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

FPGA-based SVPWM overmodulation system and method Download PDF

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CN111800051A
CN111800051A CN202010744011.6A CN202010744011A CN111800051A CN 111800051 A CN111800051 A CN 111800051A CN 202010744011 A CN202010744011 A CN 202010744011A CN 111800051 A CN111800051 A CN 111800051A
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overmodulation
voltage vector
region
amplitude
calculation module
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宋宝
周向东
唐小琦
马锐
邹益刚
唐钰
孙彬
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Huazhong University of Science and Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H02P25/024—Synchronous motors controlled by supply frequency
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation
    • H02P27/12—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation pulsing by guiding the flux vector, current vector or voltage vector on a circle or a closed curve, e.g. for direct torque control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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  • Power Engineering (AREA)
  • Control Of Ac Motors In General (AREA)

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

FPGA-based SVPWM overmodulation system and method
Technical Field
The invention relates to a driving method of a permanent magnet synchronous motor, in particular to an SVPWM overmodulation system and an SVPWM overmodulation method of the permanent magnet synchronous motor.
Background
With the continuous and deep research and development of power electronic technology and motor control theory, the alternating current servo control technology makes great progress, so that the alternating current servo control technology is widely applied to the fields of numerical control machines, industrial robots, new energy vehicles, weapon equipment, aerospace and the like. The development trend of numerical control is a high-speed processing technology, and higher requirements are put forward on high speed and high torque of a servo drive system in order to improve production efficiency and processing quality.
In an alternating current servo system based on vector control, a pulse width modulation technology controls a voltage source type inverter to output three-phase voltage, and three-phase sinusoidal current is formed through a motor stator winding, so that a rotary circular magnetic field is generated to drive a motor rotor to rotate. The control goal of the Sinusoidal Pulse Width Modulation (SPWM) technology is to make the output voltage of the inverter as close to a sine wave as possible, but the control of the current waveform is not considered, and the amplitude of the fundamental wave of the phase voltage can reach V to the maximumdc/2. The Space-Vector Modulation (SVPWM) technology integrates an inverter and an alternating current motor, the motor generates a rotating circular magnetic field by controlling the inverter, and the amplitude of a phase voltage fundamental wave can reach the maximum
Figure BDA0002607714870000011
The improvement is about 15 percent compared with the SPWM technology. The SVPWM modulation technology is widely applied due to the advantages of high utilization rate of direct-current bus voltage, low harmonic content, simple digital implementation and the like. However, the SVPWM modulation technology is only suitable for the condition that the reference voltage vector is within the regular hexagon, and after the reference voltage vector exceeds the regular hexagon, the SVPWM overmodulation algorithm is needed to be adopted for correction, and the algorithm can enable the amplitude of the fundamental wave of the output phase voltage to reach 2V at mostdcAnd/pi, the bus voltage utilization rate can be further improved by about 10 percent. The method has great significance for improving the instant overload capacity of the motor, accelerating the dynamic response speed and accelerating the flux weakening speed.
The SVPWM overmodulation algorithm can improve the voltage utilization rate of a direct current bus, so that higher torque and rotation speed are obtained and the performance of a motor is improved, and the SVPWM overmodulation algorithm becomes a research problem which is focused by numerous scholars at home and abroad. Joachim Holtz proposes a dual-mode overmodulation strategy that divides the overmodulation region into region I and region II: the overmodulation I area only corrects the amplitude of the voltage vector, and the phase keeps consistent with the reference voltage vector; overmodulation region II requires the phase and amplitude of the voltage vector to be modified to ensure the continuity of the output voltage vector. The harmonic introduced by the strategy in the overmodulation I area is smaller, but the implementation is more complicated due to the fact that the phase angle is continuously corrected in the overmodulation II area. In order to reduce the calculation difficulty, a few scholars propose to simplify the overmodulation II region, but the output voltage jumps. And the Dong-Choon Lee and the like obtain a functional relation between the amplitude of a phase voltage fundamental wave and a control angle according to Fourier expansion, obtain a crossing angle and a holding angle corresponding to different overmodulation coefficients by combining the relation between the voltage amplitude and the overmodulation coefficients, perform piecewise linear processing on the crossing angle and the holding angle, and facilitate calculation and digital realization.
At present, SVPWM overmodulation algorithms proposed by scholars at home and abroad are mainly optimized from the aspects of simplifying calculation, improving control precision, reducing harmonic waves and the like, and are almost all realized in MCU or DSP, wherein a dual-mode overmodulation strategy is adopted and improved by numerous scholars due to superior comprehensive performance.
Disclosure of Invention
In view of the problems in the prior art, the invention provides an SVPWM overmodulation system based on FPGA, which comprises: 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 module is represented by VαAnd VβAs input signal, processing and outputting to the amplitude phase angle calculation module, and outputting reference voltage vector V by the amplitude phase angle calculation modulerefAnd a phase angle θ;
calculating, by the sum over-modulation factor calculation module, the reference voltage vector VrefCalculating overmodulationA coefficient m;
the overmodulation I region calculation module calculates a voltage vector amplitude V according to the overmodulation coefficient mmCalculating 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)
Figure BDA0002607714870000031
To obtain
Figure BDA0002607714870000032
And
Figure BDA0002607714870000033
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 mmAnd a holding angle alphahCombined with said initial angle theta0Obtaining the amplitude V of the output voltage vectoroutAnd phase angle thetaoutThen the cosine calculating module calculates cos thetaoutAnd sin θoutAnd then the voltage component calculating module calculates the voltage component according to the formula (2)
Figure BDA0002607714870000034
To obtain
Figure BDA0002607714870000035
And
Figure BDA0002607714870000036
finally, the output of the output processing module is obtained by the formula (1)
Figure BDA0002607714870000037
And
Figure BDA0002607714870000038
or is obtained from the formula (2)
Figure BDA0002607714870000039
And
Figure BDA00026077148700000310
as an input voltage for the motor inverter.
Preferably, the overmodulation region i calculation module calculates the voltage vector magnitude V by looking up a table according to the overmodulation coefficient mm。
Preferably, the overmodulation region ii calculation module calculates the voltage vector magnitude V by looking up a table according to the overmodulation coefficient mmAnd a holding angle alphah。
Preferably, the magnitude V of the output voltage vectoroutObtained from the following equation:
Figure BDA00026077148700000311
preferably, the phase angle θ of the output voltage vectoroutObtained from the following equation:
Figure BDA00026077148700000312
wherein, the relative angle delta theta of the reference voltage vector in the sector is theta-theta0。
The invention also provides a method for overmodulation according to the SVPWM overmodulation system based on the FPGA, which comprises the following steps:
step 1): according to an input signal VαAnd VβThe computing module outputs a reference voltage vector VrefAnd a phase angle θ;
step 2): according to the reference voltage vector VrefCalculating an overmodulation coefficient m;
step 3): according to the reference voltage vector VrefOr 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 mmThen combining the reference voltage phase angle theta according to the formula
Figure BDA0002607714870000041
To obtain
Figure BDA0002607714870000042
And
Figure BDA0002607714870000043
when the overmodulation region is an overmodulation II region, acquiring an initial angle theta of a sector where a reference voltage vector is located0Calculating the voltage vector magnitude V according to the over-modulation coefficient mmAnd a holding angle alphahCombined with said initial angle theta0Obtaining the amplitude V of the output voltage vectoroutAnd phase angle thetaoutAccording to the formula
Figure BDA0002607714870000044
To obtain
Figure BDA0002607714870000045
And
Figure BDA0002607714870000046
step 5): output of
Figure BDA0002607714870000047
And
Figure BDA0002607714870000048
as an input voltage for the motor inverter.
Compared with the prior art, the invention at least has the following beneficial effects:
1) the SVPWM overmodulation method is improved, the calculation process is simplified, and the SVPWM overmodulation method is convenient to realize in an FPGA;
2) the voltage vector amplitude needs to be corrected in the overmodulation I area, the output voltage vector amplitude is obtained by directly looking up a table according to the overmodulation coefficient, and the calculation of a crossing angle and the correction amplitude is avoided.
3) Overmodulation II area needs to correct the voltage vector amplitude and phase angle, and the table look-up method is also adopted to simplify the calculation process. The designed amplitude phase angle correction process does not relate to division and trigonometric function operation any more, so that the consumption of a large amount of resources is avoided, and the precision can be ensured to be basically consistent with that before simplification.
Drawings
FIG. 1 is a prior art sectional view of a China linear modulation region and an over-modulation region;
FIG. 2 is a block diagram of a modulation region partition for an overmodulation block according to the present invention;
FIG. 3 is a schematic diagram of the operation of the overmodulation module of the present invention;
FIG. 4 is a plot of the overmodulation region I modified voltage vector trajectory of the present invention;
FIG. 5 is a cross angle α of the present inventionrA graph relating to an overmodulation factor m;
FIG. 6 is a vector magnitude V of the output voltage of the overmodulation region I of the present inventionmA graph relating to an overmodulation factor m;
FIG. 7 is a flow chart of the overmodulation region I of the present invention;
FIG. 8 is a plot of the overmodulation region II modified voltage vector trajectory of the present invention;
FIG. 9 is a hold angle α of the present inventionhA graph relating to an overmodulation factor m;
FIG. 10 is a plot of the overmodulation region II modified voltage vector magnitude VmA graph relating to an overmodulation factor m;
FIG. 11 is a flow chart of overmodulation region II of the present invention;
FIG. 12 is a block diagram of an overmodulation module according to the present invention.
The present invention is described in further detail below. The following examples are merely illustrative of the present invention and do not represent or limit the scope of the claims, which are defined by the claims.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
The technical scheme of the invention is further explained by the specific implementation mode in combination with the attached drawings.
When three-phase balanced sinusoidal voltage is added to the motor, the motor stator flux linkage vector can rotate at a constant amplitude and an angular speed, and the motion trail at the tail end of the flux linkage vector is circular. Since the stator resultant voltage vector always remains orthogonal to the flux linkage vector, the voltage vector rotates synchronously with the flux linkage vector. The SVPWM modulation technology is to indirectly control the rotating magnetic field of the motor stator by controlling the motion track of the voltage vector.
The essence of the SVPWM modulation technique is to control the period TPWMThe internal reference voltage vector is equivalently synthesized by two basic voltage vectors and a zero vector, and the corresponding action time is t1、t2And t0And satisfy t1+t2+t0＝TPWM。
As shown in FIG. 1, when the magnitude of the reference voltage vector is smaller than the radius of the inscribed circle of the regular hexagon, there is always t1+t2＜TPWMThe actual output voltage vector track and the reference voltage vector are kept consistent and are both circular, and the area is called a linear modulation area. Gradually increasing the vector amplitude of the reference voltage, and when the vector amplitude exceeds the radius of the inscribed circle, t can appear on the part exceeding the regular hexagon by adopting a linear modulation mode1+t2＞TPWMResult in t0Less than 0, which is physically unreasonable. This region cannot continue to use linear modulation and requires an overmodulation algorithm to re-program the output voltage vector trajectory, and is therefore referred to as an overmodulation region.
To determine the modulation region, an overmodulation coefficient is defined as:
Figure BDA0002607714870000061
the modulation factor increases along with the gradual increase of the amplitude of the reference voltage vector, and the modulation depth gradually enters an overmodulation region from a linear modulation region along with the deepening.
(1) Region i is overmodulation. Due to physical constraints, the portion of the reference voltage vector that exceeds the boundary of the regular hexagon may be constrained on the boundary of the regular hexagon, resulting in a loss of voltage. The voltage compensation is carried out by adopting a strategy of not changing the voltage phase and only increasing the voltage amplitude near the basic voltage vector, wherein the corrected voltage amplitude is equal to the reference angle alpharIt is related.
2) Overmodulation region ii. Compensating for the voltage loss by holding the voltage vector at the basic voltage vector when the reference voltage vector is in the vicinity of the basic voltage vector, wherein the time of holding is via a holding angle alphahAnd (4) determining.
Example 1
The overmodulation calculation module provided by the invention pre-corrects the reference voltage before SVPWM modulation, and other modules in the original system do not need to be modified by introducing the overmodulation module, so that the overmodulation calculation module is convenient to verify and transplant. In practical engineering, the SVPWM modulation module needs t to output1And t2Performing clipping processing, i.e. when t1+t2＞TPWMWhen, will t1And t2Carrying out equal-scale reduction according to the following formula;
Figure BDA0002607714870000062
it is possible to realize that the portion of the reference voltage vector that exceeds the regular hexagon is limited to the regular hexagon. Therefore, the over-modulation module does not need to perform limit calculation when the voltage amplitude exceeds the boundary of the regular hexagon, only needs to directly output the corrected voltage vector, and can avoid unnecessary calculation.
The reference voltage vector amplitude of the whole modulation region is 0-2VdcAnd/3, dividing the whole modulation region into a linear modulation region, an overmodulation I region and an overmodulation II region according to the overmodulation coefficient m, as shown in FIG. 2.
FIG. 3 is a schematic diagram of the operation of the overmodulation calculation module according to the present invention, first based on the reference voltage vector component VαAnd VβCalculating the voltage amplitude VrefAnd calculating an overmodulation coefficient m according to the amplitude, determining the region by the overmodulation coefficient m and adopting corresponding algorithm processing. The linear modulation region does not need to be corrected and is directly output; the overmodulation I area needs to increase a voltage vector amplitude value to compensate voltage loss, and a phase angle keeps following; overmodulation region ii requires modification of the magnitude and phase angle of the voltage vector. Finally calculating and outputting the corrected voltage vector component
Figure BDA0002607714870000071
And
Figure BDA0002607714870000072
as overmodulation correction amplitude phase angle relates to more operations such as division, trigonometric function and the like, and a large amount of resources are consumed for realizing the operations in the FPGA, the algorithm of an overmodulation region I and a overmodulation region II needs to be designed, some calculation processes in the overmodulation region I and the overmodulation region II are simplified and integrated as much as possible within a precision range, and a large amount of resources are prevented from being consumed by excessive complex calculation. The whole overmodulation module comprises addition and subtraction and multiplication which can be directly realized, and also relates to operations which cannot be directly realized, such as square-open square-root amplitude calculation, arc tangent phase calculation, sine and cosine voltage calculation and the like. The following analyses the computation scheme of various operations in an FPGA:
(1) the square root amplitude calculation can be realized by a multiplier and a square IP core in Quartus II software, wherein the square of two voltage components needs to consume 4 18 × 18 multipliers, and the square IP core needs to consume some basic logic units. The CORDIC algorithm can solve the amplitude of the vector through iteration, and the iteration process does not involve complex operation.
(2) The method for solving the phase angle through the arc tangent mainly comprises a Taylor series approximation method, a ROM table look-up method, a CORDIC algorithm and the like. The taylor series approximation requires a large number of multipliers, which is not preferred because of the tight resources of the multipliers. The arc tangent value lookup table is to pre-store the angle value in the ROM, and look up the corresponding arc tangent value by taking the ratio of the ordinate and the abscissa as an input address. The angle values of the four quadrants can be calculated through preprocessing, the table lookup method is simple and easy to implement, and the operation precision of the table lookup method is limited by resources. The CORDIC algorithm can calculate the phase angle of the vector by calculating the arc tangent, and can output the magnitude and the phase angle of the vector simultaneously through a round of iterative operation.
(3) The method for calculating the sine and cosine values of the angles mainly comprises a table look-up method and a CORDIC algorithm. The table look-up method is to store the sine and cosine values in the FPGA, take the angle value as the input address of the look-up table, and look up and output the sine and cosine values of the angle. The CORDIC algorithm may calculate the sine and cosine values simultaneously in one iteration.
Since the CORDIC has the advantages of high algorithm precision, high operation speed and capability of simultaneously solving various trigonometric function operations, the CORDIC algorithm is adopted to realize the calculation of the amplitude phase angle and the sine and cosine.
The overmodulation module of the present invention is divided into 9 sub-modules: the system comprises an input processing module, an amplitude phase angle calculation module, an overmodulation coefficient calculation module, an overmodulation I region algorithm module, an overmodulation II region algorithm module, an output correction amplitude phase angle module, a sine and cosine calculation module, a voltage component calculation module and an output processing module. Overmodulation module with VαAnd VβAs input, modified by overmodulation algorithm and output
Figure BDA0002607714870000081
And
Figure BDA0002607714870000082
the relationship between the various sub-modules is shown in FIG. 12.
Wherein the amplitude phase angle calculation module calculates the amplitude from:
Figure BDA0002607714870000083
the phase angle is calculated from:
Figure BDA0002607714870000084
the overmodulation coefficient calculation module calculates an overmodulation coefficient by:
Figure BDA0002607714870000085
how the overmodulation i region and the overmodulation ii region simplify the process of correcting the phase angle of the reference voltage vector magnitude according to the equal area method and how the trigonometric function is calculated based on CORDIC will be analyzed below.
The overmodulation region i algorithm module calculates the amplitude from:
the overmodulation I area starts from the inscribed circle of the regular hexagon, and in order to make the output still track the reference voltage, the strategy for correcting the reference voltage vector is to increase the voltage amplitude, the phase angle is kept constant, and then the reference voltage vector amplitude is increased to VmObtaining an output voltage vector, wherein the output voltage vector track intersects with the regular hexagon at a cross angle alphar. After the correction by the overmodulation I region algorithm, the radius of the output voltage vector locus circle is Vm. Due to the amplitude limiting effect of the SVPWM modulation module, the actual running track is partially on a regular hexagon and partially on a circle. Wherein the vector magnitude V of the output voltagemAngle of intersection alpharThe relationship of (1) is:
Figure BDA0002607714870000091
the key of the overmodulation I region algorithm is how to depend on the vector magnitude V of the reference voltagerefDetermining an output voltage vector magnitude VmThe size of (2). According to the volt-second balance principle, the average value of the output voltage vector in unit time is the same as the reference voltage vector, and the output voltage vector and the reference voltage vector rotate at the same speed, so that the area swept by the rotation of the output voltage vector is equal to the area swept by the rotation of the reference voltage vector. Therefore, the overmodulation I region compensates for the missing voltage by increasing the voltage amplitude, and switches to geometry to ensure that the area of the missing voltage pattern is equal to the area of the compensated voltage pattern. As shown in fig. 4, the missing voltage is composed of six portions where the reference voltage vector locus exceeds the regular hexagon, and the compensation voltage includes six portions where the output voltage vector locus is surrounded by the regular hexagon and the reference voltage vector locus near the vertex.
According to the equal area method, the area enclosed by one rotation of the reference voltage vector is equal to the area enclosed by the actual output voltage vector track, and the following equation is provided:
Figure BDA0002607714870000092
the area enclosed by the actual output voltage vector locus can be divided into six sectors and six triangles. Bonding of
Equation 2.2, obtaining the overmodulation coefficient m and the crossing angle alpharThe relationship of (1) is:
Figure BDA0002607714870000093
wherein the crossing angle alpharIs in the range of 0 to pi/6. When the vector amplitude of the reference voltage is the radius of the inscribed circle of the regular hexagon, the reference voltage begins to enter an overmodulation I area, and the crossing angle alpha is at the momentrPi/6, the overmodulation coefficient m is about 0.9069; when the corrected output voltage vector locus is a regular hexagon circumcircle, compensation can not be carried out through the vertex, and the overmodulation II area is started, so that the crossing angle alpha of the upper limit of the overmodulation I arearAt 0, the overmodulation coefficient m is about 0.9523. Since equation 3.3 is non-linear, the intersection angle α cannot be directly calculated on the chip using this equationrThe graph image of the graph is drawn by MATLAB as shown in FIG. 5.
Theoretically, linear fitting or offline point-taking processing can be performed on the curve, and then the crossing angle alpha can be obtained through overmodulation coefficient m calculation or table lookuprThen the cross angle is taken into 3.1 to calculate the output voltage vector amplitude VmThis implementation is usually applied in MCU or DSP. Since cosine and division operations are involved in equation 3.1, calculating this equation in FPGA is relatively complex and consumes much resources. And V in formula 3.1dcThe voltage of the direct current bus can be regarded as a constant after per unit processing when engineering is realized, and V can be firstly regarded asdcSeen as 1. Therefore, the overmodulation coefficient m and the output voltage amplitude V can be directly plotted by MATLAB in combination with equations 3.1 and 3.3mFIG. 6 shows the relationship of (A). Since the piecewise linear fitting needs to consume a multiplier, the mode of taking points off line and storing the points in a chip for table lookup is more beneficial to implementation and resource utilization in the FPGA. The text can be directly checked in FPGA by taking points on the curve with a certain precision and using a table look-up methodObtaining the amplitude V of the output voltage vector by looking up the table through the over-modulation coefficient mm. Thus, the accuracy of calculating the amplitude of the output voltage by looking up the table and then carrying out formula 3.1 is consistent, but the complex calculation and resource consumption of formula 3.1 are avoided.
Since the overmodulation I region does not change the phase angle, the vector of the output voltage is directly decomposed to obtain the corrected voltage
Figure BDA0002607714870000101
And
Figure BDA0002607714870000102
comprises the following steps:
Figure BDA0002607714870000103
overmodulation region II algorithm module
The overmodulation region I algorithm flow is shown in FIG. 7, where two components V of the reference voltage vectorαAnd VβAs input, after the voltage amplitude is corrected by a table look-up method, two corrected voltage components are output
Figure BDA0002607714870000104
And
Figure BDA0002607714870000105
the calculation which is difficult to be directly realized in the whole algorithm process comprises the calculation of the amplitude phase angle of the reference voltage loss and the calculation of sine and cosine in the formula 3.4, which are inevitable. The process of implementing the overmodulation algorithm in a DSP usually calculates an overmodulation coefficient from a reference voltage amplitude, then determines a crossing angle from the overmodulation coefficient, and finally calculates an output voltage amplitude from the crossing angle. The overmodulation I region algorithm designed based on the FPGA simplifies the process of calculating the amplitude of the output voltage, and the amplitude of the output voltage is directly obtained by looking up a table according to an overmodulation coefficient. The algorithm avoids the calculation of the crossing angle and the output voltage amplitude, greatly simplifies the calculation and saves resources, can ensure the calculation precision, and is more beneficial to realizing in an FPGA。
The upper limit of the overmodulation I area is that when the output voltage vector locus is a circumscribed circle of a regular hexagon, the actual running locus is completely on the regular hexagon. If the reference voltage amplitude V is continuously increasedrefAnd starts to enter overmodulation region ii. The correction strategy of the overmodulation II area is to keep the output voltage vector at the basic voltage vector for a period of time and then jump and follow the reference voltage vector to synchronously rotate. The time kept in the basic voltage vector corresponds to the rotation angle of the reference voltage vector in the space being the keeping angle alphahFrom equation 2.18, the magnitude of the correction voltage vector at the hold angle is VmOutput voltage vector and correction voltage vector magnitude VmAnd a holding angle alphahIt is related.
For example, with 3 sectors, the output voltage vector trace for overmodulation region II is analyzed as shown in FIG. 8 when the reference voltage vector is rotated to 0 to αhThe output voltage vector is always the basic voltage vector V1(ii) a When the reference voltage vector rotates to the protection alphahTo pi/3-alphahWhile the output voltage vector is along the modified voltage vector locus circle VmFrom alphahSynchronously rotate to pi/3-alphah(ii) a When the reference voltage vector rotates to pi/3-alphahWhen the voltage reaches pi/3, the output voltage vector is always the basic voltage vector V2. Wherein the output voltage vector follows a modified voltage vector locus circle VmDuring rotation, due to the amplitude limiting effect of the SVPWM module, the actual output voltage vector track can automatically move along the regular hexagon boundary, and amplitude limiting calculation is not needed.
Also according to the equal area method, the geometric area enclosed by the vector converted into the reference voltage and the actual output voltage track is equal, and the following equation exists:
Figure BDA0002607714870000111
when the output in the holding angle is the basic voltage vector, the area of the output is equivalent to the area enclosed by the rotation of the basic voltage vector and the holding angle. Combining formula 2.2, obtaining overmodulation coefficient m and holding angle alphahThe relationship of (1) is:
Figure BDA0002607714870000112
wherein the angle of holding alphahIs in the range of 0 to pi/6. When entering an overmodulation II area, the holding angle is 0, the overmodulation coefficient is 0.9523, and the output voltage vector locus is a circumscribed circle of a regular hexagon; and when the upper limit of the overmodulation II region is in an upper limit, the holding angle is pi/6, the overmodulation coefficient is 1.0472, and the output voltage vector locus has six vertexes, namely six basic voltage vectors jump. Mapping overmodulation coefficient m and holding angle alpha by MATLABhThe relationship of (2) is shown in FIG. 9.
Drawing an overmodulation coefficient m and a corrected voltage vector amplitude V through MATLAB according to an equation 2.2 and an equation 3.6mThe relationship of (2) is shown in FIG. 10. By taking points on the curve with a certain precision and using a table look-up method, the holding angle alpha can be directly obtained by looking up the table by the overmodulation coefficient mhAnd the magnitude V of the correction voltage vectormAnd the complex calculation and resource consumption are avoided.
The amplitude and phase angle of overmodulation region II need to be corrected simultaneously, and the holding angle alpha is obtained by looking up the tablehAnd the magnitude V of the correction voltage vectormThen, the amplitude V of the output voltage vector can be calculated according to the sector where the reference voltage vector is locatedoutAnd phase angle thetaout. According to the space voltage vector diagram, the initial angle theta of the sector where the reference voltage vector is located0Comprises the following steps:
Figure BDA0002607714870000121
the relative angle of the reference voltage vector within the sector is:
Δθ＝θ-θ0(3.8)
keeping the voltage vector on the basic voltage vector within the holding angle, namely, the voltage amplitude and the phase angle are fixed; beyond the holding angle, the amplitude is the vector amplitude V of the correction voltagemThe phase angle follows the same. Therefore, the amplitude V of the output voltage vector is obtained by analyzing the relation between the relative angle delta theta and the holding angleoutSize:
Figure BDA0002607714870000122
the phase angle theta can be obtained as welloutComprises the following steps:
Figure BDA0002607714870000123
amplitude V of the output voltage vector to be corrected as welloutAnd phase angle thetaoutBy decomposition, obtaining an output
Figure BDA0002607714870000124
And
Figure BDA0002607714870000131
Figure BDA0002607714870000132
the flow chart for calculating overmodulation II region is shown in FIG. 11, with reference to the voltage vector component VαAnd VβAfter correcting the voltage amplitude phase angle by an algorithm for inputting, outputting a voltage component
Figure RE-GDA0002660783900000134
And
Figure RE-GDA0002660783900000135
the whole algorithm flow does not need to calculate the amplitude phase angle of the reference voltage vector and calculate the voltage component, and the intermediate process does not relate to operations such as division, trigonometric function and the like, only relates to addition and subtraction, comparison and multiplication, and is convenient to realize in the FPGA.
And finally, jumping completely on six basic voltage vectors along with the deepening of the modulation depth, and outputting a six-beat step wave state. Because the output voltage vector of the overmodulation II area is kept at the basic voltage vector for a certain time and then jumps and follows, the amplitude and the phase angle cannot follow the reference voltage vector, and certain torque pulsation can be caused. The overmodulation region ii cannot achieve complete phase angle following, but can maximize the voltage amplitude.
The overmodulation region i output voltage vector ranges from a regular hexagonal inscribed circle to a circumscribed circle, and the overmodulation region ii modified voltage vector ranges from a regular hexagonal circumscribed circle to an inscribed circle. Because the output voltage vector of the upper limit of the overmodulation region I and the correction voltage vector which just enters the overmodulation region II are both regular hexagon circumscribed circles, the algorithm can realize smooth transition from the region I to the region II. Through the design of overmodulation I and II regions, trigonometric function and division operation in a modified voltage amplitude phase angle are avoided, but calculation of a reference voltage vector amplitude phase angle and a voltage component cannot be avoided, and the trigonometric function operation is realized through a CORDIC algorithm.
The preferred embodiments of the present invention have been described in detail, however, the present invention is not limited to the specific details of the above embodiments, and various simple modifications may be made to the technical solution of the present invention within the technical idea of the present invention, and these simple modifications are within the protective scope of the present invention.
It should be noted that the technical features described in the above embodiments can be combined in any suitable manner without contradiction, and various possible combinations of the features are not described in order to avoid unnecessary repetition.
In addition, any combination of the various embodiments of the present invention is also possible, and the same should be considered as the disclosure of the present invention as long as it does not depart from the spirit of 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 VαAnd a vertical signal VβAs 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 modulerefAnd 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 VrefCalculating 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 mmCalculating 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)
Figure FDA0002607714860000011
To obtain
Figure FDA0002607714860000012
And
Figure FDA0002607714860000013
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 mmAnd a holding angle alphahCombined with said initial angle theta0Obtaining the amplitude V of the output voltage vectoroutAnd phase angle thetaoutThen the cos theta is calculated by the sine and cosine calculation moduleoutAnd sin θoutAnd then the voltage component calculating module calculates the voltage component according to the formula (2)
Figure FDA0002607714860000014
To obtain
Figure FDA0002607714860000015
And
Figure FDA0002607714860000016
finally, the output of the output processing module is obtained by the formula (1)
Figure FDA0002607714860000017
And
Figure FDA0002607714860000018
or is obtained from the formula (2)
Figure FDA0002607714860000019
And
Figure FDA00026077148600000110
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 mm。
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 mmAnd a holding angle alphah。
4. The overmodulation system according to claim 1, wherein: magnitude V of the output voltage vectoroutObtained from the following equation:
Figure FDA0002607714860000021
wherein VdcIs the dc bus voltage.
5. The overmodulation system according to claim 1The system is characterized in that: phase angle theta of the output voltage vectoroutObtained from the following equation:
Figure FDA0002607714860000022
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 VαAnd VβThe computing module outputs a reference voltage vector VrefAnd a phase angle θ;
step 2): according to the reference voltage vector VrefCalculating an overmodulation coefficient m;
step 3): according to the reference voltage vector VrefOr 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 mmThen combining the reference voltage phase angle theta according to the formula
Figure FDA0002607714860000023
To obtain
Figure FDA0002607714860000024
And
Figure FDA0002607714860000025
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 mmAnd a holding angle alphahCombined with said initial angle theta0Obtaining the amplitude V of the output voltage vectoroutAnd phase angle thetaoutAccording to the formula
Figure FDA0002607714860000031
To obtain
Figure FDA0002607714860000032
And
Figure FDA0002607714860000033
step 5): output of
Figure FDA0002607714860000034
And
Figure FDA0002607714860000035
as an input voltage for the motor inverter.
CN202010744011.6A 2020-07-29 2020-07-29 FPGA-based SVPWM overmodulation system and method Pending CN111800051A (en)

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