RESEARCH OF PHASE-SHIFT METHOD OF RESONANT DC/DC CONVERTER POWER CONTROL

Transcription

1 ELECTRONICS 6 September, Sozopol, BLGARIA RESEARCH OF HASE-SHIFT METHOD OF RESONANT DC/DC CONVERTER OWER CONTROL Nikolay Dimitrov Bankov, Aleksanar Stoyanov Vuchev niversity of Foo Technologies, 6 Maritza Blv, 4 loviv, Bulgaria, nikolay_bankov@yahoo.com Technical niversity of Sofia, Branch loviv, 7a Br. Buckstone Str., 44 loviv, Bulgaria, vutchev@abv.bg A phase-shift metho of profoun power control of resonant DC/DC converter, operating at frequencies higher than the resonant frequency, has been suggeste. The converter consists of two inverters, parallely connecte to the line output. The metho is base on the change in the phase angle between the controlling impulses sent to the relevant vents of the two inverters. Analysis on the metho of the first harmonic has showe epenencies in the basic quantities of the DC/DC converter. A fast metho of early engineering esign of the scheme has been suggeste. The results have been confirme through computer simulation with the help of OrCAD Spice. Keywors: resonant DC/DC converters, control methos, phase-shift control. INTRODCTION A DC/DC converters operating at frequencies higher than the resonant frequency are wiely use in power sources construction for ifferent purposes [ 4]. This is ue to their power inices an high level of safe operating. There are two groups of methos of output power control of resonant DC/DC converters control at either variable or constant operating frequencies [3 5]. The secon group of methos comprehens the so-calle phase-shift metho, where two or more inverters are use parallely connecte to the line output. Because of ephasing between the controlling impulses sent to the relevant vents of the two inverters their output currents gets to be ephase as well an they have to be summe up geometrically. Thus the output power value can be obtaine though change in the phase angle between the controlling impulses. So far, researches on the phase-shift metho of resonant DC/DC converter output power control have been either insufficient or sporaic [6]. urpose of this stuy is to analyze the metho of the first harmonic of this converter using the metho of phase-shift control. Result of this analysis will be suggestion of esign methos for the converter.. ANALYSIS Basic scheme of the converter is presente on fig.. It can be conventionally ivie into three sections two ientical half-brige resonant inverters (I an II) 8

2 ELECTRONICS 6 September, Sozopol, BLGARIA parallely connecte an one brige rectifier (III) with loaing resistor, connecte to its output. The two invertors operate at constant frequency, however their controlling impulses are ephase at angle. By changing the phase angle ftom to 8 we can receive profoun power control over the converter. Fig.. Basic scheme of the DC/DC converter Voltages an currents charts for the converter are shown on fig.. Fig.. Diagrams of the voltages an currents 8

3 ELECTRONICS 6 September, Sozopol, BLGARIA We assume that all elements are ieal an accoring to the first harmonic metho, in the present scheme, the first harmonics of the currents an the voltages are the only active ones. The resonant frequency, the wave impeance an the reactance of the two oscillate circuits can be presente as follows: ω ; L ρ ; X ωs L ν ρ, () LC C ωsc ν where ν ωs ω represents the frequency istraction of inverters circuits. The following equations are vali for the researche circuit at establishe moe, where p. is equal to zero: & a() & c() + jxi& () ; & b() & c() + jxi& (), () where a(), b(), c(), I (), I () represent effective values of the first harmonics of u a, u b, u c, i, i. After summing up above equations an conversions we receive: & + & X ( ) () j I& () & a() b() e() & c() + j I& () + I& () & + c X, (3) Whereas e() represents equivalent voltage, substituting the concurrent use of both a() an b(). Due to it, the scheme can be presente as consiste of only one inverter with oscillate circuit at same resonant frequency but twice-lower reactance. With the above assumptions for the scheme, the following epenences are vali: a () b() ; c () ; I() I ; e() a () Then from equations (3) an (4) we can go to: (4) 8 + ν ρ I (5) ν With purpose to obtain summarize results, all the quantities have been normalize as following: voltages against, currents against ρ, powers against 4ρ. Thus equation (5) gives expression of normalize output characteristic of the converter: I + X I 6 ν + ν where X represent the normalize reactance of the converter, towars the loaing circuit. The relative output power value of the scheme can be obtaine from above equation after relevant conversions: I I X I (7) Maximum output power an conitions through which it can be obtaine are: max ; ( max) X I ; X ( max) (8) 83 (6)

4 ELECTRONICS 6 September, Sozopol, BLGARIA Equation (6) provie the following epenences: X I ϕ X I ; sinϕ (9) where ϕ represents the angle between voltage u () an current i (). The relative current values of the two inverters are: sin + X I + X I sin ϕ I () () 4 X I () sin + X I X I 4 X sin ϕ The voltages an currents charts (fig.) clearly show that the relevant angles ϕ an ϕ between u a(), i () an u b(), i () are: ϕ + γ ϕ γ () ; Angles γ an γ between voltage u () an currents i (), i () can be receive from the following expressions: γ sin + X I ϕ sin + X I + X I sin ϕ (3) γ sin X I ϕ sin + X I X I sin ϕ (4) The relative average values of the currents running through the switches an the ioes of the inverters are: ϕ () I () θ S ()( + ϕ I I I AV ) (5) I () θ D ()( ϕ I I I AV ) (6) ϕ ϕ I () θ S ()( + ϕ I I II AV ) (7) I () θ D ()( ϕ I I II AV ) (8) ϕ The normalize average current running through the rectifier ioes is: I I D III AV (9) The relative maximum values of the voltages across the inverters capacitors are: 84

5 ELECTRONICS 6 September, Sozopol, BLGARIA I() I() I () C () I max ω C ν / ρ ν S I () I () I () C () II max ωsc ν / ρ ν The normalize average value of the input current of the converter is efine by following expression: I [ I () sin( θ ϕ ) + I () sin( θ ϕ )] θ ( I () ϕ + I () ϕ ) () 3. DESIGN When esigning similar scheules, the following parameters are usually given: output power, output voltage an operating frequency f. Very often the supply voltage value is given an through inclusion of transformer we can obtain esire output voltage. Frequency istraction is usually chosen within the range ν,,3. If we assume that the coefficient of efficiency of this converter is unity, power source parameters are: I (3) The values of the elements of resonant tank circuit L an C can be efine by the expressions for maximum output power an frequency istraction: 8 ν ; ν f LC (4) ρ L C ν Then we receive the following epenences for L an C: 4 ν L 3 ν f ν ; C (5) 6 f The so chosen parameters for the converter efine the nominal operation point corresponing to the output power at given frequency istraction. It is significant that in this case the angle of ephasing between the controlling impulses of both of the inverters inclue in the scheme has to be chosen in avance as well. sually, at nominal loa resistance, we choose. Computer simulation of presente DC/DC converter without transformer has been conucte with the OrCAD Spice program an at the following setting ata: supply voltage 3V, nominal output voltage V, operating frequency fkhz, output power РkW, elements of both resonant tank circuit L9,3µH an C8,43nF, loaing resistance R,5Ω. The value given to 9. 85

6 ELECTRONICS 6 September, Sozopol, BLGARIA The simulation results (values of the currents in the resonant tank circuits, input current an voltages across the capacitors) are compare in Table together with theoretical estimations results. There is very goo concurrence between the results obtaine from the calculations through the suggeste methos an these from the computer simulation, where the relative error is uner 5%. Table. Theoretical results an simulation results I () I () I Cm Cm A A A V V изчислено 8,788 3,74, ,5 86, Spice 8,79 3,666, ,644 78,9 4. CONCLSIONS Analysis on the metho of the first harmonic of DC/DC converter, operating at frequencies higher than the resonant frequency has been conucte, using the phaseshift metho of output power control. Depenencies for the basic quantities of the converter have been obtaine. Fast metho of easy engineering esign of the scheme has been suggeste. Very goo concurrences between the theoretical results an the results from the computer simulation have been constitute. The metho of the first harmonic is simple an a convenient one an in this particular case, it appears to be satisfyingly correct (error is uner 5%). REFERENCES [] Anchev M., G. Maleev, Analysis of a transistor inverter functioning with a frequency higher than this of the resonance one, E+E, 5-6,, pp.-7. [] Bankov, N., Analysis of a transistor resonant inverter by using the first harmonic approximation, Cuperac lavi, Nis, 996 (in Serbian). [3] Cheron, Y., La commutation ouce ans la conversion statique e l energie electrique, Technique et Documentation - Lavoisier, 989. [4] Cheron, Y., H. Foch, J. Roux, ower transfer control methos in high frequency resonant converters, CI roceeings, Munich, 986, pp.9-3. [5] Oruganti, R., F.C. Lee, Resonant ower rocessor: art II Methos of control, roc. IEEE-LAS 84 Ann. Meet, pp , 984. [6] Savary,., M. Nakaoka, T. Maruhashi, Novel type of high-frequency link inverter for photovoltaic resiential applications, IEEE roceeings, Vol.33, t. B, 4, July