阅读说明：本技术 一种永磁同步电机系统过采样预测电流控制方法 (A kind of permanent magnet synchronous motor system over-sampling predictive-current control method ) 是由 王志强 杨明波 夏长亮 谢赛飞 金雪峰 张国政 于 2019-09-08 设计创作，主要内容包括：一种永磁同步电机系统过采样预测电流控制方法,包括：由控制系统在kT<Sub>s</Sub>、(k+0.25)T<Sub>s</Sub>、(k+0.5)T<Sub>s</Sub>、(k+0.75)T<Sub>s</Sub>时刻进行取样；计算电机参考电流q轴分量；在kT<Sub>s</Sub>、(k+0.5)T<Sub>s</Sub>时刻求解电机实际电流d、q轴分量；利用电机离散预测模型,得到预测电压d、q轴分量；采用不对称七段式两电平SVPWM调制策略,在kT<Sub>s</Sub>、(k+0.5)T<Sub>s</Sub>时刻计算六路PWM脉冲的占空比,在(k+0.25)T<Sub>s</Sub>、(k+0.5)T<Sub>s</Sub>、(k+0.75)T<Sub>s</Sub>、(k+1)T<Sub>s</Sub>时刻输出六路PWM脉冲作用于六桥臂逆变器,进而实际输出对应参考电压作用于电机。本发明通过两次电压电流采样,四次电机转子位置角采样并在一个载波周期内更新四次PWM占空比,有效的提升了低开关频率下系统的动态性能,且稳态无静差、震荡。(A kind of permanent magnet synchronous motor system over-sampling predictive-current control method, comprising: by control system in kT s 、(k+0.25)T s 、(k+0.5)T s 、(k+0.75)T s Moment is sampled；Calculate motor reference current q axis component；In kT s 、(k+0.5)T s Moment solves motor actual current d, q axis component；Using motor discrete predictive model, predicted voltage d, q axis component is obtained；Using two level SVPWM modulation strategy of asymmetric seven segmentation, in kT s 、(k+0.5)T s Moment calculates the duty ratio of six road pwm pulses, in (k+0.25) T s 、(k+0.5)T s 、(k+0.75)T s 、(k+1)T s Moment exports six road pwm pulses and acts on six leg inverters, and then reality output corresponds to reference voltage and acts on motor.The present invention is sampled by voltage and current twice, and four times motor rotor position angle samples and updates four PWM duty cycles in a carrier cycle, effectively improves the dynamic property of system under low switching frequency, and stable state floating, concussion.)

1. a kind of permanent magnet synchronous motor system over-sampling predictive-current control method, which comprises the following steps:

1) in kT_sMoment and (k+0.5) T_sMoment, by control system to motor ABC three-phase current, DC bus-bar voltage and motor Rotor angular rate is sampled；In kT_sMoment, (k+0.25) T_sMoment, (k+0.5) T_sMoment, (k+0.75) T_sMoment, by Control system is sampled rotor position angle, k=1, and 2,3 ...；

2) in the case where motor reference current d shafting component is zero control, motor reference current q axis is calculated by der Geschwindigkeitkreis pi regulator It is componentSpecifically:

Wherein,Respectively motor reference current d, q shafting component,For der Geschwindigkeitkreis pi regulator proportionality coefficient, For der Geschwindigkeitkreis pi regulator integral coefficient, ω^refFor speed reference, ω is rotor machinery angular speed；

3) according to motor ABC three-phase current, kT is solved_sMoment motor actual current d, q shafting component i_d(k)、i_q(k), it specifically asks Solution are as follows:

Wherein, x is 0 in the first half of each carrier cycle, latter half 0.5, i_d(k+x) and i_qIt (k+x) is respectively motor D, q shafting component of actual current, i_A(k)、i_B(k) and i_CIt (k) is the ABC three-phase current of motor, M_ABC/αβIt is quiet by ABC three-phase Only transformation matrix of the shafting to α β two-phase static axial system, M_αβ/dqFor by the transformation of α β two-phase static axial system to dq two-phase rotary axis Matrix, expression are as follows:

In formula, θ (k+x) is (k+x) T_sThe angle of moment d shafting and α shafting；

4) in kT_sMoment and (k+0.5) T_sMoment obtains the pre- of motor actual current d, q shafting component according to current forecasting model Measured value, including (k+0.25) T is predicted respectively_sMoment and (k+0.75) T_sMoment electric current d, q shafting componentWithAndWithCompensation of delay as voltage-prediction model；

5) voltage-prediction model is utilized, respectively according to kT_sMoment and (k+0.5) T_sThe rotor angular rate, the electricity at moment Machine reference current d shafting and q shafting componentWith the d shafting of motor actual current and the predicted value of q shafting component, obtain So that predicted current is in (k+1) T_sPredicted voltage d, the q shafting component of moment track reference electric currentWith In (k+1.5) T_sPredicted voltage d, the q shafting component of moment track reference electric currentWith

6) in each carrier cycle, using two level SVPWM modulator approach of asymmetric seven segmentation, four three-phase inverters are calculated PWM duty cycle T_a、T_bAnd T_c, and each calculated result is updated；In kT_sMoment judges (k-0.25) T_sMoment is counted The PWM duty cycle of calculation is in kT_sMoment is to (k+0.25) T_sThere are several intersection points between moment with triangular carrier, if number of hits is greater than 1, then kT_sThe three-phase PWM duty ratio that moment calculates is equal to (k-0.25) T_sMoment three-phase PWM duty ratio, if number of hits is equal to 1, Then according to kT_sMoment calculated reference voltage d, q shafting componentWith rotor position angle θ (k) with And in kT_sMoment is to (k+0.25) T_sMoment has a phase PWM duty cycle of intersection point with triangular carrier, recalculates other two-phases PWM duty cycle, according to kT if without intersection point_sMoment calculated reference voltage d, q shafting componentWith rotor position angle θ (k), three-phase PWM duty ratio is calculated；

In (k+0.25) T_sMoment is according to kT_sMoment calculated reference voltage d, q shafting componentWith (k+0.25)T_sThe rotor position angle θ (k+0.25) at moment calculates three-phase PWM duty ratio；

In (k+0.5) T_sMoment judges (k+0.25) T_sMoment, three-phase PWM duty ratio calculated was in (k+0.5) T_sMoment is to (k+ 0.75)T_sThere are several intersection points between moment with triangular carrier, if number of hits is greater than 1, (k+0.5) T_sThe three-phase that moment calculates PWM duty cycle is equal to (k+0.25) T_sMoment three-phase PWM duty ratio, if number of hits is equal to 1, according to (k+0.5) T_sMoment meter Reference voltage d, q shafting component of calculatingWith rotor position angle θ (k+0.5) and in (k+ 0.5)T_sMoment is to (k+0.75) T_sMoment has a phase PWM duty cycle of intersection point with triangular carrier, recalculates other two-phases PWM duty cycle, according to (k+0.5) T if without intersection point_sMoment calculated reference voltage d, q shafting componentWith rotor position angle θ (k+0.5), three-phase PWM duty ratio is calculated；

In (k+0.75) T_sMoment is according to (k+0.5) T_sMoment calculated reference voltage d, q shafting component (k+0.75) T_sThe rotor position angle θ (k+0.75) at moment calculates three-phase PWM duty ratio；By each moment Calculated three-phase PWM duty ratio delay 0.25T_sIt is compared afterwards with triangular carrier and exports pwm pulse and act on six bridge arms Inverter, and then reality output corresponds to reference voltage and acts on motor, and return step 1) recycled.

2. a kind of permanent magnet synchronous motor system over-sampling predictive-current control method according to claim 1, feature exist In step 4) the current forecasting model is as follows:

In formula,For (k-1) T_sD, q shafting voltage prediction value that moment is calculated, For (k-0.5) T_sD, q shafting voltage prediction value that moment is calculated, T_sFor IGBT switch periods, R_sFor stator Resistance, L_d、L_qRespectively d, q shafting component of stator inductance, ψ_fFor rotor flux, ω_eFor rotor angular rate.

3. a kind of permanent magnet synchronous motor system over-sampling predictive-current control method according to claim 1, feature exist In the step 5) voltage-prediction model is as follows:

In formula,Respectively predicted voltage d, q shafting component, subscript PR indicate predicted value, T_sFor IGBT switch periods, R_sFor stator resistance, L_d、L_qRespectively d, q shafting component of stator inductance, ψ_fFor rotor flux, ω_eFor rotor electric angle speed Degree.

4. a kind of permanent magnet synchronous motor system over-sampling predictive-current control method according to claim 1, feature exist In in step 6):

In kT_sMoment judges (k-0.25) T_sMoment, three-phase PWM duty ratio calculated was in kT_sMoment between the moment with triangle The calculation formula that carrier wave number of hits is equal to the PWM duty cycle for recalculating other two-phases when 1 is as follows:

T₃=0.5mT_ssinθ(k+0.25)+T₂+T₁

In formula, T₁For kT_sMoment is to (k+0.25) T_sWhat the phase PWM duty cycle updated between the moment intersected with triangular carrier Time, T₂、T₃It is other two phase PWM duty ratios for recalculating in (k+0.25) T_sMoment is to (k+0.5) T_sWith three between moment The time of angle carrier wave intersection,For the SVPWM index of modulation, θ (k+0.25) is (k+0.25) T_sMoment motor turns Sub- electrical angle；

In kT_sMoment judges (k+0.25) T_sMoment, three-phase PWM duty ratio calculated was at (k+0.5T)_sMoment is to (k+0.75T_s) The calculation formula for the PWM duty cycle for recalculating other two-phases when being equal to 1 with triangular carrier number of hits between the moment is as follows:

T₆=T₄-0.5mT_ssinθ(k+0.75)-T₅

In formula, T₄For (k+0.5) T_sMoment is to (k+0.75) T_sThe phase PWM duty cycle and triangular carrier updated between moment The time of intersection, T₅、T₆It is other two phase PWM duty ratios for recalculating in (k+0.75) T_sMoment is to (k+1) T_sBetween moment The time intersected with triangular carrier,For the SVPWM index of modulation, (k+0.75 is (k+0.75) T to θ_sMoment electricity Machine rotor electrical angle.

Technical field

The present invention relates to a kind of permanent magnet synchronous motors.Electricity is predicted more particularly to a kind of permanent magnet synchronous motor system over-sampling Method of flow control.

Background technique

Model Predictive Control (Model Predictive Control, abbreviation MPC) is developed in engineer application Get up, there is very strong industrial application background and wide applicability.In multiple processes such as petroleum, chemical industry, space flight and the energy This control method is all applied successfully in control field.Control system for permanent-magnet synchronous motor mostly uses revolving speed, current double closed-loop control Structure, wherein the dynamic of current inner loop, steady-state performance are to promote the key factor of control system for permanent-magnet synchronous motor performance.Model is pre- Observing and controlling system predicts that the k+1 moment should act on the voltage vector of motor by prediction model using the motor status at the k moment.It should After voltage vector acts on a cycle, current of electric can accurately follow command current value.Model Predictive Control can make motor electric Stream obtains good dynamic and steady-state response.But control delay is to restrict that current inner loop is dynamic, stable state for digital control One of principal element of performance.Under the operating condition of low switching frequency, PWM duty cycle update delay cycle is longer, at this time motor electricity Pressure, the actual value and sampled value of electric current and rotor position angle, which change greatly, to be led to control amount there are large errors will cause electric current control Existing oscillation and static difference are produced, current oscillation can cause electromechanics shake that driver can even be made to stop fortune because of overcurrent alarm Row；Electric current static difference can reduce drive system operational efficiency, and nominal torque can not be exported and can not work by resulting in drive system In problems such as torque control patterns.

Summary of the invention

Control system for permanent-magnet synchronous motor can be greatly improved the technical problem to be solved by the invention is to provide one kind to move The permanent magnet synchronous motor system over-sampling predictive-current control method of steady-state performance.

The technical scheme adopted by the invention is that: a kind of permanent magnet synchronous motor system over-sampling predictive-current control method, The following steps are included:

1) in kT_sMoment and (k+0.5) T_sMoment, by control system to motor ABC three-phase current, DC bus-bar voltage and Rotor angular rate is sampled；In kT_sMoment, (k+0.25) T_sMoment, (k+0.5) T_sMoment, (k+0.75) T_sWhen It carves, rotor position angle is sampled by control system, k=1,2,3 ...；

2) in the case where motor reference current d shafting component is zero control, motor is calculated with reference to electricity by der Geschwindigkeitkreis pi regulator Flow q shafting componentSpecifically:

Wherein,Respectively motor reference current d, q shafting component,For der Geschwindigkeitkreis pi regulator ratio system Number,For der Geschwindigkeitkreis pi regulator integral coefficient, ω^refFor speed reference, ω is rotor machinery angular speed；

3) according to motor ABC three-phase current, kT is solved_sMoment motor actual current d, q shafting component i_d(k)、i_q(k), have Body solves are as follows:

Wherein, x is 0 in the first half of each carrier cycle, latter half 0.5, i_d(k+x) and i_q(k+x) it is respectively D, q shafting component of motor actual current, i_A(k)、i_B(k) and i_CIt (k) is the ABC three-phase current of motor, M_ABC/αβFor by ABC tri- Transformation matrix of the phase static axial system to α β two-phase static axial system, M_αβ/dqFor by α β two-phase static axial system to dq two-phase rotary axis Transformation matrix, expression are as follows:

In formula, θ (k+x) is (k+x) T_sThe angle of moment d shafting and α shafting；

4) in kT_sMoment and (k+0.5) T_sMoment obtains motor actual current d, q shafting component according to current forecasting model Predicted value, including predict (k+0.25) T respectively_sMoment and (k+0.75) T_sMoment electric current d, q shafting component WithAndWithCompensation of delay as voltage-prediction model；

5) voltage-prediction model is utilized, respectively according to kT_sMoment and (k+0.5) T_sThe rotor electric angle speed at moment Degree, motor reference current d shafting and q shafting componentWith the d shafting of motor actual current and the prediction of q shafting component Value, obtains so that predicted current is in (k+1) T_sPredicted voltage d, the q shafting component of moment track reference electric currentWithIn (k+1.5) T_sPredicted voltage d, the q shafting component of moment track reference electric currentWith

6) in each carrier cycle, using two level SVPWM modulator approach of asymmetric seven segmentation, four three contraries are calculated Become the PWM duty cycle T of device_a、T_bAnd T_c, and each calculated result is updated；In kT_sMoment judges (k-0.25) T_sMoment PWM duty cycle calculated is in kT_sMoment is to (k+0.25) T_sThere are several intersection points between moment with triangular carrier, if number of hits Greater than 1, then kT_sThe three-phase PWM duty ratio that moment calculates is equal to (k-0.25) T_sMoment three-phase PWM duty ratio, if number of hits etc. In 1, then according to kT_sMoment calculated reference voltage d, q shafting componentWith rotor position angle θ (k) and in kT_sMoment is to (k+0.25) T_sMoment has a phase PWM duty cycle of intersection point with triangular carrier, recalculate other two The PWM duty cycle of phase, according to kT if without intersection point_sMoment calculated reference voltage d, q shafting componentWith rotor position angle θ (k), three-phase PWM duty ratio is calculated；

In (k+0.25) T_sMoment is according to kT_sMoment calculated reference voltage d, q shafting component(k+0.25) T_sThe rotor position angle θ (k+0.25) at moment calculates three-phase PWM duty ratio；

In (k+0.5) T_sMoment judges (k+0.25) T_sMoment, three-phase PWM duty ratio calculated was in (k+0.5) T_sMoment To (k+0.75) T_sThere are several intersection points between moment with triangular carrier, if number of hits is greater than 1, (k+0.5) T_sWhat the moment calculated Three-phase PWM duty ratio is equal to (k+0.25) T_sMoment three-phase PWM duty ratio, if number of hits is equal to 1, according to (k+0.5) T_sWhen Carve calculated reference voltage d, q shafting componentWith rotor position angle θ (k+0.5) and (k+0.5)T_sMoment is to (k+0.75) T_sMoment has a phase PWM duty cycle of intersection point with triangular carrier, recalculates other two-phases PWM duty cycle, according to (k+0.5) T if without intersection point_sMoment calculated reference voltage d, q shafting componentWith rotor position angle θ (k+0.5), three-phase PWM duty ratio is calculated；

In (k+0.75) T_sMoment is according to (k+0.5) T_sMoment calculated reference voltage d, q shafting component (k+0.75) T_sThe rotor position angle θ (k+0.75) at moment calculates three-phase PWM duty ratio； By calculated three-phase PWM duty ratio delay 0.25T of each moment_sIt is compared afterwards with triangular carrier and exports pwm pulse work For six leg inverters, and then reality output corresponds to reference voltage and acts on motor, and return step 1) it is recycled.

A kind of permanent magnet synchronous motor system over-sampling predictive-current control method of the invention is keeping switching frequency constant In the case where, the dynamic steady-state performance of control system for permanent-magnet synchronous motor can be greatly improved.Technical solution of the present invention is brought Beneficial effect be:

(1) present invention is by carrying out double sampling to motor to the busbar voltage of motor, three-phase current in one cycle Rotor position angle carries out four samplings, and obtains predicted voltage value d shafting and q shafting component by model prediction algorithm, to be The steady-state performance of system provides guarantee；

(2) present invention updates four PWM duty cycles by asymmetric SVPWM method in a carrier cycle, Reference frame is provided for the dynamic property of system；

(3) present invention is sampled by voltage and current twice, and four times motor rotor position angle samples and in a carrier cycle Four PWM duty cycles of interior update effectively improve the dynamic property of system under low switching frequency, and stable state floating, concussion.

Detailed description of the invention

Fig. 1 is two level PWM rectifier main circuit of three-phase and control system architecture figure；

Fig. 2 is that control system for permanent-magnet synchronous motor current sample and PWM duty cycle update timing diagram；

Fig. 3 is a kind of flow chart of permanent magnet synchronous motor system over-sampling predictive-current control method of the present invention.

Specific embodiment

Below with reference to embodiment and attached drawing to a kind of permanent magnet synchronous motor system over-sampling predictive-current control of the invention Method is described in detail.

As shown in figure 3, a kind of permanent magnet synchronous motor system over-sampling predictive-current control method of the invention, including it is following Step:

1) in kT_sMoment, (k+0.5) T_sMoment carries out electric current, voltage and rotor angular rate by control system Sampling, specifically includes: motor ABC three-phase current i_A(k)、i_A(k+0.5)、i_B(k)、i_B(k+0.5)、i_C(k)、i_C(k+0.5), directly Flow busbar voltage u_dc(k)、u_dc(k+1), rotor angular rate ω_e(k)、ω_e(k+0.5)；In kT_sMoment, (k+0.25) T_s Moment, (k+0.5) T_sMoment, (k+0.75) T_sMoment is sampled rotor position angle by control system, specifically includes: θ (k),θ(k+0.25),θ(k+0.5),θ(k+0.75)；K=1,2,3 ...；

2) in the case where motor reference current d shafting component is zero control, motor is calculated with reference to electricity by der Geschwindigkeitkreis pi regulator Flow q shafting componentSpecifically:

Wherein,Respectively motor reference current d, q shafting component,For der Geschwindigkeitkreis pi regulator ratio system Number,For der Geschwindigkeitkreis pi regulator integral coefficient, ω^refFor speed reference, ω is rotor machinery angular speed；

3) according to motor ABC three-phase current i_A(k+x)、i_B(k+x)、i_C(k+x), (k+x) T is solved_sThe practical electricity of moment motor Flow d, q shafting component i_d(k+x)、i_qIt is (k+x), specific to solve are as follows:

Wherein, x is 0 in the first half of each carrier cycle, latter half 0.5, i_d(k+x) and i_q(k+x) it is respectively D, q axis component of motor actual current, i_A(k)、i_B(k) and i_CIt (k) is the ABC three-phase current of motor, M_ABC/αβFor by ABC three-phase Transformation matrix of the static axial system to α β two-phase static axial system, M_αβ/dqFor by the change of α β two-phase static axial system to dq two-phase rotary axis Matrix is changed, expression is as follows:

In formula, θ (k+x) is (k+x) T_sThe angle of moment d shafting and α shafting；

4) in kT_sMoment and (k+0.5) T_sMoment obtains motor actual current d, q shafting component according to current forecasting model Predicted value, including predict (k+0.25) T respectively_sMoment and (k+0.75) T_sMoment electric current d, q shafting component WithAndWithCompensation of delay as voltage-prediction model；The electric current Prediction model is as follows:

In formula,For (k-1) T_sD, q shafting voltage prediction value that moment is calculated, For (k-0.5) T_sD, q shafting voltage prediction value that moment is calculated, T_sFor IGBT switch Period, R_sFor stator resistance, L_d、L_qRespectively d, q shafting component of stator inductance, ψ_fFor rotor flux, ω_eFor rotor electricity Angular speed.

5) voltage-prediction model is utilized, respectively according to kT_sMoment and (k+0.5) T_sThe rotor electric angle speed at moment Degree, motor reference current d shafting and q shafting componentWith the d shafting of motor actual current and the prediction of q shafting component Value, obtains so that predicted current is in (k+1) T_sPredicted voltage d, the q shafting component of moment track reference electric currentWithIn (k+1.5) T_sPredicted voltage d, the q shafting component of moment track reference electric currentWithThe voltage-prediction model is as follows:

In formula,Respectively predicted voltage d, q shafting component, subscript PR indicate predicted value, T_sWeek is switched for IGBT Phase, R_sFor stator resistance, L_d、L_qRespectively d, q shafting component of stator inductance, ψ_fFor rotor flux, ω_eFor rotor electric angle Speed.

6) in each carrier cycle, using two level SVPWM modulator approach of asymmetric seven segmentation, four three contraries are calculated Become the PWM duty cycle T of device_a、T_bAnd T_c, and each calculated result is updated；In kT_sMoment judges (k-0.25) T_sMoment PWM duty cycle calculated is in kT_sMoment is to (k+0.25) T_sThere are several intersection points between moment with triangular carrier, if number of hits Greater than 1, then kT_sThe three-phase PWM duty ratio that moment calculates is equal to (k-0.25) T_sMoment three-phase PWM duty ratio, if number of hits etc. In 1, then according to kT_sMoment calculated reference voltage d, q shafting componentWith rotor position angle θ (k) and in kT_sMoment is to (k+0.25) T_sMoment has a phase PWM duty cycle of intersection point with triangular carrier, recalculate other two The PWM duty cycle of phase, according to kT if without intersection point_sMoment calculated reference voltage d, q shafting componentWith rotor position angle θ (k), three-phase PWM duty ratio is calculated；

In (k+0.25) T_sMoment is according to kT_sMoment calculated reference voltage d, q shafting component(k+0.25) T_sThe rotor position angle θ (k+0.25) at moment calculates three-phase PWM duty ratio；

In (k+0.5) T_sMoment judges (k+0.25) T_sMoment, three-phase PWM duty ratio calculated was in (k+0.5) T_sMoment To (k+0.75) T_sThere are several intersection points between moment with triangular carrier, if number of hits is greater than 1, (k+0.5) T_sWhat the moment calculated Three-phase PWM duty ratio is equal to (k+0.25) T_sMoment three-phase PWM duty ratio, if number of hits is equal to 1, according to (k+0.5) T_sWhen Carve calculated reference voltage d, q shafting componentWith rotor position angle θ (k+0.5) and (k+0.5)T_sMoment is to (k+0.75) T_sMoment has a phase PWM duty cycle of intersection point with triangular carrier, recalculates other two-phases PWM duty cycle, according to (k+0.5) T if without intersection point_sMoment calculated reference voltage d, q shafting componentWith rotor position angle θ (k+0.5), three-phase PWM duty ratio is calculated；

In (k+0.75) T_sMoment is according to (k+0.5) T_sMoment calculated reference voltage d, q shafting component (k+0.75) T_sThe rotor position angle θ (k+0.75) at moment calculates three-phase PWM duty ratio； By calculated three-phase PWM duty ratio delay 0.25T of each moment_sIt is compared afterwards with triangular carrier and exports pwm pulse work For six leg inverters, and then reality output corresponds to reference voltage and acts on motor, and return step 1) it is recycled.Its In:

In kT_sMoment judges (k-0.25) T_sMoment, three-phase PWM duty ratio calculated was in kT_sMoment between the moment with The calculation formula that triangular carrier number of hits is equal to the PWM duty cycle for recalculating other two-phases when 1 is as follows:

In formula, T₁For kT_sMoment is to (k+0.25) T_sA phase PWM duty cycle and the triangular carrier phase updated between moment The time of friendship, T₂、T₃It is other two phase PWM duty ratios for recalculating in (k+0.25) T_sMoment is to (k+0.5) T_sBetween moment The time intersected with triangular carrier,For the SVPWM index of modulation, θ (k+0.25) is (k+0.25) T_sMoment electricity Machine rotor electrical angle；

In kT_sMoment judges (k+0.25) T_sMoment, three-phase PWM duty ratio calculated was in (k+0.5) T_sMoment is to (k+ 0.75)T_sThe calculation formula of the PWM duty cycle of other two-phases is recalculated when being equal to 1 with triangular carrier number of hits between the moment such as Shown in lower:

In formula, T₄For (k+0.5) T_sMoment is to (k+0.75) T_sThe phase PWM duty cycle and triangle updated between moment The time of carrier wave intersection, T₅、T₆It is other two phase PWM duty ratios for recalculating in (k+0.75) T_sMoment is to (k+1) T_sMoment Between time for intersecting with triangular carrier,For the SVPWM index of modulation, θ (k+0.75) is (k+0.75) T_sWhen Carve electrical angle of motor rotor.