p

cl

n

bg

m

ah ,, (16)

Therefore, set function

20

20

20 )()()(

1),,(

zzyyxxzyxf

;

then, Formula (15) can be turned into Formula (17) as follows in accordance with trapezoid formula:

]),,(8

lg[105 0 0 0

1 m n p

kjiW zyxfAAA

hglLL (17)

In Formula (17):

522

)1,,2,1(2

),0(1

mi

miAi

)1,,2,1(2

),0(1

ni

niAj

)1,,2,1(2

),0(1

pi

piAk

Therefore, in combination of the Formula (17) shown above and according to the computational model for near-field noise of substation, set dimension of some transformer in substation as (5m×10m×4m). According to the model and calculation formulas giv-en in this thesis, take the step size as 0.2. See Table 3 for the geometric attenuation results for approximate distance of the computational model:

Noise attenuation trends as shown in Figure 5 given below can be obtained according to computed results of Table 3.

In combination of Figure 5, it can be known that the attenuation speed of point sound source is the highest. In the noise attenuation trend within 14m away from sound source, attenuation speed of substation compu-ting model is lower than those of point sound source and plane sound source.

Figure 5. Schematic diagram of geometric divergence attenuation of substation computing mode.

4 CONCLUSIONS

This thesis firstly studies the shielding diffraction propagation mode of noise and provides the propaga-tion situation when acoustic wave encounters shield-ing. The acoustic wave energy loss caused by reflec-tion, projection, and diffraction of acoustic wave while encountering high-density materials, such as walls or boards, can be huge during sound propagation process.

Then, this thesis establishes geometric divergence noise attenuation model based on geometric diver-gence model principles and the main reasons of geo-metric noise attenuation; and has obtained the calcula-tion formula of noise attenuation with distance in-crease which contains great significance in solving noise interference problem of fully-sealed compact substation.

REFERENCES

[1] Gao, Y. 2014. Predictive Research on Sound Field Fea-tures and Noise Distribution of Substation. North China Electric Power University.

[2] Ruan, X.Y. 2014. Prediction Theory of Coherent Acous-tic Field Noise and Research on its Application in High-Voltage DC Transmission System. Hefei University of Technology.

[3] Wei, H.Z. 2010. Research on Audible Noise Prediction System in High-Voltage DC Transmission System. Hefei University of Technology.

[4] Huang, L. 2014. Research on the Semidefinite Relaxa-tion Successive Approximation Positioning Methods of Substation Partial Discharge Sources. Hefei University of Technology.

[5] Li, W.H. 2015. Research on Prediction and Control Techniques of High-Voltage Substation Noise Pollution. Guangdong University of Technology.

[6] Ni, Y. Zhou, B. Pei, C.M. & Zhai, G.Q. 2014. Analysis of interference patterns of acoustic wave around 1000kV extra-high voltage paralleling reactor. High Voltage En-gineering, 12: 3926-3932.

[7] Xiang, N. 2009. Mechanism and Control Study of Trans-Regional Power Grid’s Low Frequency Oscilla-tion. Wuhan University.

[8] Yang, M. 2014. Research on Nonlinear Characteristics of Ferromagnetic Resonance Overvoltage and Its Flexi-bility Restraint Strategy. Chongqing University.

[9] Fan, X.P., Li, L., Huang, C.J., Liu, J.W., Chen, M. & Deng, Q. 2014. Analysis and control of 110kV substa-tion noise pollution. Noise and Vibration Control, 05: 120-124.

[10] Wang, Y.D., Xu, L.W. & Shen, J.S. 2012. Predictive study of substation environmental noise. Environmental Engineering, S1: 179-181.

[11] Zheng, Y. 2012. Study of Human’s Subjective Feelings on Substation Noise and Its Voice Control Methods. Zhejiang University.

[12] Li, X.X., Yang, C.P. & Jiang, W. 2008. Capital asset pricing model based on investor’s sentiment behaviors. Journal of Qingdao University (Natural Science Edi-tion), 21(4): 95-98.

0

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6 7 8 9 10 11 12 13

Distance from sound source

sound pressure

Calculation model of point soundsource

Surface acoustic source model

Substation calculation model

Table 3. Close-range geometric divergence results of different sound sources.

Computing model

Weighting sound pressure level /dB

Distance between predicted positions and sound source /m(height is 1m)

1 2 3 4 5 6 7 8 9 10 12 14 15 Results of point sound source computation

80 73.98 70.45 67.96 66.02 64.44 63.1 61.94 60.92 60 58.42 57.07 56.48

Results of plane sound source computation

80 76.99 75.23 72.73 70.79 69.21 67.87 66.7 65.69 64.77 63.19 61.85 61.25

Computing model of substation

80 77.75 75.46 73.99 71.82 70.61 69.24 68.53 67.4 66.39 65.47 64.64 63.87

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