感应加热电源负载感应器模型与恒频调功研究
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摘要
能源和环保问题日益严重，世界各国在开发新能源、治理环境的同时，大力提倡节能、环保。固态感应加热电源因其高效、环保将得到更加广泛应用。感应加热理论虽然已经成熟，但是在工程应用中还有些问题需要解决，本文对被加热物体为空心圆柱体的负载感应器等效模型和串联谐振逆变电源恒频功率调节方式进行了深入研究。本文的主要研究内容如下：
采用解析法推导了被加热物体为空心圆柱体负载感应器等效数学模型；通过求解被加热物体空心圆柱体涡流场分布，推导了被加热物体等效电阻R_b和等效电抗X_b解析表达式；并对(?)r_1／δ≥10(r_1：空心圆柱体内径，δ：透入深度)时的R_b和X_b进行了简化，简化后的R_b和X_b计算公式中不再含有贝塞尔函数，公式更加简单；指出当(?)r_b／δ≥10且w≥4(w：空心圆柱体厚度)时被加热物体等效电阻R_b和等效电抗X_b相等。
推导了负载感应器等效电阻R和等效电抗X计算公式，并对其进行了仿真(采用ANSOFT MAXWELL 2D／3D有限元仿真软件进行仿真)和实验验证，仿真和实验结果表明本文推导的负载感应器数学模型正确，负载感应器等效电阻和等效电抗计算公式准确。本文推导的负载感应器等效电阻和等效电抗计算公式物理意义明确，计算公式简单，使用方便，具有较大的工程应用价值。
从磁场角度定性分析了负载感应器等效电阻和等效电感大小与线圈匝数N、流过线圈的电流频率f、被加热物体的导磁率μ_r以及感应加热线圈半径r_3之间的关系，指导感应线圈的设计和被加热物体材料的选择；指出当被加热物体为不锈钢时，从负载感应器电效率的角度来讲，应选用铁素体或马氏体不锈钢。
采用微分方程法推导出了采用恒频移相调功方式和恒频不对称电压消除法功率调节方式时，串联谐振逆变电源实现零压开通的最小归一化开关频率f_(emin)函数关系；并与采用傅立叶级数法推导得到的最小归一化开关频率f_(emin)解析表达式进行对比，仿真和实验结果表明采用微分方程法推导的最小归一化开关频率f_(emin)准确。
详细分析了串联谐振逆变电源的两种恒频率功率调节方式的工作模态；从最小归一化开关频率f_(emin)、效率以及功率调节范围等方面对串联谐振逆变电源的两种恒频率调功方式进行了对比，指出恒频移相调功方式调功范围宽，适合应用在直流母线电压变化范围大，宽范围调功场合，恒频不对称电压消除法调功范围窄。当调功范围为(0.25-1)P_n(P_n为额定功率)，采用恒频不对称电压消除法调功方式时电源效率比采用移相调功方式时高，尤其频率高采用MOSFET管时更是如此。
最后从主电路拓扑、负载匹配方式和散热器选取等方面给出了4kW串联谐振逆变电源的详细设计思路。产品长期运行结果表明，设计的串联谐振逆变电源工作可靠，效率高(电效率和热效率乘积高达90％)，与电热丝加热方式相比，效率提高近30％。
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~(1／2)r_1/δ≥10 (r_1 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~(1／2)r_1/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 r_3. 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%.
采用解析法推导了被加热物体为空心圆柱体负载感应器等效数学模型；通过求解被加热物体空心圆柱体涡流场分布，推导了被加热物体等效电阻R_b和等效电抗X_b解析表达式；并对(?)r_1／δ≥10(r_1：空心圆柱体内径，δ：透入深度)时的R_b和X_b进行了简化，简化后的R_b和X_b计算公式中不再含有贝塞尔函数，公式更加简单；指出当(?)r_b／δ≥10且w≥4(w：空心圆柱体厚度)时被加热物体等效电阻R_b和等效电抗X_b相等。
推导了负载感应器等效电阻R和等效电抗X计算公式，并对其进行了仿真(采用ANSOFT MAXWELL 2D／3D有限元仿真软件进行仿真)和实验验证，仿真和实验结果表明本文推导的负载感应器数学模型正确，负载感应器等效电阻和等效电抗计算公式准确。本文推导的负载感应器等效电阻和等效电抗计算公式物理意义明确，计算公式简单，使用方便，具有较大的工程应用价值。
从磁场角度定性分析了负载感应器等效电阻和等效电感大小与线圈匝数N、流过线圈的电流频率f、被加热物体的导磁率μ_r以及感应加热线圈半径r_3之间的关系，指导感应线圈的设计和被加热物体材料的选择；指出当被加热物体为不锈钢时，从负载感应器电效率的角度来讲，应选用铁素体或马氏体不锈钢。
采用微分方程法推导出了采用恒频移相调功方式和恒频不对称电压消除法功率调节方式时，串联谐振逆变电源实现零压开通的最小归一化开关频率f_(emin)函数关系；并与采用傅立叶级数法推导得到的最小归一化开关频率f_(emin)解析表达式进行对比，仿真和实验结果表明采用微分方程法推导的最小归一化开关频率f_(emin)准确。
详细分析了串联谐振逆变电源的两种恒频率功率调节方式的工作模态；从最小归一化开关频率f_(emin)、效率以及功率调节范围等方面对串联谐振逆变电源的两种恒频率调功方式进行了对比，指出恒频移相调功方式调功范围宽，适合应用在直流母线电压变化范围大，宽范围调功场合，恒频不对称电压消除法调功范围窄。当调功范围为(0.25-1)P_n(P_n为额定功率)，采用恒频不对称电压消除法调功方式时电源效率比采用移相调功方式时高，尤其频率高采用MOSFET管时更是如此。
最后从主电路拓扑、负载匹配方式和散热器选取等方面给出了4kW串联谐振逆变电源的详细设计思路。产品长期运行结果表明，设计的串联谐振逆变电源工作可靠，效率高(电效率和热效率乘积高达90％)，与电热丝加热方式相比，效率提高近30％。
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~(1／2)r_1/δ≥10 (r_1 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~(1／2)r_1/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 r_3. 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%.
引文
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