CN102857134B - High-frequency inverter power supply of wireless power transmission device and frequency doubling control method for inverter power supply - Google Patents
High-frequency inverter power supply of wireless power transmission device and frequency doubling control method for inverter power supply Download PDFInfo
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Abstract
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技术领域 technical field
本发明涉及一种用于无线电能传输装置的高频逆变电源及其倍频控制方法。The invention relates to a high-frequency inverter power supply for a wireless energy transmission device and a frequency multiplication control method thereof.
背景技术 Background technique
目前,电动汽车、城市轨道交通等电气化交通车辆通过接触方式充电或供电,尤其是城市轨道交通等通过触网与受电弓的移动式接触供电,因接触不良容易产生火花、摩擦带来积碳粉尘,供电的安全可靠性低、污染严重、维护工作量大,设备使用寿命也受影响,当遇到雨雪等恶劣环境影响时,接触供电更具有明显的局限性。无线供电技术可有效解决上述问题,其特点是:(1)供电电源和负载单元之间不需物理接触,电气绝缘,安全、可靠;(2)没有裸露导体存在,电能传递能力不受环境因素影响;(3)不存在机械磨损,可靠、耐用,免维护。无线供电技术可用于城市轨道交通、电动汽车、自动化装备等的无线供电,以及水下、矿井、易燃易爆等恶劣环境下的供电。At present, electrified transportation vehicles such as electric vehicles and urban rail transit are charged or powered by contact, especially urban rail transit, etc., are powered by mobile contact between catenary and pantograph. Sparks and friction are likely to cause carbon deposition due to poor contact Dust, low safety and reliability of power supply, serious pollution, heavy maintenance workload, and equipment service life are also affected. When encountering harsh environments such as rain and snow, contact power supply has obvious limitations. Wireless power supply technology can effectively solve the above problems. Its characteristics are: (1) No physical contact is required between the power supply and the load unit, electrical insulation, safety and reliability; (2) There is no exposed conductor, and the power transmission capacity is not affected by environmental factors. (3) There is no mechanical wear, reliable, durable, and maintenance-free. Wireless power supply technology can be used for wireless power supply in urban rail transit, electric vehicles, automation equipment, etc., as well as power supply in harsh environments such as underwater, mine, flammable and explosive.
无线电能传输装置的基本构成包括无接触变压器,以及高频逆变器、高频谐振电路等,为灵活、安全、可靠、方便的给电气化车辆及其他移动设备供电提供了一种有效方法。The basic composition of the wireless power transmission device includes a non-contact transformer, a high-frequency inverter, a high-frequency resonant circuit, etc., which provides an effective method for flexible, safe, reliable, and convenient power supply to electrified vehicles and other mobile devices.
无线电能传输的发展方向是大气隙、高功率、高频率、高效率。然而,目前高频电力电子器件的功率等级、开关频率都不高,单个电力电子器件的功率和频率等级很难满足大功率无线电能传输装置的需求。如何有效、经济、合理地提高并灵活调节高频逆变器的输出频率是电能无线传输的核心问题之一。另外,在无线电能传输中,初级与次级之间的互感与它们之间的耦合系数对电能传输效率起至关重要的作用。它们之间的间隙、相互位置对它们绕组之间的互感影响很大。绕组互感降低时,效率下降明显。因此如何提高无线电能传输变压器气隙的适应性,在初级与次级相互位置变动等因素导致互感下降的情况下确保较高的传输效率,是无线电能传输的另一核心问题。The development direction of wireless power transmission is large air gap, high power, high frequency and high efficiency. However, the power level and switching frequency of high-frequency power electronic devices are not high at present, and the power and frequency levels of a single power electronic device are difficult to meet the needs of high-power wireless power transmission devices. How to effectively, economically and reasonably increase and flexibly adjust the output frequency of the high-frequency inverter is one of the core issues of wireless power transmission. In addition, in wireless power transmission, the mutual inductance between primary and secondary and the coupling coefficient between them play a crucial role in power transmission efficiency. The gap and mutual position between them have a great influence on the mutual inductance between their windings. When the winding mutual inductance is reduced, the efficiency drops significantly. Therefore, how to improve the adaptability of the air gap of the wireless power transmission transformer and ensure high transmission efficiency when the mutual inductance decreases due to factors such as changes in the primary and secondary mutual positions is another core issue of wireless power transmission.
申请公开号为No.H04-317527的日本专利公开了一种非接触充电装置,为了实现高效率传递功率,次级线圈必须精确地位于相应的位置,对初次级位置关系以及空间约束很强。Japanese Patent Application Publication No. H04-317527 discloses a non-contact charging device. In order to achieve high-efficiency power transfer, the secondary coil must be precisely located at the corresponding position, which has strong constraints on the primary and secondary positional relationship and space.
中国专利200710163025.3提出的非接触电能传输装置用于电瓶车充电,其初级线圈和次级线圈均为扁平螺旋卷绕的类似圆形的平板状,仅当初次级中心正好对齐的时候才具有较高的效率,一旦初次级存在位置偏差,其传递效率会大幅下降。The non-contact power transmission device proposed in Chinese patent 200710163025.3 is used for battery car charging. Its primary coil and secondary coil are both flat and helically wound, similar to a circular flat plate. Efficiency, once there is a positional deviation between the primary and secondary stages, the transfer efficiency will drop significantly.
中国专利200810234555.7公开的非接触充电装置中,初级线圈为平行导线,次级线圈绕制在磁芯上,其中初级线圈需要穿过次级的磁芯,同样初次级的横向相对位置受到很大的局限,仅限于初级线圈固定且次级线圈有固定运动路径的场合。In the non-contact charging device disclosed in Chinese patent 200810234555.7, the primary coil is a parallel wire, and the secondary coil is wound on a magnetic core, wherein the primary coil needs to pass through the secondary magnetic core, and the lateral relative position of the primary and secondary is greatly affected Limitations, limited to the occasions where the primary coil is fixed and the secondary coil has a fixed path of motion.
以上现有技术中都存在变压器初次级位置被严重约束,实用性不强。无接触供电变压器之所以对初次级相对位置敏感,主要原因是初次级相对位置变动造成初次级之间互感的大幅变化,从而影响输出功率和效率。在同样变压器初次级相对位置情况下,提高传输频率,可以在变压器次级获得更高的电压,可有效提高传输功率和效率,解决该问题。由于无接触变压器耦合系数较普通工业用变压器小很多,属于松耦合变压器,为了提高传输效率,采用高达数十kHz的频率进行传输。In the above prior art, the primary and secondary positions of the transformer are severely constrained, and the practicability is not strong. The main reason why the non-contact power supply transformer is sensitive to the relative position of the primary and secondary is that the relative position change of the primary and secondary causes a large change in the mutual inductance between the primary and secondary, thus affecting the output power and efficiency. In the case of the same relative position of the primary and secondary of the transformer, increasing the transmission frequency can obtain a higher voltage on the secondary of the transformer, which can effectively improve the transmission power and efficiency, and solve this problem. Since the coupling coefficient of the non-contact transformer is much smaller than that of ordinary industrial transformers, it is a loosely coupled transformer. In order to improve the transmission efficiency, the frequency of up to tens of kHz is used for transmission.
为提高传输频率,可用高频MOSFET作为变流器的主开关器件形成高频逆变电源。然而,由于MOSFET的电压电流定额相对较小,大功率设备需要大量的器件串并联使用,降低了系统可靠性。IGBT器件容量远高于MOSFET,并且不存在寄生二极管不良反向恢复特性问题,适合大功率应用。但是,IGBT拖尾电流在高频开关工作状态下引起的关断损耗很大,限制其工作频率的提高。在感应加热电源领域,目前IGBT开关频率在零电流开关(ZCS)状态下可工作在100kHz。In order to increase the transmission frequency, a high-frequency MOSFET can be used as the main switching device of the converter to form a high-frequency inverter power supply. However, due to the relatively small voltage and current ratings of MOSFETs, high-power devices require a large number of devices to be used in series and parallel, which reduces system reliability. The device capacity of IGBT is much higher than that of MOSFET, and there is no problem of poor reverse recovery characteristics of parasitic diodes, which is suitable for high-power applications. However, the turn-off loss caused by the IGBT tail current in the high-frequency switching state is very large, which limits the increase of its operating frequency. In the field of induction heating power supplies, the current IGBT switching frequency can work at 100kHz in the zero current switching (ZCS) state.
文献“蔡慧,赵荣祥,陈辉明,汪世平.倍频式IGBT感应加热电源的研究[J],中国电机工程学报,2006,26(2):154-158.”中描述了一种基于IGBT依靠谐振电路振荡电流形成负载电流频率是开关管工作频率两倍的效果,该方法不但需要额外的谐振电路,而且频率提高有限,器件换流条件对谐振电路品质因数要求较高,另外功率器件定额没有得到有效利用。The literature "Cai Hui, Zhao Rongxiang, Chen Huiming, Wang Shiping. Research on double-frequency IGBT induction heating power supply [J], Chinese Journal of Electrical Engineering, 2006, 26 (2): 154-158." describes a method based on IGBT relying on resonance The oscillating current of the circuit forms the effect that the frequency of the load current is twice the operating frequency of the switching tube. This method not only requires an additional resonant circuit, but also has a limited increase in frequency. use efficiently.
文献“沈锦飞,惠晶,吴雷,颜文旭.倍频分时控制IGBT 180kHz/50kW高频感应焊接电源[J],焊接学报,2009,30(9):1-4.”中提出对逆变器每个桥臂并联的IGBT采用分时控制的方法可以提高逆变器的工作,实现逆变器倍频输出,然而该方法输出频率倍数固定,没有涉及如何变倍频运行。In the document "Shen Jinfei, Hui Jing, Wu Lei, Yan Wenxu. Frequency multiplication time-sharing control IGBT 180kHz/50kW high-frequency induction welding power supply [J], Journal of Welding, 2009, 30 (9): 1-4." The IGBT connected in parallel to each bridge arm of the inverter adopts the time-sharing control method to improve the work of the inverter and realize the frequency multiplication output of the inverter. However, the output frequency multiple of this method is fixed, and it does not involve how to change the frequency multiplication operation.
同感应加热电源相比,无线电能传输系统具有自己的特殊性:(1)效率要求不同:作为电能传输对传输效率的要求更高,因此要求电路拓扑和控制方法更高效;(2)逆变器负载不同:无线电能传输中无接触变压器初次级相对位置具有一定的变化范围,当无接触变压器初次级相对位置变动造成初次级互感下降时,通过提高传输频率可以提高效率;而当无接触变压器互感较大时,提高传输频率对效率的提升已不明显,且会带来额外的逆变器损耗;(3)电容匹配:感应加热电源频率相对固定,电容值一般不变,而无线电能传输系统由于传输频率的大范围变化,因此谐振电容电容值必须变化,以和电感、传输频率参数相匹配以保持高效率。Compared with the induction heating power supply, the wireless power transmission system has its own particularity: (1) The efficiency requirements are different: as electric energy transmission, the transmission efficiency is higher, so the circuit topology and control method are required to be more efficient; (2) Inversion The relative position of the primary and secondary of the non-contact transformer in wireless power transmission has a certain range of variation. When the relative position of the primary and secondary of the non-contact transformer changes and the mutual inductance of the primary and secondary decreases, the efficiency can be improved by increasing the transmission frequency; and when the non-contact transformer When the mutual inductance is large, increasing the transmission frequency does not improve the efficiency significantly, and will bring additional inverter losses; (3) Capacitance matching: the frequency of the induction heating power supply is relatively fixed, and the capacitance value generally remains unchanged, while wireless energy transmission Due to the wide range of transmission frequency changes in the system, the capacitance value of the resonant capacitor must be changed to match the inductance and transmission frequency parameters to maintain high efficiency.
发明内容 Contents of the invention
本发明的目的是克服现有无接触变压器对初次级相对位置适应性低以及传输效率低的问题,提出一种用于无线电能传输装置的倍频式高频逆变电源及其倍频控制方法。本发明采用多个逆变器单元并联构成逆变器倍频电路,根据无线电能传输系统中无接触变压器以及负载工况,可大范围自动调节逆变器倍频电路输出频率,在现有功率开关器件水平上产生出远高于开关频率的工作频率,通过提高工作频率,使无接触变压器在处于同样初次级相对位置情况下有更高的感应电压从而提高无接触变压器对初次级相对位置适应性。传输频率可根据无接触变压器和负载状况调节,达到最佳效率。初级谐振电容和次级谐振电容也可以随着调节频率进行调节以同电感与频率相匹配,保持高效率。本发明通过逆变器调节输出功率,无需额外的变换电路,省去直流调功环节,减少了损耗。本发明可提高供电频率和传输效率,并提高初级与次级之间相对位置的适用性,提高传输效率和系统可用性;本发明通过提高供电频率,还可减小系统尺寸和重量。The purpose of the present invention is to overcome the problems of low adaptability to primary and secondary relative positions and low transmission efficiency of existing non-contact transformers, and propose a frequency-multiplier high-frequency inverter power supply and its frequency-multiplication control method for wireless energy transmission devices . The invention adopts a plurality of inverter units connected in parallel to form an inverter frequency multiplication circuit. According to the non-contact transformer and load conditions in the wireless power transmission system, the output frequency of the inverter frequency multiplication circuit can be automatically adjusted in a large range. The switching device level produces a working frequency much higher than the switching frequency. By increasing the working frequency, the non-contact transformer has a higher induced voltage in the same relative position of the primary and secondary, thereby improving the adaptability of the non-contact transformer to the relative position of the primary and secondary. sex. The transmission frequency can be adjusted according to the non-contact transformer and load conditions to achieve the best efficiency. The primary resonant capacitor and the secondary resonant capacitor can also be adjusted with the frequency adjustment to match the inductance and frequency to maintain high efficiency. The invention adjusts the output power through the inverter, does not need an additional conversion circuit, saves the DC power adjustment link, and reduces the loss. The invention can improve power supply frequency and transmission efficiency, improve the applicability of the relative position between primary and secondary, improve transmission efficiency and system availability; the invention can also reduce system size and weight by increasing power supply frequency.
本发明解决技术问题采用的技术方案如下:The technical solution adopted by the present invention to solve technical problems is as follows:
本发明无线电能传输装置的倍频式高频逆变电源包括:直流电源、逆变器倍频电路、主控制器、次级控制器、初级谐振电容、次级谐振电容、初级电容补偿调节器、次级电容补偿调节器、无接触变压器、频率和相位检测模块、初级状态量检测传感器、次级状态量检测传感器、初级通信模块、次级通信模块、整流器、负载和驱动电路等。The frequency doubling high-frequency inverter power supply of the wireless energy transmission device of the present invention includes: a DC power supply, an inverter frequency doubling circuit, a main controller, a secondary controller, a primary resonant capacitor, a secondary resonant capacitor, and a primary capacitor compensation regulator , secondary capacitance compensation regulator, non-contact transformer, frequency and phase detection module, primary state quantity detection sensor, secondary state quantity detection sensor, primary communication module, secondary communication module, rectifier, load and drive circuit, etc.
所述的直流电源经过逆变器倍频电路后得到高频电压,再经过初级谐振电容连接到无接触变压器的初级侧。在逆变器倍频电路输出端和初级谐振电容之间设有初级状态量检测传感器。初级状态量检测传感器包括电压传感器、电流传感器、温度传感器、气隙传感器和位置传感器等,所述的电压传感器、电流传感器、温度传感器、气隙传感器和位置传感器分别检测逆变器倍频电路的输出电压、输出电流、逆变器倍频电路的温度、无接触变压器初级和次级之间的气隙以及初级和次级之间的相对位置。无接触变压器的次级经过次级谐振电容以及整流器后得到直流电,供给负载。在整流器和负载之间设有次级状态量传感器,次级状态量传感器包括电压传感器、电流传感器,所述的电压传感器、电流传感器分别检测整流器输出的电压和电流。初级状态量检测传感器检测得到的逆变器输出电压和电流信号进入频率和相位检测模块后,将得出的逆变器输出电流频率信号以及逆变器输出电压和逆变器输出电流之间的相位差信号发送给主控制器。初级状态量检测传感器检测到的所有信号都发送给主控制器。次级状态量检测传感器将整流器输出的电压和电流信号发送给次级控制器,次级控制器通过次级通信模块将整流器输出的电压信号和电流信号发送给初级通信模块,初级通信模块再将整流器输出的电压信号和电流信号传递给主控制器。主控制器综合初级状态量检测传感器和次级状态量检测传感器的信号,发出逆变器倍频电路的驱动脉冲到驱动电路,驱动电路连接到逆变器倍频电路的各个开关器件驱动接线端,驱动逆变器倍频电路的各个开关器件。在需要改变频率的倍数的情况下,主控制器给初级电容补偿调节器和次级电容补偿调节器发出指令,调节初级谐振电容和次级谐振电容的电容量。The DC power supply obtains a high-frequency voltage after passing through an inverter frequency multiplication circuit, and then connects to the primary side of the non-contact transformer through a primary resonant capacitor. A primary state quantity detection sensor is arranged between the output terminal of the frequency multiplication circuit of the inverter and the primary resonant capacitor. The primary state quantity detection sensors include voltage sensors, current sensors, temperature sensors, air gap sensors and position sensors, etc., and the voltage sensors, current sensors, temperature sensors, air gap sensors and position sensors respectively detect the Output voltage, output current, temperature of inverter frequency multiplier circuit, air gap between primary and secondary of non-contact transformer, and relative position between primary and secondary. The secondary of the non-contact transformer passes through the secondary resonant capacitor and the rectifier to obtain DC power and supply it to the load. A secondary state quantity sensor is provided between the rectifier and the load. The secondary state quantity sensor includes a voltage sensor and a current sensor, and the voltage sensor and the current sensor respectively detect the voltage and current output by the rectifier. After the inverter output voltage and current signals detected by the primary state quantity detection sensor enter the frequency and phase detection module, the obtained inverter output current frequency signal and the difference between the inverter output voltage and the inverter output current The phase difference signal is sent to the master controller. All signals detected by the primary state quantity detection sensors are sent to the main controller. The secondary state quantity detection sensor sends the voltage and current signals output by the rectifier to the secondary controller, and the secondary controller sends the voltage signal and current signal output by the rectifier to the primary communication module through the secondary communication module. The voltage signal and current signal output by the rectifier are transmitted to the main controller. The main controller synthesizes the signals of the primary state quantity detection sensor and the secondary state quantity detection sensor, and sends the driving pulse of the frequency multiplication circuit of the inverter to the driving circuit, and the driving circuit is connected to the driving terminals of each switching device of the frequency multiplication circuit of the inverter , to drive each switching device of the frequency multiplication circuit of the inverter. When the multiple of the frequency needs to be changed, the main controller sends instructions to the primary capacitance compensation regulator and the secondary capacitance compensation regulator to adjust the capacitance of the primary resonance capacitor and the secondary resonance capacitor.
所述的直流电源可以是交流电源经整流后得到的直流源,也可以是蓄电池或者电容器等直流源。直流电源可以是电压源,也可以是电流源,分别对应电压型逆变器倍频电路和电流型逆变器倍频电路。以下以电压型逆变器倍频电路为例说明本发明的结构。The DC power source may be a DC source obtained by rectifying an AC power source, or may be a DC source such as a storage battery or a capacitor. The DC power supply can be a voltage source or a current source, corresponding to the frequency multiplication circuit of the voltage source inverter and the frequency multiplication circuit of the current source inverter respectively. The structure of the present invention will be described below by taking the frequency multiplier circuit of a voltage source inverter as an example.
所述的逆变器倍频电路由n套逆变单元并联构成,从n套逆变单元中选择k套逆变单元分时驱动时,逆变器倍频电路的输出电压频率或电流频率为逆变单元输出电压频率或电流频率的k倍,构成k倍频逆变器,n为不小于1的整数,k为不小于1且不大于n的整数。对于电压型逆变器倍频电路,所述的k倍频逆变器指的是逆变器倍频电路的输出电压频率为逆变单元输出电压频率的k倍;对于电流型逆变器倍频电路,所述的k倍频逆变器指的是逆变器倍频电路的输出电流频率为逆变单元输出电流频率的k倍,k为不小于1的整数。下文均以电压型逆变器倍频电路为例。逆变器倍频电路可以是单相输出,也可以是多相输出。The inverter frequency multiplication circuit is composed of n sets of inverter units connected in parallel. When k sets of inverter units are selected from n sets of inverter units for time-sharing drive, the output voltage frequency or current frequency of the inverter frequency multiplication circuit is The inverter unit outputs k times the voltage frequency or current frequency to form a k-multiple frequency inverter, n is an integer not less than 1, and k is an integer not less than 1 and not greater than n. For voltage type inverter frequency multiplication circuit, described k frequency multiplication inverter refers to that the output voltage frequency of inverter frequency multiplication circuit is k times of inverter unit output voltage frequency; frequency circuit, the k-multiplier inverter means that the output current frequency of the inverter frequency multiplication circuit is k times the output current frequency of the inverter unit, and k is an integer not less than 1. The frequency multiplier circuit of the voltage source inverter is taken as an example below. The frequency multiplication circuit of the inverter can be a single-phase output or a multi-phase output.
所述的逆变器倍频电路的每套逆变单元可以为已知的全桥拓扑结构,或已知的半桥拓扑结构,或其他直流变换为交流的拓扑结构。每套逆变单元内的各个开关组可以为单个器件,也可以为多个器件的串联或者并联构成。逆变器倍频电路中的功率器件可以为MOSFET、IGBT、IGCT等全控型器件,器件可以自带反并联的续流二极管,也可以另加反并联的续流二极管。Each set of inverter units of the frequency multiplication circuit of the inverter can be a known full-bridge topology, a known half-bridge topology, or other topologies that convert DC to AC. Each switch group in each inverter unit can be a single device, or a series or parallel connection of multiple devices. The power device in the frequency multiplication circuit of the inverter can be a full-control device such as MOSFET, IGBT, IGCT, etc., and the device can have an anti-parallel freewheeling diode, or an antiparallel freewheeling diode can be added.
所述的初级状态量检测传感器包括检测逆变器倍频电路输出电压、逆变器倍频电路输出电流、逆变器倍频电路温度、无接触变压器初级和次级之间的气隙和相对位置等状态量的检测传感器。逆变器倍频电路输出电压传感器分别连接到逆变器倍频电路的两个输出端子上;逆变器倍频电路输出电流传感器串接入逆变器倍频电路的一个输出线上;逆变器倍频电路温度传感器嵌入逆变器倍频电路的散热片中;无接触变压器初级和次级之间的气隙和相对位置传感器分别布置在无接触变压器的初级和次级中。初级状态量检测传感器的输出信号发送到主控制器上,其中电压和电流的输出信号发送到频率和相位检测模块。次级状态量检测传感器包括无接触变压器次级侧整流器输出电压和输出电流传感器,输出电压传感器分别连接到整流器输出的两个端子上,输出电流传感器串联接入其中一个输出线上。次级状态量检测传感器的输出信号发送到次级控制器上。The primary state quantity detection sensor includes detecting the output voltage of the inverter frequency doubling circuit, the output current of the inverter frequency doubling circuit, the temperature of the inverter frequency doubling circuit, the air gap between the primary and secondary of the non-contact transformer and the relative Sensors for detection of state quantities such as position. The output voltage sensors of the inverter frequency multiplication circuit are respectively connected to the two output terminals of the inverter frequency multiplication circuit; the output current sensors of the inverter frequency multiplication circuit are connected in series to one output line of the inverter frequency multiplication circuit; The temperature sensor of the frequency doubling circuit of the inverter is embedded in the heat sink of the frequency doubling circuit of the inverter; the air gap between the primary and secondary of the non-contact transformer and the relative position sensor are respectively arranged in the primary and secondary of the non-contact transformer. The output signal of the primary state quantity detection sensor is sent to the main controller, and the output signal of voltage and current is sent to the frequency and phase detection module. The secondary state quantity detection sensor includes the output voltage and output current sensors of the rectifier on the secondary side of the non-contact transformer. The output voltage sensors are respectively connected to the two output terminals of the rectifier, and the output current sensor is connected in series to one of the output lines. The output signal of the secondary state quantity detection sensor is sent to the secondary controller.
所述的无接触变压器由初级绕组、次级绕组以及结构件组成,初级绕组和次级绕组之间有一定气隙。The non-contact transformer is composed of a primary winding, a secondary winding and structural parts, and there is a certain air gap between the primary winding and the secondary winding.
所述的初级谐振电容和次级谐振电容可以是单个或者多个电容组成;初级谐振电容可以和初级绕组串联、并联或者进行串并联连接,次级谐振电容可以和次级绕组串联、并联或者串并联连接。The primary resonant capacitor and the secondary resonant capacitor can be composed of a single or multiple capacitors; the primary resonant capacitor can be connected in series, parallel or series-parallel with the primary winding, and the secondary resonant capacitor can be connected in series, parallel or in series with the secondary winding connected in parallel.
所述的整流器可以是不控整流桥和滤波电容组成,也可以是可控整流器或者其他将交流转变为直流的拓扑。整流器可以输出为直流电压源,也可以是直流电流源。The rectifier may be composed of an uncontrolled rectifier bridge and a filter capacitor, or may be a controllable rectifier or other topologies that convert AC into DC. The output of the rectifier can be a DC voltage source or a DC current source.
所述的负载可以是实际直流负载,也可以经过其它电能变换环节后供给负载,即等效负载。The load mentioned above may be an actual DC load, or may be supplied to the load after passing through other electric energy conversion links, that is, an equivalent load.
所述的主控制器除了以上所提到的相关连接方式外,还同逆变器倍频电路驱动电路相连。主控制器根据初级状态量检测传感器和次级状态量检测传感器发来的信号进行判断处理,给初级电容补偿调节器和次级电容补偿调节器发出指令,调节电容量以和电感及频率参数相匹配;主控制器根据初级状态量检测传感器和次级状态量检测传感器发来的信号进行判断处理:决定当前逆变器倍频电路应该输出的频率,可从单倍频频率及其附近到n倍频频率及其附近之间变化;决定逆变单元输出电压的占空比,以调节输出功率;决定逆变器倍频电路输出电压和输出电流之间的相位差,以调节逆变器倍频电路输出电压和输出电流之间的相位,最后综合调整驱动脉冲的频率、占空比和相位,经过死区控制后发送到驱动电路,驱动电路连接到逆变器倍频电路的各个开关器件上驱动接线端。主控制器根据所需输出频率要求,从n套逆变单元中选择k套,分时驱动,每套逆变单元的工作频率相同,每套逆变单元内的开关组驱动脉冲占空比小于或者等于1/(2k),依次工作1/k开关周期,各逆变单元驱动脉冲依次滞后360/k度,逆变器倍频电路最后输出电压频率是单套逆变单元输出电压频率的k倍,即k倍频逆变器,其中,n为不小于1的整数,k为不小于且大于1的整数。In addition to the related connection methods mentioned above, the main controller is also connected with the drive circuit of the frequency multiplication circuit of the inverter. The main controller judges and processes according to the signals sent by the primary state quantity detection sensor and the secondary state quantity detection sensor, sends instructions to the primary capacitance compensation regulator and the secondary capacitance compensation regulator, and adjusts the capacitance to match the inductance and frequency parameters. Matching; the main controller judges and processes according to the signals sent by the primary state quantity detection sensor and the secondary state quantity detection sensor: determines the frequency that the current inverter frequency multiplication circuit should output, which can be from single frequency and its vicinity to n Change between the multiplier frequency and its vicinity; determine the duty cycle of the output voltage of the inverter unit to adjust the output power; determine the phase difference between the output voltage and output current of the inverter frequency multiplier circuit to adjust the inverter multiplier The phase between the output voltage and the output current of the frequency circuit, and finally adjust the frequency, duty cycle and phase of the driving pulse comprehensively, and send it to the driving circuit after the dead zone control, and the driving circuit is connected to each switching device of the frequency multiplication circuit of the inverter Upper drive terminal. The main controller selects k sets from n sets of inverter units according to the required output frequency requirements, and drives them in time-sharing. Or it is equal to 1/(2k), working in turn for 1/k switching cycle, the driving pulse of each inverter unit lags behind 360/k degrees in turn, and the final output voltage frequency of the inverter frequency multiplication circuit is k of the output voltage frequency of a single set of inverter units times, that is, a k-multiplier inverter, where n is an integer not less than 1, and k is an integer not less than and greater than 1.
所述的频率和相位检测模块根据初级状态量检测传感器获得的逆变器倍频电路输出电压和输出电流,计算出逆变器倍频电路输出电流的频率以及逆变器倍频电路输出电压和输出电流的相位差并发送给主控制器。The frequency and phase detection module calculates the frequency of the output current of the inverter frequency multiplication circuit and the output voltage and The phase difference of the output current is sent to the main controller.
所述的初级电容补偿调节器和次级电容补偿调节器,分别根据主控制器和次级控制器的指令,调节初级谐振电容的电容量和次级谐振电容的电容量,确保电源装置中的电容、电感和频率参数匹配。The primary capacitance compensation regulator and the secondary capacitance compensation regulator adjust the capacitance of the primary resonant capacitor and the capacitance of the secondary resonant capacitor according to the instructions of the main controller and the secondary controller respectively, so as to ensure the Capacitance, inductance and frequency parameter matching.
所述的次级控制器接收次级状态量检测传感器发来的信号,次级控制器与次级通信模块相连以和初级通信模块通信。The secondary controller receives the signal from the secondary state quantity detection sensor, and the secondary controller is connected with the secondary communication module to communicate with the primary communication module.
所述的初级通信模块可以通过RS232、RS422、RS485、CAN、以太网等方式同主控制器连接,所述的次级通信模块可以通过RS232、RS422、RS485、CAN、以太网等方式同次级控制器连接,初级通信模块和次级通信模块可以通过射频、红外、RS232、RS422、RS485、CAN、以太网等方式进行无线通信或者有线通信。The primary communication module can be connected with the main controller through RS232, RS422, RS485, CAN, Ethernet, etc., and the secondary communication module can be connected with the secondary The controller is connected, and the primary communication module and the secondary communication module can perform wireless communication or wired communication through radio frequency, infrared, RS232, RS422, RS485, CAN, Ethernet, etc.
所述的驱动电路将逆变器倍频电路发出的驱动脉冲信号经过处理后,驱动电路的输出连接到逆变器倍频电路的各个开关器件驱动接线端,驱动逆变器倍频电路的各个开关器件。After the drive circuit processes the drive pulse signal sent by the inverter frequency multiplication circuit, the output of the drive circuit is connected to each switching device drive terminal of the inverter frequency multiplication circuit to drive each of the inverter frequency multiplication circuits. switch device.
本发明高频逆变电源采用倍频逆变的拓扑结构和倍频控制方法,使逆变器输出的频率可以达到半导体器件本身开关频率的数倍,大大提高大功率变流器的输出频率范围,从而大幅提高无接触变压器次级感应电压。相比低谐振频率,减小了变压器初次级相对位置变动对输出功率和效率的影响,进而提高无接触供电系统对变压器初级与次级相对位置变化的适应性,提高系统的可用性。The high-frequency inverter power supply of the present invention adopts the topology structure of frequency multiplication inverter and the frequency multiplication control method, so that the frequency output by the inverter can reach several times the switching frequency of the semiconductor device itself, and the output frequency range of the high-power converter is greatly improved. , thereby greatly increasing the secondary induced voltage of the non-contact transformer. Compared with the low resonant frequency, it reduces the influence of the change of the relative position of the transformer primary and secondary on the output power and efficiency, thereby improving the adaptability of the contactless power supply system to the change of the relative position of the transformer primary and secondary, and improving the availability of the system.
本发明可应用于感应式无线电能传输、谐振式无线电能传输领域。The invention can be applied to the fields of inductive wireless power transmission and resonant wireless power transmission.
附图说明 Description of drawings
图1是全桥逆变器型高频逆变电源及其倍频控制方法框图;Fig. 1 is a block diagram of a full-bridge inverter-type high-frequency inverter power supply and its frequency multiplication control method;
图2是半桥逆变器型高频逆变电源及其倍频控制方法框图;Fig. 2 is a block diagram of a half-bridge inverter type high-frequency inverter power supply and its frequency multiplication control method;
图3是三倍频逆变器三倍频输出时的驱动脉冲和逆变器输出电压波形;Fig. 3 is the driving pulse and the inverter output voltage waveform when the triple frequency inverter triples the frequency output;
图4是三倍频逆变器两倍频输出时的驱动脉冲和逆变器输出电压波形;Fig. 4 is the drive pulse and the inverter output voltage waveform when the triple frequency inverter doubles the frequency output;
图5是三倍频逆变器单倍频输出时的驱动脉冲和逆变器输出电压波形;Fig. 5 is the drive pulse and the inverter output voltage waveform when the triple frequency inverter outputs single frequency;
其中,1直流电源,2逆变器倍频电路,2’逆变单元,3初级状态量检测传感器,3’次级状态量检测传感器,4无接触变压器,5初级谐振电容,5’次级谐振电容,6整流器,7负载,8主控制器,9频率和相位检测模块,10初级电容补偿调节器,10’次级电容补偿调节器,11次级控制器,12初级通信模块,12’次级通信模块,13驱动电路。Among them, 1 DC power supply, 2 inverter frequency multiplication circuit, 2' inverter unit, 3 primary state quantity detection sensor, 3' secondary state quantity detection sensor, 4 non-contact transformer, 5 primary resonance capacitor, 5' secondary Resonant Capacitor, 6 Rectifier, 7 Load, 8 Main Controller, 9 Frequency and Phase Detection Module, 10 Primary Capacitor Compensation Regulator, 10' Secondary Capacitor Compensation Regulator, 11 Secondary Controller, 12 Primary Communication Module, 12' secondary communication module, 13 drive circuits.
具体实施方式 Detailed ways
以下结合附图和具体实施方式对本发明做进一步说明。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.
图1所示为本发明实施例一:全桥逆变器型无线电能传输装置的倍频式高频逆变电源及其倍频控制方法框图,其基本组成和连接方式如下。Fig. 1 is a block diagram of the first embodiment of the present invention: a frequency multiplication high-frequency inverter power supply of a full-bridge inverter type wireless power transmission device and its frequency multiplication control method, and its basic composition and connection method are as follows.
本发明的高频逆变电源包括:直流电源1、逆变器倍频电路2、主控制器8、次级控制器11、初级谐振电容5、次级谐振电容5’、初级电容补偿调节器10、次级电容补偿调节器10’、无接触变压器4、频率和相位检测模块9、初级状态量检测传感器3、次级状态量检测传感器3’、初级通信模块12、次级通信模块12’、整流器6、负载7和驱动电路13等。The high-frequency inverter power supply of the present invention includes: a DC power supply 1, an inverter frequency multiplication circuit 2, a main controller 8, a secondary controller 11, a primary resonant capacitor 5, a secondary resonant capacitor 5', and a primary capacitor compensation regulator 10. Secondary capacitance compensation regulator 10', non-contact transformer 4, frequency and phase detection module 9, primary state quantity detection sensor 3, secondary state quantity detection sensor 3', primary communication module 12, secondary communication module 12' , rectifier 6, load 7 and drive circuit 13, etc.
直流电源1的正负端分别连接到逆变器倍频电路2的直流输入端,逆变器倍频电路2输出单相高频电压,经串联或者并联同初级谐振电容5的两个端子相连,初级谐振电容5同无接触变压器4的初级串联或者并联连接,在逆变器倍频电路2的输出端和初级谐振电容5之间设有初级状态量检测传感器3,初级状态量检测传感器3包括电压传感器、电流传感器、温度传感器、气隙传感器和位置传感器等,分别检测逆变器倍频电路的输出电压、输出电流、逆变器倍频电路的温度、无接触变压器初级和次级的气隙以及初次级之间的相对位置。无接触变压器4的次级经串联或者并联同次级谐振电容5’相连后的两个输出端子连接到整流器6的输入端,整流器6的输出连接到负载7的正负极,在整流器6和负载7之间设有次级状态量传感器3’。次级状态量传感器3’包括电压传感器和电流传感器,电压传感器和电流传感器分别检测整流器输出的电压和电流。初级状态量检测传感器3检测到的逆变器输出电压和电流信号进入频率和相位检测模块9后,频率和相位检测模块9将得到的逆变器输出电流的频率信号以及逆变器输出电压和逆变器输出电流之间的相位差信号发送给主控制器8。初级状态量检测传感器3检测到的所有信号都发送给主控制器8。次级状态量检测传感器3’将整流器6输出的电压和电流信号发送给次级控制器11,次级控制器11通过次级通信模块12’发送给初级通信模块12,初级通信模块12再将信号传递给主控制器8。主控制器8综合初级状态量检测传感器3和次级状态量检测传感器3’的信号,发出逆变器倍频电路2的驱动脉冲,经过死区控制后发送到驱动电路13,驱动电路13连接到逆变器倍频电路2的各个开关器件驱动接线端。初级电容补偿调节器10的一侧同主控制器8相连,另一侧同初级谐振电容5相连。次级电容补偿调节器10’的一侧同次级控制器11相连,另一侧同次级谐振电容5’相连。The positive and negative terminals of the DC power supply 1 are respectively connected to the DC input terminals of the inverter frequency multiplication circuit 2, and the inverter frequency multiplication circuit 2 outputs a single-phase high-frequency voltage, which is connected to the two terminals of the primary resonant capacitor 5 in series or in parallel , the primary resonant capacitor 5 is connected in series or in parallel with the primary of the non-contact transformer 4, and a primary state quantity detection sensor 3 is provided between the output terminal of the inverter frequency multiplication circuit 2 and the primary resonant capacitor 5, and the primary state quantity detection sensor 3 Including voltage sensor, current sensor, temperature sensor, air gap sensor and position sensor, etc., respectively detect the output voltage and output current of the frequency multiplication circuit of the inverter, the temperature of the frequency multiplication circuit of the inverter, and the primary and secondary temperature of the non-contact transformer. Air gap and relative position between primary and secondary. The secondary of the non-contact transformer 4 is connected to the input terminal of the rectifier 6 through the two output terminals connected in series or in parallel with the secondary resonant capacitor 5', and the output of the rectifier 6 is connected to the positive and negative poles of the load 7, between the rectifier 6 and A secondary state quantity sensor 3' is arranged between the loads 7 . The secondary state quantity sensor 3' comprises a voltage sensor and a current sensor, and the voltage sensor and the current sensor respectively detect the voltage and current output by the rectifier. After the inverter output voltage and current signal detected by the primary state quantity detection sensor 3 enters the frequency and phase detection module 9, the frequency and phase detection module 9 will obtain the frequency signal of the inverter output current and the inverter output voltage and The phase difference signal between the inverter output currents is sent to the main controller 8 . All the signals detected by the primary state quantity detection sensor 3 are sent to the main controller 8 . The secondary state quantity detection sensor 3' sends the voltage and current signal output by the rectifier 6 to the secondary controller 11, and the secondary controller 11 sends it to the primary communication module 12 through the secondary communication module 12', and the primary communication module 12 sends the signal to the primary communication module 12. The signal is passed to the master controller 8. The main controller 8 synthesizes the signals of the primary state quantity detection sensor 3 and the secondary state quantity detection sensor 3', sends out the driving pulse of the inverter frequency multiplication circuit 2, and sends it to the driving circuit 13 after the dead zone control, and the driving circuit 13 is connected to To the respective switching device drive terminals of the frequency multiplying circuit 2 of the inverter. One side of the primary capacitance compensation regulator 10 is connected to the main controller 8 , and the other side is connected to the primary resonant capacitor 5 . One side of the secondary capacitance compensation regulator 10' is connected to the secondary controller 11, and the other side is connected to the secondary resonant capacitor 5'.
直流电源1可以是交流电源经整流后得到的直流源,也可以是蓄电池或者电容器等直流源。直流电源可以是电压源,也可以是电流源,分别对应电压型逆变器倍频电路和电流型逆变器倍频电路,以下以电压型逆变器倍频电路为例说明本发明的结构。The DC power source 1 may be a DC source obtained by rectifying an AC power source, or may be a DC source such as a storage battery or a capacitor. The DC power supply can be a voltage source or a current source, respectively corresponding to the frequency multiplication circuit of the voltage type inverter and the frequency multiplication circuit of the current type inverter. The structure of the present invention will be described below by taking the frequency multiplication circuit of the voltage type inverter as an example. .
所述的逆变器倍频电路2由n套逆变单元并联构成,从n套逆变单元2’中选择k套逆变单元2’分时驱动时,逆变器倍频电路2的输出电压频率为逆变单元(2’)输出电压频率的k倍,构成k倍频逆变器,n为不小于1的整数,k为不小于1且不大于n的整数。对于电压型逆变器倍频电路,所述的k倍频逆变器指的是逆变器倍频电路的输出电压频率为逆变单元输出电压频率的k倍;对于电流型逆变器倍频电路,所述的k倍频逆变器指的是逆变器倍频电路的输出电流频率为逆变单元输出电流频率的k倍,k为不小于1的整数。下文均以电压型逆变器倍频电路为例。逆变器倍频电路2可以是单相输出,也可以是多相输出。The inverter frequency multiplication circuit 2 is composed of n sets of inverter units connected in parallel, and when k sets of inverter units 2' are selected from n sets of inverter units 2' for time-sharing driving, the output of the inverter frequency multiplication circuit 2 The voltage frequency is k times the output voltage frequency of the inverter unit (2'), forming a k-multiple frequency inverter, n is an integer not less than 1, and k is an integer not less than 1 and not greater than n. For voltage type inverter frequency multiplication circuit, described k frequency multiplication inverter refers to that the output voltage frequency of inverter frequency multiplication circuit is k times of inverter unit output voltage frequency; frequency circuit, the k-multiplier inverter refers to the frequency of the output current of the inverter frequency multiplication circuit is k times the frequency of the output current of the inverter unit, and k is an integer not less than 1. The frequency multiplier circuit of the voltage source inverter is taken as an example below. The frequency multiplication circuit 2 of the inverter can be a single-phase output or a multi-phase output.
所述的逆变单元2’可以为已知的全桥拓扑结构,或已知的半桥拓扑结构,或其他直流变换为交流的拓扑结构。每套逆变单元内的各个开关组可以为单个器件,也可以为多个器件的串联或者并联构成。逆变器倍频电路中的功率器件可以为MOSFET、IGBT、IGCT等全控型器件,器件可以自带反并联的续流二极管,也可以另加反并联的续流二极管。The inverter unit 2' can be a known full-bridge topology, or a known half-bridge topology, or other DC-to-AC topology. Each switch group in each inverter unit can be a single device, or a series or parallel connection of multiple devices. The power device in the frequency multiplication circuit of the inverter can be a full-control device such as MOSFET, IGBT, IGCT, etc., and the device can have an anti-parallel freewheeling diode, or an antiparallel freewheeling diode can be added.
所述的初级状态量检测传感器3包括检测逆变器倍频电路2输出电压、逆变器倍频电路2输出电流、逆变器倍频电路2温度、无接触变压器4初级和次级之间的气隙和相对位置等状态量的检测传感器。逆变器倍频电路2输出电压传感器分别连接到逆变器倍频电路2的两个输出端子上;逆变器倍频电路输出电流传感器串接入逆变器倍频电路的一个输出线上;逆变器倍频电路温度传感器嵌入逆变器倍频电路2的散热片中;无接触变压器4初级和次级之间的气隙和相对位置传感器分别布置在无接触变压器的初级和次级中。初级状态量检测传感器的输出信号发送到主控制器上,其中电压、电流输出信号发送到频率和相位检测模块。次级状态量检测传感器3’包括无接触变压器次级侧整流器输出电压和输出电流传感器,输出电压传感器分别连接到整流器输出的两个端子上,输出电流传感器串联接入其中一个输出线上。次级状态量检测传感器3’的输出信号发送到次级控制器11上。The primary state quantity detection sensor 3 includes detecting the output voltage of the inverter frequency doubling circuit 2, the output current of the inverter frequency doubling circuit 2, the temperature of the inverter frequency doubling circuit 2, the contactless transformer 4 between the primary and the secondary Sensors for detection of state quantities such as air gap and relative position. The output voltage sensor of the inverter frequency multiplication circuit 2 is respectively connected to the two output terminals of the inverter frequency multiplication circuit 2; the output current sensor of the inverter frequency multiplication circuit is connected in series to one output line of the inverter frequency multiplication circuit The temperature sensor of the frequency doubling circuit of the inverter is embedded in the heat sink of the frequency doubling circuit of the inverter 2; the air gap between the primary and secondary of the non-contact transformer 4 and the relative position sensor are respectively arranged in the primary and secondary of the non-contact transformer middle. The output signal of the primary state quantity detection sensor is sent to the main controller, and the voltage and current output signals are sent to the frequency and phase detection module. The secondary state quantity detection sensor 3' includes a contactless transformer secondary side rectifier output voltage and an output current sensor, the output voltage sensor is respectively connected to the two terminals of the rectifier output, and the output current sensor is connected in series to one of the output lines. The output signal of the secondary state quantity detection sensor 3' is sent to the secondary controller 11.
所述的无接触变压器4由初级绕组、次级绕组以及结构件组成,初级绕组和次级绕组之间有一定气隙。The non-contact transformer 4 is composed of a primary winding, a secondary winding and structural components, and there is a certain air gap between the primary winding and the secondary winding.
所述的初级谐振电容5和次级谐振电容5’可以是单个或者多个电容组成;初级谐振电容5可以和初级绕组串联、并联或者进行串并联连接,次级谐振电容5’可以和次级绕组串联、并联或者串并联连接。The primary resonant capacitor 5 and the secondary resonant capacitor 5' can be composed of a single or multiple capacitors; the primary resonant capacitor 5 can be connected in series, in parallel or in parallel with the primary winding, and the secondary resonant capacitor 5' can be connected with the secondary The windings are connected in series, parallel or series-parallel.
所述的整流器6可以是不控整流桥和滤波电容组成,也可以是可控整流器或者其他将交流转变为直流的拓扑。整流器可以输出为直流电压源,也可以是直流电流源。The rectifier 6 may be composed of an uncontrolled rectifier bridge and a filter capacitor, or may be a controllable rectifier or other topologies that convert AC to DC. The output of the rectifier can be a DC voltage source or a DC current source.
所述的负载7可以是实际直流负载,也可以经过其它电能变换环节后供给负载,即等效负载。The load 7 may be an actual DC load, or it may be supplied to the load after passing through other electric energy conversion links, that is, an equivalent load.
所述的主控制器8除了以上所提到的相关连接方式外,还与逆变器倍频电路2驱动电路相连。主控制器8根据初级状态量检测传感器3和次级状态量检测传感器3’发来的信号进行判断处理,得到变压器初次级之间的气隙、初次级之间的相对位置以及负载状况等,决定当前逆变器倍频电路2’应该输出的频率,可从单倍频频率及其附近到n倍频频率及其附近之间变化;决定逆变单元2’输出电压的占空比,以调节输出功率;决定逆变器倍频电路2输出电压和输出电流之间的相位差,以调节逆变器倍频电路2输出电压和输出电流之间的相位,最后综合调整驱动脉冲的频率、占空比和相位,经过死区控制后发送到驱动电路13,驱动电路13连接到逆变器倍频电路2的各个开关器件上驱动接线端。为了让整个系统工作在较高效率,主控制器8还需根据逆变器倍频电路2的输出频率,决定向初级电容补偿调节器10和次级电容补偿调节器10’发出指令,调节初级谐振电容5和次级谐振电容5’的电容量,以和电感及频率参数相匹配。主控制器8根据逆变器倍频电路输出频率要求,从n套逆变单元2’中选择k套,分时驱动相应逆变器的逆变单元2’,每个逆变单元2’的工作频率相同,每个逆变单元内的开关组驱动脉冲占空比小于或者等于1/(2k),依次工作1/k开关周期,各逆变单元驱动脉冲依次滞后360/k度;k倍频逆变器倍频电路的输出电压频率是每个逆变单元2’输出电压频率的k倍,其中,n为不小于1的整数,k为不小于且不大于n的整数。The main controller 8 is also connected to the driving circuit of the frequency multiplication circuit 2 of the inverter in addition to the related connection methods mentioned above. The main controller 8 performs judgment processing according to the signals sent by the primary state quantity detection sensor 3 and the secondary state quantity detection sensor 3', and obtains the air gap between the primary and secondary stages of the transformer, the relative position between the primary and secondary stages, and the load status, etc. Determine the frequency that the inverter frequency multiplier circuit 2' should output, which can be changed from the single multiplier frequency and its vicinity to the n multiplier frequency and its vicinity; determine the duty cycle of the inverter unit 2' output voltage, to Adjust the output power; determine the phase difference between the output voltage and the output current of the frequency multiplication circuit 2 of the inverter, to adjust the phase between the output voltage and the output current of the frequency multiplication circuit 2 of the inverter, and finally adjust the frequency of the driving pulse comprehensively, The duty cycle and phase are sent to the driving circuit 13 after being controlled by the dead zone, and the driving circuit 13 is connected to the driving terminal of each switching device of the frequency multiplication circuit 2 of the inverter. In order to make the whole system work at a higher efficiency, the main controller 8 also needs to decide to issue instructions to the primary capacitor compensation regulator 10 and the secondary capacitor compensation regulator 10' according to the output frequency of the inverter frequency multiplier circuit 2 to adjust the primary The capacitance of the resonant capacitor 5 and the secondary resonant capacitor 5' is matched with the inductance and frequency parameters. The main controller 8 selects k sets from n sets of inverter units 2' according to the output frequency requirements of the frequency multiplication circuit of the inverter, and drives the inverter units 2' of the corresponding inverter in time-sharing, and each inverter unit 2' The working frequency is the same, the duty cycle of the driving pulse of the switching group in each inverter unit is less than or equal to 1/(2k), and the switching cycle is 1/k in sequence, and the driving pulse of each inverter unit lags behind by 360/k degrees; k times The output voltage frequency of the frequency inverter frequency multiplication circuit is k times the output voltage frequency of each inverter unit 2', wherein n is an integer not less than 1, and k is an integer not less than and not greater than n.
所述的频率和相位检测模块9根据初级状态量检测传感器3获得的逆变器倍频电路输出电压和输出电流,计算出逆变器倍频电路输出电流的频率以及逆变器倍频电路输出电压和输出电流的相位差并发送给主控制器8,以实现所述的频率和相位差的闭环控制。The frequency and phase detection module 9 calculates the frequency of the output current of the inverter frequency multiplication circuit and the output frequency of the inverter frequency multiplication circuit according to the output voltage and output current of the inverter frequency multiplication circuit obtained by the primary state quantity detection sensor 3 The phase difference of the voltage and the output current is sent to the main controller 8 to realize the closed-loop control of the frequency and the phase difference.
所述的初级电容补偿调节器10的一侧同主控制器8相连,另一侧同初级谐振电容5相连。次级电容补偿调节器10’一侧和次级控制器11相连,另一侧同次级谐振电容5’相连。初级电容补偿调节器10和次级电容补偿调节器10’分别根据主控制器8和次级控制器11的指令,调整接入的初级谐振电容5电容量和次级谐振电容5’的电容量,确保电源装置中的电容、电感和频率参数匹配。One side of the primary capacitance compensation regulator 10 is connected to the main controller 8 , and the other side is connected to the primary resonance capacitor 5 . One side of the secondary capacitance compensation regulator 10' is connected to the secondary controller 11, and the other side is connected to the secondary resonant capacitor 5'. The primary capacitance compensation regulator 10 and the secondary capacitance compensation regulator 10' adjust the capacitance of the connected primary resonant capacitor 5 and the secondary resonant capacitor 5' according to the instructions of the main controller 8 and the secondary controller 11 respectively , to ensure that the capacitance, inductance and frequency parameters in the power supply unit match.
所述的次级控制器11接收次级状态量检测传感器3’发来的信号,次级控制器11与次级通信模块12’相连以和初级通信模块12通信。The secondary controller 11 receives the signal from the secondary state quantity detection sensor 3', and the secondary controller 11 is connected with the secondary communication module 12' to communicate with the primary communication module 12.
所述的初级通信模块12可以通过RS232、RS422、RS485、CAN、以太网等方式同主控制器8连接。所述的次级通信模块12’可以通过RS232、RS422、RS485、CAN、以太网等方式同次级控制器11连接,初级通信模块和次级通信模块可以通过射频、红外、RS232、RS422、RS485、CAN、以太网等方式进行无线通信或者有线通信。The primary communication module 12 can be connected with the main controller 8 through RS232, RS422, RS485, CAN, Ethernet and the like. The secondary communication module 12' can be connected with the secondary controller 11 through RS232, RS422, RS485, CAN, Ethernet, etc., and the primary communication module and the secondary communication module can be connected through radio frequency, infrared, RS232, RS422, RS485 , CAN, Ethernet, etc. for wireless or wired communication.
所述的驱动电路13将逆变器倍频电路发出的驱动脉冲信号经过处理后,驱动电路的输出连接到逆变器倍频电路的各个开关器件驱动接线端,驱动逆变器倍频电路的各个开关器件。After the drive circuit 13 processes the drive pulse signal sent by the inverter frequency multiplication circuit, the output of the drive circuit is connected to each switching device drive terminal of the inverter frequency multiplication circuit to drive the inverter frequency multiplication circuit. individual switching devices.
如图1所示的全桥逆变器型无线电能传输装置的倍频式高频逆变电源的逆变器倍频电路2由n套全桥逆变单元构成,每套全桥逆变单元由4个开关组构成。开关组S1_1、S1_2、S1_3和S1_4构成逆变器第一套逆变单元2’,开关组S2_1、S2_2、S2_3和S2_4构成逆变器第二套逆变单元2’,以此类推,开关组Sn_1、Sn_2、Sn_3和Sn_4构成逆变器第n套逆变单元2’。n倍频运行模式如下:n套逆变单元2’分时动作,每套逆变单元2’的工作频率相同,每套逆变单元2’内的开关组驱动脉冲占空比小于或者等于1/(2n),依次工作1/n开关周期,各逆变单元驱动脉冲依次滞后360/n度;n倍频逆变器倍频电路的输出电压频率是每个逆变单元2’输出电压频率的n倍,即n倍频逆变器,其中,n为不小于1的整数。The inverter frequency doubling circuit 2 of the frequency doubling high-frequency inverter power supply of the full-bridge inverter type wireless power transmission device shown in Figure 1 is composed of n sets of full-bridge inverter units, and each set of full-bridge inverter units Consists of 4 switch groups. The switch groups S1_1, S1_2, S1_3 and S1_4 constitute the first inverter unit 2' of the inverter, the switch groups S2_1, S2_2, S2_3 and S2_4 constitute the second inverter unit 2' of the inverter, and so on, the switch group Sn_1, Sn_2, Sn_3 and Sn_4 constitute the nth set of inverter unit 2' of the inverter. The n-multiple frequency operation mode is as follows: n sets of inverter units 2' time-sharing action, each set of inverter units 2' has the same operating frequency, and the duty cycle of the switch group drive pulse in each set of inverter units 2' is less than or equal to 1 /(2n), work in turn for 1/n switching cycle, the driving pulse of each inverter unit lags behind 360/n degrees in turn; the output voltage frequency of the frequency multiplication circuit of the n-multiplier inverter is the output voltage frequency of each inverter unit 2' n times of , that is, an n-multiple frequency inverter, where n is an integer not less than 1.
所述的逆变器倍频电路2的n套逆变单元2’可以按上述方式分时驱动形成n倍频逆变器,也可以从中选择k套逆变单元2’,构成k倍频逆变器,其中k为不小于1且不大于n的整数,从而逆变器倍频电路2输出电压频率可以从1到n倍的逆变单元输出电压频率范围变化。The n sets of inverter units 2' of the inverter frequency multiplication circuit 2 can be time-divisionally driven to form an n frequency multiplication inverter, and k sets of inverter units 2' can also be selected to form a k frequency multiplication inverter. Inverter, wherein k is an integer not less than 1 and not greater than n, so that the output voltage frequency of the inverter frequency multiplication circuit 2 can vary from 1 to n times the output voltage frequency range of the inverter unit.
随着逆变倍频电路2的输出频率变化,主控制器8向初级电容补偿调节器10和次级电容补偿调节器10’发出指令,调节初级谐振电容5和次级谐振电容5’的电容量,以和电感及频率参数相匹配,从而保持能量传递的高效化。As the output frequency of the inverter frequency multiplier circuit 2 changes, the main controller 8 sends instructions to the primary capacitance compensation regulator 10 and the secondary capacitance compensation regulator 10' to adjust the electric current of the primary resonance capacitor 5 and the secondary resonance capacitor 5'. Capacity, to match the inductance and frequency parameters, so as to maintain the high efficiency of energy transfer.
所述的逆变器倍频电路2通过调节逆变单元对角线开关组驱动频率的相位差来调节逆变器倍频电路的输出功率。也可以令逆变单元对角线开关组驱动脉冲一致,调节其驱动脉冲的占空比来调节逆变器倍频电路的输出功率。The inverter frequency multiplication circuit 2 adjusts the output power of the inverter frequency multiplication circuit by adjusting the phase difference of the driving frequency of the diagonal switch group of the inverter unit. It is also possible to make the driving pulses of the diagonal switch groups of the inverter unit consistent, and adjust the duty ratio of the driving pulses to adjust the output power of the frequency multiplication circuit of the inverter.
图2所示为本发明实施例二:半桥型倍频式高频逆变电源及其倍频控制方法,其基本组成和连接方式除了逆变单元2’以及相应的功率调节方式外同实施例一相同。Fig. 2 shows the second embodiment of the present invention: half-bridge frequency multiplication type high-frequency inverter power supply and its frequency multiplication control method, its basic composition and connection method are the same as the implementation except the inverter unit 2' and the corresponding power adjustment method Example 1 is the same.
如图2所示的半桥型逆变器倍频电路2由n套半桥逆变单元2’以及串联连接的电容和串联连接的均压电阻构成,每套半桥逆变单元由2个开关组构成,连接方式见图2。第一开关组S1_1和S1_2构成第一套逆变单元2’第二开关组S2_1和S2_2构成第二套逆变单元2’,以此类推,第n开关组Sn_1和Sn_2构成第n套逆变单元2’。n倍频运行模式如下:每个逆变单元内的开关组驱动脉冲占空比小于或者等于1/(2n),依次工作1/n开关周期,各逆变单元驱动脉冲依次滞后360/n度;n倍频逆变器倍频电路的输出电压频率是每个逆变单元2’输出电压频率的n倍,构成n倍频逆变器,其中,n为不小于1的整数。The half-bridge inverter frequency multiplication circuit 2 shown in Figure 2 is composed of n sets of half-bridge inverter units 2', capacitors connected in series and voltage equalizing resistors connected in series, and each set of half-bridge inverter units consists of 2 The switch group is composed, and the connection method is shown in Figure 2. The first switch group S1_1 and S1_2 constitute the first set of inverter unit 2', the second switch group S2_1 and S2_2 constitute the second set of inverter unit 2', and so on, the nth switch group Sn_1 and Sn_2 constitute the nth set of inverter Unit 2'. The n-multiple frequency operation mode is as follows: the duty cycle of the driving pulse of the switching group in each inverter unit is less than or equal to 1/(2n), and it works sequentially for 1/n switching period, and the driving pulse of each inverter unit lags behind by 360/n degrees in turn The frequency of the output voltage of the n-multiple frequency inverter frequency multiplication circuit is n times the output voltage frequency of each inverter unit 2', forming an n-multiple frequency inverter, where n is an integer not less than 1.
同实施例一,实施例二的逆变器倍频电路2输出电压频率可以从1到n倍的逆变单元2’输出电压频率范围变化。随着逆变倍频电路2的输出电压频率变化,主控制器8向初级电容补偿调节器10和次级电容补偿调节器10’发出指令,调节初级谐振电容5和次级谐振电容5’的电容量,以和电感及频率参数相匹配,从而保持能量传递的高效化。Same as the first embodiment, the output voltage frequency of the inverter frequency multiplication circuit 2 of the second embodiment can vary from 1 to n times the output voltage frequency range of the inverter unit 2'. As the frequency of the output voltage of the inverter frequency multiplier circuit 2 changes, the main controller 8 issues instructions to the primary capacitance compensation regulator 10 and the secondary capacitance compensation regulator 10' to adjust the primary resonance capacitor 5 and the secondary resonance capacitor 5'. Capacitance, to match the inductance and frequency parameters, so as to maintain the high efficiency of energy transfer.
所述的半桥型逆变器倍频电路2各逆变单元2’对角线开关组驱动脉冲一致,通过调节其驱动脉冲的占空比来调节逆变器倍频电路2的输出功率。The drive pulses of the diagonal switch groups of each inverter unit 2' of the half-bridge inverter frequency multiplier circuit 2 are consistent, and the output power of the inverter frequency multiplier circuit 2 is adjusted by adjusting the duty ratio of the drive pulses.
以实施例一和实施例二为对象介绍三倍频和n倍频逆变器倍频电路2的倍频控制方法。Taking Embodiment 1 and Embodiment 2 as objects, the frequency multiplication control method of the frequency multiplication circuit 2 of the triple frequency and n-multiplication inverters is introduced.
根据实施例一所述,三倍频逆变器倍频电路可以以三倍频模式,也可以两倍频模式或者单倍频模式运行,相应的控制方法如下。According to Embodiment 1, the frequency multiplication circuit of the triple frequency inverter can operate in triple frequency mode, double frequency mode or single frequency mode, and the corresponding control method is as follows.
三倍频模式,三倍频逆变器倍频电路由三套逆变单元2’组成。每个开关组的驱动脉冲占空比小于或者等于1/6,依次工作1/3开关周期;未经死区控制的驱动脉冲以及逆变器倍频电路2输出波形如图3所示,其中P14a和P23a为第一套逆变单元2’的驱动脉冲,P14b和P23b为第二套逆变单元2’的驱动脉冲,P14c和P23c为第三套逆变单元2’的驱动脉冲,各个开关组驱动脉冲依次滞后120度。三倍频逆变器的输出电压频率是单套逆变单元2’输出电压频率的3倍。(1)对于全桥型逆变单元2’,P14a是第一套逆变单元2’内的第一开关组的第一开关S1_1和第一开关组的第四开关S1_4的驱动脉冲;P23a是第一套逆变单元2’内的第一开关组的第二开关S1_2和的第一开关组的第三开关S1_3的驱动脉冲;P14b是第二套逆变单元2’内的第二开关组的第一开关S2_1和的第二开关组的第四开关S2_4的驱动脉冲;P23b是第二套逆变单元2’内的第二开关组的第二开关S22和的第二开关组的第三开关S2_3的驱动脉冲;P14c是第三套逆变单元2’内第三开关组第一开关S3_1和第四开关S3_4的驱动脉冲;P23c是第三套逆变单元2’内第三开关组第二开关S32和第三开关组第三开关S3_3的驱动脉冲;Up是逆变器倍频电路2输出电压波形。(2)对于半桥型逆变单元2’,P14a是第一套逆变单元2’内第一开关组第一开关S1_1的驱动脉冲;P23a是第一套逆变单元2’内第一开关组第二开关S1_2的驱动脉冲;P14b是第二套逆变单元2’第二开关组第一开关内S2_1的驱动脉冲;P23b是第二套逆变单元2’内第二开关组第开关S2_2的驱动脉冲;P14c是第三套逆变单元2’内第三开关组第一开关S3_1的驱动脉冲;P23c是第三套逆变单元2’内第三开关组第二开关S3_2的驱动脉冲;Up是逆变器倍频电路2输出电压波形。可以看到三倍频逆变器倍频电路2输出电压频率是单套逆变单元2’输出电压频率的三倍。Triple frequency mode, triple frequency inverter frequency multiplication circuit is composed of three sets of inverter units 2'. The duty cycle of the driving pulse of each switch group is less than or equal to 1/6, and it works sequentially for 1/3 switching period; the driving pulse without dead zone control and the output waveform of the inverter frequency multiplication circuit 2 are shown in Figure 3, where P14a and P23a are the drive pulses of the first set of inverter unit 2', P14b and P23b are the drive pulses of the second set of inverter unit 2', P14c and P23c are the drive pulses of the third set of inverter unit 2', each switch The group drive pulses are sequentially delayed by 120 degrees. The output voltage frequency of the triple frequency inverter is 3 times of the output voltage frequency of a single set of inverter unit 2'. (1) For the full-bridge inverter unit 2', P14a is the driving pulse of the first switch S1_1 of the first switch group and the fourth switch S1_4 of the first switch group in the first set of inverter unit 2'; P23a is The driving pulse of the second switch S1_2 of the first switch group in the first set of inverter unit 2' and the third switch S1_3 of the first switch group; P14b is the second switch group in the second set of inverter unit 2' P23b is the driving pulse of the first switch S2_1 of the second switch group and the fourth switch S2_4 of the second switch group; P23b is the second switch S22 of the second switch group in the second set of inverter unit 2' and the third The drive pulse of switch S2_3; P14c is the drive pulse of the first switch S3_1 and the fourth switch S3_4 of the third switch group in the third set of inverter unit 2'; P23c is the drive pulse of the third switch group in the third set of inverter unit 2'. The driving pulses of the second switch S32 and the third switch S3_3 of the third switch group; Up is the output voltage waveform of the frequency multiplication circuit 2 of the inverter. (2) For the half-bridge inverter unit 2', P14a is the driving pulse of the first switch S1_1 of the first switch group in the first set of inverter unit 2'; P23a is the first switch in the first set of inverter unit 2' The driving pulse of the second switch S1_2 in the group; P14b is the driving pulse of S2_1 in the first switch of the second switch group of the second set of inverter unit 2'; P23b is the second switch S2_2 of the second switch group in the second set of inverter unit 2' P14c is the driving pulse of the first switch S3_1 of the third switch group in the third set of inverter unit 2'; P23c is the driving pulse of the second switch S3_2 of the third switch group in the third set of inverter unit 2'; Up is the output voltage waveform of the frequency multiplication circuit 2 of the inverter. It can be seen that the output voltage frequency of the frequency multiplication circuit 2 of the triple frequency inverter is three times that of the output voltage frequency of a single set of inverter unit 2'.
两倍频模式,从三套逆变单元2’中任意选择两套,例如选择第一套和第二套逆变单元运行。每个开关组的驱动脉冲占空比小于或者等于1/4,依次工作1/2个开关周期;未经死区控制的驱动脉冲以及逆变器倍频电路输出波形如图4所示,其中P14a和P23a为第一套逆变单元2’驱动脉冲,P14b和P23b为第二套逆变单元2’驱动脉冲,滞后第一套逆变单元2’驱动脉冲180度。两倍频逆变器倍频电路的输出电压频率是单套逆变单元2’输出电压频率的两倍。(1)对于全桥型逆变单元,P14a是逆变器第一套逆变单元2’内的第一开关组的第一开关S1_1和第四开关S1_4的驱动脉冲;P23a是第一套逆变单元2’内的第一开关组的第二开关S1_2和第三开关S1_3的驱动脉冲;P14b是第二套逆变单元2’内的第二开关组的第一开关S2_1和第四开关S2_4的驱动脉冲;P23b是第二套逆变单元2’内的第二开关组的第二开关S2_2和第三开关S2_3的驱动脉冲;Up是逆变器倍频电路2的输出电压波形。(2)对于半桥型逆变单元2’,P14a是第一套逆变单元2’内的第一开关组的第一开关S1_1的驱动脉冲;P23a是第一套逆变单元2’内的第一开关组的第二开关S1_2的驱动脉冲;P14b是第二套逆变单元2’内的第二开关组的第一开关S2_1的驱动脉冲;P23b是第二套逆变单元2’内的第二开关组的第二开关S2_2的驱动脉冲;Up是逆变器倍频电路2的输出电压波形。可以看到两倍频逆变器倍频电路2输出电压频率是每套运行的逆变单元2’输出电压频率的两倍。In the double frequency mode, two sets are randomly selected from three sets of inverter units 2', for example, the first set and the second set of inverter units are selected for operation. The duty cycle of the driving pulse of each switch group is less than or equal to 1/4, and it works sequentially for 1/2 switching period; the driving pulse without dead zone control and the output waveform of the frequency multiplication circuit of the inverter are shown in Figure 4, where P14a and P23a are the driving pulses of the first set of inverter unit 2', P14b and P23b are the driving pulses of the second set of inverter unit 2', lagging behind the driving pulse of the first set of inverter unit 2' by 180 degrees. The output voltage frequency of the double frequency inverter frequency multiplier circuit is twice the output voltage frequency of a single set of inverter unit 2'. (1) For the full-bridge inverter unit, P14a is the driving pulse of the first switch S1_1 and the fourth switch S1_4 of the first switch group in the first set of inverter unit 2' of the inverter; P23a is the driving pulse of the first set of inverter The driving pulse of the second switch S1_2 and the third switch S1_3 of the first switch group in the inverter unit 2'; P14b is the first switch S2_1 and the fourth switch S2_4 of the second switch group in the second set of inverter unit 2' P23b is the driving pulse of the second switch S2_2 and the third switch S2_3 of the second switch group in the second set of inverter unit 2'; Up is the output voltage waveform of the frequency multiplication circuit 2 of the inverter. (2) For the half-bridge inverter unit 2', P14a is the driving pulse of the first switch S1_1 of the first switch group in the first set of inverter unit 2'; P23a is the driving pulse of the first switch S1_1 in the first set of inverter unit 2'. The drive pulse of the second switch S1_2 of the first switch group; P14b is the drive pulse of the first switch S2_1 of the second switch group in the second set of inverter unit 2'; P23b is the drive pulse of the second switch group in the second set of inverter unit 2' The driving pulse of the second switch S2_2 of the second switch group; Up is the output voltage waveform of the frequency multiplication circuit 2 of the inverter. It can be seen that the output voltage frequency of the double-frequency inverter frequency multiplication circuit 2 is twice that of the output voltage frequency of each set of running inverter units 2'.
单倍频模式,从三套逆变单元2’中任意选择一套运行,例如选择第一套逆变单元运行。每个开关组的驱动脉冲占空比小于或者等于1/2,未经死区控制的驱动脉冲以及逆变器倍频电路输出波形如图5所示,其中P14a和P23a为第一套逆变单元2’驱动脉冲。(1)对于全桥型逆变单元,P14a是逆变器第一套逆变单元2’内的第一开关组的第一开关S1_1和第四开关S1_4的驱动脉冲;P23a是第一套逆变单元2’内的第一开关组的第二开关S1_2和第三开关S1_3的驱动脉冲。(2)对于半桥型逆变单元2’,P14a是第一套逆变单元2’内的第一开关组的第一开关S1_1的驱动脉冲;P23a是第一套逆变单元2’内的第一开关组的第二开关组S1_2的驱动脉冲;Up是逆变器倍频电路2的输出电压波形。逆变单元独立运行模式下,逆变器倍频电路2输出电压频率和运行的逆变单元2’输出电压频率相同。In the single multiplier mode, one of the three sets of inverter units 2' is randomly selected to operate, for example, the first set of inverter units is selected to operate. The driving pulse duty cycle of each switch group is less than or equal to 1/2, the driving pulse without dead zone control and the output waveform of the inverter frequency multiplication circuit are shown in Figure 5, where P14a and P23a are the first set of inverter Unit 2' drive pulse. (1) For the full-bridge inverter unit, P14a is the driving pulse of the first switch S1_1 and the fourth switch S1_4 of the first switch group in the first set of inverter unit 2' of the inverter; P23a is the driving pulse of the first set of inverter The driving pulses of the second switch S1_2 and the third switch S1_3 of the first switch group in the switching unit 2'. (2) For the half-bridge inverter unit 2', P14a is the driving pulse of the first switch S1_1 of the first switch group in the first set of inverter unit 2'; P23a is the driving pulse of the first switch S1_1 in the first set of inverter unit 2'. The driving pulse of the second switch group S1_2 of the first switch group; Up is the output voltage waveform of the frequency multiplication circuit 2 of the inverter. In the independent operation mode of the inverter unit, the output voltage frequency of the inverter frequency multiplication circuit 2 is the same as the output voltage frequency of the running inverter unit 2'.
根据以上介绍,很容易推导出n倍频逆变器倍频电路2的k倍频模式控制方法如下:According to the above introduction, it is easy to deduce the control method of the k-multiplier mode of the n-multiplier inverter frequency multiplier circuit 2 as follows:
k倍频模式:从n套逆变单元2’中任意选择k套运行。每套逆变单元2’内的开关组驱动脉冲占空比小于或者等于1/(2k),依次工作1/k开关周期,各逆变单元2’驱动脉冲依次滞后360/k度。k倍频运行模式下逆变器倍频电路2的输出电压频率是每套运行的逆变单元2’输出电压频率的k倍,k为不小于1且不大于n的整数。k frequency multiplication mode: randomly select k sets of operation from n sets of inverter units 2'. The duty ratio of the driving pulses of the switching groups in each set of inverter units 2' is less than or equal to 1/(2k), and the switching cycles are sequentially operated for 1/k, and the driving pulses of each inverter unit 2' are sequentially delayed by 360/k degrees. The output voltage frequency of the inverter frequency multiplication circuit 2 under the k-multiplication operation mode is k times of the output voltage frequency of the inverter unit 2' of each set of operation, and k is an integer not less than 1 and not greater than n.
对于全桥型逆变器倍频电路,以上实施例所介绍倍频控制方法中没有施加全桥移相控制,采用全桥移相控制时,每个逆变单元对角线开关组驱动脉冲存在一定的相位差,以调节输出功率。例如,n倍频全桥逆变器倍频电路中,第k个逆变单元2’中,Sk_4的驱动脉冲滞后Sk_1驱动脉冲一定相位角,Sk_2的驱动脉冲滞后Sk_3驱动脉冲同样的相位角,n为不小于1的整数,k为不小于1且不大于n的整数。For the frequency multiplication circuit of the full-bridge inverter, the frequency multiplication control method introduced in the above embodiments does not apply the full-bridge phase-shift control. When the full-bridge phase-shift control is used, the driving pulses of the diagonal switch groups of each inverter unit exist A certain phase difference to adjust the output power. For example, in the n-multiple frequency full-bridge inverter frequency multiplication circuit, in the kth inverter unit 2', the driving pulse of Sk_4 lags behind the driving pulse of Sk_1 by a certain phase angle, and the driving pulse of Sk_2 lags behind the driving pulse of Sk_3 by the same phase angle, n is an integer not less than 1, and k is an integer not less than 1 and not greater than n.
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