Minimum Switching Losses Based On Voltage Space Vector Pulse Width Modulation Technique.doc

Minimum Switching Losses Based On Voltage Space Vector Pulse Width Modulation Technique基于电压空间矢量PWM技术的最小开关损耗研究孙闯（上海发电设备成套设计研究院，学号P200909071）Minimum Switching Losses Based On Voltage Space Vector Pulse Width Modulation TechniqueSun Chuang (Shanghai Power Equipment Research Institute, Minhang District, Shanghai,200240,China)ABSTRACT: Through studying the literature of Minimum Switching Losses VSVPWM techniques, the research content, research methods and findings of the minimum switching losses of the voltage space vector PWM technology (VSVPWM) can be summarized.KEY WORDS: voltage space vector PWM; switching losses; research content; research methods; technique Findings1. Research contentIn the literature of study and simulation of minimum switching losses VSVPWM technology, through analysis the distribution of eight vectors of the voltage space vector PWM technology (VSVPWM), it can be found that the location of non-switching sectors can continuously vary within a certain range. On the basis, a program of VSVPWM depending on the load power factor angle of dynamic adjustment of non-switching sectors is put forward, and it can make the non-switching sectors fell over the area of loading resistor as much as possible. The program not only reduces switching frequency, but also reduces switching current. So it could achieve the purpose of the minimal switching losses1.2. Research methods2.1 The basic principles and characteristics of VSVPWM1-4VSVPWM has high utilization rate of DC voltage、convenience of digital realization、clarity of physical conceptual and so on. Its concrete realization is that line voltage or phase voltage can be synthesized. Compare with the traditional SPWM, this paper is according to phase voltage synthesis. To simplify the problem, as shown in Fig.1, Voltage source inverter is the objet of study.The expected output three-phase voltage is （1）The definition for the synthesis voltage vector is （2）Let us to put equation (1) into equation (2), the final expression for the expected output voltage vector is （3）When bipolar modulation, the inverter could has total eight kinds of switch state. If two switches: one upper and one lower conduct at the same time such that the output voltage is , the switch state is 1,whereas if these switches are off at the same time , the switch is 0. So the eight kinds of switch states are 100、110、010、011、001、101、000、111. The equation (2) shows zero-sequence component does not affect the synthesis of vector, it is convenient to select the midpoint of DC side as a reference neutral point. So it can be gained six non-zero vectors and two zero vectors whose phase follow by a difference of .The fig.2 shows the eight space vectors.According to the parallelogram law of vector synthesis and the equal-area principle of PWM, the space vector which is arbitrary angle and limited module can be synthesized by the eight space vectors. In other words the expected output voltage vector can be synthesized by the eight space vectors, so the expected output phase voltage 、 can be gained.For example, the fig.2 shows at the sector I. And is the action time of vector , is the action time of vector , is the sampling period. According to the sine rule, the consequence is （4）The total action time of vector and vector can not exceed the sampling period. So the constraints is （5）When taking equation (4) into equation(5), the consequence is （6）The equation (1) shows A is the fundamental amplitude of the expected output phase voltage and is the fundamental amplitude of the expected output Line voltage. So the equation (6) shows the maximum fundamental amplitude of the output Line voltage for Voltage Source Inverter is DC-side voltage according to VSVPWM.Because ,. And is the acting time of zero vectors and . （7）Space vector sequence should be followed by the principle of the least switching times.If is phase advance of the vector and is the acting time , and is phase lag of the vector and is the acting time, the general laws of the control of VSVPWM are （8） （9） （10） （） （11）The tab.1 shows the space vector sequence for sectors 、 and.The tab.2 shows the space vector sequence for sectors 、 and VI.2.2 Study of Minimum Switching Losses VSVPWM1According to VSVPWM, if we distribute zero vectors appropriate and keep the same sampling period, per cycle per phase can has non-switching sectors. So it can be reduced one-third of the total number of switches.There are many kinds of zero vector distribution programs which can reduce one-third of the total number of switches. The following are several typical programs.2.2.1 When k =1, we select zero vector . At sectors and , A phase always keep the upper arm on and keep the lower arm off. At sectors II and , B phase always keep the upper arm on and keep the lower arm off. At sectors and V, C phase always keep the upper arm on and keep the lower arm off. So each phase-arm has non-switching sectors at the positive half cycle of the phase voltage. And it can be reduced one-third of the total number of switches.2.2.2 When k =0, we select zero vector. At sectors and , A phase always keep the upper arm off and keep the lower arm on. At sectors V and , B phase always keep the upper arm off and keep the lower arm on. At sectors and , C phase always keep the upper arm off and keep the lower arm on. So each phase-arm has non-switching sectors at the positive half cycle of the phase voltage. And it can be reduced one-third of the total number of switches.2.2.3 At sectors I、III and V, we select zero vector and k=1. At sectors II、and , we select zero vector and k=0. So A、B and C keep the upper arm on and keep the lower arm off at sectors I、III and V. And A、B and C keep the upper arm off and keep the lower arm on at sectors II、and . Thus each phase each cycle has two non-switching sectors which keep the interval and the width. And it can be reduced one-third of the total number of switches.2.2.4 At sectors I、III and V, we select zero vector and k=0. At sectors II、and , we select zero vector and k=1. So A、B and C keep the upper arm off and keep the lower arm on at sectors I、III and V. And A、B and C keep the upper arm on and keep the lower arm off at sectors II、and . Thus each phase each cycle has two non-switching sectors which keep the interval and the width. And it can be reduced one-third of the total number of switches.In order to discuss the situation comfortably, we give the following concept. According to the Inverter Circuit, when the given voltage is three-phase symmetrical sine wave as shown in equation (1) and it use the control of VSVPWM, if the reference phase voltage has each one of the non-switching sectors at the positive and negative half-cycle, so the definition of the lag angle of non-switching sectors is the angle that the mid-point of non-switching sectors at the positive half-cycle file over the positive peak point of the given voltage. It can be shown in fig.3. According to the above definition, at the program (3); at the program (4). If is the switching loss of switching device, the relation is as follows2-3. （12）In equation (12), is the monotonically increasing function of 、, and is the switching voltage, is the switching current and is the practical switching frequency. Because is fixed according to Voltage Source Inverter and according to VSVPWM ( k=0.5 ).In the programs （1）、(2)、(3)、(4), , thus it greatly reduce the switching losses. But do we further reduce the switching losses? According to foregoing discussion, is at least and is also fixed, so the only way is to reduce the switching current. The only way to reduce the switching current is to switch the device as far as possible in the smaller load current of the sector. is the power factor angle of Inverter three-phase symmetrical load ().If =,two non-switching sectors of per cycle per phase fall over the maximum current amplitude at plus or minus half-cycle of load current . So it can reduce the switching current, and reduce the switching losses. The key is whether continuously vary within a certain range. If is variable within a certain range, range? For three-phase symmetrical, A phase is the research object. Can be seen from Fig.3, when =, it is the maximum Lag angle; when =-, it is the Maximum Lead angle. So the range of is -，.In order to put two non-switching sectors of into the area of the maximum load current, 、k should be the next value. The program can be called fifth program. （13） （14）The fifth program both reduce to the minimize number of switching, and reduce to the minimum switching losses. When (), twonon-switching sectors of the maximum load current amplitude each cycle Just are not switching sectors. And therefore the maximum the switching current can be reduced by 1 3% (). As long as (), positive and negative peak of load current will fall within the non-switching sectors, thereby reducing the maximum switching current. Motor load power factor is typically more than 0.8, with the mechanical load varies, so the fifth program not only make the minimum switching loss, but also effectively reduce the maximum switching current of the switching device.3. Research FindingsIn VSVPWM, the choice of zero vectors is flexible. While maintaining the same sampling period, the maximum switching frequency can be reduced by one third by proper selection of zero vectors. And there are many zero-vector distribution programs. But merely reduc