KR20130086443A - Low current ripple current controller for independent multiphase permanent magnet synchronous motor drives - Google Patents

Abstract

PURPOSE: A low current ripple controller is provided to consistently maintain a switching frequency by controlling the output voltage of an inverter. CONSTITUTION: A current controller includes all bridge inverters. The current controller obtains the reference voltage of the all bridge inverters based on the feed forward of a variable model including the inductance matrix of the independence poly permanent magnet synchronous motor. [Reference numerals] (AA) 1/45+1/4500 [sec]

Description

Low current ripple current controller for independent multiphase permanent magnet synchronous motor drives

The present invention relates to a current control for driving a multiphase synchronous motor, and more particularly, to a current controller having a low current ripple characteristic for driving an independent polyphase permanent magnet synchronous motor, which is recently developed for submarine or ship propulsion. .

Introduction to Prior Art Literature

The concept of so-called independent polyphase AC motors, with no neutral connection in the windings of the phases, was previously proposed by JAHNS in Non-Patent Document 1 in 1980. However, the study of independent polyphase permanent magnet synchronous motors began in earnest in 2000, when MARTIN et al. Proposed the results of applying this type of motor to the high power electric propulsion of a ship in Non-Patent Document 2.

In 2006, Kim Dong-suk presented the results of a study on the design of an independent multiphase permanent magnet synchronous motor of 5MW class 24 phase 32 pole 384 slots for electric propulsion of general ships, warships and submarines. In 2009, Mr. Ho-Yong Choi presented the design results of a multi-permanent multi-phase permanent magnet synchronous motor of several-MW 24 phase 36 pole 432 slots for ship propulsion in Non-Patent Document 4. In 2010, Byung-Kook Cho et al. Presented the results of research on the driving of the motor in Non-Patent Document 5, and Park, Sun-Jung et al. Presented the results of the research on the inverter design of the motor in Non-Patent Document 6.

Key Features of Independent Polyphase Permanent Magnet Synchronous Motor

As the motors of the present invention, the main features of the motors presented from Non-Patent Document 2 to Non-Patent Document 6 are as follows.

1) It is a polyphase method. The polyphase approach allows the use of small power inverters, which are easy to manufacture, to drive large power motors.

2) It is an independent method. Independent phase approach allows the use of single-phase full-bridge inverters, which is advantageous for high capacity implementations.

3) The waveform of electromotive force is close to the trapezoidal wave, not the sinusoidal wave. Trapezoidal waves can produce greater torque under the same conditions. Therefore, higher efficiency can be realized.

Difficulty of Current Control

While the independent polyphase permanent magnet synchronous motor as described above has the advantage of effectively realizing the driving of a large power motor, the current control is particularly difficult for the following reasons.

1) In multiphase, the magnetic coupling between phases is very large. The larger the number of phases, the greater the magnetic coupling. Large magnetic coupling between phases is difficult to control because the current of each phase is greatly changed by the currents of the other phases that are magnetically coupled.

2) The waveform of electromotive force is a trapezoidal wave, not a sinusoidal wave, and the reference current waveform is also a trapezoidal wave, not a sinusoidal wave. Therefore, various current control techniques developed under the sine wave cannot be applied.

Introduction to Current Control Prior Art

Current control prior art for driving permanent magnet synchronous motors is almost always for three-phase Y-connected motors. Basically, the magnetic coupling between phases is small in three phases, but in Y-connection mode, this is canceled out and does not appear in operation. As such, current control techniques applied to motors without magnetic coupling between phases do not show good performance when applied to an independent polyphase permanent magnet synchronous motor having a large magnetic coupling between phases. (The current control techniques described in Patent Documents 1 and 2 are related to independent polyphase permanent magnet synchronous motors, but so-called non-redundant fractional slot motors. Unlike the motors of the present invention, the magnetic coupling between the phases is very small.The current control technique of Patent Documents 1 and 2 is applied to the motors of the present invention where the magnetic coupling between the phases is very large. Does not look like.)

These points are also mentioned in Non-Patent Document 2, and Non-Patent Document 2 proposes a hysteresis controller as a method for solving this problem. In addition, the non-patent document 6 and the non-patent document 7 also proposed a hysteresis controller. Fundamentally, hysteresis controllers have the advantage of being particularly adaptable and of their ability to follow reference current waveforms rather than sinusoids.

Problems of Current Control Prior Art

However, when the hysteresis controller is applied to an independent polyphase permanent magnet synchronous motor having a very large magnetic coupling between phases, the following serious problems arise.

1) The inverter's switching frequency is very irregular.

2) Very large switching ripple occurs in the current waveform.

3) Large switching ripple occurs on the torque waveform.

4) In an all-phase motor with an even number N, the magnetic coupling between the m and m + N / 2 phases is particularly large and does not work properly unless the leakage inductance is large enough.

US 6727668 B1 (MASLOV, B. A. et al.) Apr. 27, 2004. US 7312592 B2 (MASLOV, B. A. et al.) Dec. 25, 2007.

JAHNS, T. M. 'Improved reliability in solid-state ac drives by means of multiple independent phase-drive units', IEEE Transactions on Industry Applications. Vol. IA-16, No. 3, 1980, p 321-331. MARTIN, J.-P .; MEIBODY-TABAR, F .; DAVAT, B. 'Multiple-phase permanent magnet synchronous machine supplied by VSIs, working under fault conditions'. In: Industry Applications Conference, 2000. Conference Record of the 2000 IEEE, 2000, p. 1710-1717. Kim, Dongseok; Gourd, watering; Kim, Handle; God, flagstone. 'A Study on the Design of Large Capacity Permanent Magnet Ship Propulsion Motor with Phase Conversion'. Korean Institute of Electrical Engineers 37th Summer Conference B, 2006, p. 835-836. CHOI, Ho-Yong; PARK, Sun-Jung; KONG, Young-Kyung; Jae-Goo, BIN. 'Design of multi-phase permanent magnet motor for ship propulsion', In: Electrical Machines and Systems, 2009. ICEMS 2009. International Conference on, 2009, p. 1-4. CHO, Byung-Geuk; YOON, Young-Doo; SUL, Seung-Ki; KONG, Young-Kyung; BIN, Jae-Goo; PARK, Sun-Jung; LEE, Man-Li. 'A separate double-winding 12-phase brushless DC motor drive fed from individual H-bridge inverters', In: Energy Conversion Congress and Exposition (ECCE), 2010 IEEE, p. 3889-3895. PARK, Sun-Jung; SONG, Jong-Hwan; CHOI, Ho-Yong; LEE, Man-Li; KONG, Young-Kyung; Jae-Goo, BIN. 'A study on design of inverter for multi-phase brushless DC ship propulsion motor', Vehicle Power and Propulsion Conference (VPPC), IEEE, 2010, p. 1-5. Jung, Sung Young; Ball, mirror; Empty, restoring; God, flagstone; Kim, Jangmok; Choi, Hong Soon; Oh, Jinseok. 'Study on the Characteristic Analysis of Independent 6-Phase BLDC Motors'. Korean Society of Marine Engineers, Vol. 33, No. 6, 2009, p. 939-945. KATO, T .; MIYAO, K. 'Modified hysteresis control with minor loops for single-phase full-bridge inverters', In: Industry Applications Society Annual Meeting, 1988., Conference Record of the 1988 IEEE, 1988, p. 689-693.

An object of the present invention is to solve the problems of the current control prior art for driving an independent polyphase permanent magnet synchronous motor. That is, an object of the present invention is a current control technique for driving an independent polyphase permanent magnet synchronous motor, which can maintain a constant switching frequency of the inverter, does not generate large switching ripple in the current waveform and the torque waveform, and has an even number of phases. It is to provide a new technology without problems in the phase-in progress motor.

The current controller for driving the independent multi-phase permanent magnet synchronous motor of the present invention controls the output voltage of the inverter so that the current follows the reference current by receiving necessary signals from the upper controller and the measurement unit. The main features of the technology are as follows. .

The reference voltage vector v ^* (t) is obtained by the following equation.

In the above formula

L is a previously obtained inductance matrix;

i ^* (t) is the input reference current vector; And

e (t) is the received electromotive force vector.

The output voltage vector v (t) is controlled by pulse width modulating the reference voltage vector v ^* (t).

In the pulse width modulation method, the differential voltages between the phases may equalize the center positions of voltage pulses of all the phases in order to reduce the magnitude of the circulating current ripple occurring through the magnetic coupling between the phases.

The electromotive force vector e (t) of Equation 1 may be obtained as in the following equation.

In the above formula

ψ ( θ _r ) is a coil flux flux distribution vector obtained in advance;

θ _r is the angle of the rotor measured; And

ω _r is the measured angular velocity of the rotor.

The reference current derivative vector of Equation 1 may also be obtained by the following Equation.

Δt in the above formula is a predefined finite time difference.

The reference current derivative vector of Equation 1 may also be obtained by the following Equation.

The reference current derivative vector of Equation 1 can also be obtained with the differentiation of a well-known analog electronic circuit.

The reference current vector i ^* (t) of Equation 1 may be obtained as in the following equation.

In the above formula

α ( θ _r ) is a previously obtained current shape vector; And

T ^* is the reference torque received.

When using Equation 5, the reference current derivative vector of Equation 1 may be obtained as in the following Equation.

When using Equation 5, the product of the inductance matrix of Equation 1 and the reference current derivative vector may be obtained as in the following Equation.

In the above formula

β ( θ _r ) is a previously obtained voltage shape vector.

Feedback may be added to the reference voltage vector v ^* (t) of Equation 1 as in the following equation.

In the above formula

i (t) is the measured current vector; And

r is a predetermined proportional gain.

An equivalent resistance of the winding may be added to the reference voltage vector v ^* (t) of Equation 1 as shown in the following equation.

In the above formula

R is the equivalent resistance of the winding obtained in advance.

Feedback may be added to the reference voltage vector v ^* (t) of Equation 9 as shown in the following equation.

In a full-phase motor with an even number of phases N, the output voltages v _m (t) and v _{m + N / 2} (t) are opposite polarities, especially when the magnetic coupling between m and m + N / 2 phases is large. The same control can be used.

Compared to the hysteresis controller of the current control prior art, the main effects of the present invention are as follows.

1) The inverter's switching frequency can be kept constant.

2) The magnitude of the switching ripple in the current waveform is particularly reduced.

3) The magnitude of the switching ripple in the torque waveform is also greatly reduced.

4) There is no problem even in a full-phase motor with an even number of phases.

1 to 5 are cross-sectional views showing the structure of the electric motors of the present invention.
6 and 7 are part of the drive circuits of the electric motors of the present invention.
8 shows a series connection of windings in a 12 phase mode.
9 is a cross-sectional view showing the structure of a 12-phase electric motor of a half-phase running system.
10 and 11 are auxiliary views for modeling the electric motor of FIG.
12 is an inductance matrix of a full-phase progressive 24 phase electric motor.
13 is an example of a normal void flux density function.
14 is a bond ratio function for FIG. 13.
FIG. 15 is an inductance matrix of 24 phase shift mode with the coupling ratio function of FIG.
16 is another example of a normal void flux density function.
17 is a bond ratio function for FIG. 16.
18 is an example of coil transformer flux distribution.
19 is a simulation result of a hysteresis controller for a phase shift mode 12 phases.
20 to 22 are simulation results of the controller of the present invention with respect to the half-phase progression scheme 12 phases.
23 to 25 are simulation results of the controller of the present invention with respect to the 24 phase shift mode.

Structure of electric motor

In order to illustrate the motors shown in Non-Patent Documents 2 to 6, a cross-sectional view of a permanent magnet synchronous motor of 12 phase 18 pole 108 slots is shown in FIG. The cut portion of the right figure of FIG. 1 is the dashed line AA of the left figure, and the cut part of the left figure is the dashed line BB of the right figure. Reference numeral 101 is a stator, 102 is a permanent magnet, and 103 is a rotor. The motor of FIG. 1 differs only in the number of phases and the number of poles compared to the motors shown in Non-Patent Documents 2 to 6, and other features are the same.

2 is a cross-sectional view of a permanent magnet synchronous motor of 24 phase 2-pole 24 slot. In Fig. 2, the numbers written in the circumferential direction give the phase numbers to the coil sides in the slots. The circumferential number of the small radius is the number of the coil side at the small radius position in the slot of the angle, respectively, and the circumferential number of the large radius is the number of the coil side of the large radius position in the slot of the angle, respectively. Coil sides of the same number but without prime and coil sides of the prime number are connected in series to form a coil circuit, i.e., a winding, of that number. As an example, the connection of the first phase is shown in FIG. 3.

4 is a cross-sectional view of a permanent magnet synchronous motor of 24 phase 4 pole 48 slot. The number written in the circumferential direction in FIG. 4 is also given the number of the phase on the coil side in the slot by the same rule as in FIG. 2. Coil sides of the same number but without prime and coil sides of the number with primes are connected in series to form a coil circuit, i.e., a winding, of that number. As an example, the connection of the first phase is shown in FIG. 5.

The motors of FIGS. 2 to 5 and the motors shown in Non-Patent Documents 2 to 6 differ only in the number of phases or the number of poles, and other features are the same. In the present specification, specific contents will be described as representative of the electric motor of FIG. 2.

Drive circuit of electric motor

6 shows a driving circuit of the electric motor shown in Non-Patent Documents 3 to 6. As shown in FIG. 61st and the 13th on the driving circuit is connected via a switch SW _1. FIG. 6 shows only the driving circuits of the first phase and the thirteenth phase. In general, the driving circuits of the m-th phase and the m + 12th phases are also the same as those of FIG. In Fig. 6, reference numeral 201 denotes an inverter of the first phase, and reference numeral 213 denotes an inverter of the thirteenth phase. The inverters are single phase full bridge voltage source inverters, each of which also consists of four switching elements. The outputs of the inverters are each connected to two coil sides of the corresponding phase. In Fig. 6, the DC side voltage source of the two inverters is common. The DC-side voltage source of all phase inverters may be common, and two or more separate voltage sources may be used to increase reliability. As shown in FIG. 7, non-patent documents 3 to 6 show how to connect the mth phase and the m + 12th phase to two voltage sources, respectively. If SW ₁ and all phases SW _{m in} Figs. 6 and 7 are in the blocking state, the windings of all phases are electrically disconnected and are in the 24 phase mode. However, if SW ₁ and SW _m of all phases are in a conductive state, the winding of the mth phase and the winding of the m + 12th phases are connected in series, which is in the 12 phase mode. 8 shows that the windings of the first phase and the thirteenth phase are connected in series when SW ₁ is in a conductive state. In the 12-phase mode, the motor of FIG. 2 has only twice the number of turns, and is equivalent to the motor of FIG. 9. In the 12-phase mode, the number of turns of each phase doubles, thus doubling the electromotive force. In 12-phase mode, only half of the inverter's switching elements are active. In the case of FIG. 6 or FIG. 7, S ₁ , S ₄ , S ₅ , and S ₈ constitute one full bridge inverter. The 12-phase mode has a lower maximum speed and maximum power than the 24-phase mode, but has the effect of less power loss in the switching elements.

The full bridge inverter can output three kinds of voltages depending on the cases of the conducting switches. Taking the inverter 201 of FIG. 6 as an example, Table 1 shows the output characteristics of the inverter according to the control of the switching elements. In practice, the positive voltage, negative voltage, and zero voltage are not exactly V _dc , -V _dc , and 0 because of the voltage drop in the switching elements, but in this specification the switching element is to avoid the complexity of the description and formula. Ignore the voltage drop across these fields.

When the circuit of FIG. 6 is in the 12-phase mode, the output characteristics according to the control of the switching elements are shown in Table 2.

And when the circuit of Figure 7 in the 12-phase mode, the output characteristics according to the control of the switching elements are shown in Table 3.

In Tables 2 and 3, the output voltage v _1.13 is the voltage from coil side 1 to coil side 13 as shown in FIG.

Definition of a polyphase circuit

If there are two or more single-phase AC circuits, and the desired voltage or current waveforms of each phase have different phase angles, it can be defined as a multiphase circuit. In the AC steady state, an equilibrium condition may be defined when the magnitudes of desired voltages or currents of all phases are the same and the phase angles are multiples of a constant value. By the way, it is preferable to divide the two-phase circuit of the AC steady state and the equilibrium condition according to the type of phase angle. The first kind is the traditional one, called the phase inversion method, and the phase angle θ _m of each phase is obtained by the following equation.

In the above formula, N is the number of phases as the number of single-phase circuits. As an example, FIG. 2 is 24 phases of the full-phase propagation method. The second kind is less well known, called the antiphase process, and the phase angle θ _m of each phase is given by the following equation.

As an example, FIG. 9 is a 12-phase electric motor of a half-phase running system.

By the way, in the phase shift method, when the number of phases N is an even number, there is a special point that the following equation holds in the steady state of alternating current and equilibrium conditions.

In the case where the above formula holds, the N phase is equal to two N / 2 phases overlapping each other.

Now, considering the case where the voltages and currents are the AC steady state, the equilibrium, and the pure sine wave, the voltage and current of each phase can be written as follows.

Then, instantaneous power p _s (t) is as follows.

In other words, in the case of the AC steady state, the equilibrium, and the pure sine wave, the instantaneous power of the polyphase circuit is constant with no change over time. On the other hand, even in the case of not the AC steady state, the equilibrium, or the pure sine wave, if the voltage and current of each phase are properly controlled, the instantaneous power of the polyphase circuit can be constant without change over time.

Model of electric motor

First, in order to avoid too complicated descriptions and formulas, it is assumed that each phase of the motor satisfies the same, i.e., phase symmetry, condition in all respects except for the difference in angle. Faraday's law in differential form is

Now, the equivalent resistance of each phase is ignored once and will be considered later. Then, the relationship between the magnetic flux φ _m that links the winding of the m-th phase and the voltage v _m on the phase is derived from the above equation.

In the above formula, n is the same number of turns of each phase winding.

Next, write the ampere round law in differential form:

The relationship between the current i _k of the k-th phase and the magnetic flux Φ _k from which the current is generated is derived from the above equation from the following equation.

In the above formula, L _s is the same magnetic inductance of each phase winding. The magnetic flux generated by the current in each phase is distributed in the form of magnetic flux density in the voids. As an example, in FIG. 10, the magnetic flux density generated in the void by the current i ₁ of the first phase is indicated by an arrow.

Now, it is considered that the magnetic flux density generated in the air gap in the first phase is represented by the function B ₁ ( θ ) of the angle θ . Let B ₁ ( θ ) be the pore flux density function in which the current in the first phase occurs. Now, the reference line of the angle θ is made into a straight line passing through the coil side from the center of the circle, and the counterclockwise direction is determined as the positive direction. The value of B ₁ ( θ ) is the magnitude at θ of the magnetic flux density at which the current in the first phase is generated in the void, and the sign is positive when the direction of the magnetic flux density enters the rotor, and exits the rotor. Direction is negative. Then you can write

In the above formula, l is the length in the direction of the axis of rotation of the void and r is the radius of the void. In order to normalize the void magnetic flux density function B ₁ ( θ ), a normal void magnetic flux density function b ₁ ( θ ) satisfying the following equation is defined.

Then, the pore magnetic flux density function B _k ( θ ) at which the k-th phase current is generated can be written as follows by applying the phase symmetry condition.

Next, the magnetic flux generated by the rotor to which the permanent magnet is attached is also distributed in the form of magnetic flux density in the void. However, the magnetic flux density rotates in accordance with the rotation of the rotor. Now, the reference line of the angle θ _r of the rotor is also set as the counter-linear line passing through the coil side 1 from the center of the circle, and the counterclockwise direction is set as the positive direction. This is shown in FIG. And when θ _r = 0, it is assumed that the magnetic flux density generated in the voids is represented by the function B _r ( θ ) of the angle θ . Let B _r ( θ ) be the void flux density function in which the rotor is generated. The value of B _r ( θ ) is the magnitude of the magnetic flux density occurring in the void at θ , and the sign is positive when the direction of the magnetic flux density enters the rotor, and when the direction exits the rotor. Negative sign.

In a situation where both the magnetic flux generated by the N-phase currents in the gap and the magnetic flux generated by the rotor are overlapped and distributed, the magnetic flux φ ₁ that bridges the winding of the first phase can be written as the following equation.

Substituting the above formula into Faraday's law, the voltage v ₁ of the first phase is

The integral part of the first term on the right side of the above equation is summarized as follows.

In the above equation, c ( θ _k ) represents the ratio of the magnetic flux portion that links the winding of the first phase among the magnetic flux Φ _k where the current of the k-th phase occurs. Let c ( θ _k ) be called the coupling ratio function.

The second term on the right side of the equation in the preceding paragraph is summarized as follows.

In the above formula, ψ ₁ ( θ _r ) is proportional to the value of magnetic flux density acting on the two coil sides of the first phase when the angle of the rotor is θ _r . Let ψ ₁ ( θ _r ) be the coil flux distribution of the first phase. ω _r is the angular velocity of the rotor and e ₁ (t) is the electromotive force of the first phase. Then you get

The voltage v _{m of the} m-th phase can also be obtained in the same manner by applying the phase symmetry condition, and the following equation is obtained.

Write the above formula as follows:

Now, the same equivalent resistance of each phase is called R, and considering this effect, the above equation becomes as follows.

In the above formula, v (t) is a voltage vector, L is an inductance matrix, i (t) is a current vector, e (t) is an electromotive force vector, ψ ( θ _r ) is a coil transformer flux distribution vector. The diagonal elements of L are magnetic inductances, and the non-diagonal elements are mutual inductances. As an example, the inductance matrix of the 24-phase electric motor of the full-phase propagation method is shown in FIG. 12.

Torque Generation Model

The power p (t) converted from electrical energy to mechanical energy can be written as the following equation.

This power is equal to the product of the torque T (t) of the rotor and the angular velocity ω _r (t) of the rotor.

Therefore, the torque T (t) can be written as

Referring to the above, the above formula can be written as follows.

Current optimization method

Given the angle θ _r of the rotor and thus given the coil flux distribution ψ _m ( θ _r ) of each phase, the current i _m (t) of each phase must be equal to produce any desired torque T (t). The formula must be satisfied. However, the current i _m (t) of each phase satisfying the above formula is not unique but is numerous. Thus, in a multiphase motor having a phase redundancy, an additional purpose may be provided in addition to generating a desired torque. As a further object, a method of minimizing power loss in an equivalent resistance is known, and is also disclosed in Non-Patent Document 2. The optimization problem can be written as

Then, the optimum current of each phase is obtained as follows.

Write the above formula as follows:

As shown in the above equation, the optimum current vector i (t) at time t is proportional to the desired torque T (t), and is proportional to α ( θ _r ) which is a function of the angle of the rotor θ _r . Let α ( θ _r ) be called the current shape vector. On the other hand, it is known that such an optimization method can be applied to fault tolerance operation, and is also disclosed in Non-Patent Document 2.

Real electric motor

The foregoing is a hydraulic model of the motor. We do not know exactly how a real motor works. However, it is conceivable that the function f [] to the virtual, the output voltage of the inverter vector v (t) is applied to the motor, the current vector i (t) generated when the images of the following:

In the above formula,

In order to avoid ambiguity of the formula, the formula is written in two notation forms of the determinant. The same is true for future equations.

Step of the Current Controller of the Invention

Previously described optimization methods, or when turned the reference current vector i ^* (t) obtained by some other method, the current vector i (t) is based on the current vector i ^* (t) a well output voltage of the inverter so as to follow vector v ( Controlling t) is called current control. However, as described above, each phase single-phase full bridge voltage source inverter can output only three types of voltages. Therefore, the voltage of each phase is pulse-width modulated to control the output voltage vector v (t).

The current controller of the present invention has two steps as follows.

1) the current vector i (t) is calculated based on the current vector i ^* (t) so as to follow a well reference voltage vector v ^* (t).

2) The output voltage vector v (t) is controlled by pulse width modulating the reference voltage vector v ^* (t) so that the voltage of each phase approximates the reference voltage well.

Find Reference Voltage Vector

The current controller of the present invention obtains the reference voltage vector v ^* (t) as follows.

In the above formula

L is a previously obtained inductance matrix;

i ^* (t) is the input reference current vector; And

e (t) is the received electromotive force vector.

The same is true for future equations.

The inductance matrix L is obtained by selecting from the following models.

Inductance Matrix Model 1

It is a model that assumes that the magnitude of the magnetic flux density generated by the current in one phase of the void is constant with respect to the circumferential position of the void. The normal void magnetic flux density function b ₁ ( θ ) of this model is shown in FIG. 13. Calculating the coupling ratio function c ( θ _k ) described in the previous model of the motor for this normal void flux density function,

The above formula is shown in a graph as shown in FIG. In the case of 24 phases of the phase shift mode, the inductance matrix L is obtained as shown in FIG. 15. Using this model, all the values of the inductance matrix L can be found by measuring or estimating the same magnetic inductance L _s of each phase winding.

Inductance Matrix Model 2

It is a model in which the magnitude of the magnetic flux density generated in the air in one phase is not constant with respect to the circumferential position of the air. To create an example, a function such as the following expression is used.

16 shows b ₁ ( θ ) with a = 0.05 and q = 4. Calculating the coupling ratio function c ( θ _k ) described in the previous model of the motor for this normal void flux density function,

The above equation is shown in a graph as shown in FIG. 17. Even with this model, all values of the inductance matrix L can be found by measuring or estimating the same magnetic inductance L _s of each phase winding.

Inductance Matrix Model 3

Measure the pore flux density function B ₁ ( θ ) or the normal pore flux density function b ₁ ( θ ) where the current in one phase is generated, or estimate it by a numerical method such as the finite element method, and measure the value of the magnetic inductance L _s in one phase. By estimating, all the values of the inductance matrix L can be found using the equations described in the previous model of the motor . Alternatively, it is also possible to directly measure and use the values of the magnetic inductances and mutual inductances of the inductance matrix L.

Modulating Pulse Width

The output voltage vector v (t) is controlled by pulse width modulating the reference voltage vector v ^* (t) obtained in the previous step. Pulse width modulation methods for single phase full bridge voltage source inverters are well known and all methods are available.

In pulse width modulation methods, the differential voltage between phases may equalize the center position of voltage pulses of all phases in order to reduce the magnitude of circulating current ripple occurring through magnetic coupling between phases. By equalizing the center positions of the voltage pulses of all the phases, the differential voltage between the phases is minimal, thus minimizing the magnitude of the circulating current ripple through the magnetic coupling between the phases.

As the pulse width modulation method, carrier methods may be used, and among them, a three-level triangular carrier method known to have good performance may be used. The carriers of each phase may use independent ones between the phases, and the phase angles of the carriers of all phases may be equalized in order to reduce the magnitude of the circulating current ripple caused by the magnetic coupling between the phases. . The center positions of the voltage pulses of all phases are then almost identical.

The modulation period or carrier period of the pulse width modulation method may be kept constant or may be adjusted for some purpose. Modulation period may be adjusted for the purpose of reducing power loss in switching elements, modulation period may be adjusted for the purpose of reducing switching ripple of torque, modulation period for irregularity of switching ripple of torque You can also make it irregular.

Finding EMF Vectors

The electromotive force vector e (t) of the previous reference voltage vector can be obtained by the following equation.

In the above formula

ψ ( θ _r ) is a coil flux flux distribution vector obtained in advance;

θ _r is the angle of the rotor measured; And

ω _r is the measured angular velocity of the rotor.

Find coil flux flux vector

It is possible to directly measure the coil flux distribution generated by the permanent magnet of the rotor or to estimate it by numerical methods such as finite element method. Alternatively, the electromotive force can be measured and divided by the rotational angular velocity. 18 shows an example of the coil transformer flux distribution ψ ₁ ( θ _r ).

Find Reference Current Derivative Vector

The reference current derivative vector of the previous reference voltage vector can be obtained using the finite time forward difference method as shown in the following equation.

Δt in the above formula is a predefined finite time difference.

The reference current derivative vector may also be obtained using the finite time backward difference method as follows.

The reference current derivative vector can also be found with the differentiation of well-known analog electronic circuits.

Find Reference Current Vector

The reference current vector i ^* (t) in the previous reference voltage vector can be obtained by the following equation with reference to the current optimization method .

In the above formula

α ( θ _r ) is a previously obtained current shape vector; And

T ^* is the reference torque received.

When the above equation is used, the reference current derivative vector of the previous reference voltage vector can be obtained as shown in the following equation.

When using the above equation, the product of the inductance matrix and the reference current derivative vector of the previous reference voltage vector can be obtained as shown in the following equation. By multiplying the inductance matrix and the reference current derivative vector in advance, it is possible to reduce the burden of real-time computation.

In the above formula

β ( θ _r ) is a previously obtained voltage shape vector.

Adding feedback

If the actual motor having a small equivalent resistance when there is transient response speed of the current and the torque slowly Using a reference voltage vector for obtaining the previous reference voltage vector. The smaller the equivalent resistance, the slower the transient response. In this case, feedback may be added to the reference voltage vector v ^* (t) of the previous reference voltage vector calculation as in the following equation.

In the above formula

i (t) is the measured current vector; And

r is a predetermined proportional gain.

The larger the proportional gain r, the faster the transient response, but the noise that can be included in the measured current vector i (t) is amplified to affect the waveform of current and torque. Therefore, it is desirable to set the magnitude of the proportional gain r to a small value as long as the desired transient response speed can be obtained.

Adding the equivalent resistance of the winding

If the actual motor has a large equivalent resistance, the steady-state error appears in the current waveform by using the reference voltage vector in the previous reference voltage vector calculation. The larger the equivalent resistance, the greater the steady state error. In this case, the equivalent resistance of the winding may be added to the reference voltage vector v ^* (t) in the previous reference voltage vector calculation as in the following equation.

In the above formula

R is the equivalent resistance of the winding obtained in advance.

If the equivalent resistance of each phase is not the same, the equivalent resistance R _m of each phase may be used instead of R of the above formula.

Adding equivalent resistance and feedback of windings

As described above, when the actual motor has a large equivalent resistance, the transient response speed of the current and the torque appears quickly. However, when the transient response speed does not reach the desired transient response speed, feedback may be added to the reference voltage vector v ^* (t) of the above equation as shown in the following equation.

Controlling m and m + N / 2 Phases with Same Polarity

The magnetic coupling between m phase and m + N / 2 phase is particularly large in an all-phase motor with even number N of phases. In this case, if there is a differential voltage between the phases, a large cyclic current ripple occurs through the magnetic coupling between the phases. The smaller the leakage inductance between m and m + 12 phases, the larger the magnitude of the circulating current ripple. In this case, the output voltages v _m (t) and v _{m + N / 2} (t) may be controlled equally with the opposite polarity. Then there is no cyclic current ripple between m and m + 12 phases.

Simulation program 1-half-phase motor

In order to more clearly disclose the current controller technology of the present invention, we propose a basic simulation program using Matlab, a computer programming language. Simulation program 1 is for a typical half-phase motor. In particular, a program applied to the 12-phase mode of the electric motor of FIG. The current controller used as an example the addition of equivalent resistance and feedback of the windings. The pulse width modulation method used to equalize the center positions of voltage pulses of all the phases in order to reduce the magnitude of the circulating current ripple caused by the differential voltages between the phases through magnetic coupling between the phases.

As explained earlier, it is not possible to accurately model a real motor, and we have no choice but to simulate a model. However, even in the virtual model, the current controller can be used to evaluate the performance of the current controller by intentionally placing errors on various physical quantities of the model. In this simulation, the following equation is used as a virtual model of the actual motor. Since the change in the angular velocity ω _r of the rotor has little to do with the performance of the current controller, it was kept constant.

Data entry

The data input part of the program is as follows.

In the above program, t1 is the simulation start time, t2 is the end time, NK is the number of times between start and end, dt is the finite time difference, N is the number of phases, Vdc is the DC voltage, and f is the frequency of the rotor. , w is the angular velocity of the rotor, Tmax is the maximum torque, Tr is the reference torque, fs is the modulation frequency, Ts is the modulation period, Ks is the discrete time value of the modulation period, i is the current vector, v is the output voltage vector, e is The electromotive force vector, ir is the reference current vector, T is the torque, vr is the reference voltage vector, vc is the carrier voltage vector, t is the current time, and r is the proportional gain.

Inductance matrix model

The creation part of inductance matrix model 1 is as follows.

In the above program, Ls is the magnetic inductance common to each phase, Lg is the leakage inductance common to each phase, R is the equivalent resistance common to each phase, thk is the phase angle of the kth phase, c is the coupling ratio function, and L1 is the inductance matrix. Model 1, L1inv, is the inverse of inductance matrix model 1.

The creation part of inductance matrix model 2 is as follows.

In the above program, L2 is the inductance matrix model 2 and L2inv is the inverse of the inductance matrix model 2.

Electric Motor System Simulation

The part of the program that simulates the motor system including the current controller is as follows.

In the above program, ext_time is the number of times to increase the simulation time, th is the angle of the rotor, PsiH (th, N) is the function to obtain the coil variable flux distribution vector, and AlpH (th, N) is the function to obtain the current shape vector. .

Find coil coil flux distribution vector

If you save the program to obtain the coil flux distribution vector as a file named PsiH.m, the matlab program will recognize it as a built-in function. The formula of the function is made to approximate the electromotive force waveforms presented from Non-Patent Document 3 to Non-Patent Document 6.

In the above program, n is the number of turns of each phase, Vmax is the maximum value of the electromotive force, and wmax is the maximum value of the angular velocity of the rotor.

Function to find reference current derivative vector

If you save the program to obtain the reference current derivative vector as a file named AlpH.m, Matlab program recognizes it as a built-in function.

Function to generate reference torque

If you save the program that generates the reference torque as a file named Tref.m, Matlab program recognizes it as a built-in function.

Program that shows waveforms graphically

The program to display the waveform as follows is as follows. You can check the waveform by inserting it at the end or in the middle of the program.

Simulation result-12 phase motor with half phase

Although many simulations and robust control characteristics have been confirmed during the technology development process, it is difficult to present in this specification, and the basic program is provided instead. However, simulation results of the high speed rotation state and the low speed rotation state, respectively, in which the reference torque increases linearly from the zero torque state to the maximum torque for 1/90 second are shown in FIGS. 19 to 21. 19 shows the result of using the prior art hysteresis controller, and FIGS. 20 and 21 show the result of using the controller of the present invention. 22 shows the output voltages of all phases within the modulation period. It can be seen that the center positions of voltage pulses of all phases are almost the same.

Simulation program 2-electric motor

Simulation program 2 is for a general electric motor of general phase advance. In particular, a program applied to the 24-phase mode of the motor of FIG. The current controller used as an example the addition of equivalent resistance and feedback of the windings. The pulse width modulation method used to equalize the center positions of voltage pulses of all the phases in order to reduce the magnitude of the circulating current ripple caused by the differential voltages between the phases through magnetic coupling between the phases.

Data entry

The data input part of the program is as follows.

Inductance matrix model

The creation part of inductance matrix model 1 is as follows.

The creation part of inductance matrix model 2 is as follows.

Electric Motor System Simulation

The part of the program that simulates the motor system including the current controller is as follows.

Find coil coil flux distribution vector

If you save the program to obtain the coil flux distribution vector as a file named PsiF.m, the matlab program will recognize it as a built-in function.

Function to find reference current derivative vector

If you save the program to obtain the reference current derivative vector as a file named AlpF.m, Matlab program recognizes it as a built-in function.

Simulation result-24 phase electric motor

Although many simulations and robust control characteristics have been confirmed during the technology development process, it is difficult to present in this specification, and the basic program is provided instead. However, simulation results of the high speed rotation state and the low speed rotation state, respectively, in which the reference torque increases linearly from the zero torque state to the maximum torque during 1/90 second are shown in FIGS. 23 to 24. 25 shows the output voltages of all phases within the modulation period. It can be seen that the center positions of voltage pulses of all phases are almost the same.

On the other hand, the prior art hysteresis controller not only performs poorly in a 24-phase electric motor, but also does not work properly at all when the leakage inductance is small. The reason is that the magnetic coupling between m phase and m + 12 phase is too large for a 24 phase electric motor. In this case, if there is a differential voltage between the phases, too large cyclic current ripple occurs through the magnetic coupling between the phases, so it is necessary to make the voltages of the m phase and the m + 12 phases the same with the opposite polarity.

Claims (1)

A current controller for driving an independent polyphase permanent magnet synchronous motor with full bridge inverters, comprising: a reference voltage of the full bridge inverters including a feedforward of a phase variable model including an inductance matrix of the independent polyphase permanent magnet synchronous motor; And a method for driving an independent polyphase permanent magnet synchronous motor.

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