COMPUTATION OF CURRENT PULSED SOURCES WITH INDUCTIVE ENERGY STORAGES

Transcription

1 Power enineerin REFERENCES. Apasov A.M. Valuev D.V. Danilov V.I. On possible reasons of defects of lare-capacity billets of low-carbon ananese steel at «Yurash» // Bulletin of the Tosk Polytechnic University V P Tushinskiy L.I. Bataev A.A. Tikhoirova L.B. Perlite structure and constructive strenth of steel. Novosibirsk: Nauka p. 3. Lyubiova L.L. The technique of roentenoetric analysis of instructure stresses // Bulletin of the Tosk Polytechnic University V P Malinina R.I. Malyutina E.S. Novikov V.Yu. et al. Practical etalloraphy. Moscow: Interet Enineerin p. 5. Structural-phase states of etal systes / Ed. by A.I. Potekaeva. Tosk: Press of NTL p. 6. Metal research and steel theral treatent. Reference book. V. II. The fundaentals of theral treatent / Ed. by M.L. Bernshtein A.G. Rathshtadt. Moscow: Metalluriya p. 7. Sorokin V.G. Gervasiev M.A. Paeev V.S. et al. Steels and alloys. Moscow: Interet Enineerin p. Received on..006 UDC COMPUTATION OF CURRENT PULSED SOURCES ITH INDUCTIVE ENERGY STORAGES G.V. Nosov Tosk Polytechnic University E-ail: nosov@elti.tpu.ru Forulas for coputation of efficiency and paraeters of current pulsed sources at charin and discharin of the inductive enery storae on active loadin have been obtained. For charin the inductive storae the electric and capacitor batteries unipolar and synchronous electric enerators with the rectifier equivalent circuit of which can be presented by consecutive connection of equivalent capacity inductance and resistance are considered. Forulas at which hih efficiency of chare is reached are obtained for coputation of paraeters of the inductive storae in the for of the ultilayered coil. It is shown that current pulsed sources are the ost effective at oscillatory charin of the inductive storae when ore than 50 % of the enerator enery can be transferred to loadin. Currently pulsed sources with resistive («hot» inductive storaes of electroanetic enery and open (explosive switches К (Fi. are one of the ost powerful current pulse enerators with specific accuulated enery in inductive storae to 5 J/ and ore [ 3]. Therefore coputation of the efficiency and paraeters of such source is the topical proble. To chare the inductive storae with enery let us exaine such electroanetic enery enerators as accuulator and capacitor batteries chared fro internal source as well as unipolar and synchronous electric enerators with rectifier in electrodynaic brakin ode [ 3]. Fi.. Diara of charin inductive storae and pulse loadin supply: Г is the electroanetic enery enerator; Н is the loadin; К and К are the switches; L and r are the inductance and resistance of storae wire The equivalent circuit of these enerators ay be approxiately introduced in the for of series connection of capacity C inductance L and resistance r [ 3] then for equivalent paraeters of a circuit of inductive storae loadin C ( = ; r = r + r; Le = L + L U when switches К and К are closed one deterines the roots of characteristic equations r r p ( = ± Le 4Le LC e and charin tie of inductive storae (p p ln( p/ p t = (3 p p correspondin to current axial value i(t CU ( pp I [ pt p t = i t = e e ] (4 p p and axial enery accuulated by the storae LI = (5 at voltae anitude at capacitance C U ( p pt p U p t = uc t = e e (6 p p p where and U are the initial values of accuulated enery and voltae of enerator at open switch К respectively (Fi.. 69

2 Bulletin of the Томsк Pоlytеchnic University V For all types of enerators on charin tie intervals of inductive storae 0<t<t current i(t ay be taken equal to pt pt q I( e e πt it ( = I sin (7 pt pt e e t where q 05 at aperiodic chare when roots of p are real neative and different; and q at oscillatin chare when roots of p are coplex and conjuate. If heat enery loss in inductive storae and enerator are taken into account t T = = 0 r i( t dt I r t (8 where I is the effective (quadratic current value on tie interval 0<t<t then at total accuulated enery in anetic field of enerator and storae LI e (9 Ì = the efficiency of accuulation (charin of enery in anetic field subject to ( 7 9 we deterine as Ì η = = Ì + T t I + τ I (0 t( + r r + τ ( + L L( + q 3 where τ =L e /r and τ=l/r are the constants of chare and storae respectively. At charin takin into account (0 averae power of enerator equals T + Ì Ì P = =. ( t tη Then if we assue that the switch К opens at point of tie t=t instantly rapidly and the load Н (Fi. is characteried by constant resistance r H then at equivalent resistance of enerator and storae dischare circuit rp = r + rh ( the roots of characteristic equation rp rp p (3 34 = ± Le 4Le LC e and current at initial conditions i(t =I and u C (t =U ay be deterined: Cp4 U p3 ( t t e + pi I 3 it ( =. (4 p3 p 4 p C 4 p4 U p4 ( t t + e p3 I As a result at axiu values of voltae U = r I H (5 and load capacity P = IrH (6 fro conditions of transforation of all anetic field enery into heat after openin the switch К LI e Irpt p= we et the desin duration of enerator and storae dischare to the load τ p t p = (7 and deterine the efficiency of enerator enery transfer to the load M η = (8 where τ p =L e /r p is the constant of dischare. The power aplification due to current pulse copression (t p <t subject to (0 aounts to P rh t K p = = (9 P r η τ and this coefficient increases by rowin of load resistance r H. The calculations were carried out and the diaras were plotted (Fi. by the forulas ( 9 at chane of the equivalent inductance L e. It follows fro the that pulsed source functionin is the ost efficient at oscillatin charin when L e is rather lower than critical inductance (λ=l e /L kp << 4τ Lkp = (0 C i.e. the inductance supportin equal roots (. However at L e reduction the chare tie t decreases in coparison with τ that results in increase of enerator averae power Р. Fi.. The desin dependences of efficiencies η η and relative chare tie t /τ Thus to support hih efficiencies η and η at lower averae enerator power Р it is necessary to have L e <<L kp at axial constant of the chare τ. 70

3 Power enineerin As then obviously the constant of the storae τ should be axial as well. Let us deterine the inductive storae paraeters at which the constant τ is axial. Let us consider that the inductive storae is ade in the for of ultilayer coil of rectanular cross-section (Fi. 3 the inductance of which is calculated by the approxiate forula [4]: Rw L ( 6R+ 9l+ 0a and if the suands in denoinator are of the sae order then the calculatin error does not exceed %. Fi. 3. L / L τ = τ + + r / r The coil of rectanular cross-section: w is the nuber of turns; R is the averae radius of turns; a is the windin thickness; l is the coil lenth; and rk are the coordinate axes Let us denote the coil lenth l=ka by a certain coefficient k>0 then the coil resistance aounts to π Rw r = ( γ Kka Z where γ is the specific conductivity of the conductor aterial; K Z is the coefficient of fillin the windin section with the conductor. As a result takin into account ( and ( we write down the constant of the storae 4 L 06 0 γ kra τ = (3 r π[6 R+ (9k+ 0 a] whence π(9k+ 0 aτ R. ( γ ka 6πτ As the internal radius of windin is R =R 05a 0 then R/a 05 then on the basis of (4 we obtain γ ka τ n (5 π[9k + 3] where n is the certain coefficient. Let us write down the axial value of current as al I (6 = w where j is the axial current density in windin conductor. Substitution of forulas ( (4 6 into (5 allows obtainin the ratio for calculation of windin thickness 0 (9k+ 3(9k+ 3 3 n a. ( kn (9k + 0 (7 The volue of windin γ V = π Ral = τ (8 and ass of the conductor with specific volue density ρ is deterined by the forulas ( (3 (5 and (6 γρ = ρv =. τ (9 Then takin into account (9 let us et specific stored enery j pw = = τ γρ (30 and specific constant of the storae τ j pτ = = τ. γρ (3 It is obvious that the axiu of the constant (5 corresponds to the axial specific paraeters (30 and (3. It is written down as follows γ τ f ( k n (3 takin into account (7 where kn(9k n f( k n = (33 3. (9k + 3 (9k + 0 The desin function of the coil (33 which is shown in Fi. 4 has axial value equals approxiately 069 at k and n 5. Fi. 4. The desin function of the coil As a result we finally obtain the thickness of windin equal the coil lenth fro the forulas (6 8 3 at f(kn a = l 4 6 ( averae radius of windin turns 0 7

4 Bulletin of the Томsк Pоlytеchnic University V R 643a and axial constant of the storae (35 4 γ τ 06 0 (36 08 and the inductance 4 L aw (37 and resistance of the coil are obtained fro the forulas (. w r 0 3. γ K (38 Z a It should be noted that the obtained ratios of the coil sies a=l and R 643a coincide with the results iven in [5] where it is appointed as well that the coils with such sies have rather hih constant τ than the toroids. If the values I and are specified then L ay be calculated fro (5. And then usin the forulas (34 37 the nuber of coil turns ay be deterined selectin such current density j that this nuber coes out to be the interal: 0 0 w L. 0 (39 Total teperature of coil windin conductor is deterined by charin and in tie point t=t at adiabatic heatin and constant specific conductivity γ aounts to θ jt 0 ( + q 3 C ρ ργ θ (40 I λu + 06 ( λ 00 r λ U r γ r + 4( λ 00 (44 and accuulated enery of enerator are obtained 06 ( 00 4 ( L / L λ +. (45 λ So if the values = MJ; K Z =05; γ=58 Mho/; ρ=8900 k/ 3 ; С ρ =3855 J/k. С; θ 0 =0 С; r Н = Oh; λ=03 are specified and the enerator with U =50 V r =0 Oh and L =0 khn is used then at j =45 A/ by the forulas ( 45 the paraeters of the pulsed source: I = МА; L= khn; a=l 066 ; R 073 ; w= turns; r 857 koh; τ 33 s; τ 9 s; τ p 76 s; t =7 s; t p =088 s; θ 09 C; В =664 T; σ =399 MPa; V ; k; pw 47 J/; pτ s/k; С =807 F; М =05 MJ; =5 MJ; η 05; η 047; Р M; Р 086 M; K p 9; U =086 V ay be calculated. For the source with the iven paraeters the typical diara of standard current pulse calculated by the forulas (7 and (4 is introduced in Fi. 5. And dependences for its axial value obtained by the ratio (44 are shown in Fi. 6. where θ 0 is the initial teperature; C ρ is the specific heat capacity of conductor aterial. On the basis of calculation of the coil anetic field (fi. 3 the approxiate forulas for deterinin axial values of inductance LI B (4 3π wa and anetic field pressure on coil internal turns are obtained BI σ (4. a At specified paraeters U L r of enerator and j K Z γ of the storae for oscillatin charin when 00<λ<05 fro forulas ( at equivalent enerator capacity τ λ ( + L / L C = 4 (43 L ( + r / r the approxiate ratios for calculatin axial values of current Fi. 5. Fi. 6. The desin standard current pulse of the source Maxial values of current pulse 7

5 Power enineerin Thus the derived forulas ay be used for calculatin paraeters of pulsed current sources with inductive enery storaes. On the basis of analysis of forulas and carried out calculations the followin conclusions ay be stated.. The oscillatin chare is the ost efficient when the equivalent inductance is rather lower than the critical one (λ<< and ore than 50 % of enerator enery ay be transferred to the load.. To support hih efficiency of the source at low averae power of enerator it is necessary to have axial constants of the chare τ and storae τ. 3. Increasin initial stress of enerator U at constant paraeters j γ K Z and r the efficiencies of the chare η and enerator enery transfer to the load η row as the current achieves the required axial value I at low anitudes of λ. 4. Application of accuulator batteries unipolar and synchronous enerators as enerators for aperiodic chare of inductive storae is inefficient owin to low anitudes η and η; use of these enerators at oscillatin chare requires ipleentation of special constructive solutions directed to increase of rate of current rise i.e. to increase of stress U and decrease of inductance L and resistance r. 5. Oscillatin chare of inductive storae fro a capacitor bank is the ost efficient and appropriate especially if the battery has hih density of accuulated enery which can exceed 3 J/ [6]. REFERENCES. Explosive enerators of electric current power pulses / E.I. Asinovskiy E.F. Lebedev A.A. Leontiev et al; ed. by V.E. Fortov. Moscow: Nauka p.. Hih power pulsed systes / Ed. by E.I. Asinovskiy. Moscow: Mir p. 3. Glebov I.A. Kasharskiy E.G. Rutber F.G. Synchronous enerators of short-ter and ipact action. Leninrad: Nauka p. 4. Electrotechnical reference book: 3 volues V.. General questions. Electrotechnical aterials / Ed. by professor of MEI V.I. Gerasiov et al. Moscow: Eneroatoidat p. 5. Physics and enineerin of power pulsed systes / Ed. by E.P. Velikhov. Moscow: Eneroatoidat p. 6. Aviation week and space technoloy V P Received on UDC UNIVERSAL MATHEMATICAL MODEL OF POER THREE-PHASE TRANSFORMERS AND AUTOTRANSFORMERS A.S. Gusev S.V. Svechkarev I.L. Plodistiy Tosk Polytechnic University E-ail: Svech@tpu.ru The substantiation of necessity in essential increase of copleteness and reliability of odelin processes in enery systes has been shown. The results of synthesis of universal atheatical odel of one of the ain eleents of enery systes power transforers and autotransforers are iven. The deanded quality of reproduction of processes is confired by experience of usin the developed odel in structure of all-ode ultiprocessin odelin coplexes of real tie of the hybrid type. The exaples illustratin quality of process odelin are shown. Accordin to statistics [ ] about 50 % of severe failures in electric systes (ES includin EES occurs due to incorrect actions of dispatcher staff relayin anufacturin and eerency autoation the ain reason of which is the use of under-coplete and under-reliable inforation on possible processes especially eerency ones in EES at desin coissionin and aintenance. EES specific character excludes practically a possibility of obtainin this inforation in a full-scale way and extraordinary coplication of up-to-date EES restricts considerably applicability of their physical odelin. As a result the ain ethod of obtainin inforation on various noral and eerency processes in EES is atheatical odelin the possibilities of which depend on presence: and use of rather accurate atheatical odels for all kinds and types of equipent; eans capable of solvin reliably and efficiently the EES equation systes fored by these odels. The stated constantly hih eerency coponent in EES indicates objectively the fact that the existin ipleentations of these factors do not support the copleteness and reliability of atheatical odelin required for its considerable decrease and in particular for efficient dispatcher control of its operability. The detailed analysis of these facts and their interaction is iven in [3 8]; the urent need and topicality of further developent of these factors follows fro this. It is obvious also that the first of the becoes loically first-priority. 73