Virtual sound barrier for indoor transformers

Transcription

1 Virtual soud barrier for idoor trasformers Jiaheg TAO 1 ; Shupig WANG 2 ; Xiaoju QIU 3 ; Nig HAN 4 ; Like ZHANG 5 1,2,3 Key Laboratory of Moder Aoustis ad Istitute of Aoustis, Najig Uiversity, Najig, , Chia 4 Shool of iformatio siee ad egieerig, Southeast Uiversity, Najig, , Chia 5 Shool of Eergy ad Power Egieerig, Wuha Uiversity of Tehology, Wuha, , Chia ABSTRACT Power trasformers sometimes loate i a elosed room with a opeig surfae for the vetilatio purpose. Uder these situatios, most oise radiates out from the opeig, so a virtual soud barrier a be built to suppress the soud radiatio outside by employig a multiple-hael ative oise otrol system. Based o the soud radiatio model of idoor moopoles, the oise redutio performaes of both etralized ad deetralized otrol systems are ivestigated ad ompared. Cosiderig the hael umber requiremet, a virtual soud barrier is built for a atual idoor trasformer, where both the etralized ad the deetralized strategies are ivestigated. Simulatio results show that the fully idepedet virtual soud barrier is effetive for the idoor trasformer oise otrol. Keywords: Virtual soud barrier, Trasformer oise I-INCE Classifiatio of Subjets Number(s): INTRODUCTION Trasformer oise is domiated by low frequey harmoi ompoets 1, whih is harmful to people ad eviromet ad hard to be otrolled with traditioal passive methods. Ative oise otrol (ANC) tehologies a provide better performae with low ost ad easy maiteae 2-7. For the idoor trasformer loatig i a avity with oe opeig, a multi-hael ANC system defied as virtual soud barrier 8 (VSB) a be implemeted at the opeig to blok the soud radiatio outward. Although oly the soud radiatio through the opeig eeds to be osidered, huge hael umber is required for a large trasformer, whih makes the storage ad omputatio load of the otroller beome too heavy to be implemeted. Takig a 110 kv trasformer for example, the opeig area is about 48 m 2 ad at least 265 haels are required osiderig that the otrol soure iterval should be less tha a quarter of the wavelegth 9 (about 0.85 m for 200 Hz). Waveform sythesis algorithms istead of the ommoly used filtered-x LMS algorithm a be used to derease the proessig power requiremet; however the ross ouplig betwee the otrol soure ad error mirophoes still eeds to be osidered. A alterative method is to deetralize the VSB system, that is, implemet may idepedet ANC systems istead of the multiple-iput ad multiple-output system. Lebouher et al. aalyzed the stability of the deetralized feedbak ANC system of siusoidal soud i free spae ad derived pratial oditios from both the small gai theorem ad the Nyquist riterio 12. Zhag et al. ivestigated the performae of deetralized multi-hael feedbak aalog otrol systems ad obtaied a suffiiet stability oditio i terms of the predefied maximum oise amplifiatio ad the geometrial ofiguratio of the idepedet otrollers 13. It was also demostrated that there is a optimum leakage oeffiiet that results i the best 1 [email protected]. 2 [email protected] 3 [email protected]. 4 [email protected]. 5 [email protected] Iter-oise 2014 Page 1 of 7

2 Page 2 of 7 Iter-oise 2014 oise redutio performae ad the performae dereases with the further irease of the leakage oeffiiet for a deetralized ANC system i the trasformer oise otrol 14. Besides,the feasibility of applyig ANC tehology o a staggered double glazig widow was ivestigated ad the measured extra oise redutio i the room is about 10 db 15. Sixtee idepedet ANC systems were istalled at a 1 m 2 ope widow to protet the buildig iterior from the exteral oise. The oise redutio of more tha 10 db was ahieved for the frequey rage of 200~700 Hz at the error sesors while the extra oise redutio is oly 2~3 db i the room iterior 16. Despite all the researh metioed i the preedig text, o researh is foud o the VSB, espeially the deetralized VSB, o the opeig of a avity for iterior soure. This will be ivestigated i this paper. A theoretial model for preditig the soud radiatio through the opeig from the soure i the avity will be established first; the this model will be used to alulate the trasfer futios employed for VSB performae evaluatio. Fially the oise redutio of both deetralized ad deetralized VSBs will be ivestigated ad ompared based o the umerial simulatios. 2. THEORETICAL MODEL 2.1 Soud radiatio from the soures i the elosure with a opeig Figure 1 shows oe primary soure represetig the trasformer loates i a elosure with a opeig at the surfae z= L z. The elosure dimesio is L x L y L z, ad the moopole loatio is r s (x s, y s, z s ) with a stregth of q 0. The virtual barrier is omposed by a otrol soure array at the plae z=l ad a error mirophoe array at the elosure opeig. Assume that the opeig is embedded i a ifiite baffle ad both the primary soure ad the otrol soures a be osidered as moopoles, the soud pressure from oe moopole soure i the elosure a be preseted as p Figure 1 Idoor moopole with a baffled opeig i jkzz r jkzz ( P e + P e ) ( x y) ( x, y) ( x, y ) φ φ φ ( jk z ) (1) s s i =, + ρ 0ωq0 exp z zs 2SΛk z i jkzlz r jkzlz ( P e + P e ) ( x, y ) ( x, y ) φ ( x, y ) ( ) exp( jkr) 1 φ 0 0 s s jkz lz zs pout = jkz φ 0 0 jρ0ωq0 e ds (2) 0 2π 0 2 S SΛ r i where p i ad p out stad for the soud pressure iside ad outside the avity, P ad P r are the x y os π l os π l, k z is the mode oeffiiets of the th mode, ( ) φ is the mode shape ( ) ( ) wave umber i the z diretio ad equals k ( π l ) 2 ( π l ) 2, 2 x x y y the agular frequey, S is the opeig area, ρ 0 is the air desity, ad y ( x = y = 0, Λ =1; x = 0 or y = 0, Λ =0.5; x 0 ad y 0, the field poit to the itegratio poit (x 0, y 0, l z ) o the opeig area S 0. x x y, k is the wave umber, ω is Λ is a ostat depedig o x Λ =0.25), r is the distae from y Page 2 of 7 Iter-oise 2014

3 Iter-oise 2014 Page 3 of Virtual soud barrier based o ative oise otrol For the virtual barrier based o the ANC system, the error sigals a be expressed as e = p + ZQ (3) where p is the soud pressure from the primary soure, Z is the matrix omposed by the atual trasfer futios from the otrol soures to the error mirophoes ad Q is the stregth vetor of the otrol soures. Q is ormally obtaied by miimizig the ost futio H H J = e e + βq Q (4) where β is the leakage oeffiiet ad the supersript H deotes matrix traspose. Normally, a modelig proess is performed first to aquire the trasfer futios of seodary paths ad these trasfer futios are used to alulate the error gradiet i the otrol proess. The matrix of the trasfer futios of seodary paths, Z e is equal to the atual trasfer futio matrix Z for the fully oupled ANC system with ideal modelig oditio. For the deetralized system, the values of the trasfer futio betwee the otrol soures ad the error mirophoes from other idepedet systems are zero. If the VSB is omposed by fully idepedet ANC systems with the same ost futio ad leakage oeffiiet as Eq. (4), Z e is the diagoal matrix of trasfer futio matrix Z ad the off-diagoal elemets are zero. Eq. (1) a thus be rewritte as e = p + Z Q (5) e The gradiet of the ost futio therefore a be writte as J J H J = + = 2Z R I e e + 2βQ (6) q q R where q ad q I are the real ad image part of the otrol soure stregth. Cosider the algorithm Q ( k + 1) = Q ( k) μ J (k is the iteratio umber ad μ is the step size) ad the system overgee oditio Q κ 1) = Q ( κ ), the otrol soure stregth a be obtaied as 13 ( + κ H 1 H ( ) = [ Z Z + I] Z p Q e β e (7) It is lear that whe the leakage oeffiiet β equals zero, the soure stregth a be expressed as 1 Q ( ) = Z p ad is idepedet o the implemetatio matrix Z e. Substitutig Eq. (7) ito Eq. (3), the soud pressure whe ANC is applied a be obtaied ad the the oise redutio by the virtual barrier a be evaluated by usig the formulatio Ne Ne 2 2 ΔW = 10 log 10 e m ( ) ( p ) (8) m m= 1 m= 1 where N e is the umber of evaluatio poits. 3. SIMULATIONS 3.1 Trasfer futio alulatio The proposed aalytial formulatio i setio 2.1 has bee implemeted i a Matlab ode. The values of L x, L y ad L z are m, m ad m. The primary soure is plaed at (0.12, 0.12, 0.16) m to exite the avity modes as muh as possible ad the stregth is m 3 /s. Besides, a boudary elemet model is also built i LMS Vitual Lab, ad the predited results at two radom hose field poits (iside ad outside the avity) are ompared with those obtaied employig Eqs. (1) ad (2) as show i Figure 2. Iter-oise 2014 Page 3 of 7

4 Page 4 of 7 Iter-oise 2014 Figure 2 Predited soud pressure level by both aalytial ad boudary elemet methods It is obvious from Figure 2 that the predited soud pressure level employig the proposed aalytial model agrees well with those alulated by BEM ad therefore the auray of the proposed aalytial model is validated. The value differee above 400 Hz is due to the truatio of the mode order, where oly 10 modes are osidered i the aalytial model simulatios. Aother possible reaso is that the elemet umber i BEM is ot suffiiet at high frequeies. The trasfer futios from the stregth of both the primary soure ad the otrol soures to the soud pressure of field poits iludig the error mirophoes are alulated based o Eqs. (1) ad (2) i the followig alulatios. 3.2 Effet of ANC system type As show i Figure 1, it is assumed that 6 otrol soures are adopted i a horizotal plae, whih is 10 m below the elosure opeig. The earest oe to the z axis loates at (0.108, , 0.598) m ad the itervals i x ad y axis are m ad m. The error mirophoes are usually paired with the otrol soures, ad they are plaed at the elosure opeig ad 10 m above the otrol soures aordigly. 380 itersetios of evely distributed logitude ad latitude lies o a semi-sphere surfae are hose for oise redutio performae evaluatio. The semi sphere eters at the opeig eter ad the radius is 10 m. It is kow that the oise redutio dereases with the irease of the leakage oeffiiet β i geeral. The reaso is that the otrol soure stregths drift away from the optimum value whih a be obtaied whe the leakage oeffiiet ireases. The VSB a be implemeted with two differet otrol strategies, fully oupled (6 hael etralized), ad fully idepedet, where β is set as 0 or a radomly hose value For the fully idepedet VSB, eah otrol soure ad the error mirophoe above it ostitute oe idepedet ANC system. The performae with differet type VSBs is preseted i Figure 3. (a) (b) Figure 3 Noise redutio performae of differet type VSBs (a) β is zero (b) β is 1e7 It is lear from Figure 3(a) that whe the leakage oeffiiet equals zero, the oise redutio performae is the same for both fully oupled ad idepedet VSBs. The reaso is that the otrol Page 4 of 7 Iter-oise 2014

5 Iter-oise 2014 Page 5 of 7 soure stregth i Eq. (5) a be expressed as Q ( ) = Z p 1, whih has o relatioship with the implemetatio trasfer futio matrix Z e. It is also preseted that the oise redutio dereases with the frequey i geeral while the oise redutio peaks ours at the frequeies of the radiated soud power, suh as 104 Hz, 280 Hz, 415 Hz ad so o. Whe the leakage oeffiiet equals , the oise redutio is depressed ad maily appears at the peak frequeies of the soud power. The oise redutio performae of the fully oupled VSB is better tha that of the idepedet VSB, while the oise amplifiatio of oupled VSB is also larger at the frequeies aroud 135 Hz, 295 Hz, 425 Hz ad so o, whih are little higher tha the peak frequeies of the soud power. I pratial appliatios, the oise spetrum after broadbad otrol is almost flat ad the maximum oise redutio at the origial oise peaks is usually below 30 db whe the ANC system is tured o due to the bakgroud oise ad the soud radiatio harateristi of ormal soures. Therefore it is assumed that the oise spetrum whe the fully oupled VSB is implemeted remais a ostat value over the frequey bad. This assumptio is realized by optimizig the leakage oeffiiet for eah frequey. The ostat oise level is set as 32.2 db, whih is the miimum soud power above 70 Hz ad the redutio at the oise peaks is about 20 db i the simulatio. The VSB is tured off ad the otrol soure stregth is set to be zero whe the frequey is below 70 Hz. The soud oise redutio of the idepedet VSB with the optimized leakage oeffiiet is plotted i Figure 4. Figure 4 Noise redutio performae of differet type VSBs with optimized β It is lear from Figure 4 that the whe the oise redutio of the idepedet VSB is poorer tha that of the fully oupled VSB i geeral. It a also be foud that the idepedet VSB idues the oise amplifiatio i the frequey bad betwee 200 Hz ad 260 Hz. The soud pressure level at six error mirophoes at 250 Hz is preseted i Figure 5, where it is obvious that the soud pressure at all the error mirophoes is ehaed whe the idepedet VSB is applied while the soud pressure redutio at error mirophoes is diffiult to distiguish. This meas that the reaso for the oise amplifiatio of idepedet VSB is the oise redutio riterio for leakage oeffiiet determiatio based o oupled VSB is too low at the frequeies from 200 Hz to 260 Hz. Figure 5 Soud pressure level at the error mirophoes whe the peak oise redutio is 20 db Iter-oise 2014 Page 5 of 7

6 Page 6 of 7 Iter-oise 2014 Whe the oise redutio riterio is ehaed to 30 db for oise peaks, the soud oise redutio of the idepedet VSB with the optimized leakage oeffiiet is plotted i Figure 6. It is lear that the oise a be depressed at frequeies from 200 Hz to 260 Hz. Cosider the results i Figure 4, it a be oluded that whe the radiated oise level is high eough (30 db above the bakgroud oise level), the idepedet VSB a effetively redue the soud radiatio from the idoor soud soure at most frequey; whe the oise level is low, the idepedet VSB may amplify the oise at the frequeies where the valley of the radiated soud power ours. It may also be oted that there still exists some oise amplifiatio i the frequey rage 35 Hz to 80 Hz for the idepedet VSB ad the reaso eeds to be ivestigated further. It is also foud that i both Figures 4 ad 5 that the performae of the fully oupled VSB is better at the frequeies where the peaks of the radiatio power appear. Whe the 20 db riterio is adopted, the oise redutio is 9.5 db, 5.4 db higher ompared to the idepedet VSB at 105 Hz ad 280 Hz. Whe the 30 db riterio is adopted, the oise redutio is 10.4 db ad 15.1 db higher aordigly. Figure 6 Soud pressure level at the error mirophoes whe the peak oise redutio is 30 db 4. CONCLUSIONS A theoretial mode for preditig the soud radiatio through the opeig from a moopole soure i a elosure is established ad the performae of both etralized ad deetralized virtual soud barrier at the opeig surfae is ivestigated. It is show that the idepedet virtual soud barrier is effetive at most frequeies although the oise redutio is at least 5.4 db lower tha that of the fully oupled oe at the frequeies where the soud power peaks appear. Besides, there exists a oise amplifiatio risk at the frequeies where the radiated soud power is ot high eough. The feasibility of applyig the deetralized virtual soud barrier for idoor trasformer is validated ad experimetal validatios eeds to be further ivestigated. ACKNOWLEDGEMENTS The work is supported by the Natioal Natural Siee Foudatio of Chia ( ). REFERENCES 1. Mig RS, Pa J, Norto MP, Wede S, Huag H. The soud field haraterisatio of a power trasformer. Appl Aoust. 1999;56(4): Coover WB. Fightig oise with oise. Noise Cotrol. 1956;2: Ross CF. Experimets o the ative otrol of trasformer oise. J Soud Vib. 1978;61: Hesselma N. Ivestigatio of oise redutio o a 100 kva trasformer tak by meas of ative methods. Appl Aoust. 1978;11: Agevie OL. Ative aellatio of the hum of large eletri trasformers. Pro INTER-NOISE 92; 1992; Toroto, Caada p Page 6 of 7 Iter-oise 2014

7 Iter-oise 2014 Page 7 of 7 6. Marti V, Roure A. Ative oise otrol of aousti soures usig spherial harmois expasio ad a geeti algorithm simulatio ad experimet. J Soud Vib. 1998;212(3): Qiu X., Zhag LM, Tao J. Progress i researh o ative otrol of trasformer oise. Pro INTER-NOISE 2012; August 2012; New York, USA Zou H, Qiu X, Lu J, Niu F. A prelimiary experimetal study o virtual soud barrier system. J Soud Vib. 2007;307(1): Nelso PA, Curtis ARD, Elliot SJ, Bullmore AJ. The miimum power output of free field poit soures ad the ative otrol of soud. J Soud Vib. 1987;116(3): Qiu X, Hase CH. A algorithm for ative otrol of trasformer oise with olie aellatio path modellig based o perturbatio method. J Soud Vib. 2000;240(4): Qiu X, Li X, Ai YT, Hase CH. A waveform sythesis algorithm for ative otrol of trasformer oise: implemetatio. Appl Aoust. 2002;63: Lebouher E, Miheau P, Berry A, ĽEspérae A. A stability aalysis of a deetralized adaptive feedbak ative otrol system of siusoidal soud i free spae. J Aoust So Am. 2002;111(1): Zhag L, Tao J, Qiu X. Performae aalysis of deetralized multi-hael feedbak systems for ative oise otrol i free spae. Appl Aoust. 2013;74: Cordioli JA, Hase CH, Li X, Qiu X. Numerial evaluatio of a deetralised feedforward ative otrol system for eletrial trasformer oise. Iteratioal J Aoust Vib. 2002;7(2): Huag H, Qiu X, Kag J. Ative oise atteuatio i vetilatio widows. J Aoust So Am. 2011;130(1): Ise S. The boudary surfae otrol priiple ad its appliatios. IEICE Tras. Fudametals E88-A. 2005; Iter-oise 2014 Page 7 of 7