Research On Load Inductor Mathematical Model Of Induction Heating Power Source And Constant Frequency Power Modulation

With the situation of energy source exhaustion and environmental pollution, manycountries around the world advocate energy-saving and environmental protection industry.Solid induction heating source is extensively applied for its high efficiency andenvironment-friendly. Although the theory of induction heating is mature, some problemsin engineering application need be solved. This dissertation studies the equivalent modelof load inductor which has a hollow cylinder as the heated object and the constantfrequency power regulation methods of the series resonant inverter power source. Theprimary contents and original contributions of this dissertation are as follows.This dissertation deduces the mathematical equivalent model of load inductor whichhas a hollow cylinder as the heated object based on magnetic field analysis. At first, itsolves the eddy magnetic field distribution of the heated hollow cylinder, then it deducesthe analytic expression of the heated hollow cylinder equivalent resistance R_b and equivalentreactance X_b based on Poynting theorem for the first time, and simplifies the expression ofR_b and X_b while 2^1／2r₁/δ≥10 (r₁ is the internal diameter of the hollow cylinder andδis the penetration depth of the hollow cylinder). The simplified computational formulaes ofR_b and X_b do not contain Bessel function so they can be easily used. And it also indicatesthat equivalent resistance is equal to the equivalent reactance of the heated object while2^1／2r₁/δ≥10 and w/δ≥2 (w is the thickness of the heated object) for the first time.This dissertation qualitatively analyzes the relation of load inductor equivalentresistance and inductance, the coil number N, the frequency of coil current f, themagnetoconductivityμ_r of the heated object and the semidiameter of the inductionheating coil r₃. The conclusion can efficiently guide the dimension design and materialselection of the induction heating coil in engineering application. In order to increaseelectrical efficiency of the load inductor, it should choose ferrite steel or martensite steelwhen the material of the heated object is made of stainless steel.Based on differential equation method, this dissertation deduces the analyticexpression of minimum normalization switch frequency f_emin of the constant frequency shift-phase power modulation method and constant frequency asymmetricalvoltage-cancellation power modulation method, respectively, while all swithes of theseries resonant inverter power source are zero voltage turn-on. It contrasts the analyticexpression of f_emin deduced by fourier series method with that deduced by differentialequation method. The simulation and experimental results show that the f_emin deducedby differential equation method is more accurate.The operative modes of two constant frequency power modulation methods of theseries resonant inverter power source are analyzed in detail. And minimum normalizationswitch frequency f_emin, power efficiency and power modulation range of two constantfrequency power modulation methods are compared. The dissertation indicates that theconstant frequency shift-phase power modulation method has wide power modulationrange and is suitable for the occasion which has large variation of the direct current busvoltage and wide power modulation range, and the constant frequency asymmetricalvoltage-cancellation power modulation method has narrow power modulation range and issuitable for the occasion which has little variation of bus voltage. But the efficiency of theconstant frequency asymmetrical voltage-cancellation power modulation method is higherthan that of the constant frequency shift-phase power modulation method while the powermodulation range is within 25% to 100% power rating, especially adopting the MOSFETon the occasion of high frequency.At last, it gives the detailed design of a 4kW series resonant inverter power sourcewhich includes the main curcuit topology, load matching and radiator selecion. Thelong-term operation results of the product shows that the designed series resonant inverterpower source has high reliability and high efficiency. Compared with strip heater, theseries resonant inverter power source increases the efficiency about 30%.