Information Technology Journal

Year: 2014 | Volume: 13 | Issue: 5 | Page No.: 927-933
DOI: 10.3923/itj.2014.927.933

A New Sector Positioning Method of the SVPWM Reference Voltage Space Vector

Gaoming He, Mei Wang, Jinming Gan and Chaoxiang Liang

Abstract: Induction motor speed control is an important means to improve the efficiency of electric power and the Space Vector Pulse Width Modulation (SVPWM) control technology is widely used in induction motor speed control. In this study, synthesis method of the SVPWM reference voltage space vectors and sectors positioning method are analyzed, three condition factors which control the sector positions of the reference voltage space vectors are digitized and traditional Look-Up Table (LUT) method to posit the sectors of the reference voltage space vectors is derived. On this basis, digital forms of the three condition factors are combined and analyzed, therefore a new sector positioning method of the SVPWM reference voltage space vectors is proposed. This study proves that the presented method can be used to determine the switch sequences of the inverter directly according to the three condition factors and the traditional LUT method shall be omitted in programming, so it will reduce the code memory space effectively.

Keywords: SVPWM, voltage space vector and sector

INTRODUCTION

The space vector pulse width modulation (SVPWM) is a common control method for frequency speed regulation of the three-phase induction motor (Vlatkovic and Borojevic, 1994; Shu et al., 2007; Chen and Li, 1999; Lopez et al., 2008; Holmes, 1996; Wang et al., 2004; Trzynadlowski et al., 1997). It considers the inverter and the motor as a whole. And the ideal flux circle of the alternating current motor is taken as a bench mark upon power supply by the symmetric three-phase sine wave voltage. The aim of SVPWM is to control the motor to obtain the round rotating magnetic field with constant amplitude. Thus, a constant electromagnetic torque is produced. (Vlatkovic and Borojevic, 1994). In practical application, the voltage vector synthesis method, which is a common method to realize SVPWM (Shu et al., 2007), synthesizes the target vector by two adjacent standard voltage space vectors. Its key process is to determine the sectors where the reference voltage vectors are located (Wang et al., 2004) and look-up Table method is used in general in the actual programming. An improved synthesis method of SVPWM reference voltage space vectors is proposed in this study and the switch control sequence of the inverter can be directly synthesized according to the reference voltage vectors.

CONTROL THEORY OF THE SVPWM

It is a common control mode with the Voltage Source Inverter (VSI) among induction motor frequency speed regulation systems (Vlatkovic and Borojevic, 1994). The control model is shown in Fig. 1. There are three bridge arms for control in the inverter. And each bridge arm has two switch tubes, so the totally 6 switch tubes are S_a, S_b, S_c, . Among the above the states in the pairs of S_a and , S_b and the pairs of S_c and are opposite with each other. If one switch tube in the bridge arm is closed, another one must be disconnected at the same time. a, b and c are used to represent three windings of the induction motor.

According to the above, there are eight switch states of the inverter, as shown in Table 1. Among them, if the S_a is closed, the corresponding state is represented with 1, otherwise in 0, as well as S_b and S_c.

As shown in Fig. 1, when S_a , S_b , S_c are all closed, there isn’t any pressure drop of the three windings on the induction motor, conversely, when are all shut, there is also no pressure drop. Thus, the state 0 and 7 belong to the same state called the zero state, which is equivalent to connecting three-phase windings of the motor a, b and c to the same potential at the same time. And the asynchronous motor produces no rotating magnetic field.

While state 1 to 6 are known as the working states which will make some of the windings of the induction motor power up. So, there are seven different states of the voltage inverter.

Suppose the voltages of the three coils of the induction motor are respectively u_a , u_b and u_c and there is:

There are three stator windings in the three-phase induction motor. At working time each winding connects a one-phase voltage and the differences in each pairs of the voltages are all 120 degrees. As a result, it is complex to make quantitative analysis on this three-dimensional voltage vector. And the three-dimensional voltage vector is converted into the two-dimensional vector by Park transform usually, result two dimensional vector u_s (t) is:

From Eq. 1 and 2 and taking into account the power constant factors, there is:

From Eq. 3, when the switch state of the inverter is 001, there is:

Similarly voltages of the others can be calculated as follows:

It can be seen from Eq. 5 to 9 that six of the eight vectors have the same amplitude in the two-dimensional plane, but the phase are differed of 60 degrees, as shown in Fig. 2a. Vectors are rotated in counter-clockwise order, u(111) and u(000) in the center of the hexagon are the zero voltage vectors.

U_ref is the reference voltage vector for a single moment, whose projection on the α-β coordinates are u_α and u_β, respectively.

SECTOR JUDGMENT OF VOLTAGE SPACE VECTOR

Figure 2b is a standard diagram of hexagonal voltage space vector. Most common induction motor control technologies at present are carried out through the two-dimensional vectors of the two-phase coordinates, so it’s needed to transform the three-phase static coordinate to the two-phase α-β static coordinate system. U_ref in Fig. 2b is the reference voltage vector for a single moment, whose projection on the α-β coordinates are respectively u_α and u_β and to are sector numbers. As induction motor stator flux linkage is the accumulation of voltage space vector to the time, stator flux linkage corresponded to the timing producing U_ref could be gotten from the combination of the loading time of the two standard voltage space vector which are adjacent to U_ref . In order to synthesize this voltage space vector, it is needed to make sure that two adjacent standard voltage space vectors are contained, that is the sector of the U_ref needed confirmation.

Seen from Fig. 2b that angles of every sector are all 60 degrees, therefore there are certain distribution characteristics of the size and plus-minus of the sector of U_ref and the projection components u_α and u_β in α-β coordinates. From Fig. 2b, when u_β>0, U_ref must be at one of the sector , or .

As a result, the sector distribution can be roughly determined through the plus-minus of the u_β. And further judgment will be made according to the projection components u_α and u_β of each sector. With sector as example, analysis is as follows.

When U_ref is in sector , the angle between U_ref and axis α is less than 60 degrees, the u_α and u_β are both positive. Suppose the size of U_ref is U, there is:

On the other hand, due to u_α>0 and u_β>0, U_ref must be located in the zone between 0 to 90 degrees and it is further confirmed through:

that U_ref must be located in the zone between 0 to 60 degrees, therefore:

is a necessary and sufficient condition of voltage space vector U_ref locating in sector .

To:

in Eq. 10, both sides multiplied by at the same time, there is:

Equation 11 can be further simplified into following form:

That is:

From Eq. 13, when u_β>0 and:

the voltage space vector U_ref is located in the sector . According to the methods described above, conditions through which U_ref are located in the other five sectors can be obtained:

When u_β>0 and:

or:

U_ref is located in section .
When u_β>0 and:

U_ref is located in section .
When u_β<0 and:

is located in section .
When u_β<0 and:

or:

U_ref is located in section .
When u_β<0 and:

U_ref is located in section .

According to the analysis above, the serial number of the sectors where U_ref is located is decided by the plus-minus of the three factors including u_β,

and:

The conditions listed above are shown in Table 2.

It is worth noticing that the three condition factors u_β:

and:

can’t be larger or less than zero all at the same time. Analysis with set theory to Table 2 is shown as follows:

When u_β>0, there is:

When:

there is:

Combine the two condition factors above, (there must be:

at the time) and there is:

And so results in U_ref∈{}, namely that U_ref must be located in sector .

In the same way, other two combinations with either two of the three condition factors can be used to determine the sector number where U_ref is located in. Suppose the three condition factors u_β:

and:

are expressed, respectively in A, B and C, which are made to be expressed in 1 when the value is larger than 0 and 0 when the value is less than 0. As a result, Table 2 can be simplified as shown in Table 3.

The three conditions factors u_β:

and:

can't be greater or less than zero at the same time, so ABC in Table 2 can’t be 000 or 111. Via method of setting, the U_ref sector's location can be determined through various combinations of A, B and C values as follows:

Indicated in Table 4 for the above situations.

Methods above can also be represented as:

Set F = 4A+2B+C, so F value is just equal with the value of the binary number consisted of ABC, whose scope is from 1-6. Therefore, F value can also be used to determine the sector of U_ref , which is also the method to determine the sector in many teaching materials and documents and is commonly realized through look-up Table method in actual programming.

RELATIONSHIP BETWEEN THE ADJACENT TWO STANDARD VOLTAGE SPACE VECTORS AND THE COMBINATIONS OF DIFFERENT ABC VALUE

Look-up Table method is commonly used to determine the sectors which the reference voltage space vector are located in. But if we can omit the look-up of the sector number, directly determine the standard voltage space vector loading time through the combinations of the values when ABC change their locations, it will reduce the code length. Binary numbers directly represented in the combination order of ABC listed as below in Table 5.

Results from the analysis of Table 5 as shown below.

Set Y₁ as standard voltage space vectors 1 and Y₂ as standard voltage space vectors 2. Set X as combination of BAC. Set Y₁ = f₁ (X), Y₂ = f₂ (X), f₂ (X). There is:

Set F₇ = 4B+2A+C, according to Eq. 18, there comes out Y₂ = F₇.

Results from the analysis of Table 6 as shown below.

Set Y₁ as standard voltage space vectors 1, Y₂ as Standard voltage space vectors 2, X = Combination of CBA, Y₁ = f₁ (X), Y₂ = f₂ (X).

There is:

Set F₆ = 4C+2B+A, according to Eq. 20, there comes out Y₁ = 7-F₆.

The serial number’s orders of the sectors are same in Table 5, 6, 7, 8, 9 and 10 and therefore, two adjacent standard voltage space vectors can be determined according to the different Tables. Through the analysis above, two standard voltage space vectors Y₁ and Y₂ which are used to U_ref synthesis is simply corresponded with the combination of CBA and BAC, as shown in Eq. 21:

When symmetric PWM waveform is output, there are two kinds of switch sequences of the outer inverter, which are 000->Y₁->Y₂->111->Y₂->Y₁->000 and 000->Y₂->Y₁->111->Y₁->Y₂->000. There is only one difference between the adjacent switch sequences and the switch control of the inverter in each PMW cycle started from 000, so the second switch sequence must be less of 1 than the third one, that is the value of the binary number represented the second switch sequence must be less than that of the third switch sequences. So, when Y₁>Y₂, the control mode is 000->Y₂->Y₁->111->Y₁-> Y₂->000, while when Y₁<Y₂, it is 000->Y₁->Y₂->111->Y₂->Y₁->000. As a result, this method can be used to determine the switch sequence which controls the inverter, omit the steps of look-up table in the programming and save code storage space through the validation of the actual programming.

CONCLUSION

There is a relatively deep analysis to the synthesis method of space voltage vectors in this study, sector positioning method of the reference voltage space vector which used to using traditional look-up Table method is deduced from the set theory. And on the basis of it, further analysis is made to the determining method of the two standard voltage space vectors which are used to synthesis the reference voltage space vector. The method can directly determine the switch sequence of the inverter and save code storage space and running time of the program in programming realization process, which is of certain application value.

ACKNOWLEDGMENTS

This study is supported by science and Technology Department of Guangxi Zhuang Autonomous Region of China under Grant No. 10123012-4 and Education Department of Guangxi Zhuang Autonomous Region of China under Grant No. 2013YB224 and No. 201106LX556. We would like to give our special thanks to Prof. Dr. Zhenming Yu at the Wuzhou University, Wuzhou, China for his in valuable assistance also.

REFERENCES