CN111800051A - An FPGA-based SVPWM overmodulation system and method - Google Patents

Abstract

The invention relates to an SVPWM overmodulation system and method based on FPGA, belonging to the technical field of motor control; the modulation methods in the prior art are all based on MCU or DSP, and have complex calculation and long time; the overmodulation system comprises an input processing module, an amplitude phase angle calculation module, an overmodulation coefficient calculation module, an overmodulation I region calculation module, an overmodulation II region calculation module, an output correction amplitude phase angle module, a sine and cosine calculation module, a voltage component calculation module and an output processing module; the calculation process of the algorithm is simplified, and the algorithm is convenient to realize in the FPGA.

Description

An FPGA-based SVPWM overmodulation system and method

technical field

The present invention relates to a driving method of a permanent magnet synchronous motor, in particular to a SVPWM overmodulation system and method of a permanent magnet synchronous motor.

Background technique

With the continuous in-depth research and development of power electronic technology and motor control theory, AC servo control technology has made great progress, which is widely used in CNC machine tools, industrial robots, new energy vehicles, weapons and equipment, aerospace and other fields. The development trend of numerical control is high-speed machining technology. In order to improve production efficiency and improve machining quality, higher requirements are placed on the high-speed and high-torque servo drive system.

比SPWM技术提高约15％。SVPWM调制技术由于直流母线电压利用率较高、谐波含量较小、数字化实现较简单等优点被广泛应用。但SVPWM调制技术 只适用于参考电压矢量在正六边形以内的情况，超过正六边形后需要采用SVPWM 过调制算法进行修正，该算法可以使输出相电压基波幅值最大达到2V_dc/π，可 进一步提高母线电压利用率约10％。这对提高电机的瞬间过载能力，加快动态响 应速度以及弱磁升速都意义重大。In the AC servo system based on vector control, the pulse width modulation technology controls the voltage source inverter to output the three-phase voltage, and the three-phase sinusoidal current is formed through the motor stator winding, thereby generating a rotating circular magnetic field to drive the motor rotor to rotate. The control goal of the sinusoidal pulse width modulation (SPWM, Sinual Pluse Width Modulation) technology is to make the output voltage of the inverter as close to a sine wave as possible, but without considering the control of the current waveform, the amplitude of the fundamental phase voltage can reach V _dc /2. Space-Vector Pluse Width Modulation (SVPWM, Space-Vector Pluse Width Modulation) technology treats the inverter and the AC motor as one, and controls the inverter to make the motor generate a rotating circular magnetic field. The maximum amplitude of the phase voltage fundamental wave can reach

About 15% improvement over SPWM technology. SVPWM modulation technology is widely used due to the advantages of high DC bus voltage utilization, small harmonic content, and simple digital implementation. However, the SVPWM modulation technology is only suitable for the case where the reference voltage vector is within the regular hexagon. After exceeding the regular hexagon, the SVPWM over-modulation algorithm needs to be used for correction. This algorithm can make the output phase voltage fundamental wave amplitude up to 2V _dc /π, The utilization rate of busbar voltage can be further improved by about 10%. This is of great significance for improving the instantaneous overload capacity of the motor, speeding up the dynamic response speed and increasing the speed of the field weakening.

The SVPWM over-modulation algorithm can improve the utilization rate of the DC bus voltage, thereby obtaining greater torque and speed and improving the motor performance, so it has become a research problem that many scholars at home and abroad focus on. Joachim Holtz proposed a dual-mode overmodulation strategy that divides the overmodulation region into region I and region II: the overmodulation region I only corrects the amplitude of the voltage vector, while the phase remains consistent with the reference voltage vector; the overmodulation region II needs to be corrected Phase and amplitude of the voltage vector to ensure the continuity of the output voltage vector. The harmonics introduced by this strategy in the overmodulation I region are small, but the implementation is cumbersome due to the constant correction of the phase angle in the overmodulation II region. In order to reduce the computational difficulty, many scholars propose to simplify the overmodulation II region, but the output voltage will jump. According to the Fourier expansion, Dong-Choon Lee et al. obtained the functional relationship between the amplitude of the phase voltage fundamental wave and the control angle, and combined the relationship between the voltage amplitude and the overmodulation coefficient to obtain the crossover angle and the hold angle corresponding to different overmodulation coefficients, and carried out their calculations. Piecewise linear processing is adopted, which is convenient for calculation and digital realization.

At present, the SVPWM overmodulation algorithm proposed by domestic and foreign scholars is mainly optimized from the aspects of simplifying calculation, improving control accuracy and reducing harmonics, and almost all of them are implemented in MCU or DSP. Among them, the dual-mode overmodulation strategy has been widely used by many scholars due to its excellent comprehensive performance Adopt and improve.

SUMMARY OF THE INVENTION

In view of the problems existing in the prior art, the present invention provides an FPGA-based SVPWM overmodulation system, the overmodulation system includes: an input processing module, an amplitude phase angle calculation module, an overmodulation coefficient calculation module, and an overmodulation I area calculation module. module, overmodulation Ⅱ area calculation module, output correction amplitude phase angle module, sine and cosine calculation module, calculation voltage component module, output processing module;

The overmodulation module takes V _α and V _β as input signals, and outputs to the amplitude and phase angle calculation module after processing, and the reference voltage vector V _ref and the phase angle θ are output from the amplitude and phase angle calculation module;

calculating the overmodulation coefficient m according to the reference voltage vector _Vref by the sum overmodulation coefficient calculation module;

得到

和

The overmodulation I area calculation module calculates the voltage vector amplitude V _m according to the overmodulation coefficient m, and then calculates cosθ and sinθ by the sine and cosine calculation module, and then calculates the voltage component by the calculation module according to formula (1)

get

and

得到

和

The output correction amplitude phase angle module obtains the initial angle θ ₀ of the sector where the reference voltage vector is located, and then the overmodulation II area calculation module calculates the voltage vector amplitude Vm and the holding angle α according to the overmodulation coefficient _{m h} , the amplitude V _out and the phase angle θ _out of the output voltage vector are obtained in combination with the initial angle θ ₀ , and then the cos θ _out and sin θ _out are calculated by the sine and cosine calculation module, and then the calculation voltage component module is calculated according to the formula ( 2)

get

and

和

或由所述公式(2) 得到

和

作为所述电机逆变器的输入电压。Finally, the output of the output processing module is obtained from the formula (1)

and

or obtained from the formula (2)

and

as the input voltage of the motor inverter.

Preferably, the overmodulation I region calculation module calculates the voltage vector magnitude Vm by looking up a table according to the overmodulation coefficient _m .

Preferably, the overmodulation zone II calculation module calculates the voltage vector amplitude V _m and the hold angle α _h by looking up a table according to the overmodulation coefficient m.

Preferably, the amplitude V _out of the output voltage vector is obtained by the following formula:

Preferably, the phase angle θ _out of the output voltage vector is obtained by the following formula:

其中，参考电压矢量在扇区内的相对角度 Δθ＝θ-θ₀。

Wherein, the relative angle of the reference voltage vector in the sector Δθ=θ−θ ₀ .

The present invention also provides a kind of method that carries out overmodulation according to the SVPWM overmodulation system based on FPGA, and described method comprises the following steps:

Step 1): according to the input signals V _α and V _β , the calculation module outputs the reference voltage vector V _ref and the phase angle θ;

Step 2): calculate the overmodulation coefficient m according to the reference voltage vector V _ref ;

Step 3): determine the overmodulation region according to the reference voltage vector _Vref or the overmodulation coefficient m;

得到

和

当过调 制区域为过调制Ⅱ区时，获取参考电压矢量所在扇区的初始角度θ₀，根据所述过 调制系数m计算电压矢量幅值V_m和保持角α_h，结合所述初始角度θ₀得到输出电压 矢量的幅值V_out与相角θ_out，依据公式

得到

和

Step 4): when the overmodulation region is the overmodulation I region, the voltage vector amplitude Vm is calculated according to the overmodulation coefficient _m and combined with the reference voltage phase angle θ, according to the formula

get

and

When the overmodulation region is the overmodulation II region, obtain the initial angle θ ₀ of the sector where the reference voltage vector is located, calculate the voltage vector amplitude V _m and the holding angle α _h according to the overmodulation coefficient m, and combine the initial angle θ ₀ to get the amplitude V _out and the phase angle θ _out of the output voltage vector, according to the formula

get

and

和

作为所述电机逆变器的输入电压。Step 5): Output

and

as the input voltage of the motor inverter.

Compared with the prior art solutions, the present invention at least has the following beneficial effects:

1) the present invention improves the SVPWM overmodulation method, simplifies the calculation process, and is easy to realize in FPGA;

2) The voltage vector amplitude value needs to be corrected in the overmodulation I area, and the output voltage vector amplitude value is obtained by directly looking up the table according to the overmodulation coefficient, avoiding the calculation of the cross angle and the correction amplitude value.

3) The voltage vector amplitude and phase angle need to be corrected in the overmodulation II region, and the table look-up method is also used to simplify the calculation process. The designed amplitude and phase angle correction process no longer involves division and trigonometric function operations, avoiding the consumption of a lot of resources, and the accuracy can be guaranteed to be basically the same as before the simplification.

Description of drawings

Fig. 1 is the division diagram of prior art China linear modulation area and over-modulation area;

Fig. 2 is the modulation area division diagram of overmodulation module of the present invention;

Fig. 3 is the working schematic diagram of the overmodulation module of the present invention;

Fig. 4 is the correction voltage vector locus diagram of overmodulation I region of the present invention;

Fig. 5 is the relation diagram of intersection angle α _r and overmodulation coefficient m of the present invention;

6 is a graph showing the relationship between the output voltage vector amplitude V _m and the overmodulation coefficient m of the overmodulation I region of the present invention;

Fig. 7 is the flow chart of overmodulation I area of the present invention;

Fig. 8 is the locus diagram of correction voltage vector of overmodulation II region of the present invention;

Fig. 9 is the relation diagram of the present invention holding angle α _h and overmodulation coefficient m;

Fig. 10 is a graph showing the relationship between the correction voltage vector amplitude V _m and the overmodulation coefficient m in the overmodulation II region;

Fig. 11 is the flow chart of overmodulation II area of the present invention;

Figure 12 is a block diagram of the overmodulation module of the present invention.

The present invention will be described in further detail below. However, the following examples are only simple examples of the present invention, and do not represent or limit the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

specific embodiment

The technical solutions of the present invention are further described below with reference to the accompanying drawings and through specific embodiments.

When a three-phase balanced sinusoidal voltage is added to the motor, the stator flux vector of the motor will rotate with a constant amplitude and angular velocity, and the motion trajectory of the end of the flux vector is circular. Since the stator resultant voltage vector is always kept orthogonal to the flux vector, the voltage vector rotates synchronously with the flux vector. The SVPWM modulation technology indirectly controls the rotating magnetic field of the motor stator by controlling the motion trajectory of the voltage vector.

The essence of SVPWM modulation technology is to synthesize the reference voltage vector in the control period T _PWM by two basic voltage vectors and zero vector equivalently, the corresponding action times are t ₁ , t ₂ and t ₀ respectively, and t ₁ +t ₂ +t ₀ =T _PWM .

As shown in Figure 1, when the amplitude of the reference voltage vector is smaller than the radius of the inscribed circle of the regular hexagon, there is always t ₁ +t ₂ <T _PWM , and the actual output voltage vector trajectory is consistent with the reference voltage vector, both of which are circular. The area is called the linear modulation area. Gradually increase the amplitude of the reference voltage vector. When the radius of the inscribed circle is exceeded, the part exceeding the regular hexagon adopts the linear modulation method, and t ₁ +t ₂ >T _PWM will cause t ₀ to be less than 0. This is physically unreasonable. Therefore, this area cannot continue to use linear modulation, and an overmodulation algorithm needs to be used to re-plan the output voltage vector trajectory, so this area is called the overmodulation area.

In order to judge the modulation area, the overmodulation coefficient is defined as:

The modulation coefficient increases with the gradual increase of the reference voltage vector amplitude, and the modulation depth increases gradually from the linear modulation region to the overmodulation region.

(1) Overmodulation I region. Due to physical limitations, the portion of the reference voltage vector beyond the boundary of the regular hexagon will be confined to the boundary of the regular hexagon, resulting in a loss of voltage. The voltage compensation is performed by adopting a strategy of not changing the voltage phase, but only increasing the voltage amplitude near the basic voltage vector, where the corrected voltage amplitude is related to the reference angle α _r .

2) Overmodulation II area. When the reference voltage vector is in the vicinity of the base voltage vector, the voltage loss is compensated by holding the voltage vector at the base voltage vector for a time determined by the hold angle _αh .

Example 1

The overmodulation calculation module provided by the present invention pre-corrects the reference voltage before the SVPWM modulation, and the introduction of the overmodulation module does not require any modification to other modules in the original system, which is convenient for verification and transplantation. In practical engineering, the SVPWM modulation module needs to limit the output t ₁ and t ₂ , that is, when t ₁ +t ₂ >T _PWM , t ₁ and t ₂ are proportionally reduced according to the following formula;

It is possible to confine the portion of the reference voltage vector beyond the regular hexagon to the regular hexagon. Therefore, the overmodulation module does not need to perform limit calculation when the voltage amplitude exceeds the boundary of the regular hexagon, and only needs to directly output the corrected voltage vector, which can avoid unnecessary calculations.

The reference voltage vector amplitude range of the entire modulation region is 0 to 2V _dc /3, and the entire modulation region is divided into linear modulation region, overmodulation I region and overmodulation II region according to the overmodulation coefficient m, as shown in Figure 2.

和

As shown in Figure 3, it is the working schematic diagram of the over-modulation calculation module of the present invention. First, the voltage amplitude V _ref and the phase angle θ are calculated according to the reference voltage vector components V _α and V _β , and then the over-modulation coefficient m is calculated from the amplitude. The modulation coefficient m determines the region where it is located and adopts the corresponding algorithm for processing. The linear modulation area does not need any correction, and outputs directly; the overmodulation I area needs to increase the voltage vector amplitude to compensate for the voltage loss, and the phase angle keeps following; the overmodulation II area needs to correct the voltage vector amplitude and phase angle. Finally calculate and output the corrected voltage vector component

and

Since the overmodulation correction amplitude phase angle involves many operations such as division and trigonometric functions, the implementation of these operations in the FPGA needs to consume a lot of resources. Therefore, it is necessary to design the algorithms for the overmodulation area I and II, within the accuracy range. Try to simplify and integrate some of these computing processes to avoid too many complex calculations that consume a lot of resources. The entire overmodulation module includes addition, subtraction and multiplication that can be directly implemented, and involves some operations that cannot be directly implemented, such as square root to find amplitude, arc tangent to find phase angle, sine and cosine to find voltage components, etc. The following analyzes the calculation scheme of various operations in FPGA:

(1) The magnitude of the square root can be obtained through the multiplier and the square root IP core in the Quartus II software. The square of the two voltage components needs to consume 4 18×18 multipliers, and the square root IP core needs to consume some basic logic units. The CORDIC algorithm can iteratively find the magnitude of the vector, and the iterative process does not involve complex operations.

(2) The methods of obtaining the phase angle by arctangent mainly include Taylor series approximation method, ROM look-up table method, CORDIC algorithm and so on. The Taylor series approximation method needs to consume a large number of multipliers, and this method is not desirable because the multiplier resources are relatively tight. The arc tangent lookup table stores the angle value in the ROM in advance, and uses the ratio of the ordinate to the abscissa as the input address to search for the corresponding arc tangent. The angle values of the four quadrants can be calculated through preprocessing, and the look-up table method is simple and easy to implement, but its operation accuracy is limited by resources. The CORDIC algorithm can calculate the phase angle of the vector by calculating the arctangent, and can output the amplitude and phase angle of the vector at the same time through one round of iterative operation.

(3) Calculate the sine and cosine value of the angle mainly including the look-up table method and the CORDIC algorithm. The look-up table method is to store the sine and cosine values in the FPGA, and use the angle value as the input address of the look-up table to find and output the sine and cosine values of the angle. One iteration of the CORDIC algorithm can calculate the sine and cosine values at the same time.

Because CORDIC has the advantages of high algorithm precision, fast operation speed, and can solve a variety of trigonometric function operations at the same time, this paper adopts the CORDIC algorithm to calculate the amplitude, phase angle and sine and cosine.

和

各个子模块间的 关系如图12所示。The overmodulation module of the present invention is divided into 9 sub-modules: an input processing module, an amplitude phase angle calculation module, an overmodulation coefficient calculation module, an overmodulation I area algorithm module, an overmodulation II area algorithm module, and an output correction amplitude phase angle module. , sine and cosine calculation module, calculation voltage component module, output processing module. The overmodulation module takes V _α and V _β as input, and the output is corrected by the overmodulation algorithm

and

The relationship between each sub-module is shown in Figure 12.

Among them, the amplitude phase angle calculation module calculates the amplitude by the following formula:

Calculate the phase angle from:

The overmodulation coefficient calculation module calculates the overmodulation coefficient by the following formula:

The following will analyze how the overmodulation I area and the overmodulation II area simplify the process of correcting the phase angle of the reference voltage vector amplitude according to the equal area method, and how to calculate the trigonometric function based on CORDIC.

The overmodulation zone I algorithm module calculates the amplitude by the following formula:

The overmodulation I area starts from the inscribed circle of the regular hexagon. In order to make the output still track the reference voltage, the correction strategy for the reference voltage vector is to increase the voltage amplitude, and the phase angle remains unchanged, so the reference voltage vector amplitude is changed. Adding to V _m yields an output voltage vector whose locus intersects the regular hexagon at the intersection angle α _r . The radius of the output voltage vector track circle is V _m after being corrected by the overmodulation I area algorithm. Due to the limiting effect of the SVPWM modulation module, the actual running track will be partly on the regular hexagon and partly on the circle. The relationship between the output voltage vector amplitude V _m and the crossing angle α _r is:

The key to the algorithm of overmodulation I area is how to determine the magnitude of the output voltage vector magnitude V _m according to the reference voltage vector magnitude V _ref . According to the principle of volt-second balance, the average value of the output voltage vector per unit time is the same as the reference voltage vector, and the rotation speed of the output voltage vector and the reference voltage vector is the same, so the area swept by the rotation of the output voltage vector should be equal to the rotation sweep of the reference voltage vector. area passed. Therefore, in the overmodulation I region, the missing voltage is compensated by increasing the voltage amplitude, and when it is converted into geometry, it is necessary to ensure that the area of the missing voltage pattern is equal to the area of the compensation voltage pattern. As shown in Fig. 4, the missing voltage consists of six parts of the reference voltage vector trajectory exceeding the regular hexagon, and the compensation voltage includes the six parts of the output voltage vector trace surrounded by the regular hexagon and the reference voltage vector trace near the vertex.

According to the equal-area method, the area formed by the rotation of the reference voltage vector is equal to the area enclosed by the actual output voltage vector trace, which has the following equation:

The area enclosed by the actual output voltage vector trace can be divided into six sectors and six triangles. combine

Equation 2.2, the relationship between the overmodulation coefficient m and the cross angle α _r is obtained as:

where the intersection angle α _r ranges from 0 to π/6. When the reference voltage vector amplitude is the radius of the inscribed circle of the regular hexagon, it begins to enter the overmodulation I region, the intersection angle α _r at this time is π/6, and the overmodulation coefficient m is about 0.9069; when the corrected output voltage vector trace When it is a regular hexagon circumscribed circle, it cannot continue to pass through the vertex for compensation, and it begins to enter the overmodulation II zone, so the upper cross angle α _r of the overmodulation I zone is 0, and the overmodulation coefficient m is about 0.9523. Since Equation 3.3 is nonlinear, the intersection angle α _r cannot be calculated directly in the chip using this formula, and its curve image is drawn through MATLAB as shown in Figure 5.

In theory, linear fitting or offline point processing can be performed on this curve, and then the cross angle α _r can be obtained by calculating the overmodulation coefficient m or looking up the table, and then the cross angle can be brought into Equation 3.1 to calculate the output voltage vector amplitude V _m , this realization method is usually applied in MCU or DSP. Since the cosine and division operations are involved in Equation 3.1, calculating this formula in an FPGA is more complicated and consumes more resources. In Equation 3.1, V _dc is the DC bus voltage, which can be regarded as a constant after per-unit processing during engineering implementation, and V _dc can be regarded as 1 first. Therefore, the relationship between the overmodulation coefficient m and the output voltage amplitude V _m can be directly drawn through MATLAB by combining Equation 3.1 and Equation 3.3, as shown in Figure 6. Since piecewise linear fitting needs to consume multipliers, it is more beneficial to implement and utilize resources in FPGA by taking offline points and storing them in the chip to look up the table. In this paper, we select points on this curve according to a certain precision and use the table lookup method, and we can directly look up the table through the overmodulation coefficient m to obtain the amplitude V _m of the output voltage vector in the FPGA. This is consistent with the accuracy of calculating the output voltage amplitude by looking up the table to obtain the cross angle first, and then bringing it into Equation 3.1, but it avoids the complex calculation and resource consumption of Equation 3.1.

和

为：Since the overmodulation I region does not change the phase angle, the output voltage vector is directly decomposed to obtain the corrected

and

for:

Overmodulation Ⅱ Region Algorithm Module

和

整个算法流 程中的难以直接实现的运算包括计算参考电压失量的幅值相角，以及式3.4中计 算正余弦，这些运算都是无法避免的。通常在DSP中实现过调制算法的流程是 根据参考电压幅值计算过调制系数，然后通过过调制系数确定交叉角，最后由 交叉角计算输出电压幅值。本节基于FPGA设计的过调制Ⅰ区算法简化了计算 输出电压幅值的过程，直接根据过调制系数查表得到输出电压幅值。该算法避 免了交叉角和输出电压幅值的计算，很大程度上简化了计算和节省资源，同时 可以保证计算精度，更利于在FPGA中实现。The algorithm flow of the overmodulation I region is shown in Figure 7. The two components V _α and V _β of the reference voltage vector are used as inputs. After the voltage amplitude is corrected by the look-up table method, the corrected two voltage components are output.

and

The operations that are difficult to implement directly in the entire algorithm flow include calculating the amplitude and phase angle of the reference voltage loss, and calculating the sine and cosine in Equation 3.4. These operations are unavoidable. Usually, the process of implementing the overmodulation algorithm in DSP is to calculate the overmodulation coefficient according to the reference voltage amplitude, then determine the crossover angle through the overmodulation coefficient, and finally calculate the output voltage amplitude from the crossover angle. In this section, the algorithm of overmodulation I area based on FPGA design simplifies the process of calculating the output voltage amplitude, and directly obtains the output voltage amplitude according to the overmodulation coefficient look-up table. The algorithm avoids the calculation of the crossing angle and the output voltage amplitude, which simplifies the calculation and saves resources to a large extent. At the same time, the calculation accuracy can be guaranteed, which is more conducive to the realization in FPGA.

The upper limit of the overmodulation I region is that when the output voltage vector trajectory is a regular hexagon circumscribed circle, the actual running track is completely on the regular hexagon. If the reference voltage amplitude V _ref continues to increase, it begins to enter the overmodulation II region. The correction strategy in overmodulation II is to keep the output voltage vector at the basic voltage vector for a period of time, and then the jump follows the reference voltage vector to rotate synchronously. The angle at which the reference voltage vector rotates in space during the period of time remaining at the basic voltage vector is the holding angle α _h . According to Equation 2.18, the corrected voltage vector amplitude at the holding angle can be obtained as V _m , and the output voltage vector is the same as the corrected voltage vector. The amplitude V _m is related to the hold angle α _h .

Taking 3 sectors as an example, the trace of the output voltage vector in the analysis area II is shown in Figure 8. When the reference voltage vector rotates to within 0 to _αh , the output voltage vector is always the basic voltage vector V ₁ ; When rotated to keep α _h to π/3-α _h , the output voltage vector rotates synchronously from α _h to π/3-α _h along the correction voltage vector trajectory circle V _m ; when the reference voltage vector rotates to π/3-α _h To π/3, the output voltage vector is always the base voltage vector V ₂ . When the output voltage vector rotates along the corrected voltage vector trajectory circle V _m , due to the limiting effect of the SVPWM module, the actual output voltage vector trajectory will automatically move along the regular hexagon boundary, and no limit calculation is required.

Also according to the equal area method, the geometric area enclosed by the reference voltage vector and the actual output voltage trace is equal to the following equation:

When the output in the holding angle is the basic voltage vector, its area is equivalent to the area enclosed by the rotation holding angle of the basic voltage vector. Combined with Equation 2.2, the relationship between the overmodulation coefficient m and the holding angle α _h is obtained as:

where the holding angle α _h ranges from 0 to π/6. When entering the overmodulation II zone, the hold angle is 0, the overmodulation coefficient is 0.9523, and the output voltage vector trace is the circumscribed circle of the regular hexagon; when the upper limit of the overmodulation zone II is the hold angle is π/6, the overmodulation coefficient is 1.0472, The output voltage vector locus has six vertices, that is, jumps in the six basic voltage vectors. The relationship between the overmodulation coefficient m and the holding angle α _h is drawn by MATLAB as shown in Figure 9.

Also according to Equation 2.2 and Equation 3.6, the relationship between the overmodulation coefficient m and the corrected voltage vector amplitude V _m is drawn through MATLAB, as shown in Figure 10. Taking points on this curve according to a certain precision and using the table look-up method, the holding angle α _h and the amplitude V _m of the corrected voltage vector can be directly obtained by looking up the table by the overmodulation coefficient m, avoiding complex calculation and resource consumption .

Overmodulation II needs to correct the amplitude and phase angle at the same time. After obtaining the holding angle α _h and the corrected voltage vector amplitude V _m by looking up the table, the amplitude V _out of the output voltage vector can be calculated according to the sector where the reference voltage vector is located. Phase angle θ _out . According to the space voltage vector diagram in the figure, the initial angle θ ₀ of the sector where the reference voltage vector is located is:

The relative angle of the reference voltage vector within the sector is:

Δθ=θ-θ ₀ (3.8)

Within the holding angle, it remains on the basic voltage vector, that is, the voltage amplitude and phase angle are fixed; outside the holding angle, the amplitude is the corrected voltage vector amplitude V _m , and the phase angle follows the same unchanged. Therefore, by analyzing the relationship between the relative angle Δθ and the holding angle, the amplitude V _out of the output voltage vector is obtained:

Similarly, the phase angle θ _out can be obtained as:

和

Similarly, the amplitude V _out and phase angle θ _out of the corrected output voltage vector are decomposed to obtain the output

and

和

The calculation flow chart of the overmodulation II region is shown in Figure 11. Taking the reference voltage vector components V _α and V _β as the input, after correcting the voltage amplitude and phase angle through the algorithm, the output voltage component

and

In addition to calculating the magnitude and phase angle of the reference voltage loss and calculating the voltage component, the entire algorithm process does not involve division and trigonometric functions in the intermediate process, but only involves addition, subtraction, comparison and multiplication, which is easy to implement in FPGA.

With the deepening of the modulation depth, it finally jumps on the six basic voltage vectors, and the output is a six-beat staircase wave state. Since the output voltage vector in the overmodulation II region remains at the basic voltage vector for a certain period of time and then jumps to follow, the amplitude and phase angle cannot follow the reference voltage vector, which will cause a certain torque ripple. The phase angle cannot be completely followed in the overmodulation II region, but the voltage amplitude can be maximized.

The range of the output voltage vector in the overmodulation I region is from the inscribed circle to the circumscribed circle of the regular hexagon, while the range of the corrected voltage vector in the overmodulation II region is from the circumscribed circle to the inscribed circle of the regular hexagon. Since the output voltage vector at the upper limit of the overmodulation I region and the corrected voltage vector just entering the overmodulation II region are both regular hexagon circumscribed circles, the algorithm can achieve a smooth transition from the I region to the II region. Through the design of the overmodulation zone I and zone II, the trigonometric function and division operation in the correction of the voltage amplitude phase angle are avoided, but the calculation of the reference voltage vector amplitude phase angle and voltage component cannot be avoided. CORDIC algorithm implementation.

The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the specific details of the above-mentioned embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solutions of the present invention. These simple modifications All belong to the protection scope of the present invention.

In addition, it should be noted that the specific technical features described in the above-mentioned specific embodiments can be combined in any suitable manner unless they are inconsistent. The combination method will not be specified otherwise.

In addition, the various embodiments of the present invention can also be combined arbitrarily, as long as it does not violate the spirit of the present invention, it should also be regarded as the content disclosed by the present invention.

Claims (6)

1. An SVPWM overmodulation system based on FPGA is characterized in that: the overmodulation system includes: the system comprises an input processing module, an amplitude phase angle calculation module, an overmodulation coefficient calculation module, an overmodulation I region calculation module, an overmodulation II region calculation module, an output correction amplitude phase angle module, a sine and cosine calculation module, a voltage component calculation module and an output processing module;

the overmodulation system uses a horizontal signal V_αAnd a vertical signal V_βAs an input signal, processing the input signal and outputting the processed signal to the amplitude phase angle calculation module, and outputting a reference voltage vector V by the amplitude phase angle calculation module_refAnd a phase angle θ, wherein phase angle θ is the angle of the input signal with respect to the horizontal axis α.

Calculating, by the overmodulation coefficient calculation module, the reference voltage vector V_refCalculating an overmodulation coefficient m; when 0.9523>When m is greater than or equal to 0.9069, the region is an overmodulation I, when 1.0472>When m is greater than or equal to 0.9523, the region I is overmodulation;

the overmodulation I region calculation module calculates a voltage vector amplitude V according to the overmodulation coefficient m_mCalculating cos theta and sin theta by a sine and cosine calculating module, and calculating a voltage component by the voltage component calculating module according to a formula (1)

To obtain

And

the output correction amplitude phase angle module acquires an initial angle theta of a sector where a reference voltage vector is located₀And then the overmodulation II region calculation module calculates the voltage vector amplitude V according to the overmodulation coefficient m_mAnd a holding angle alpha_hCombined with said initial angle theta₀Obtaining the amplitude V of the output voltage vector_outAnd phase angle theta_outThen the cos theta is calculated by the sine and cosine calculation module_outAnd sin θ_outAnd then the voltage component calculating module calculates the voltage component according to the formula (2)

To obtain

And

finally, the output of the output processing module is obtained by the formula (1)

And

or is obtained from the formula (2)

And

as the input voltage to the motor inverter.

2. The overmodulation system according to claim 1, wherein: the overmodulation I region calculation module calculates the voltage vector amplitude V through table lookup according to the overmodulation coefficient m_m。

3. The overmodulation system according to claim 1, wherein: the overmodulation II area calculation module calculates the voltage vector amplitude V through table lookup according to the overmodulation coefficient m_mAnd a holding angle alpha_h。

4. The overmodulation system according to claim 1, wherein: magnitude V of the output voltage vector_outObtained from the following equation:

wherein V_dcIs the dc bus voltage.

5. The overmodulation system according to claim 1The system is characterized in that: phase angle theta of the output voltage vector_outObtained from the following equation:

wherein, the relative angle delta theta of the reference voltage vector in the sector is theta-theta₀。

6. A method of overmodulation by an SVPWM overmodulation system according to a permanent magnet synchronous machine according to any of claims 1-5, characterized in that it comprises the following steps:

step 1): according to an input signal V_αAnd V_βThe computing module outputs a reference voltage vector V_refAnd a phase angle θ;

step 2): according to the reference voltage vector V_refCalculating an overmodulation coefficient m;

step 3): according to the reference voltage vector V_refOr the overmodulation coefficient m judges an overmodulation region;

step 4): when the overmodulation region is an overmodulation I region, calculating a voltage vector amplitude V according to the overmodulation coefficient m_mThen combining the reference voltage phase angle theta according to the formula

To obtain

And

when the overmodulation region is overmodulation II region, acquiring the initial angle theta of the sector where the reference voltage vector is located₀Calculating the voltage vector magnitude V according to the overmodulation coefficient m_mAnd a holding angle alpha_hCombined with said initial angle theta₀Obtaining the amplitude V of the output voltage vector_outAnd phase angle theta_outAccording to the formula

To obtain

And

step 5): output of

And

as an input voltage for the motor inverter.

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