CN114865975B - A Linear Inductance Model Optimization Method for Rotor Position Estimation of Three-Phase Switched Reluctance Motor - Google Patents

Abstract

The present invention is a linear inductance model optimization method for estimating the rotor position of a three-phase switched reluctance motor. When the three-phase switched reluctance motor is running under high load, there are six intervals divided according to the logical relationship between the three-phase inductances in one inductance cycle. Each interval always has one phase saturated inductance and two phases unsaturated inductance. The saturated inductance will cause the rotor position estimation accuracy of the traditional linear inductance model to be seriously reduced. Therefore, the present method estimates the sum of the three-phase unsaturated inductances. Based on the fact that the sum of the three-phase unsaturated inductances is a constant at any position, the virtual inductance of each phase is defined as the difference between the sum of the three-phase unsaturated inductances and the estimated phase inductances of the other two phases. When the magnetic circuit is saturated, the virtual inductance is used to replace the saturated phase inductance in a given interval to participate in the interval division of the inductance cycle, and the linear inductance model is reconstructed. This effectively improves the rotor position estimation accuracy under magnetic saturation conditions and ensures the reliable driving of the three-phase switched reluctance motor when it is running at medium and low speeds without a position sensor.

Description

Optimization method of linear inductance model for rotor position estimation of three-phase switched reluctance motor

Technical Field

The present invention belongs to the technical field of motor control, and in particular relates to a linear inductance model optimization method for estimating the rotor position of a three-phase switched reluctance motor.

Background Art

Switched reluctance motor (SRM) has the advantages of simple structure, low cost, wide speed regulation range, and strong fault tolerance. It is widely used in electric vehicles and industrial applications. The high-performance control of switched reluctance motors requires accurate rotor position information as a basis, and the rotor position information is currently mainly obtained through position sensors. Commonly used mechanical position sensors increase the size and cost of the entire motor control system to a certain extent, and are prone to failure in extremely harsh environments such as high temperature, oil pollution, and dust. Therefore, position sensorless control technology has important research value.

In recent years, a large number of switched reluctance motor position sensorless control technologies have been proposed based on the mapping relationship between electromagnetic characteristics and rotor position. In practical applications, the magnetic circuit of the switched reluctance motor is usually in a saturated state. Inductance distortion can cause the accuracy of most rotor position estimation based on the excitation phase inductance to decrease, and in severe cases, the algorithm fails. The traditional rotor position estimation method based on the linear inductance model is only applicable to the non-saturated magnetic circuit condition. In order to accurately identify the rotor position when the magnetic circuit is saturated, the existing model optimization method usually requires a large amount of offline detection and mathematical calculations to compensate for the rotor position estimation error accordingly. This optimization process is relatively complicated and the measurement data is not universal.

Therefore, this application proposes a linear inductance model optimization method for estimating the rotor position of a three-phase switched reluctance motor. The method has simple logic and is easy to implement. It can effectively avoid the influence of magnetic saturation and achieve high-precision identification of the rotor position by relying solely on the distribution characteristics of the three-phase inductance.

Summary of the invention

In view of the deficiencies in the prior art, the technical problem to be solved by the present invention is to provide a linear inductance model optimization method for rotor position estimation of a three-phase switched reluctance motor.

The technical solution adopted by the present invention to solve the technical problem is as follows:

A linear inductance model optimization method for three-phase switched reluctance motor rotor position estimation includes linear inductance models in two cases: unsaturated and saturated magnetic circuits. The method is characterized in that the method includes the following contents:

Based on the asymmetric half-bridge power converter, the windings of the three-phase switched reluctance motor are turned on in turn according to a certain conduction interval. The conducting phase winding adopts the current chopping control method, and the non-conducting phase winding is injected with high-frequency pulses. The three-phase full-cycle inductance is estimated by formula (1) to obtain the three-phase estimated phase inductance L _A , L _B , L _C ;

Where, L is the estimated phase inductance, i(t) represents the relationship function between phase current and time, U _dc is the bus voltage, V _D and _VT are the diode voltage drop and power switch voltage drop of the power converter, respectively, and di(t)/dt| _on and di(t)/dt| _off represent the current slopes at the instants of winding opening and closing, respectively;

When the magnetic circuit is not saturated, one inductance cycle of the three-phase switched reluctance motor is divided into 6 intervals according to the logical relationship between the three-phase inductances. Then, there are 6 phase inductance intersections in one inductance cycle, and each interval is 60°/N _r mechanical angle, where N _r represents the number of rotor poles of the three-phase switched reluctance motor. When the conduction phase sequence is ABC, taking phase B as an example, the 6 intervals are R1: [0°, 60°/N _r ), R2: [60°/N _r , 120°/N _r ), R3: [120°/N _r , 180°/N _r ), R4: [180°/N _r , 240°/N _r ), R5: [240°/N _r , 300°/N _r ), R6: [300°/N _r , 0°);

When the magnetic circuit is unsaturated, measure the upper and lower inductance intersection thresholds _Lm and _Ln , and estimate _{the sum} of the three-phase unsaturated inductances Lsum by formula (2);

L _sum = L _A + L _B + L _C (2)

Assume that the three-phase virtual inductance is L _A ', L _B ' and L _C ', and define the virtual inductance of each phase as the difference between the sum of the three-phase unsaturated inductance L _sum and the estimated phase inductance of the other two phases. Then the three-phase virtual inductance is:

When the conduction phase sequence is A-B-C, in the case of magnetic circuit saturation, in intervals R2 and R3, the virtual inductance of phase B is used to replace the saturated estimated phase inductance of phase B to participate in interval division, in intervals R4 and R5, the virtual inductance of phase C is used to replace the saturated estimated phase inductance of phase C to participate in interval division, and in intervals R6 and R1, the virtual inductance of phase A is used to replace the saturated estimated phase inductance of phase A to participate in interval division; that is, the intervals R2 and R3 are logically divided according to the size of the estimated phase inductances of phase A and phase C and the virtual inductance of phase B, the intervals R4 and R5 are logically divided according to the size of the estimated phase inductances of phase A and phase B and the virtual inductance of phase C, and the intervals R6 and R1 are logically divided according to the size of the estimated phase inductances of phase B and phase C and the virtual inductance of phase A;

When the conduction phase sequence is C-B-A, in the case of magnetic circuit saturation, in intervals R2 and R3, the virtual inductance of phase B is used to replace the saturated estimated phase inductance of phase B to participate in interval division, in intervals R4 and R5, the virtual inductance of phase A is used to replace the saturated estimated phase inductance of phase A to participate in interval division, and in intervals R6 and R1, the virtual inductance of phase C is used to replace the saturated estimated phase inductance of phase C to participate in interval division; that is, according to the size logic of the estimated phase inductances of phase A and phase C and the virtual inductance of phase B, the intervals R2 and R3 are divided according to the size logic of the estimated phase inductances of phase B and phase C and the virtual inductance of phase A, and the intervals R4 and R5 are divided according to the size logic of the estimated phase inductances of phase B and phase C and the virtual inductance of phase A, and the intervals R6 and R1 are divided according to the size logic of the estimated phase inductances of phase A and phase B and the virtual inductance of phase C;

When the magnetic circuit is saturated, a linear inductance model shown in formula (14) is constructed with the participation of virtual inductance to estimate the rotor position in real time, and then the rotor speed is estimated according to formula (4) to realize the position-free operation of the three-phase switched reluctance motor;

Wherein, θ represents the estimated rotor position, k ₁ =-(L _m -L _n )N _r /60 represents the phase inductance slope in the odd interval, k ₂ =(L _m -L _n )N _r /60 represents the phase inductance slope in the even interval, p and q represent the odd and even intervals respectively, u and v represent the phase in the odd and even intervals respectively, _Lu (θ) represents the estimated phase inductance of the u phase with the rotor position as the independent variable, and _Lv ′(θ) represents the virtual inductance of the v phase with the rotor position as the independent variable;

Where f is the sampling frequency, ω(n) is the rotor speed, θ(n) and θ(n-1) represent the rotor position information in the nth and n-1th sampling periods respectively.

Compared with the prior art, the present invention has the following beneficial effects:

1. For the three-phase switched reluctance motor, in order to prevent the generation of unexpected negative torque, the phase current level in the inductance decrease interval will not be higher than the saturation current threshold, otherwise the working efficiency of the motor will be greatly reduced; on the other hand, the influence of magnetic saturation on the bottom area where the estimated phase inductance is less than the lower inductance intersection threshold is negligible, that is, the inductance of each phase is unsaturated in the decrease and bottom areas, while in the positive torque area where the estimated phase inductance is greater than the lower inductance intersection threshold, the current level is high, and the estimated phase inductance is usually in a saturated and distorted state. Therefore, when the three-phase switched reluctance motor is running at high load, there is always one phase saturated inductance and two phases unsaturated inductance in each interval divided according to the logical relationship between the three-phase inductances in one inductance cycle. The saturated inductance will cause the accuracy of rotor position estimation of the traditional linear inductance model to be seriously reduced. Since the sum of the three-phase unsaturated inductances is a constant at any position, the virtual inductance obtained based on the two-phase unsaturated inductances is also unsaturated. Therefore, when the magnetic circuit is saturated, the virtual inductance is used to replace the saturated phase inductance in a given interval to participate in interval division and reconstruct the linear inductance model, which can effectively avoid the influence of magnetic saturation on the accuracy of rotor position estimation.

2. Based on the distribution characteristics of the inductance curve, the present invention proposes a linear inductance model optimization method for three-phase switched reluctance motor rotor position estimation. When the magnetic circuit is saturated, a virtual inductance is used to replace the saturated phase inductance in a given interval to participate in the construction of the linear inductance model, which effectively improves the rotor position estimation accuracy under magnetic saturation conditions and ensures reliable driving of the three-phase switched reluctance motor without position sensor at low and medium speeds. The method is simple in logic and has universal applicability to three-phase switched reluctance motors.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a three-phase inductance curve when the magnetic circuit is unsaturated;

FIG2 is a three-phase inductance curve diagram when the magnetic circuit is saturated;

FIG3 is a schematic diagram of virtual inductance replacement in each interval when the conduction phase sequence is A-B-C.

DETAILED DESCRIPTION

The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods, but the protection scope of the present application is not limited thereto.

The present invention is a linear inductance model optimization method for three-phase switched reluctance motor rotor position estimation, including linear inductance models in two conditions: unsaturated and saturated magnetic circuits;

1) Establish a linear inductance model when the magnetic circuit is not saturated;

Based on the asymmetric half-bridge power converter, the windings of the three-phase switched reluctance motor are turned on in turn according to a certain conduction interval. The winding current of the three-phase switched reluctance motor generates electromagnetic torque. During the operation of the three-phase switched reluctance motor, the conducting phase winding adopts the current chopping control method, and the non-conducting phase winding injects high-frequency pulses; the current slope difference method is used to estimate the three-phase full-cycle inductance, and the three-phase estimated phase inductance L _A , L _B , L _C are obtained. The general formula is:

Where, L is the estimated phase inductance, i(t) represents the relationship function between phase current and time, U _dc is the bus voltage, V _D and _VT are the diode voltage drop and power switch voltage drop of the power converter, respectively, and di(t)/dt| _on and di(t)/dt| _off represent the current slopes at the instants of winding opening and closing, respectively;

When the magnetic circuit is not saturated, one inductance cycle of the three-phase _Ns / _{Nr pole} switched reluctance motor is divided into 6 intervals according to the logical relationship of the three-phase inductance. One inductance cycle has 6 phase inductance intersections. When the conduction phase sequence is ABC, taking phase B as an example, the 6 intervals are R1: [0°, 60°/ _Nr ), R2: [60°/ _Nr , 120°/ _Nr ), R3: [120°/ _Nr , 180°/ _Nr ), R4: [180°/ _Nr , 240°/ _Nr ), R5: [240°/ _Nr , 300°/ _Nr ), R6: [300°/ _Nr , 0°); _Ns represents the number of stator poles, and _Nr represents the number of rotor poles; as shown in Figure 1, taking the three-phase 12/8 pole switched reluctance motor as an example, each interval is 7.5° mechanical angle;

When the magnetic circuit is unsaturated, measure the upper and lower inductance intersection thresholds _Lm and _Ln , and estimate _{the sum} of the three-phase unsaturated inductances Lsum by formula (2);

L _sum = L _A + L _B + L _C (2)

A traditional linear inductance model is constructed to estimate the rotor position information in real time, and its expression is:

Wherein, θ represents the estimated rotor position, k ₁ =-(L _m -L _n )N _r /60 represents the phase inductance slope in the odd interval, k ₂ =(L _m -L _n )N _r /60 represents the phase inductance slope in the even interval, p and q represent the odd and even intervals respectively, u and v represent the phases in the odd and even intervals respectively, _Lu (θ) and _Lv (θ) represent the estimated phase inductances of the u and v phases respectively with the rotor position as the independent variable;

The rotor speed is estimated based on the rotor position, and its expression is:

Where f is the sampling frequency, ω(n) is the rotor speed, θ(n) and θ(n-1) represent the rotor position information in the nth and n-1th sampling periods respectively;

Without considering magnetic circuit saturation, the estimated relationship between phase inductance and rotor position can be expressed by Fourier series as follows:

Where, L _j (i) represents the coefficient function of the phase inductance DC component, fundamental component and each order harmonic component, i represents the phase current, j represents the order, represents the initial phase;

Usually, the harmonic component is much smaller than the fundamental component. Ignoring the third-order and higher harmonic components, when the conduction phase sequence is A-B-C, the estimated phase inductance of the three phases can be expressed as:

L _B (θ)＝L ₀ (i _B )+L ₁ (i _B )cosN _r θ+L ₂ (i _B )cos2N _r θ (7)

Wherein, L _A (θ), L _B (θ), L _C (θ) represent the functions of A-phase, B-phase, and C-phase inductances and rotor positions, respectively; L ₀ (i _A ), L ₁ (i _A ), and L ₂ (i _A ) represent the DC component, first-order fundamental component, and second-order harmonic component of the estimated phase inductance of phase A, respectively; i _A represents the A-phase current; L ₀ (i _B ), L ₁ (i _B ), and L ₂ (i _B ) represent the DC component, first-order fundamental component, and second-order harmonic component of the estimated phase inductance of phase B, respectively; i _B represents the B-phase current; L ₀ (i _C ), L ₁ (i _C ), and L ₂ (i _C ) represent the DC component, first-order fundamental component, and second-order harmonic component of the estimated phase inductance of phase C, respectively; i _C represents the C-phase current;

The DC component, first-order fundamental component and second-order harmonic component of the estimated phase inductance of each phase can be expressed as:

Wherein, L _max (i) and L _min (i) represent the maximum phase inductance and the minimum phase inductance respectively, and L _mid (i) represents the middle value between the maximum inductance and the minimum inductance;

The sum of the three-phase unsaturated inductance is a constant and satisfies the following formula:

L _A (θ)+L _B (θ)+L _C (θ)＝3L ₀ (i)＝L _sum (12)

It can be seen from formula (12) that the sum of the three-phase unsaturated inductances is equal to the constant value L _sum at any position; further, assuming that the three-phase virtual inductances are L _A ', L _B ' and L _C ', and defining the virtual inductance of each phase as the difference between the sum of the three-phase unsaturated inductances L _sum and the estimated phase inductances of the other two phases, the three-phase virtual inductances are respectively:

2) Establish a linear inductance model when the magnetic circuit is saturated;

As shown in Figure 2, taking phase B as an example, when the phase current exceeds the saturation current threshold, the degree of magnetic circuit saturation increases with the increase of phase current, and the estimated phase inductance in the rising interval gradually decreases, which leads to an increasingly obvious difference between the actual inductance slope and the phase inductance slope _k2 , thus causing a significant local rotor position estimation error.

In order to eliminate the error in the estimation of the rotor position, as shown in FIG3 , when the conduction phase sequence is ABC, in the case of magnetic circuit saturation, in intervals R2 and R3, the virtual inductance _LB ′ of phase B is used to replace the saturated estimated phase inductance of phase B to participate in the interval division, in intervals R4 and R5, the virtual inductance _LC ′ of phase C is used to replace the saturated estimated phase inductance of phase C to participate in the interval division, and in intervals R6 and R1, the virtual inductance _LA ′ of phase A is used to replace the saturated estimated phase inductance of phase A to participate in the interval division, and the inductance options corresponding to each interval are shown in Table 1, that is, according to the size of the estimated phase inductance of phase A and phase C and the virtual inductance of phase B, the intervals R2 and R3 are logically divided according to the size of the estimated phase inductance of phase A and phase C and the virtual inductance of phase C, and the intervals R4 and R5 are logically divided according to the size of the estimated phase inductance of phase A and phase B and the virtual inductance of phase C, and the intervals R6 and R1 are logically divided according to the size of the estimated phase inductance of phase B and phase C and the virtual inductance of phase A;

Table 1 Inductance options corresponding to each range

When the conduction phase sequence is CBA, in the case of magnetic circuit saturation, in intervals R2 and R3, the virtual inductance L _B ′ of phase B is used to replace the saturated estimated phase inductance of phase B to participate in interval division, in intervals R4 and R5, the virtual inductance L _A ′ of phase A is used to replace the saturated estimated phase inductance of phase A to participate in interval division, and in intervals R6 and R1, the virtual inductance L _C ′ of phase C is used to replace the saturated estimated phase inductance of phase C to participate in interval division; that is, the intervals R2 and R3 are logically divided according to the size of the estimated phase inductances of phases A and C and the virtual inductance of phase B, the intervals R4 and R5 are logically divided according to the size of the estimated phase inductances of phases B and C and the virtual inductance of phase A, and the intervals R6 and R1 are logically divided according to the size of the estimated phase inductances of phases A and B and the virtual inductance of phase C;

When the magnetic circuit is saturated, that is, when the phase current exceeds the saturation current threshold, a linear inductance model shown in formula (14) is constructed with the participation of virtual inductance to estimate the rotor position in real time, and then the rotor speed is estimated according to formula (4) to realize the position-free operation of the three-phase switched reluctance motor;

Wherein, L _v ′(θ) represents the v-phase virtual inductance with the rotor position as the independent variable.

Any matters not described in the present invention are applicable to the prior art.

Claims (2)

1. A linear inductance model optimization method for three-phase switched reluctance motor rotor position estimation, including linear inductance models in two cases of unsaturated and saturated magnetic circuits; characterized in that the method includes the following contents: Based on the asymmetric half-bridge power converter, the windings of the three-phase switched reluctance motor are turned on in turn according to a certain conduction interval. The conducting phase winding adopts the current chopping control method, and the non-conducting phase winding is injected with high-frequency pulses. The three-phase full-cycle inductance is estimated by formula (1) to obtain the three-phase estimated phase inductance L _A , L _B , L _C ; Where, L is the estimated phase inductance, i(t) represents the relationship function between phase current and time, U _dc is the bus voltage, V _D and _VT are the diode voltage drop and power switch voltage drop of the power converter, respectively, and di(t)/dt| _on and di(t)/dt| _off represent the current slopes at the instants of winding opening and closing, respectively; When the magnetic circuit is not saturated, one inductance cycle of the three-phase switched reluctance motor is divided into 6 intervals according to the logical relationship between the three-phase inductances. Then, there are 6 phase inductance intersections in one inductance cycle, and each interval is 60°/N _r mechanical angle, where N _r represents the number of rotor poles of the three-phase switched reluctance motor. When the conduction phase sequence is ABC, taking phase B as an example, the 6 intervals are R1: [0°, 60°/N _r ), R2: [60°/N _r , 120°/N _r ), R3: [120°/N _r , 180°/N _r ), R4: [180°/N _r , 240°/N _r ), R5: [240°/N _r , 300°/N _r ), R6: [300°/N _r , 0°); When the magnetic circuit is unsaturated, measure the upper and lower inductance intersection thresholds _Lm and _Ln , and estimate _{the sum} of the three-phase unsaturated inductances Lsum by formula (2); L _sum = L _A + L _B + L _C (2) Assume that the three-phase virtual inductance is L _A ', L _B ' and L _C ', and define the virtual inductance of each phase as the difference between the sum of the three-phase unsaturated inductance L _sum and the estimated phase inductance of the other two phases. Then the three-phase virtual inductance is: When the conduction phase sequence is A-B-C, in the case of magnetic circuit saturation, in intervals R2 and R3, the virtual inductance of phase B is used to replace the saturated estimated phase inductance of phase B to participate in interval division, in intervals R4 and R5, the virtual inductance of phase C is used to replace the saturated estimated phase inductance of phase C to participate in interval division, and in intervals R6 and R1, the virtual inductance of phase A is used to replace the saturated estimated phase inductance of phase A to participate in interval division; that is, the intervals R2 and R3 are logically divided according to the size of the estimated phase inductances of phase A and phase C and the virtual inductance of phase B, the intervals R4 and R5 are logically divided according to the size of the estimated phase inductances of phase A and phase B and the virtual inductance of phase C, and the intervals R6 and R1 are logically divided according to the size of the estimated phase inductances of phase B and phase C and the virtual inductance of phase A; When the conduction phase sequence is C-B-A, in the case of magnetic circuit saturation, in intervals R2 and R3, the virtual inductance of phase B is used to replace the saturated estimated phase inductance of phase B to participate in interval division, in intervals R4 and R5, the virtual inductance of phase A is used to replace the saturated estimated phase inductance of phase A to participate in interval division, and in intervals R6 and R1, the virtual inductance of phase C is used to replace the saturated estimated phase inductance of phase C to participate in interval division; that is, according to the size logic of the estimated phase inductances of phase A and phase C and the virtual inductance of phase B, the intervals R2 and R3 are divided according to the size logic of the estimated phase inductances of phase B and phase C and the virtual inductance of phase A, and the intervals R4 and R5 are divided according to the size logic of the estimated phase inductances of phase B and phase C and the virtual inductance of phase A, and the intervals R6 and R1 are divided according to the size logic of the estimated phase inductances of phase A and phase B and the virtual inductance of phase C; When the magnetic circuit is saturated, a linear inductance model shown in formula (14) is constructed with the participation of virtual inductance to estimate the rotor position in real time, and then the rotor speed is estimated according to formula (4) to realize the position-free operation of the three-phase switched reluctance motor; Wherein, θ represents the estimated rotor position, k ₁ =-(L _m -L _n )N _r /60 represents the phase inductance slope in the odd interval, k ₂ =(L _m -L _n )N _r /60 represents the phase inductance slope in the even interval, p and q represent the odd and even intervals respectively, u and v represent the phase in the odd and even intervals respectively, _Lu (θ) represents the estimated phase inductance of the u phase with the rotor position as the independent variable, and _Lv ′(θ) represents the virtual inductance of the v phase with the rotor position as the independent variable; Where f is the sampling frequency, ω(n) is the rotor speed, θ(n) and θ(n-1) represent the rotor position information in the nth and n-1th sampling periods respectively. 2. The linear inductance model optimization method for three-phase switched reluctance motor rotor position estimation according to claim 1, characterized in that the linear inductance model established when the magnetic circuit is unsaturated is: Where L _v (θ) represents the estimated inductance of the v phase with the rotor position as the independent variable.