Torque ripple optimization control method for SRM based on quasi-sine wave current excitation

Abstract

This invention presents an optimized control method for SRM torque ripple based on quasi-sinusoidal current excitation. First, the rotor position electrical angle and actual three-phase current values ​​are acquired. The actual motor speed is calculated based on the rotor position electrical angle, and the speed deviation between the actual speed and the given speed is calculated. This speed deviation is then processed by PI control to obtain the reference value of the q-axis component of the base frequency virtual current. Based on the rotor position electrical angle and the base frequency virtual current vector reference value, the three-phase virtual current reference values ​​are calculated. Next, the inductance of each phase of the switched reluctance motor is obtained through simulation, and the inductance of each phase is Fourier decomposed. A second-order virtual current vector is selected as the compensation quantity and superimposed with the base frequency virtual current vector to obtain the three-phase virtual current. Finally, the error between the three-phase virtual current reference value and the actual value is calculated. This three-phase virtual current error is then processed by hysteresis control to generate drive signals for each switch of the power converter, enabling switching control of the power converter. This method suppresses torque ripple by generating a quasi-sinusoidal phase current.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, specifically relating to an SRM torque ripple optimization control method based on quasi-sinusoidal current excitation. Background Technology

[0002] Switched reluctance motors (SRMs) are widely used in various fields such as electric vehicles, home appliances, and spacecraft starters due to their advantages of simple structure, low manufacturing cost, high reliability, large starting torque, and high efficiency. (See also...) Figure 1 A switched reluctance motor drive (SRD) system includes a switched reluctance motor (SRM), a power converter, a position sensor, a current sensor, and a controller. The switched reluctance motor is responsible for electromechanical energy conversion, the power converter excites the stator windings of the switched reluctance motor, the controller provides drive signals to the switching devices of the power converter, the encoder detects the rotor position in real time, and the current sensor detects the three-phase current of the motor in real time.

[0003] The simple yet unique doubly salient pole structure of switched reluctance motors (SRMs) generates nonlinear electromagnetic characteristics that lead to significant torque ripple at low speeds, limiting their further promotion and application. Current excitation to suppress torque ripple is an important control method, which achieves this by injecting virtual currents of other orders into the fundamental frequency virtual current. Classic methods for torque ripple control based on current excitation include quasi-square wave current excitation and sinusoidal current excitation with a DC bias component. For the phase current and phase inductance waveforms of traditional quasi-square wave current excitation control, see [reference needed]. Figure 2 The phase current is typically adjusted to a quasi-square wave waveform, and current is turned on when the inductor slope is positive to obtain positive torque. This control method has strong torque output capability, but the discontinuous current waveform can cause large torque ripple. It also requires precise electromagnetic characteristic data of the motor, such as high-speed, high-accuracy sampling and extremely low step sizes, to modulate the current or torque in real time, placing higher demands on both the hardware and software of the control system. See [link to relevant documentation] for the phase current and phase inductance waveforms of sinusoidal current excitation control with DC bias components. Figure 3 Following the control logic of AC motors, the phase inductance is simplified into a sinusoidal model, and the phase current is a sinusoidal wave with DC bias. Although the waveform of this control method is continuous, its control mode is based on permanent magnet synchronous motors and has inherent third torque harmonics, resulting in large torque ripple. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the technical problem this invention aims to solve is to provide an optimized control method for SRM torque ripple based on quasi-sinusoidal current excitation, so as to reduce SRM torque ripple and enable SRM to achieve higher operational stability.

[0005] The technical solution adopted by the present invention to solve the aforementioned technical problem is as follows:

[0006] A torque ripple optimization control method for SRM based on quasi-sinusoidal current excitation includes the following steps:

[0007] Step 1: Collect the rotor position electrical angle and the actual value of the three-phase current of the switched reluctance motor; calculate the actual speed of the motor based on the rotor position electrical angle, and calculate the speed deviation between the actual speed and the given speed. The speed deviation is controlled by PI to obtain the reference value of the q-axis component of the base frequency virtual current.

[0008] Based on the rotor position electrical angle and the fundamental frequency virtual current vector reference value, the three-phase virtual current reference value is calculated using equation (1);

[0009]

[0010] In the formula, θ e Indicates the rotor position electrical angle, [i' a *,i′ b *,i′ c *] T Represents the three-phase virtual current reference value, T represents the matrix transpose, [i' d_1 *,i' q_1 *,i′ 0_1 *] T Indicates the reference value of the virtual current vector at the fundamental frequency, i′ d_1 *、i′ q_1 *、i′ 0_1 *These are the reference values ​​for the d-axis, q-axis, and 0-axis components of the fundamental frequency virtual current, respectively.

[0011] Substitute the three-phase virtual current reference values ​​into equation (2) to calculate the motor torque:

[0012]

[0013] In the formula, T e N represents the motor torque. r Indicates the number of rotor poles, i j Indicates the actual phase current, i′ j Represents the virtual phase current, W′(i j ,θ e ) represents magnetic co-energy, L jThe phase inductance is represented by j, the phase number of the switched reluctance motor is represented by j = 1, 2, ..., m, and the phases A, B, ..., M of the switched reluctance motor are represented by m, which represents the total number of phases of the switched reluctance motor.

[0014] Step 2: Obtain the inductance of each phase of the switched reluctance motor through simulation, and perform Fourier decomposition on each phase inductance to obtain the components of each phase inductance. Based on the effect of different orders of virtual current vectors on motor torque harmonics, select the second-order virtual current vector as the compensation quantity, and superimpose it with the fundamental frequency virtual current vector to obtain the three-phase virtual current. The expression for the reference value of the three-phase virtual current is as follows:

[0015]

[0016] i′ q_2 *=K·i′ q_1 * (14)

[0017] i′0*=i′ 0_1 *+i′ 0_2 * (15)

[0018]

[0019] In the formula, i′ d_2 *、i′ q_2 *、i′ 0_2 *These represent the reference values ​​for the d-axis, q-axis, and 0-axis components of the second-order virtual current; i′ d_1 * and i′ d_2 * represents a given value, all of which are 0; L1, L2, L4, and L5 represent first-order, second-order, fourth-order, and fifth-order phase inductances, respectively.

[0020] Step 3: Calculate the error between the three-phase virtual current reference value and the actual value. The three-phase virtual current error is controlled by hysteresis to generate drive signals for each switch of the power converter, which is then used to control the switching of the power converter and in turn control the switched reluctance motor.

[0021] Furthermore, the virtual phase current is the square of the actual phase current.

[0022] Furthermore, in step 2, the motor torque generated by the interaction between the compensated virtual current vector and the phase inductance is expressed as:

[0023]

[0024] +(4L4i′ q_2 -(5L5-7L7)i′ q_1 cos(6θ) e )-6(L3 sin(3θ e)+2L6 sin(6θ e ))i′0+7L7i′ q_ 2cos(9θ e )]

[0025] In the formula, T e_1 T e_2 i′ represents the torque of the first-order and second-order motors, respectively. q_1 、i′ q_2 L1, L2, and L3 represent the q-axis components of the first-order and second-order virtual currents, respectively; L4 represents the sum of the 0-axis components of the first-order and second-order virtual currents; and L5, L6, and L7 represent the third-order, sixth-order, and seventh-order phase inductances, respectively.

[0026] Compared with the prior art, the beneficial effects of the present invention are:

[0027] 1. This invention proposes a torque control method based on virtual current. It analyzes the effect of virtual current vectors of different orders on torque harmonics, selects the second-order virtual current vector as the compensation quantity according to the effect law, and superimposes it with the fundamental frequency virtual current vector. Then, it interacts with the phase inductance to generate motor torque, thereby suppressing torque pulsation.

[0028] 2. Based on the analysis of the motor torque formula, this invention derives a current waveform that maximizes the reduction of torque ripple, namely a quasi-sine waveform between a square wave and a standard sine wave. This not only solves the problem of large torque ripple caused by the discontinuity of the traditional quasi-square wave current, but also avoids the problems of complex control methods and large torque ripple associated with sinusoidal current excitation with DC bias. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the structure of a switched reluctance motor drive system;

[0030] Figure 2 Waveforms of phase current and phase inductance for quasi-square wave current excitation;

[0031] Figure 3 Waveforms of phase current and phase inductance for sinusoidal current excitation with DC bias;

[0032] Figure 4 This is a schematic diagram of an asymmetric half-bridge power converter.

[0033] Figure 5(a) is a schematic diagram of the stator winding conduction stage;

[0034] Figure 5(b) is a schematic diagram of the stator winding freewheeling demagnetization stage;

[0035] Figure 6 This is an overall flowchart of the present invention;

[0036] Figure 7(a) is a graph of rotor position electrical angle versus inductance;

[0037] Figure 7 (b) is a diagram of inductor harmonic amplitude;

[0038] Figure 8 This is a schematic diagram of the Park transform.

[0039] Figure 9 This is a schematic diagram illustrating the relationship between a rotating coordinate system and a stationary coordinate system.

[0040] Figure 10 This is a diagram showing the actual three-phase current waveforms of the present invention. Detailed Implementation

[0041] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, but this does not limit the scope of protection of this application.

[0042] The power converter adopts an asymmetric half-bridge power converter; see the structure below. Figure 4 It includes a DC bus capacitor C, six diodes D1 to D6, and six switching transistors S1 to S6; wherein, one end of the DC bus capacitor C is connected to the DC power supply U. dc The positive terminal, one end of switching transistor S1, one end of switching transistor S3, one end of switching transistor S5, the cathodes of diodes D2, D4, and D6 are connected together. The other end of the DC bus capacitor C is connected to the DC power supply U. dc The negative terminal of the switch S1 to S6 is connected to the anode of diode D1, the anode of diode D3, the anode of diode D5, one end of switch S2, one end of switch S4, and one end of switch S6. One end of the A-phase stator winding of the switch reluctance motor is connected to the other end of switch S1 and the cathode of diode D1, and the other end of the A-phase stator winding is connected to the anode of diode D2 and the other end of switch S2. One end of the B-phase stator winding of the switch reluctance motor is connected to the other end of switch S3 and the cathode of diode D3, and the other end of the B-phase stator winding is connected to the anode of diode D4 and the other end of switch S4. One end of the C-phase stator winding of the switch reluctance motor is connected to the other end of switch S5 and the cathode of diode D5, and the other end of the C-phase stator winding is connected to the anode of diode D6 and the other end of switch S6. The control terminals of the six switches S1 to S6 receive the drive signals provided by the controller.

[0043] During operation, the switched reluctance motor of this invention requires two operating states for the voltage of each phase stator winding: 1) In the stator winding conduction stage, both switching transistors connected to the stator winding are turned on, the DC power supply supplies power to the electronic winding, and the stator winding is subjected to a positive voltage (U). dcAs shown in Figure 5(a); 2) During the freewheeling demagnetization stage, both switching transistors connected to the stator winding are turned off, and the current flows through the two diodes connected to the stator winding for freewheeling demagnetization. The winding is subjected to a negative voltage (-U) across its terminals. dc As shown in Figure 5(b).

[0044] The SRM torque ripple optimization control method based on quasi-sinusoidal current excitation of the present invention includes the following steps:

[0045] Step 1: Collect the actual values ​​of rotor position electrical angle and three-phase current using position and current sensors respectively; differentiate the rotor position electrical angle to obtain the actual motor speed; calculate the speed deviation between the actual speed and the given speed; pass the speed deviation through PI control to obtain the reference value i′ of the q-axis component of the base frequency virtual current. q_1 *;Based on the rotor position electrical angle and the fundamental frequency virtual current vector reference value, the three-phase virtual current reference value is calculated using equation (1). At this time, the three-phase virtual current is a standard sine wave with DC component.

[0046]

[0047] In the formula, θ e Indicates the rotor position electrical angle, [i' a *,i′ b *,i′ c *] T Represents the three-phase virtual current reference value, T represents the matrix transpose, [i′ d_1 *,i' q_1 *,i′ 0_1 *] T This represents the reference value of the virtual current vector at the fundamental frequency.

[0048] During the operation of the motor, the motor torque is calculated by substituting the reference value of the three-phase virtual current into equation (2) according to the principle of electromechanical energy conversion.

[0049]

[0050] In the formula, T e N represents the motor torque. r Indicates the number of rotor poles, i j Indicates the actual phase current, i′ j Represents the virtual phase current, W′(i j ,θ e ) represents magnetic co-energy, L j The phase inductance is represented by j, the phase number of the switched reluctance motor is represented by j = 1, 2, ..., m, and the phases A, B, ..., M of the switched reluctance motor are represented by m, which represents the total number of phases of the switched reluctance motor.

[0051] Step 2: Obtain the inductance of each phase of the switched reluctance motor through simulation, perform Fourier decomposition on each phase inductance to obtain the components of each phase inductance, and the Fourier decomposition results of each phase inductance are the same. Figure 7 (a) and (b) show the inductance waveform and harmonic analysis, respectively. Based on the waveform and harmonic analysis, the phase inductance can be expressed by the following formula:

[0052]

[0053] In the formula, L k L0 represents the amplitude of the k-th phase inductance. When k = 0, L0 is the DC component of the phase inductance. In equation (3), j on the right side of the equation takes the values ​​1, 2, and 3, which represent the A, B, and C phases of the switched reluctance motor, respectively.

[0054] The following analysis uses the most widely used three-phase motor as an example:

[0055] After Fourier transform, the fundamental component of the phase inductance accounts for the largest proportion of all alternating variables. According to the motor torque formula, when the phase inductance is simplified to only the DC bias and the fundamental frequency sinusoidal quantity, the product-sum formula shows that when the virtual phase current is a sinusoidal quantity lagging by 2π / 3 electrical angles, the SRM electromagnetic torque is constant and the torque ripple is zero. However, the fundamental frequency virtual current vector will interact with the second-order and higher-order phase inductances to produce torque ripple. Similarly, theoretically, the interaction between the virtual current of different orders of standard sinusoidal waveforms and the phase inductances of different orders can also produce motor torques of different orders. In this case, the motor torque is expressed as:

[0056]

[0057] In the formula, T e_x =[T a_x ,T b_x ,T c_x ] T T represents the motor torque matrix generated by the x-th order three-phase virtual current. a_x T b_x T c_x L represents the motor torque generated by the x-th order three-phase virtual current, L = diag[L a ,L b ,…,L m ] represents the diagonal matrix of phase inductance, L a ,L b ,…,L m Represents the inductance of each phase, diag[·] represents the diagonal matrix, i′ x =[i′ a_x ,i′ b_x ,i′ c_x ] T Let i′ represent the x-order virtual current matrix in the abc stationary coordinate system.a_x 、i′ b_x 、i′ c_x Let i′ represent the virtual currents of phases A, B, and C of order x, respectively. dq0_x =[i′ d_x ,i′ q_x ,i′ 0_x ] T Let i′ represent the x-order virtual current matrix in the dq0 rotating coordinate system. d_x 、i′ q_x 、i′ 0_x P represents the d-axis, q-axis, and 0-axis components of the x-order virtual current, respectively. x Represents the x-order Park transformation matrix;

[0058] The phase inductance matrix after differentiation Represented as:

[0059]

[0060] By summing all the elements in each motor torque matrix using equation (6), the motor torque generated by each order of virtual current is obtained;

[0061]

[0062] In the formula, T e_x L represents the motor torque generated by the x-th order virtual current; 3k L 3k+1 L 3k+2 Let n represent the phase inductances of order 3k, 3k+1, and 3k+2, respectively, where n = 1, 2, ..., ∞;

[0063] Define the 3k+1th order phase inductance as the positive sequence inductance, the 3k+2nd order phase inductance as the negative sequence inductance, and the 3kth order phase inductance as the zero sequence inductance; from equation (6), it can be seen that when x≠3n, the order of the motor torque decreases or increases by x after the interaction of the xth order virtual current with the positive sequence inductance, and the order of the motor torque increases or decreases by x after the interaction of the xth order virtual current with the negative sequence inductance; the initial positive or negative sign in the parentheses of the trigonometric function terms depends on the rotation direction of the virtual current vector. For a counterclockwise rotating virtual current vector, the initial signs of the motor torque generated by the interaction with the positive and negative sequence inductances are negative and positive, respectively; for a clockwise rotating virtual current vector, the initial signs of the motor torque generated by the interaction with the positive and negative sequence inductances are positive and negative, respectively; when x=3n, the interaction of the xth order virtual current with the zero sequence inductance simultaneously generates the 3k+x and 3k-x order components of the motor torque, i' q_x The ± indicates whether the direction of the virtual current vector rotation is positive or negative; the order of the motor torque generated by the interaction between the virtual current 0-axis component and the zero-sequence inductance is the same as the order of the zero-sequence inductance.

[0064] To reduce torque ripple caused by inductor harmonics, a corresponding virtual current vector is constructed and injected into the winding to generate mutually canceling torque harmonic components. The fundamental frequency virtual current vector interacts with the high-amplitude second and fourth harmonics in the inductor harmonics, generating third-order harmonic torque. Therefore, the rotational speed is -2ω e The second-order virtual current vector is used as a compensation quantity, and after being superimposed with the fundamental frequency virtual current vector, it interacts with the inductor to reduce torque harmonics, thereby reducing torque ripple; where ω e The electric angular velocity represents the virtual current vector; "-" indicates the direction of rotation.

[0065] The Park transformation is used to transform the virtual phase current in the abc stationary coordinate system to the dq0 rotating coordinate system. The relationship between the two coordinate systems is described in [reference needed]. Figure 8 For a rotational speed of -2ω e The second-order virtual current vector, using the second-order Park transformation matrix, is:

[0066]

[0067] By ignoring the low-amplitude inductor harmonics, the d-axis components of the first and second-order virtual currents are both set to zero, i.e., i' d_1 =i' d_2 =0; From equation (6), the motor torque generated by the interaction between the compensated virtual current vector and the phase inductance can be further expressed as:

[0068]

[0069] In the formula, T e_1 T e_2 i' represents the torque of the first-order and second-order motors, respectively. q_1 、i' q_2 These represent the q-axis components of the first-order and second-order virtual currents, respectively. This represents the sum of the zero-axis components of the first-order and second-order virtual currents;

[0070] Since torque control is based on virtual current, and the virtual phase current is the square of the actual phase current, the phase current should be unipolar as the square root of the controlled virtual current waveform. As can be seen from equation (8), the 0-axis component of the virtual current does not generate average torque as the DC bias of the virtual phase current. Moreover, an excessively high virtual current will lead to high motor losses and poor torque capability. Therefore, the 0-axis virtual current should be minimized as much as possible, while ensuring the unipolarity of the phase current. The three-phase virtual current i' is calculated according to equation (9). a 、i' b and i' c ;

[0071]

[0072] In equation (9), i' q_2 It should satisfy equation (10):

[0073]

[0074] The virtual currents in each phase should also satisfy the following set of equations:

[0075]

[0076] make And according to equations (9) to (11), we can solve for:

[0077]

[0078] The three-phase virtual current reference values ​​also satisfy equations (9) to (12), therefore, equations (10) and (12) and the reference value i' of the q-axis component of the fundamental frequency virtual current are combined. q_1 Substituting into equation (9), we obtain the three-phase virtual current reference value i'. a *、i' b * and i' c *;

[0079] The formula for calculating the three-phase virtual current reference value can also be expressed as:

[0080]

[0081]

[0082] i′0*=i′ 0_1 *+i′ 0_2 *(15)

[0083]

[0084] In the formula, i' d_1 * and i' d_2 * All values ​​are given and can all be 0;

[0085] Step 3: Calculate the error Δi' between the reference value and the actual value of the three-phase virtual current. a ,Δi' b ,Δi' c The three-phase virtual current error is controlled by hysteresis to generate drive signals for the six switching transistors of the power converter, thereby controlling the switching of the power converter.

[0086] Figure 9 , Figure 10 The waveforms of the virtual phase current and the actual phase current obtained by this invention are shown respectively.

[0087] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for optimizing SRM torque ripple control based on quasi-sinusoidal current excitation, characterized in that, The method includes the following steps: Step 1: Collect the rotor position electrical angle and the actual value of the three-phase current of the switched reluctance motor; calculate the actual speed of the motor based on the rotor position electrical angle, and calculate the speed deviation between the actual speed and the given speed. The speed deviation is controlled by PI to obtain the virtual current reference value of the q-axis base frequency. Based on the rotor position electrical angle and the fundamental frequency virtual current vector reference value, the three-phase virtual current reference value is calculated using equation (1); In the formula, θ e Indicates the rotor position electrical angle, [i' a *,i' b *,i' c *] T Represents the three-phase virtual current reference value, T represents the matrix transpose, [i' d_1 *,i' q_1 *,i' 0_1 *] T i' represents the reference value of the virtual current vector at the fundamental frequency. d_1 *、i' q_1 *、i' 0_1 *These are the reference values ​​for the d-axis, q-axis, and 0-axis components of the fundamental frequency virtual current, respectively. Substitute the three-phase virtual current reference values ​​into equation (2) to calculate the motor torque: In the formula, T e N represents the motor torque. r Indicates the number of rotor poles, i j i' represents the actual phase current. j Represents the virtual phase current, W′(i j ,θ e ) represents magnetic co-energy, L j The phase inductance is represented by j, the phase number of the switched reluctance motor is represented by j = 1, 2, ..., m, and the phases A, B, ..., M of the switched reluctance motor are represented by m. Step 2: Obtain the inductance of each phase of the switched reluctance motor through simulation, and perform Fourier decomposition on each phase inductance to obtain the components of each phase inductance. Based on the effect of different orders of virtual current vectors on motor torque harmonics, select the second-order virtual current vector as the compensation quantity, and superimpose it with the fundamental frequency virtual current vector to obtain the three-phase virtual current. The expression for the reference value of the three-phase virtual current is as follows: i' q_2 *=K·i' q_1 * (14) i'0*=i' 0_1 *+i' 0_2 * (15) In the formula, i' d_2 *、i' q_2 *、i' 0_2 *These represent the reference values ​​for the d-axis, q-axis, and 0-axis components of the second-order virtual current; i' d_1 * and i' d_2 * represents a given value, all of which are 0; L1, L2, L4, and L5 represent first-order, second-order, fourth-order, and fifth-order phase inductances, respectively. Step 3: Calculate the error between the three-phase virtual current reference value and the actual value. The three-phase virtual current error is controlled by hysteresis to generate drive signals for each switch of the power converter, which is then used to control the switching of the power converter and in turn control the switched reluctance motor.

2. The SRM torque ripple optimization control method based on quasi-sinusoidal current excitation according to claim 1, characterized in that, The virtual phase current is the square of the actual phase current.

3. The SRM torque ripple optimization control method based on quasi-sinusoidal current excitation according to claim 1, characterized in that, In step 2, the motor torque generated by the interaction between the compensated virtual current vector and the phase inductance is expressed as: In the formula, T e_1 T e_2 i' represents the torque of the first-order and second-order motors, respectively. q_1 、i' q_2 L1, L2, and L3 represent the q-axis components of the first-order and second-order virtual currents, respectively; L3, L6, and L7 represent the third-order, sixth-order, and seventh-order phase inductances, respectively.

Images