ELECTRONICS 005 1 3 Septembe, Sozopol, BULGARIA A DETAILED STUDY OF THE HIGH ORDER SERIAL RESONANT INVERTER FOR INDUCTION HEATING Evgeniy Ivanov Popov, Liliya Ivanova Pindeva, Elisaveta Histova Mileva, Boislav Nikolaev Tsankovski Depatment of Powe Electonics, Technical Univesity of Sofia, Kl. Ohidski Bul. No.8, 1000 Sofia, Bulgaia, phone: 359 96564, e-mail: epopov@tu-sofia.bg The eal high ode powe cicuit of the seial esonant invete without fee- wheeling diodes widely applied fo induction heating and melting is analyzed assuming a sine-wave shape of the load voltage. The load cicuit is eplaced by seially connected equivalent esistance and eactance. The paametes of the invete cicuit, especially the load voltage, the voltage acoss the powe semiconducto devices and in the thyisto vaiant the cicuit tun-off time ae detemined. A MATLAB pogam calculates and gaphically displays the fequency contolling chaacteistics. A diect steady state simulation of the invete opeation confims the esults. The equiements towads the closed loop automatic system of fequency contol can be easily defined. Keywods: seial invete, esonant invete, high-ode cicuit, chaacteistics 1. INTRODUCTION The seial esonant invete without fee - wheeling diodes applies widely fo induction heating and melting due to its convenience fo high fequency pefomance. The invete may be constucted with seially connected fully contollable devices (tansistos o GTO thyistos) and diodes. Fo cheape and not so high fequency applications when thee is a negative voltage acoss the devices ight away afte thei conduction inteval the powe cicuit can be built with thyistos. The seial esonant invete [1] has not been fully analyzed in the pactical case when the invete cicuit is of high ode. That s why this aticle is aimed at investigation of the high ode powe cicuit of the seial esonant invete fo induction heating and obtaining the fequency contol chaacteistics of the main paametes. That will allow the powe cicuit to be coectly designed taking into account the lage vaiations of the load and the estictions of the powe cicuit. The equiements towads the contolling system can also be defined. Simulations and possibly expeiments should confim the esults.. MAIN ASSUMPTIONS A half bidge cicuit (Fig. 1) is unde study but it can be easily conveted into the bidge one. The powe losses in the invete ae neglected. The commutation of the powe semiconducto devices is instantaneous. A paallel equivalent cicuit epesents the induction heate. The quality facto of the load cicuit is sufficiently high that the voltage acoss the load has a close to the sine wave shape. A combination of the method of tansitoy values and the Fouie tansfomation is applied in the analysis.
ELECTRONICS 005 1 3 Septembe, Sozopol, BULGARIA 3. REPRESENTATION OF THE LOAD CIRCUIT A paallel equivalent cicuit containing the active esistance R l and the inductance L l that ae fequency dependent epesents the inducto heate: n (1) R ( ) 1 l R n 1 () ( ) L l L, whee is the esonant fequency of the load cicuit R l, Ll, Cl 1 (3) Cl L R, L ae the inducto paametes fo the esonant fequency. π f is the contolling fequency. The values of n 1 and n ae given in []. If the quality facto of the load cicuit R l, Ll, Cl at esonance (index ) C (4) Q l R L is high enough the load voltage is almost sine wave and the load cicuit can be epesented by a seial equivalent cicuit containing the paametes R eq, X eq (Fig.). n ( ) 1 Req (5) R (n 1) 1 ( ) 1 n Q ( 1 n ( n1 ) Q ( ) ( X eq (6) R (n 1) 1 ( ) 1 n Q ( Below the esonance of the load cicuit the equivalent eactance X eq is in fact a seial equivalent inductance 1 n ( ) n1 Q ( ) ( 1) Leq (7) L (n 1) 1 ( ) 1 n Q ( Theefoe the seial invete cicuit consists of R Req, L L eq LS, C CS. Above the esonance of the load cicuit the equivalent eactance X eq is a seial equivalent capacitance
ELECTRONICS 005 1 3 Septembe, Sozopol, BULGARIA (n 1 ( ) 1 n 1) Q ( ) C eq (8) C 1 n l (n ) 1 Q ( ) ( 1) CeqCS and the seial invete cicuit consists of R Req, L LS, C, Ceq CS α C /C eq. Then the voltage acoss the invete capacito C is divided between the capacitos C S and C eq in accodance with the theoy of electical engineeing [3]. Gaphical epesentations of the functions (5), (6), (7) and (8) ae given in Fig., Fig. 3, Fig. 4 and Fig. 5 espectively. 4. PARAMETERS OF THE SERIAL INVERTER CIRCUIT The whole fouth ode invete cicuit is educed to a second ode RLC esonant ( R eq < L / C ) cicuit. This invete is analyzed in [4], [5], [1], [6]. 5. CALCULATION OF THE LOAD VOLTAGE The RMS of the load voltage can be detemined fom its hamonic components as follows (11) V l V l ( m) m 1,3,5,... Each hamonic component of the load voltage is c( m) (1) V l( m) Inom.. R eq( m) X eq( m) whee R eq(m) and X eq(m) ae calculated fom (5) and (6), exchanging / with m /. I nom Vd / Req fo natual commutation ( 0 ) and Inom Vd /( 0L) fo foced commutation ( > 0 ) whee 0 1/( LC) Req /(4L ) is the inheent fequency of the seial invete cicuit and πf is the contolling fequency. The nomalized peak value of the m hamonic component (m1,3,5, ) of the invete cuent c ( m) a ( m) b ( m) is given in [1] fo natual commutation and in [7] fo foced commutation. 6. VOLTAGE ACROSS THE POWER SEMICONDUCTOR DEVICES At natual commutation duing the inteuption inteval t X1 0 to tp π / π / 0 the voltage of the tuned-off devices is c(1) Vd (13) VVS 0.5Vd m ( k 0.5)(1 α ) Vd ± sin( tx1 tp ϕ(1) ϕeq ) cosϕeq
ELECTRONICS 005 1 3 Septembe, Sozopol, BULGARIA whee the uppe sign coesponds to the just tuned-off devices, ϕ ( 1) actg( a(1) / b(1) ), ϕ eq actg( X eq / Req ). When the othe device conducts t X 0 to π / 0 the voltage of the tuned-off device is δ t δ V 0.5 (1 ) [0.5 VS Vd α Vd ke X ( sin0t X cos0t X )] 0 (14) c(1) Vd sin( tx ϕ(1) ϕeq ) cosϕeq R eq 1 whee δ is the damping coefficient and k is the coefficient of L π δ 1 e 0 hesitation. Expessions (13) and (14) ae applied fo calculation of the maximal device voltage and in the thyisto vaiant the cicuit tun-off time. Fo foced commutation the necessay expession is given in [6]. 7. FREQUENCY CHARACTERISTICS A MATLAB pogam pocesses all the mathematical infomation descibing the steady-state opeation of the invete togethe with its load cicuit in the allowed fequency ange. The fequency chaacteistics of the invete ae obtained and gaphically displayed in Fig. 6. These paticula chaacteistics coespond to a pactically implemented invete with the following data: V d 500 V; L S 45 µh; C S 84 µf; R 0.4739599 Ω, f 083 Hz, L 8.8717 µh, C l,657.88 µf,n 1 0, n 1, f1600-600 Hz. The fist set of gaphics shows: two times the aveage input cuent of the invete I d [A] (solid line), two times the load voltage V l [V] (dashed line), ten times the cicuit tun-off time of the thyistos 10 t q.c. [µs] (dotted line). The second set of gaphics shows: the peak seial capacito voltage V CSm [V] (dash-dotted line), the maximal device voltage V VSm (solid line). The same MATLAB pogam can calculate fequency chaacteistics fo diffeent input data. Othe paametes of the cicuit can also be calculated and displayed. The calculation is moe pecise if the shape of the load voltage is close to the sine-wave fom. That is checked fo each paticula fequency. The stability and efficiency of the invete can be studied fom the chaacteistics. In geneal thee is a minimum of the input cuent and powe, load voltage, seial capacito voltage and device voltage aound the esonance of the load cicuit. If the paametes of the inducto heate vay duing the induction heating pocess it is advisable to maintain almost constant input cuent (powe) in a slight capacitive deangement of the load cicuit R l, L l, C l, whee the opeation is stable, by execising an influence on the contolling fequency. The calculated slope of the fequency chaacteistic of the input cuent is used fo detemining the paametes of the closed loop automatic contol system [1].
ELECTRONICS 005 1 3 Septembe, Sozopol, BULGARIA 8. DIRECT SIMULATION OF THE STEADY STATE The steady state is simulated by a MATLAB pogam based on the method descibed in [8] that is expeimentally confimed. The esults fom the fequency chaacteistics and fom the simulation ae in good ageement accoding to Table 1. That confims the coectness of the whole study. The detailed simulation esults of the powe invete ae gaphically displayed (Fig. 7) fo f195 Hz. The fist set of diagams shows: the seial capacito voltage v CS [V] (solid line), invete cuent i CS [A] (dashed line) and twice the load voltage v l [V] (dotted line). The second set of diagams shows: a quate of the load inductance cuent i Ll [A] (dotted line) and the voltage acoss a device v VS1 [V] (solid line). The simulation esults fo the same cicuit at f694,4 Hz displaying an inefficient but possible opeation in an inductive deangement of the load geneally with the thid hamonic component of the invete cuent (a case that is difficult to be studied analytically) ae given in Fig. 8. Table 1. f[hz] 694,4 183 018 083 Recom. 195 394 Study Sim. F.ch. Sim. F.ch. Sim. F.ch. Sim. F.ch. Sim. F.ch. Sim. Load Ind. Ind. Ind. Res. Cap. Cap I d [A] 169,5 400,7 388,7 00 196,5 178, 180,1 199,8 08, 400,6 416,3 V l [V] 00,4 304,4 303,5 15,4 15,8 01,7 06,6 11,9,1 30, 314,1 t q.c. [µs] 604 113,6 15,9 61 68,3 63,8 7,5 8,9 89,9 97,3 99,6 V CSm [V] 1456 1308 170 590 580 509 515 54 565 996 1034 V VSm [V] 197 134 134 866 875 863 886 1003 1045 1636 1689 9. CONCLUSION A detailed study of the eal seial esonant invete without fee - wheeling diodes fo induction heating is pefomed. The steady state paametes and chaacteistics ae detemined. The equiements fo the contol system can be defined. 10. REFERENCES [1] Popov E., Automatic Contol of Seial Thyisto Invetes with Vaying Load, Ph.D. Thesis, VMEI, Sofia, 1978 (in Bulg.). [] E. I. Bekovitch, G. V. Ivenskiy, Yu. S. Yoffe, A T. Matchak, V. V. Mogun, Highe fequency thyisto convetes fo electo technology applications, Leningad, Enegoatomizdat, 1983 (in Russian), pp. 8-13. [3] G. I. Atabekov, Fundamentals of cicuit theoy, Moscow, Enegy, 1969 (in Russian), pp.131-13, 100. [4] Nachev N., G. Maleev, Powe Electonics, Technica, Sofia, 1979 (in Bulg.). [5] Kusteva A., Investigation of the system seial thyisto invete induction heate, Ph.D. Thesis, VMEI, Sofia, 1974 (in Bulg.). [6] Popov E., Investgation and Analysis of Seial Thyisto RLC Invetes, Jounal Electical Engineeing and Electonics EE,vol.7-9, 003 (in Bulg.), pp.39-43. [7] Popov E., A. Popova, Study of Seial Thyisto RLC Invetes. Nomalized Examples, Poceedings of the Eleventh National Scientific and Applied Science Confeence with Intenational Paticipation ELECTRONICS ET 00, Sozopol, Bulgaia, Septembe 00 (in Bulg.). [8] Popov E., Diect detemination of the steady-state mode in autonomous invetes, Scientific Jounal Electical Engineeing and Electonics EE, vol. 11-1, 004, Sofia, Bulgaia, (In Bulg.).
ELECTRONICS 005 1-3 Septembe, Sozopol, BULGARIA i d VS1 V d / L l R l i L S1 o V d / C l C S L S v l VS Fig. 1. Fig. 5. Fig.. Fig. 6. Fig. 3. Fig. 7. Fig. 4. Fig. 8.