CN100433536C - Voltage space vector-based modulation method - Google Patents

Abstract

The invention relates to a modulation method based on a voltage space vector, belonging to a vector modulation scheme in the field of AC frequency conversion. This method uses a two-phase 120° coordinate system, uses the corresponding relationship between the three-phase bridge arm voltage and the reference voltage vector, and directly solves the action time of the three-phase bridge arm voltage through a certain vector algorithm, and finally obtains the control signals of each switch tube . The digital implementation of this method is simple, and its versatility and real-time performance are greatly improved compared with the traditional SVPWM, and it has practical value for AC frequency conversion systems.

Description

Modulation Method Based on Voltage Space Vector

1. Technical field

The invention relates to a vector modulation method in the field of AC frequency conversion

2. Background technology

Voltage space vector pulse width modulation (SVPWM) and sinusoidal pulse width modulation (SPWM) are the two most commonly used modulation methods in three-phase inverter circuits. In the field of variable frequency speed regulation, SVPWM regards the inverter and the motor as a whole, so that a rotating magnetic field with a constant amplitude is generated in the motor. This modulation method synthesizes the output voltage of the three-phase inverter into a voltage space vector on the complex plane, and approaches the command voltage space vector through different switch vector combinations. Compared with SPWM, the switching times of the switching device can be reduced by 1/3, the utilization rate of DC voltage can be increased by 15%, and it can obtain better harmonic suppression effect, fast response, less harmonic content, and DC voltage Features such as high utilization rate.

However, the traditional implementation of SVPWM is complex and must be implemented with a high-speed processor. Scholars at home and abroad have proposed many simplified methods for the digital realization of this modulation method, mainly including simplifying the sector judgment rule, using addition and subtraction operations to replace part of multiplication operations, etc. But the essence of these methods is to judge the sector first, and then use the vector of each sector to synthesize. Although there is a certain simplification, the overall structure of the program is still composed of a large number of branch programs, and the modulation algorithm of each sector has no uniform rules to follow.

How to simplify its digital implementation while adopting SVPWM is a hot spot of current research. There are few effective solutions at home and abroad, and the implementation scheme is still relatively cumbersome, and the versatility and real-time performance of the program are poor.

3. Contents of the invention

The purpose of the present invention is to propose a new type of SVPWM implementation scheme, and fundamentally simplify its implementation form, replace the concept of sectors in traditional SVPWM with a unified expression, this scheme greatly reduces the amount of calculation of the program, and Very easy to implement digitally. This implementation is characterized by:

1, a kind of modulation method based on voltage space vector, it is characterized in that:

① Use the combination of three-phase bridge arm voltages to directly synthesize the reference voltage vector, and its synthesis relationship should satisfy:

T _PWM U _ref =T _a U _a +T _b U _b +T _c U _c (1)

In the formula, T _PWM is the carrier cycle, U _ref is the reference voltage vector; U _a , U _b , U _c are the three-phase phase voltages; T _a , T _b , T _c are the functions of U _a , U _b , U _c respectively Time, that is, directly use the above-mentioned synthesis relation (1) of the three-phase bridge arm voltage to the reference voltage vector, directly solve the action time of the three-phase bridge arm voltage through the algorithm, and obtain the control signals of each switch tube;

②The composition of the new two-phase 120° coordinate system:

In the conventional three-phase coordinate system, the difference between the axes is 120°, choose any two-phase axis in the conventional three-phase coordinate system to coincide with the axis of the new two-phase 120° coordinate system, and the third phase in the conventional three-phase coordinate system The axis is projected onto the coordinate axis of the new two-phase 120° coordinate system according to the geometric relationship. The axes of the new two-phase 120° coordinate system are represented by axes m and n, and the axes A and B of the conventional three-phase coordinate system are selected to coincide with the axes m and n of the new two-phase 120° coordinate system, so that the reference voltage vector is in the new two-phase coordinate system The decomposition under the coordinate axis of the phase 120° coordinate system is deterministic, and the composite relationship under the new two-phase 120° coordinate system is:

T _PWM U _ref =T _m U _m +T _n U _n (2)

According to the sine law, the projection formula of the reference voltage vector in the new two-phase 120° coordinate system is:

The transformation relationship from the conventional three-phase coordinate system to the new two-phase 120° coordinate system is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the above formula, U _a , U _b , U _c are three-phase phase voltages; T _a , T _b , T _c correspond to the action time of U _a , U _b , U _c respectively; U _m , U _n are three-phase phase voltages In the projection under the new two-phase 120° coordinate system, T _m , T _n correspond to U _m , U _n action time respectively; θ is the angle between U _ref and m-axis, other symbols: T _PWM , U _ref and the above formula ( The definitions in 1) are the same, thus, through the above transformation, the solution to the above formula (1) is transformed into the solution to the above formula (3) and formula (4), and the three-phase voltage action time T a obtained by the solution _is , T _b and T _c respectively correspond to the switching time of the three-phase bridge arms;

③Setting of additional conditions

In order to make the above formula (4) not only have a solution, but its solution must meet the requirements of engineering realization, so the implicit additional condition of the formula (4) is:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Since T _a , T _b , and T _c are all greater than or equal to zero, additional conditions can be set:

Min(T _a , T _b , T _c )=0 (6)

Substituting this additional condition (6) into the above formula (4), the final solution formula is obtained:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\\ \mathrm{<span\; class="notranslate">\; Min</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

4. Description of drawings

Fig. 1 Synthesis of conventional three-phase coordinate system.

Fig. 2 Uncertainty of conventional three-phase coordinate system decomposition, where Fig. 2(a) is the projection of reference voltage vector U _ref on axes U _a , U _b , U _c , Fig. 2(b) is the reference voltage vector U _ref at Projection on axes U _a , U _b .

Figure 3 is a schematic diagram of the transformation from the conventional three-phase coordinate system to the new two-phase 120° coordinate system.

Figure 4 software implementation flow chart.

Fig. 5 is a flowchart for solving equation group (7).

Figure 6 Modulation waveforms of the two algorithms.

Figure 7 Execution time of the two algorithms.

5. Specific implementation

5.1 Synthesis of new space vector modulation

In a three-phase full-bridge inverter, the space vector pulse width modulation algorithm needs to solve the switching signals of the three bridge arms. The eight basic voltage vectors of the traditional modulation algorithm are actually intermediate quantities introduced for the convenience of calculation. The new space vector modulation algorithm proposed in this paper does not need to solve the action time of the eight basic voltage vectors as intermediate quantities, and directly uses the corresponding switch states of the three-phase bridge arms to synthesize the reference voltage vector, which greatly simplifies the vector modulation algorithm.

In the voltage vector space, the three-phase bridge arm voltages U _a , U _b , and U _c of the inverter are spaced exactly 120° apart, as shown in Figure 1. The reference voltage vector can be synthesized directly by using the combination of three-phase bridge arm voltages, and the synthesis relationship satisfies:

T _PWM U _ref =T _a U _a +T _b U _b +T _c U _c (1)

Where U _ref is the reference voltage vector; T _a , T _b , T _c are the action time of U _a , U _b , U _c respectively; T _PWM is the carrier period.

The essence of the present invention is to directly use the synthesis relation (1) of the three-phase bridge arm voltage to the reference voltage vector, and directly solve the action time of the three-phase bridge arm voltage through a certain algorithm to obtain the control signals of each switch tube. The key to the realization of this method is to use a special new two-phase 120° coordinate system defined in this paper, and to perform vector operations in it, thus simplifying the solution process of the modulation algorithm.

5.2 Construction of a new two-phase 120° coordinate system

According to the linear equation solving theory, the number of equations in formula (1) is less than the number of unknowns (Ta, Tb and Tc), and the linear equation has no unique solution. The non-uniqueness of the solution is reflected in the vector diagram, that is, the projection method of the reference voltage vector U _ref to the three coordinate axes is not unique, as shown in FIG. 2 .

In order to obtain the unique projection method of U _ref to the three coordinate axes, a special two-phase 120° coordinate system is defined in this paper. As shown in Figure 3. In the conventional three-phase coordinate system, the difference between the axes is 120°, choose any two-phase axis in the conventional three-phase coordinate system to coincide with the axis of the new two-phase 120° coordinate system, and the third phase in the conventional three-phase coordinate system The axis is projected onto the coordinate axis of the new two-phase 120° coordinate system according to the geometric relationship. The axes of the new two-phase 120° coordinate system are represented by axes m and n, and the axes A and B of the conventional three-phase coordinate system are selected to coincide with the axes m and n of the new two-phase 120° coordinate system, as shown in Figure 3.

Since the coordinate system changes from three-phase to two-phase, the decomposition of the reference voltage vector in the new two-phase 120° coordinate system is deterministic, and the resultant relationship in the new two-phase 120° coordinate system is:

T _pwm U _ref =T _m U _m +T _n U _n (2)

According to the sine law, the projection formula of the reference voltage vector in the new two-phase 120° coordinate system is:

In the formula, T _m and T _n correspond to the action time of U _m and U _n respectively; U _m and U _n are the projections of the three-phase phase voltage on the new two-phase 120° coordinate; θ is the angle between U _ref and the m axis.

The transformation relationship from the conventional three-phase coordinate system to the new two-phase 120° coordinate system is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them T _a , T _b , T _c correspond to the action time of U _a , U _b , U _c respectively; U _a , U _b , U _c are three-phase phase voltages.

After the above transformation, the solution to formula (1) can be transformed into the solution to the two formulas (3) and (4). First solve the coordinate axis components in the new two-phase 120° coordinate system through formula (3), and then substitute into equation group (4) to solve. The obtained three-phase voltage action times T _a , T _b , and T _c respectively correspond to the switching times of the three-phase bridge arms.

5.3 Setting of additional conditions

According to the existing known conditions, the equation group (4) not only must have a solution, but its solution must also meet the requirements of engineering realization, so an implicit additional condition can be obtained:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

However, when the solution of equation group (4) is required, further restrictions on equation (5) are required. Because the solutions of equations (4) satisfying the implicit additional condition (5) are all reasonable. According to the form of equation group (4), if one of the items is 0, the solution will be the simplest. Since T _a , T _b , and T _c are all greater than or equal to 0, additional conditions can be set:

Min(T _a , T _b , T _c )=0 (6)

When solving the values of T _a , T _b , and T _c in the formula, it is only necessary to judge the signs of T _m and T _n . Substituting the additional conditions into the equation group (4), the solution formula is finally obtained:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\\ \mathrm{<span\; class="notranslate">\; Min</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

It can be seen from the above formula that, compared with the traditional SVPWM, the equation group (7) replaces the concept of the sector. The solution rule is consistent in the whole coordinate space, and the expression is extremely simple, which is easy to implement digitally. Its main software flowchart is shown in Fig. 4, 5.

5.4 Experimental verification

The experiment is verified by 2407A DSP of TI Company, and the scheme proposed by the present invention and the traditional SVPWM are implemented in the same timer interrupt, and the modulated wave is output through D/A, as shown in Figure 6, wherein CH1 is the traditional SVPWM The voltage modulation waveform below is the voltage modulation waveform under the new algorithm, and CH2 is the voltage modulation waveform under the new algorithm.

Compared with the traditional algorithm, the new algorithm is not only simpler in software implementation, but also has improved real-time performance. Figure 7 compares the execution time of the two algorithms. Set two different I/O% ports to calculate the execution time of the two algorithms. When the algorithm program starts to be executed, the I/O level is pulled down to complete the execution program. When the I/O level is pulled high, the respective execution times of the two algorithms are detected. CH1 is the execution time of the traditional algorithm, which is about 20.2us, and CH1 is the execution time of the new algorithm, which is about 17.8us. Comparing the two, the operation time of the new algorithm is reduced by 11.9%.

Claims (1)

1, a kind of modulator approach based on space vector of voltage is characterized in that:

1. utilize the direct synthesized reference voltage vector of combination of three-phase bridge arm voltage, its compositive relation should satisfy:

T _PWMU _ref＝T _aU _a+T _bU _b+T _cU _c (1)

T in the formula _PWMBe carrier cycle, U _RefBe reference voltage vector; U _a, U _b, U _cBe respectively three-phase phase voltage; T _a, T _b, T _cBe respectively U _a, U _b, U _cAction time, promptly directly utilize the above-mentioned compositive relation formula (1) of three-phase bridge arm voltage to reference voltage vector, directly find the solution action time of three-phase bridge arm voltage by algorithm, obtain the control signal of each switching tube;

The formation of 120 ° of coordinate systems of 2. novel two-phase:

In conventional three phase coordinate systems, differ 120 ° between each axis, select the dead in line of any two phase axis and 120 ° of coordinate systems of novel two-phase in conventional three phase coordinate systems, third phase axis in conventional three phase coordinate systems then projects on the reference axis of 120 ° of coordinate systems of novel two-phase according to geometrical relationship, the axis of 120 ° of coordinate systems of novel two-phase is with axle m, n represents, choose the axis A of conventional three phase coordinate systems, the axis m of B and 120 ° of coordinate systems of novel two-phase, n overlaps, make the decomposition of reference voltage vector under the reference axis of 120 ° of coordinate systems of novel two-phase have certainty, the compositive relation under 120 ° of coordinate systems of then novel two-phase is:

T _PWMU _ref＝T _mU _m+T _nU _n (2)

Can get the projection formula of reference voltage vector in 120 ° of coordinate systems of novel two-phase according to sine is:

The transformation relation that is converted into 120 ° of coordinate systems of novel two-phase by conventional three phase coordinate systems is:

$\left\{\begin{array}{c}{T}_m=T_a-T_c\\ T_n=T_b-T_c\end{array}\right.---\left(4\right)$

In the above-mentioned formula, U _a, U _b, U _cBe three-phase phase voltage; T _a, T _b, T _cThe corresponding U of difference _a, U _b, U _cAction time; U _m, U _nBe the projection of three-phase phase voltage under 120 ° of coordinate systems of novel two-phase, T _m, T _nThe corresponding U of difference _m, U _nAction time; θ is U _RefWith the angle of m axle, other symbol: T _PWM, U _RefIdentical with the definition in the above-mentioned formula (1), thus,,, find the solution three-phase voltage T action time that obtains by finding the solution of above-mentioned formula (1) being converted into to the finding the solution of above-mentioned formula (3) and formula (4) by above-mentioned conversion _a, T _b, T _cJust distinguish the switching time of corresponding three-phase brachium pontis;

3. the setting of additional conditions

For above-mentioned formula (4) is not only separated, and it separate the requirement that must satisfy Project Realization, so the implicit additional conditions of this formula (4) are:

$\left\{\begin{array}{c}0\&le;T_a\&le;T_{\mathrm{PWM}}\\ 0\&le;T_b\&le;T_{\mathrm{PWM}}\\ 0\&le;T_c\&le;T_{\mathrm{PWM}}\end{array}\right.---\left(5\right)$

Because T _a, T _b, T _cAll, therefore additional conditions can be set more than or equal to zero:

Min(T _a，T _b，T _c)＝0 (6)

With the above-mentioned formula of these additional conditions (6) substitution (4), get solution formula to the end:

$\left\{\begin{array}{c}{T}_m=T_a-T_c\\ T_n=T_b-T_c\\ \mathrm{Min}(T_a,T_b,T_c)=0\end{array}\right.---\left(7\right).$

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