CN109347358B - Neutral point potential balance control method for three-level NPC converter - Google Patents

Neutral point potential balance control method for three-level NPC converter Download PDF

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CN109347358B
CN109347358B CN201811265428.3A CN201811265428A CN109347358B CN 109347358 B CN109347358 B CN 109347358B CN 201811265428 A CN201811265428 A CN 201811265428A CN 109347358 B CN109347358 B CN 109347358B
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midpoint potential
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CN109347358A (en
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葛琼璇
高瞻
赵鲁
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Institute of Electrical Engineering of CAS
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/66—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal
    • H02M7/68—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal by static converters
    • H02M7/72—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • H02M7/487—Neutral point clamped inverters

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Abstract

A neutral point potential balance control method for a three-level NPC converter. When the midpoint potential oscillation exceeds a limit value, the control method takes the midpoint potential oscillation in each sampling period as a calculation target to be kept zero, and obtains corresponding midpoint potential balance formulas in different sectors and areas; in order to adjust the neutral potential balance in real time, the control method firstly judges the position of a sector and a region where the current command voltage is located, then detects a three-phase current value and a space vector angle, substitutes the three-phase current value and the space vector angle into a neutral potential balance formula corresponding to the current sector and region to calculate, obtains an action time factor of the redundant small vectors, controls the action time of the two redundant small vectors by utilizing the action time factor, and can realize the dynamic balance adjustment of the neutral potential. The control method can control the midpoint potential deviation of the three-level NPC converter within a small range, and improves the reliability of the three-level NPC converter.

Description

Neutral point potential balance control method for three-level NPC converter
Technical Field
The invention relates to a neutral point potential balance control method, in particular to a neutral point potential balance control method of a three-level NPC converter.
Background
The topology of the three-level NPC (neutral Point clamped) converter is shown in fig. 1, and the three-level NPC converter can output three different level states by controlling the on and off of four switching devices P1, P2, P3 and P4 from top to bottom of three phases. The three-level NPC converter has the advantages of small size, simple structure and easiness in realizing bidirectional energy flow, and is generally applied to speed regulation occasions of medium-high voltage high-power motors at present.
Svpwm (space Vector Pulse Width modulation) is a modulation strategy often used by three-level NPC converters. The classical SVPWM method is based on the recent three-vector principle, namely, the command voltage V is obtained through three-phase voltage dq conversionrefThen the command voltage V is appliedrefThe product of the three voltage space vectors and the sampling period is decomposed into products of the three voltage space vectors and respective action time, and the target voltage is output by reasonably arranging the action sequence of the three voltage space vectors, so that modulation is realized.
The voltage space vector distribution of the three-level NPC converter in each space angle interval is shown in fig. 2. In FIG. 2VA、VB、VCPhase voltages respectively corresponding to the A phase, the B phase and the C phase, wherein angles such as 0 degree and 90 degrees represent space vector angles of corresponding degrees, namely command voltage V obtained after three-phase voltage dq changesrefAnd the included angle between the phase voltage of the A phase. Defining a command voltage VrefThe spatial vector angle when coinciding with phase a is 0 deg., and the 360 deg. spatial vector angle corresponds to one voltage fundamental period. Fig. 2, such as PPP, PPO, etc., represent the corresponding voltage space vectors, and the switching states corresponding to the voltage space vectors in fig. 2 are summarized in table 1.
TABLE 1 SVPWM Voltage space vectors and corresponding switch states
Figure GDA0002514713920000011
Figure GDA0002514713920000021
As shown in table 1, each voltage space vector of the SVPWM can be divided into a zero vector, a small vector, a medium vector and a large vector according to the magnitude, wherein the zero vector and the small vector have a redundant state. For small vectors, two P-type small vectors and N-type small vectors with the same space vector angular phase are mutually redundant small vectors. Each of the redundant small vectors and their corresponding current flowing through the midpoint are summarized in table 2.
TABLE 2 redundant Small vectors and their corresponding midpoint currents
Figure GDA0002514713920000022
In Table 2, ioCorresponding to the midpoint current, i, flowing through the midpointa、ib、icCorresponding to phase currents of phase A, phase B and phase C. As shown in Table 2, the two redundant small vectors have opposite directions of current flowing through the midpoint, so that the two redundant small vectors have opposite effects on the midpoint potential.
For the three-level NPC converter of fig. 1, if the product of the current flowing into the midpoint and the time is not equal to the product of the current flowing out of the midpoint and the time in one sampling period, the charging voltage and the discharging voltage of the capacitors C1 and C2 are not equal, and the midpoint potential is unbalanced. Unbalanced midpoint potential can generate low-order harmonic in output voltage and cause a switching device of a certain half bridge arm of the three-level NPC converter to bear overhigh voltage, so that the operation safety is endangered, and therefore measures must be taken to ensure the midpoint potential balance of the three-level NPC converter.
Existing midpoint potential balance control methods can be classified into hardware methods and software methods. The literature "NPC three-level inverter midpoint voltage balance control based on hybrid SVPWM method" (shore rainbow, D. tianjin: tianjin university, 2012:4-7) compares common hardware and software methods in detail. Compared with a hardware method, the software method can control the midpoint voltage balance without adding additional hardware equipment and a control system, can reduce the volume and save the cost, and is a better choice. Software methods commonly used by three-level NPC converters can be divided into two categories:
1) controlling hysteresis: the basic principle is that when the neutral point potential is unbalanced, the redundant small vector switch state which is beneficial to neutral point potential balance is selected to regulate and control according to the direction of three-phase current. The hysteresis control has the advantage of not increasing the switching frequency, and has the disadvantage of having an uncontrollable area when the modulation is large or the power factor angle is low.
2) Active control: the representative method is a virtual space vector method. The active control has the advantages that the midpoint potential balance can be regulated and controlled in the full modulation ratio and power factor angle range, and the disadvantage that the switching frequency is increased by one third.
For a high-power three-level NPC converter, the switching loss of the switching device in each operation is not negligible, so the switching frequency of the switching device is to be reduced as much as possible. The hysteresis control only has an uncontrollable area when the modulation is large or the power factor angle is low, and the neutral point potential balance can be effectively controlled under most conditions. Therefore, for a high-power three-level NPC converter, hysteresis control is the most common midpoint potential balance control method.
Hysteresis control requires designing hysteresis control parameters, and proper design of the hysteresis control parameter values directly influences the control effect of the system on the midpoint potential balance. When the design of the hysteresis control parameter value is not precise enough, the robustness of the system is poor, and the control effect on the balance of the midpoint potential is poor. And under different working conditions, the hysteresis control parameter value may be different, and needs to be redesigned.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a neutral point potential balance control method of a three-level NPC converter. The principle of the neutral point potential balance control method of the three-level NPC converter is the same as that of hysteresis control, the neutral point potential balance is maintained by redistributing the action time of two redundant small vectors, but the neutral point potential balance control method is different from the traditional hysteresis method, the control method of the three-level NPC converter does not need to design hysteresis control parameters, and the action time factors of the two redundant small vectors can be calculated on line only by knowing the three-phase current value and the space vector angle value. The control method can control the midpoint potential deviation of the three-level NPC converter within a small range, and improves the reliability of the three-level NPC converter.
When the midpoint potential oscillation exceeds a limit value, the midpoint potential oscillation in each sampling period is kept to be zero as a calculation target, and corresponding midpoint potential balance formulas in different sectors and areas are obtained; in order to adjust the neutral potential balance in real time, the control method firstly judges the position of a sector and a region where the current instruction voltage is located, then detects a three-phase current value and a space vector angle, substitutes the three-phase current value and the space vector angle into a neutral potential balance formula corresponding to the current sector and the region to calculate, obtains a redundant small vector action time factor, controls the action time of two redundant small vectors by utilizing the redundant small vector action time factor, and can realize the dynamic balance adjustment of the neutral potential.
When the oscillation of the midpoint potential exceeds a limit value, the method for controlling the midpoint potential balance of the three-level NPC converter specifically comprises the following steps:
1. judging the position number of the sector where the current instruction voltage is located;
the control method of the invention judges the position number of each sector by utilizing the value of the space vector angle theta, and the specific judging method is as follows:
1) when theta is more than or equal to 0 and less than pi/3, the current sector number is sector 0;
2) when the pi/3 is more than or equal to theta and less than 2 pi/3, the current sector is numbered as sector 1;
3) when theta is more than or equal to 2 pi/3 and less than pi, the current sector is numbered as sector 2;
4) when the pi is more than or equal to the theta and less than 4 pi/3, the current sector is numbered as sector 3;
5) when theta is more than or equal to 4 pi/3 and less than 5 pi/3, the current sector is numbered as sector 4;
6) when theta is more than or equal to 5 pi/3 and less than 2 pi, the current sector is numbered as sector 5.
2. Judging the position number of the area where the current instruction voltage is located;
the control method of the invention utilizes t1, t2, t3 and theta1The area position number in each sector is judged by the specific judgment method as follows:
Figure GDA0002514713920000041
in the formula (1), TsM is a modulation ratio, t1, t2 and t3 are time factors for determining the position of the region in each sector, and θ is the sampling period1Rotate to the angle corresponding to sector 0 for the current spatial vector angle θ, having θ1θ -int (θ/(pi/3)), int denotes rounding a value down to the nearest integer.
1) When t1 is more than or equal to 0, t2 is less than 0, t3 is more than or equal to 0, and theta is more than or equal to 01Less than pi/6, and the current area number is area 1;
2) when t1 is more than or equal to 0, t2 is less than 0, t3 is more than or equal to 0, pi/6 is more than theta1Is less than or equal to pi/3, and the number of the current area is area 2;
3) when t1 is more than or equal to 0, t2 is more than or equal to 0, t3 is more than or equal to 0, theta is more than or equal to 01Less than pi/6, and the current area is numbered as area 3;
4) when t1 is more than or equal to 0, t2 is more than or equal to 0, t3 is more than or equal to 0, and phi/6 is more than or equal to theta1Is less than or equal to pi/3, and the number of the current area is area 4;
5) when t1 is more than or equal to 0, t2 is more than or equal to 0, t3 is less than 0, and theta is more than or equal to 01Less than pi/6, and the current area number is area 5;
6) when t1 is less than 0, t2 is more than or equal to 0, t3 is more than or equal to 0, pi/6 is more than or equal to theta1Less than or equal to pi/3, at presentThe area is numbered area 6.
The area number, e.g., area 1 location for sector 0, is indicated as 0.1 and the area 1 location for sector 1 is indicated as 1.1.
3. Detecting a three-phase current value and a space vector angle, substituting the three-phase current value and the space vector angle into a corresponding midpoint potential balance formula of the current sector and region to calculate, and obtaining an action time factor k of a redundant small vector;
the control method of the invention takes the midpoint voltage oscillation in each sampling period as a calculation target, and calculates the corresponding midpoint potential balance formulas in different sectors and areas. When the midpoint potential oscillation exceeds a limit value, the control method of the invention substitutes the three-phase current value and the space vector angle into a corresponding midpoint potential balance formula of the current sector and region for calculation by detecting the three-phase current value and the space vector angle, and obtains a redundant small vector action time factor k. The equation for the midpoint potential balance for each sector and region is shown in table 3.
TABLE 3 corresponding midpoint potential balance formulas for each sector and region
Figure GDA0002514713920000051
Figure GDA0002514713920000061
Figure GDA0002514713920000071
In Table 3, m is the modulation ratio, θ1And theta-int (theta/(pi/3)) is an angle corresponding to the rotation of the current space vector angle theta to the sector 0, ia, ib and ic are currents of the A phase, the B phase and the C phase respectively, and k represents a redundant small vector action time factor in each sector area. The k value range calculated by the midpoint potential balance formula is limited to 0 to 1, namely:
Figure GDA0002514713920000081
4. controlling the action time of two redundant small vectors by using the redundant small vector action time factor k, thereby realizing the dynamic balance adjustment of the central potential;
two redundant small vectors of the same spatial vector angle correspond to opposite directions of current flowing through the midpoint, and the effects of the current on the midpoint potential are opposite. The control method maintains the balance of the midpoint potential of the three-level NPC converter by redistributing the action time of two redundant small vectors. Let Tx be the total action time of two redundant small vectors, and the specific method for controlling the action time of the redundant small vectors by using time factor k in different sector areas is as follows:
1) for the redundant small vectors POO/ONN, the POO action time is (1-k) Tx, and the ONN action time is k Tx;
2) for redundant small vectors PPO/OON, OON action time is (1-k) Tx, and PPO action time is k Tx;
3) for the redundant small vectors OPO/NON, the OPO action time is (1-k) Tx, and the NON action time is k Tx;
4) for the redundant small vectors OPP/NOO, the NOO action time is (1-k) Tx, and the OPP action time is k Tx;
5) for redundant small vectors OOP/NNO, OOP action time is (1-k) Tx, and NNO action time is k Tx;
6) for the redundant small vector POP/ONO, the ONO action time is (1-k) Tx, and the POP action time is k Tx;
in the above specific manner, Tx represents total action time of two redundant small vectors, P corresponds to a level state of conduction output of two switching devices P1 and P2 of an upper bridge arm of a certain phase of the three-level NPC converter, O corresponds to a level state of conduction output of a switching device P2 below the upper bridge arm of the certain phase of the three-level NPC converter and a switching device P3 above a lower bridge arm of the certain phase of the three-level NPC converter, and N corresponds to a level state of conduction output of two switching devices P3 and P4 of a lower bridge arm of the certain phase of the three-level NPC converter.
5. When the oscillation of the midpoint potential is reduced to be within a limit value, the action time factor k of the redundant small vector is made to be 0.5;
the control method only calculates when the midpoint potential oscillation exceeds a limit value, selects a corresponding midpoint potential balance formula according to the position of a sector and an area where the current instruction voltage is located to calculate a redundant small vector action time factor k, and controls the action time of two redundant small vectors by using the time factor k to maintain the balance of the midpoint potential of the three-level NPC converter. After the oscillation of the midpoint potential is reduced to be within the limit value, in order to obtain better harmonic performance, the control method of the invention does not use the midpoint potential balance formula to calculate k, but leads k to be 0.5.
Drawings
FIG. 1 three-level NPC converter topology;
fig. 2 is a SVPWM space voltage vector diagram for a three-level NPC converter;
FIG. 3 is a flowchart illustrating an embodiment of a method for controlling the neutral point potential balance of a three-level NPC converter according to the present invention;
FIG. 4 illustrates the division of the voltage space vectors corresponding to the division of the location of each region at sector 0 of SVPWM;
FIG. 5 shows the change of the fundamental frequency of 24Hz, the modulation ratio of 0.38, the initial value of the DC bus upper arm capacitor C1 voltage Udc 1V, the initial value of the DC bus lower arm capacitor C2 voltage Udc 2V, and Udc1 and Udc2 without adding midpoint potential balance protection measures;
6a, 6b and 6C show fundamental frequency 24Hz, modulation ratio fixed 0.38, initial value 3500V of DC bus upper bridge arm capacitance C1 voltage Udc1 voltage, initial value 1500V of DC bus lower bridge arm capacitance C2 voltage Udc2 voltage, and result of the embodiment under the action of the control method of the invention, wherein FIG. 6a shows the change situation of C1 voltage Udc1 and C2 voltage Udc2, FIG. 6b shows midpoint potential oscillation value Vo and midpoint potential oscillation limit value, and FIG. 6C shows the redundant small vector action time factor k calculated by the invention;
FIG. 7 shows the change conditions of the DC1 and the DC2 under the condition that the fundamental frequency of the embodiment is 24Hz, the modulation ratio is fixed to be 0.38, the initial values of the DC bus upper bridge arm capacitor C1 voltage Udc1 and the DC bus lower bridge arm capacitor voltage Udc2 are 2500V, and no midpoint potential balance protection measures are added;
8a and 8b show the fundamental frequency of 24Hz, the modulation ratio is fixed to be 0.38, the initial value of the DC bus upper bridge arm capacitor C1 voltage Udc1 and the lower bridge arm capacitor C2 voltage Udc2 voltage 2500V, and the result of the embodiment under the action of the control method of the invention, wherein, in the graph, FIG. 8a shows the change situation of the capacitor C1 voltage Udc1 and the capacitor C2 voltage Udc2, and FIG. 8b shows the midpoint potential oscillation value Vo and the midpoint potential oscillation limit value;
FIG. 9 shows the change of the fundamental frequency of 24Hz, the modulation ratio of 0.1-0.9, the initial values of the DC bus upper bridge arm capacitance C1 voltage Udc1 and lower bridge arm capacitance voltage Udc2 voltage 2500V, Udc1, Udc2 and modulation ratio m without adding midpoint potential balance protection measures;
10a, 10b and 10C show the fundamental frequency of 24Hz, the modulation ratio of 0.1-0.9 cyclically changes, the initial value of the capacitor C1 voltage Udc1 and the initial value of the capacitor voltage Udc2 of the upper bridge arm of the direct current bus is 2500V, and the result of the embodiment under the action of the control method of the invention is shown in the figures, wherein the figure 10a shows the change situation of the capacitor C1 voltage Udc1 and the capacitor C2 voltage Udc2, the figure 10b shows the change situation of the midpoint potential oscillation value Vo, the midpoint potential oscillation limit value and the modulation ratio m, and the figure 10C shows the redundant small vector action time factor k obtained by calculation.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
When the midpoint potential oscillation exceeds a limit value, the midpoint potential oscillation in each sampling period is kept to be zero as a calculation target, and corresponding midpoint potential balance formulas in different sectors and areas are obtained; in order to adjust the neutral potential balance in real time, the control method firstly judges the position of a sector and a region where the current instruction voltage is located, then detects a three-phase current value and a space vector angle, substitutes the three-phase current value and the space vector angle into a neutral potential balance formula corresponding to the current sector and the region to calculate, obtains a redundant small vector action time factor, controls the action time of two redundant small vectors by utilizing the redundant small vector action time factor, and realizes the dynamic balance adjustment of the neutral potential.
The flow of the neutral point potential balance control method based on the calculated three-level NPC converter is shown in FIG. 3:
firstly, judging whether the oscillation value of the midpoint potential exceeds a limit value, if so, executing the following steps, and if not, setting the action time factor k of the redundant small vector to be 0.5.
When the midpoint potential oscillation exceeds a limit value, the control method of the invention comprises the following steps:
1. and (3) taking the midpoint potential oscillation in each sampling period as a calculation target to obtain corresponding midpoint potential balance formulas in different sectors and regions:
(1) corresponding midpoint potential balance formula when the area number of the command voltage is 1
Assuming the command voltage falls in sector 0.1 as shown in FIG. 4, the voltage space vector action sequence of the resultant command voltage is POO-OOO-OON-ONN under the recent three-vector principle. Let the sampling period be TsThe sum of the action time of the redundancy small vectors POO and ONN in one sampling period is TS1OOO action time of T0OON action time TS2Then, there are:
Figure GDA0002514713920000101
in the formula (2), m represents a modulation ratio, θ represents a spatial vector angle, and TsFor a sampling period, TS1Is the sum of the action time of the redundant small vectors POO and ONN in a sampling period, T0For OOO duration, TS2OON is active for a time within one sampling period. Let ONN act for a time k TS1The POO action time is (1-k). times.TS1Then, there are:
Figure GDA0002514713920000102
in the formula (3), TONNONN action time, TPOOFor POO duration in one sampling period, TOONOON, k is the redundant small vector action time factor.
ONN, the midpoint current corresponding to POO is ia, the midpoint current corresponding to POO is-ia, the midpoint current corresponding to OON is-ic, and the oscillation value of the midpoint potential in one sampling period can be obtained as follows:
VO＝TS*((2k-1)*2m*sin(π/3-θ)*ia-2m*sin(θ)*ic)/C (4)
in the formula (4), VOThe oscillation value of the midpoint potential is ia, ib and ic are phase voltages of an A phase, a B phase and a C phase respectively, and C is the sum of capacitance values of an upper capacitor C1 and a lower capacitor C2 of a direct current bus of the three-level NPC converter. When the midpoint potential oscillation is zero in each sampling period, there is VOWhen 0 is substituted for formula (4), the following compounds can be obtained:
Figure GDA0002514713920000103
equation (5) is the corresponding midpoint potential balance equation for the command voltage position 0.1 when the midpoint potential oscillation is zero in each sampling period. By the same principle, midpoint potential balance formulas corresponding to the command voltage positions 1.1, 2.1, 3.1, 4.1 and 5.1 can be obtained, and then the midpoint potential balance formula corresponding to the region number of the command voltage is 1 is obtained.
(2) Corresponding midpoint potential balance formula when the area number of the command voltage is 2
Assuming that the command voltage falls in sector 0.2 as shown in FIG. 4, the voltage space vector order of action of the resultant command voltage is PPO-POO-OOO-OON under the recent three-vector principle. Let the sampling period be TsThe sum of the action time of the redundant small vectors PPO and OON in one sampling period is TS2OOO action time of T0POO action time of TS1Then, there are:
Figure GDA0002514713920000111
in the formula (6), m represents a modulation ratio, θ represents a spatial vector angle, and TsFor a sampling period, TS1For POO action time, T0For OOO duration, TS2Is the sum of the action time of the redundant small vectors PPO and OON in one sampling period. Let the PPO action time be k × TS2OON the action time is (1-k) × TS2Then, there are:
Figure GDA0002514713920000112
in the formula (7), TPPOFor PPO duration, TOONOON acting for a time, T, within a sampling periodPOOK is a redundant small vector action time factor for the action time of the POO in one sampling period.
When the PPO corresponding midpoint current is ic, the OON corresponding midpoint current is-ic, and the POO corresponding midpoint current is-ia, the oscillation value of the midpoint potential in one sampling period can be obtained as follows:
VO＝TS*((2k-1)*2m*sin(θ)*ic-2m*sin(π/3-θ)*ia)/C (8)
in the formula (8), VOThe oscillation value of the midpoint potential is ia, ib and ic are phase voltages of an A phase, a B phase and a C phase respectively, and C is the sum of capacitance values of an upper capacitor C1 and a lower capacitor C2 of a direct current bus of the three-level NPC converter. When the midpoint potential oscillation is zero in each sampling period, there is VOWhen 0 is substituted for formula (8), the following compounds are obtained:
Figure GDA0002514713920000113
equation (9) is the corresponding midpoint potential balance equation for the command voltage position 0.2 when the midpoint potential oscillation is zero in each sampling period. By the same principle, midpoint potential balance formulas corresponding to the command voltage positions 1.2, 2.2, 3.2, 4.2 and 5.2 can be obtained, and then the midpoint potential balance formula corresponding to the command voltage region with the number of 2 is obtained.
(3) Corresponding midpoint potential balance formula when the area number of the command voltage is 3
Assuming that the command voltage falls in sector 0.3 as shown in fig. 4, the voltage space vector action sequence of the resultant command voltage is POO-PON-OON-ONN by the latest three-vector principle. Let the sampling period be TsThe sum of the action time of the redundancy small vectors POO and ONN in one sampling period is TS1PON with a time TMOON action time TS2Then, there are:
Figure GDA0002514713920000121
in the formula (10), m represents a modulation ratio, θ represents a spatial vector angle, and TsFor a sampling period, TS1Is the sum of the action time of the redundant small vectors POO and ONN in a sampling period, TMFor PON action time, TS2OON is active for a time within one sampling period. Let ONN act for a time k TS1The POO action time is (1-k). times.TS1Then, there are:
Figure GDA0002514713920000122
in formula (11), TONNONN action time, TPOOFor POO duration in one sampling period, TOONOON acting for a time, T, within a sampling periodPONAnd k is the action time of the PON in one sampling period, and is a redundant small vector action time factor.
ONN, the midpoint current corresponding to POO is ia, the midpoint current corresponding to POO is-ia, the midpoint current corresponding to OON is-ic, and the midpoint current corresponding to PON is ib, then the oscillation value of the midpoint potential in one sampling period can be obtained as follows:
Figure GDA0002514713920000123
in the formula (12), VOThe oscillation value of the midpoint potential is ia, ib and ic are phase voltages of an A phase, a B phase and a C phase respectively, and C is the sum of capacitance values of an upper capacitor C1 and a lower capacitor C2 of a direct current bus of the three-level NPC converter. When the midpoint potential oscillation is zero in each sampling period, there is VOWhen 0 is substituted for formula (12), the following compounds are obtained:
Figure GDA0002514713920000124
equation (13) is the corresponding midpoint potential balance equation for the command voltage position 0.3 when the midpoint potential oscillation is zero in each sampling period. By the same principle, midpoint potential balance formulas corresponding to the instruction voltage positions of 1.3, 2.3, 3.3, 4.3 and 5.3 can be obtained, and then the midpoint potential balance formula corresponding to the area with the instruction voltage is numbered as 3 is obtained.
(4) Corresponding midpoint potential balance formula when the area number of the command voltage is 4
Assuming that the command voltage falls in sector 0.4 as shown in fig. 4, the voltage space vector action sequence of the resultant command voltage is PPO-POO-PON-OON by the latest three-vector principle. Let the sampling period be TsThe sum of the action time of the redundant small vectors PPO and OON in one sampling period is TS2PON with a time TMPOO action time of TS1Then, there are:
Figure GDA0002514713920000131
in the formula (14), m represents a modulation ratio, θ represents a spatial vector angle, and TsFor a sampling period, TS2Is the sum of the action time of the redundant small vectors PPO and OON in a sampling period, TMFor PON action time, TS1For the POO to be active for one sampling period. Let the PPO action time be k × TS2OON the action time is (1-k) × TS2Then, there are:
Figure GDA0002514713920000132
in formula (15), TPPOFor PPO duration, TOONOON acting for a time, T, within a sampling periodPOOFor POO duration in one sampling period, TPONAnd k is the action time of the PON in one sampling period, and is a redundant small vector action time factor.
When the PPO corresponding midpoint current is ic, the OON corresponding midpoint current is-ic, the POO corresponding midpoint current is-ia, and the PON corresponding midpoint current is ib, the oscillation value of the midpoint potential in one sampling period can be obtained as follows:
Figure GDA0002514713920000133
in the formula (16), VOThe oscillation value of the midpoint potential is ia, ib and ic are phase voltage of A phase, B phase and C phase respectively, and C is the sum of capacitance values of an upper capacitor C1 and a lower capacitor C2 of a direct current bus of the three-level NPC converter. When the midpoint potential oscillation is zero in each sampling period, there is VOWhen 0 is substituted for formula (16), the following compounds can be obtained:
Figure GDA0002514713920000134
equation (17) is the corresponding midpoint potential balance equation for the command voltage position 0.4 when the midpoint potential oscillation is zero in each sampling period. By the same principle, midpoint potential balance formulas corresponding to the instruction voltage positions of 1.4, 2.4, 3.4, 4.4 and 5.4 can be obtained, and then a midpoint potential balance formula corresponding to the area where the instruction voltage is located is numbered 4 is obtained.
(5) Corresponding midpoint potential balance formula when the area number of the command voltage is 5
Assuming that the command voltage falls in sector 0.5 as shown in fig. 4, the voltage space vector action sequence of the resultant command voltage is POO-PON-PNN-ONN by the latest three-vector principle. Let the sampling period be TsThe sum of the action time of the redundancy small vectors POO and ONN in one sampling period is TS1PON with a time TMPNN action time of TL1Then, there are:
Figure GDA0002514713920000141
in the formula (18), m represents a modulation ratio, θ represents a spatial vector angle, and TsFor a sampling period, TS1Is the sum of the action time of the redundant small vectors POO and ONN in a sampling period, TMFor PON action time, TL1The PNN is acted upon for a time within one sampling period. Let ONN act for a time k TS1The POO action time is (1-k). times.TS1Then, there are:
Figure GDA0002514713920000142
in formula (19), TONNONN action time, TPOOFor POO duration in one sampling period, TPONAnd k is the action time of the PON in one sampling period, and is a redundant small vector action time factor.
ONN, the midpoint current corresponding to POO is ia, the midpoint current corresponding to POO is-ia, the midpoint current corresponding to PON is ib, and the oscillation value of the midpoint potential in one sampling period can be obtained as follows:
VO＝TS*((2k-1)*(2-2m*sin(π/3+θ))*ia+(2m*sin(θ))*ib)/C (20)
in the formula (20), VOThe oscillation value of the midpoint potential is ia, ib and ic are phase voltage of A phase, B phase and C phase respectively, and C is the sum of capacitance values of an upper capacitor C1 and a lower capacitor C2 of a direct current bus of the three-level NPC converter. When the midpoint potential oscillation is zero in each sampling period, there is VOWhen 0 is substituted for formula (20), the following compounds are obtained:
Figure GDA0002514713920000143
equation (21) is the midpoint potential balance equation corresponding to the command voltage position of 0.5 when the midpoint potential oscillation is zero in each sampling period. By the same principle, midpoint potential balance formulas corresponding to the command voltage positions 1.5, 2.5, 3.5, 4.5 and 5.5 can be obtained, and then the midpoint potential balance formula corresponding to the command voltage region with the number of 5 is obtained.
(6) Corresponding midpoint potential balance formula when the area number of the command voltage is 6
Assuming that the command voltage falls in sector 0.6 as shown in fig. 4, the voltage space vector action sequence of the resultant command voltage is PPO-PPN-PON-OON by the latest three-vector principle. Let the sampling period be TsThe sum of the action time of the redundant small vectors PPO and OON in one sampling period is TS2PON with a time TMThe PPN action time is TL2Then, there are:
Figure GDA0002514713920000151
in the formula (22), m represents a modulation ratio, θ represents a spatial vector angle, and TsFor a sampling period, TS2Is the sum of the action time of the redundant small vectors PPO and OON in a sampling period, TMFor PON action time, TL2Is the time that the PPN is active in one sampling period. Let the PPO action time be k × TS2OON the action time is (1-k) × TS2Then, there are:
Figure GDA0002514713920000152
in the formula (23), TPPOFor PPO duration, TOONOON acting for a time, T, within a sampling periodPONAnd k is the action time of the PON in one sampling period, and is a redundant small vector action time factor.
When the PPO corresponding midpoint current is ic, the OON corresponding midpoint current is-ic, and the PON corresponding midpoint current is ib, the oscillation value of the midpoint potential in one sampling period can be obtained as follows:
VO＝TS*((2k-1)*(2-2m*sin(π/3+θ))*ic+(2m*sin(π/3-θ))*ib)/C (24)
in the formula (24), VOThe oscillation value of the midpoint potential is ia, ib and ic are phase voltage of A phase, B phase and C phase respectively, and C is the sum of capacitance values of an upper capacitor C1 and a lower capacitor C2 of a direct current bus of the three-level NPC converter. When the midpoint potential oscillation is zero in each sampling period, there is VOWhen formula (24) is substituted with 0, the following can be obtained:
Figure GDA0002514713920000153
equation (25) is the midpoint potential balance equation corresponding to the command voltage position 0.6 when the midpoint potential oscillation is zero in each sampling period. By the same principle, midpoint potential balance formulas corresponding to the command voltage positions of 1.6, 2.6, 3.6, 4.6 and 5.6 can be obtained, and then the midpoint potential balance formula corresponding to the command voltage region with the number of 6 is obtained.
Through the calculation, a midpoint potential balance formula in each sector and region position is obtained.
2. The invention utilizes the action time factor k of the redundant small vectors to control the action time of the two redundant small vectors, thereby realizing the dynamic balance adjustment of the central potential.
Let Tx be the total action time of two redundant small vectors, and the specific way of controlling the action time of the redundant small vectors by using the redundant small vector action time factor k in different sector areas is as follows:
1) for the redundant small vectors POO/ONN, the POO action time is (1-k) Tx, and the ONN action time is k Tx;
2) for redundant small vectors PPO/OON, OON action time is (1-k) Tx, and PPO action time is k Tx;
3) for the redundant small vectors OPO/NON, the OPO action time is (1-k) Tx, and the NON action time is k Tx;
4) for the redundant small vectors OPP/NOO, the NOO action time is (1-k) Tx, and the OPP action time is k Tx;
5) for redundant small vectors OOP/NNO, OOP action time is (1-k) Tx, and NNO action time is k Tx;
6) for the redundant small vector POP/ONO, the ONO action time is (1-k) Tx, and the POP action time is k Tx;
namely ONN, PPO, NON, OPP, NNO, POP correspond to action time k Tx, POO, OON, OPO, NOO, OOP, ONO correspond to action time (1-k) Tx. The reason is that the neutral point current values corresponding to ONN, PPO, NON, OPP, NNO and POP are phase current values, and the neutral point current values corresponding to POO, OON, OPO, NOO, OOP and ONO are opposite numbers of the phase current values. In the derivation of the neutral potential balance equation, the redundant small vectors act on the redundant small vectors corresponding to the time factor k value, wherein the neutral current is a certain phase current value, the redundant small vectors corresponding to the 1-k values act on the neutral current, and the neutral current is the inverse number of the certain phase current value, so that the action time distribution mode of the redundant small vectors can be obtained.
In the above specific manner, Tx represents total action time of two redundant small vectors, P corresponds to a level state of conduction output of two switching devices P1 and P2 of an upper bridge arm of a certain phase of the three-level NPC converter, O corresponds to a level state of conduction output of a switching device P2 below the upper bridge arm of the certain phase of the three-level NPC converter and a switching device P3 above a lower bridge arm of the certain phase of the three-level NPC converter, and N corresponds to a level state of conduction output of two switching devices P3 and P4 of a lower bridge arm of the certain phase of the three-level NPC converter.
The neutral point potential balance control method of the three-level NPC converter utilizes the principle that the effects of two redundant small vectors on neutral point potential are opposite, the neutral point potential oscillation in each period is controlled to be zero as a calculation target, and the action time factors of the two redundant small vectors can be calculated on line only by knowing the three-phase current value and the space vector angle value. The control method can control the midpoint potential deviation of the three-level NPC converter within a small range, and improves the reliability of the three-level NPC converter.
The following examples are provided to illustrate the effects of the present invention.
According to the embodiment of the invention, a three-level NPC inverter model is built by means of PSIM software, and the effectiveness of the neutral point potential balance control method of the three-level NPC converter provided by the invention is verified by using a simulation experiment.
The simulation experiment conditions are as follows: the voltage of a direct current side bus is 5000V, the capacitance values of an upper bridge arm capacitor and a lower bridge arm capacitor of the direct current bus are both 10mF, and the load of an inversion output side is a 5 omega resistor connected with a 10mH inductor in series. The system simulates step size 10us and samples are taken at a frequency of 1200 Hz.
Fig. 5 shows the change conditions of the fundamental wave frequency of 24Hz, the modulation ratio of 0.38, the initial value of the dc bus upper arm capacitor C1 voltage Udc 1V, the initial value of the dc bus lower arm capacitor C2 voltage Udc2 voltage 1500V, and Udc1 and Udc2 without adding neutral point potential balance protection measures. The results of fig. 5 show that when the difference between Udc1 and Udc2 is large and the midpoint potential imbalance problem occurs, if the midpoint potential balance protection measure is not added, the imbalance phenomena of Udc1 and Udc2 always exist, so the midpoint potential balance protection measure needs to be added to restore the midpoint potential to be balanced.
Fig. 6a, fig. 6b and fig. 6C show the fundamental frequency 24Hz, the modulation ratio is fixed to 0.38, the initial value of the voltage Udc1 of the upper arm capacitor C1 of the dc bus is 3500V, and the initial value of the voltage Udc2 of the lower arm capacitor C2 of the dc bus is 1500V. Wherein, fig. 6a is the change condition of Udc1 and Udc2, fig. 6b is the oscillation value Vo of the midpoint potential and the oscillation limit value of the midpoint potential, and fig. 6c is the action time factor k of the redundant small vector calculated by the invention. The simulation sets the midpoint potential oscillation limit value to (Udc1+ Udc2) × 0.05, namely when the midpoint potential oscillation value exceeds the direct current bus voltage by 5%, the midpoint potential balance control method is started. The results of the embodiments of fig. 6a, 6b and 6c show that, under the condition that the difference between Udc1 and Udc2 is large, that is, the midpoint potential is unbalanced, the midpoint potential oscillation value can be gradually reduced to within 5% of the direct-current bus voltage by using the midpoint potential balance control method of the invention, and the midpoint potential balance is effectively ensured. The redundant small vector action time factor k calculated by the method is assigned to 0.5 when the midpoint potential oscillation value is less than 5% of the direct current bus voltage, the online calculation is carried out only under the condition of unbalanced midpoint potential, and the value is limited to 0 to 1.
FIG. 7 shows changes of a Udc1 and a Udc2 under the condition that fundamental wave frequency is 24Hz, modulation ratio is fixed to be 0.38, voltage of a direct current bus upper bridge arm capacitor C1 is Udc1, voltage of a lower bridge arm capacitor is Udc2, and initial value is 2500V, and neutral point potential balance protection measures are not added. Fig. 7 shows that even though the initial values of Udc1 and Udc2 are the same, if a midpoint potential balance protection measure is not added, a midpoint potential imbalance problem may occur in the operation of the three-level NPC converter, which is reflected in that the difference between Udc1 and Udc2 is larger and larger, so that the midpoint potential balance protection measure needs to be added to prevent the midpoint potential imbalance problem in the operation process of the three-level NPC converter.
8a and 8b show fundamental wave frequency 24Hz, modulation ratio fixed 0.38, initial value 2500V of upper bridge arm capacitor C1 voltage Udc1 and lower bridge arm capacitor C2 voltage Udc2 of direct current bus, and result of the embodiment under the action of the control method of the invention. Fig. 8a shows changes in Udc1 and Udc2, and fig. 8b shows the midpoint potential oscillation value Vo and the midpoint potential oscillation limit value. The simulation sets the midpoint potential oscillation limit value to (Udc1+ Udc2) × 0.05, namely when the midpoint potential oscillation value exceeds the direct current bus voltage by 5%, the midpoint potential balance control method is started. The results of the embodiments of fig. 8a and 8b show that, under the condition that the initial values of Udc1 and Udc2 are the same, the midpoint potential oscillation value can be always limited within 5% of the direct-current bus voltage by using the method for controlling the midpoint potential balance in the invention, and the problem of midpoint potential imbalance of the three-level NPC converter can not occur in the operation process.
FIG. 9 shows the change conditions of the fundamental wave frequency of 24Hz, the modulation ratio of 0.1-0.9, the initial values of the DC bus upper bridge arm capacitor C1 voltage Udc1 and the DC bus lower bridge arm capacitor voltage Udc2 voltage of 2500V, and Udc1 and Udc2 under the condition of not adding the midpoint potential balance protection measure. The result of fig. 9 shows that when the modulation ratio is continuously changed, if the midpoint potential balance protection measure is not added, the midpoint potential imbalance problem may occur in the operation of the three-level NPC converter, so the midpoint potential balance protection measure needs to be added to prevent the three-level NPC converter from the midpoint potential imbalance problem in the modulation ratio changing process.
10a, 10b and 10C show fundamental wave frequency 24Hz, modulation ratio 0.1-0.9 cycle change, DC bus upper bridge arm capacitance C1 voltage Udc1 and lower bridge arm capacitance C2 voltage Udc2 initial value 2500V, and result of the embodiment under the action of the control method of the invention. Wherein, fig. 10a is the change situation of Udc1 and Udc2, fig. 10b is the change situation of the midpoint potential oscillation value Vo, the midpoint potential oscillation limit value and the modulation ratio m, and fig. 10c is the redundant small vector action time factor k calculated by the invention. The modulation ratio m is set to be cyclically changed between 0.1 and 0.9 in a simulation mode, the midpoint potential oscillation limit value is set to be (Udc1+ Udc2) × 0.05, namely, when the midpoint potential oscillation value exceeds 5 percent of the direct-current bus voltage, the midpoint potential balance control method is started. The results of the embodiments in fig. 10a, 10b, and 10c show that when the modulation ratio is constantly changed, the midpoint potential oscillation value can be always limited within 5% of the dc bus voltage by using the midpoint potential balance control method in the present invention, and the midpoint potential imbalance problem does not occur in the modulation ratio change process of the three-level NPC converter. The redundant small vector action time factor k calculated by the method is assigned to 0.5 when the midpoint potential oscillation value is less than 5% of the direct current bus voltage, the online calculation is carried out only under the condition of unbalanced midpoint potential, and the value is limited to 0 to 1.
As shown in fig. 5 to 10a, 10b and 10C, the results of the embodiments verify the effectiveness of the neutral point potential balance control method of the three-level NPC converter, and when the voltage Udc1 of the upper arm capacitor C1 and the voltage Udc2 of the lower arm capacitor C2 of the direct-current bus are close, the neutral point potential imbalance problem of the three-level NPC converter is avoided in the operation process; when the initial difference value between Udc1 and Udc2 is large, namely the midpoint potential imbalance problem occurs, the midpoint potential oscillation value can be effectively limited to be within 5% of the direct-current bus voltage by calculating a redundant small vector action time factor k on line; when the modulation ratio is changed continuously, the problem of neutral point potential imbalance of the three-level NPC converter in the modulation ratio changing process can be solved by calculating the redundant small vector action time factor k on line. According to the invention, hysteresis control parameters are not required to be designed, and the action time factors of two redundant small vectors can be calculated on line only by knowing the three-phase current value and the space vector angle value. The method can control the midpoint potential deviation of the three-level NPC converter within a small range, and improves the reliability of the three-level NPC converter.

Claims (4)

1. A neutral point potential balance control method of a three-level NPC converter is characterized in that when neutral point potential oscillation of the three-level NPC converter exceeds a limit value, the control method takes the neutral point potential oscillation in each sampling period as a calculation target to keep zero, and corresponding neutral point potential balance formulas in different sectors and areas are obtained; judging the position of a sector and a region where the current command voltage is located, then detecting a three-phase current value and a space vector angle, substituting the three-phase current value and the space vector angle into a corresponding midpoint potential balance formula of the current sector and the region, calculating to obtain a redundant small vector action time factor, and controlling the action time of two redundant small vectors by using the redundant small vector action time factor to realize dynamic balance adjustment on the midpoint potential;
when the midpoint potential oscillation exceeds a limit value, the control method substitutes the current three-phase current value and the space vector angle into the midpoint potential balance formula corresponding to the current sector and region to calculate, and obtains a redundant small vector action time factor k in each sector region; the k value range calculated by the midpoint potential balance formula is limited to 0 to 1, namely:
Figure FDA0002514713910000011
Figure FDA0002514713910000012
when the neutral point potential oscillation value of the three-level NPC converter is in a limited range, the action time of two redundant small vectors is the same, k is 0.5, and k is a redundant small vector action time factor;
the control method utilizes the action time factor k of the redundant small vectors to control the action time of the two redundant small vectors, and realizes the dynamic balance adjustment of the central potential; let Tx be the total action time of two redundant small vectors, the method for controlling the action time of the redundant small vectors by k in different sector areas is as follows:
1) for the redundant small vectors POO/ONN, the POO action time is (1-k) Tx, and the ONN action time is k Tx;
2) for redundant small vectors PPO/OON, OON action time is (1-k) Tx, and PPO action time is k Tx;
3) for the redundant small vectors OPO/NON, the OPO action time is (1-k) Tx, and the NON action time is k Tx;
4) for the redundant small vectors OPP/NOO, the NOO action time is (1-k) Tx, and the OPP action time is k Tx;
5) for redundant small vectors OOP/NNO, OOP action time is (1-k) Tx, and NNO action time is k Tx;
6) for the redundant small vector POP/ONO, the ONO action time is (1-k) Tx, and the POP action time is k Tx;
in the method, Tx represents the total action time of two redundant small vectors, P corresponds to the level state of the conducted output of two switching devices P1 and P2 of an upper bridge arm of a certain phase of the three-level NPC converter, O corresponds to the level state of the conducted output of the switching device P2 of the upper bridge arm of the certain phase of the three-level NPC converter and the switching device P3 of a lower bridge arm of the certain phase of the three-level NPC converter, and N corresponds to the level state of the conducted output of the two switching devices P3 and P4 of the lower bridge arm of the certain phase of the three-level.
2. The method for controlling the neutral point potential balance of the three-level NPC converter as claimed in claim 1, wherein the method for determining the position number of each sector is as follows:
1) when theta is more than or equal to 0 and less than pi/3, the current sector number is sector 0;
2) when the pi/3 is more than or equal to theta and less than 2 pi/3, the current sector is numbered as sector 1;
3) when theta is more than or equal to 2 pi/3 and less than pi, the current sector is numbered as sector 2;
4) when the pi is more than or equal to the theta and less than 4 pi/3, the current sector is numbered as sector 3;
5) when theta is more than or equal to 4 pi/3 and less than 5 pi/3, the current sector is numbered as sector 4;
6) when theta is more than or equal to 5 pi/3 and less than 2 pi, the current sector is numbered as sector 5;
in the above determination method, θ is the current spatial vector angle.
3. The method for controlling the neutral point potential balance of the three-level NPC converter as claimed in claim 1, wherein the method for determining the position number of each zone is as follows:
Figure FDA0002514713910000021
in the above formula, TsM is a modulation ratio, t1, t2 and t3 are time factors for determining the position of the region in each sector, and θ is the sampling period1Rotate to the angle corresponding to sector 0 for the current spatial vector angle θ, having θ1θ -int (θ/(pi/3)), int denotes rounding a value down to the nearest integer;
rotation to sector 0 by time factors t1, t2, t3 and current spatial vector angle theta1The method for judging the area position number in each sector comprises the following steps:
1) when t1 is more than or equal to 0, t2 is less than 0, t3 is more than or equal to 0, and theta is more than or equal to 01Less than pi/6, and the current area number is area 1;
2) when t1 is more than or equal to 0, t2 is less than 0, t3 is more than or equal to 0, pi/6 is more than theta1Is less than or equal to pi/3, and the number of the current area is area 2;
3) when t1 is more than or equal to 0, t2 is more than or equal to 0, t3 is more than or equal to 0, theta is more than or equal to 01Less than pi/6, and the current area is numbered as area 3;
4) when t1 is more than or equal to 0, t2 is more than or equal to 0, t3 is more than or equal to 0, and phi/6 is more than or equal to theta1Is less than or equal to pi/3, and the number of the current area is area 4;
5) when t1 is more than or equal to 0, t2 is more than or equal to 0, t3 is less than 0, and theta is more than or equal to 01Less than pi/6, and the current area number is area 5;
6) when t1 is less than 0, t2 is more than or equal to 0, t3 is more than or equal to 0, pi/6 is more than or equal to theta1Is less than or equal to pi/3, and the number of the current area is area 6;
the sector number, area 1 position of sector 0, is indicated as 0.1, and area 1 position of sector 1 is indicated as 1.1.
4. The method as claimed in claim 3, wherein when the oscillation of the midpoint potential of the three-level NPC converter exceeds a limit value, the midpoint potential balance formula corresponding to each sector and each region is obtained by taking the midpoint voltage oscillation in each sampling period as a calculation target, as follows:
at the position of 0.1, the position of the first,
Figure FDA0002514713910000031
at the position 0.2 of the first stage,
Figure FDA0002514713910000032
at the position 0.3 of the first position,
Figure FDA0002514713910000033
at the position 0.4 of the first position,
Figure FDA0002514713910000034
at the position of 0.5, the position of the first,
Figure FDA0002514713910000035
at the position 0.6 of the first position,
Figure FDA0002514713910000036
at the position 1.1, the position of the first,
Figure FDA0002514713910000037
at the position 1.2, the position of the first,
Figure FDA0002514713910000038
at the position 1.3 of the first stage,
Figure FDA0002514713910000039
at the position 1.4 of the first stage,
Figure FDA00025147139100000310
at the position 1.5, the position of the first,
Figure FDA00025147139100000311
at the position 1.6 of the first stage,
Figure FDA00025147139100000312
at the position 2.1, the position of the first,
Figure FDA00025147139100000313
at the position 2.2, the position of the first,
Figure FDA00025147139100000314
at the position 2.3 of the first stage,
Figure FDA00025147139100000315
at the position 2.4 of the first position,
Figure FDA0002514713910000041
at the position 2.5, the position of the first,
Figure FDA0002514713910000042
at the position 2.6 of the first position,
Figure FDA0002514713910000043
at the position 3.1, the position of the first,
Figure FDA0002514713910000044
at the position 3.2, the position of the first,
Figure FDA0002514713910000045
at the position 3.3, the position of the first,
Figure FDA0002514713910000046
at the position 3.4 of the first position,
Figure FDA0002514713910000047
at the position 3.5, the position of the first,
Figure FDA0002514713910000048
at the position 3.6 of the first position,
Figure FDA0002514713910000049
at the position 4.1, the position of the first,
Figure FDA00025147139100000410
at the position 4.2, the position of the first,
Figure FDA00025147139100000411
at the position 4.3 of the first position,
Figure FDA00025147139100000412
at the location of the position 4.4,
Figure FDA00025147139100000413
at the position 4.5, the position of the movable part,
Figure FDA00025147139100000414
at the position 4.6 of the first position,
Figure FDA00025147139100000415
at the position 5.1, the position of the first,
Figure FDA0002514713910000051
at the position 5.2, the position of the first,
Figure FDA0002514713910000052
at the position 5.3 of the first position,
Figure FDA0002514713910000053
at the position 5.4 of the first position,
Figure FDA0002514713910000054
at the position 5.5, the position of the guide rail is,
Figure FDA0002514713910000055
at the position 5.6 of the first position,
Figure FDA0002514713910000056
in the above formula, m is the modulation ratio, θ1θ -int (θ/(pi/3)) is an angle corresponding to the rotation of the current space vector angle θ to sector 0, int represents a value rounded down to the nearest integer, ia, ib, and ic are currents of the a, B, and C phases, respectively, and k is a generationAnd (4) applying time factors to the redundant small vectors in each sector area.
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