Permanent magnet synchronous motor MTPA control method based on double virtual direct current signal injection mode

Abstract

The invention relates to a permanent magnet synchronous motor MTPA control method based on a double-virtual direct current signal injection mode, in particular to a motor control method, and particularly relates to a control method of a built-in permanent magnet synchronous motor. A pair of virtual direct-current signals with the same amplitude and opposite polarities are injected into a current vector angle beta, Taylor expansion is carried out on electromagnetic torque containing the pair of signals, subtraction is carried out on the two signals to obtain an approximate value of the torque to a first-order partial derivative of the current vector angle, and the approximate value is input into an integral regulator; when the input quantity is controlled to be 0, the optimal current vector angle beta mtpa can be obtained, and MTPA control is achieved. In order to improve the dynamic performance and the steady-state performance of control at the same time, virtual direct-current signals with different amplitudes are selected for injection under different working conditions, the motor can be made to rapidly approach the working state of the optimal current vector angle, and fluctuation of the current vector angle in the stable state is reduced.

Description

Technical Field

[0001] The present invention relates to the field of motor control, and in particular to a control strategy for a built-in permanent magnet synchronous motor. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) feature high power density and power factor. They can be categorized by structure as surface-mounted and interior-mounted PMSMs. The interior-mounted PMSMs, with permanent magnets embedded within the rotor, have unequal direct-axis and quadrature-axis inductances. Consequently, interior-mounted PMSMs contain a reluctance torque component. Maximum torque-to-current ratio control (MTC) is a commonly used control strategy that maximizes the combined output torque of reluctance and electromagnetic torque while maintaining constant current.

[0003] Due to the influence of temperature, magnetic saturation, and saliency, the optimal current vector angle varies with load. Currently, methods for determining the optimal current vector angle in MTPA control are divided into offline and online identification methods. Offline identification involves obtaining motor parameters under different operating conditions through extensive experiments. These data are then compiled into tables for subsequent lookup. Table lookup methods require a significant amount of time for preliminary experiments and are not universally applicable to different motors. Online identification methods, including model reference adaptation, sliding mode observer, and extended Kalman, significantly reduce the workload required for each step compared to offline identification methods. However, these methods are theoretically complex, computationally intensive, and place high demands on controller performance. In recent years, signal injection methods for MTPA have garnered widespread attention. By injecting an actual high-frequency signal, the difference between the ideal and actual current angles can be extracted. However, this method can increase unnecessary power loss and torque ripple in the motor. Virtual signal injection methods, on the other hand, do not rely on actual power response and, therefore, do not inject actual current signals, but instead determine the optimal current vector angle solely through computation. Virtual signals typically include high-frequency sinusoidal signals, high-frequency square wave signals, and DC signals. High-frequency sinusoidal signals require a bandpass filter and a low-pass filter to extract the effective signal, which inevitably leads to recognition lag. High-frequency square wave signals offer a wider bandwidth, but the approximation process can produce high-frequency oscillations. Compared to the previous two, the traditional virtual DC signal injection method (hereinafter referred to as VDSIC) offers better overall control performance, but its performance deteriorates as the load increases. To address this issue, this paper proposes a bipolar virtual DC signal injection method (hereinafter referred to as DVDSIC), which simultaneously injects positive and negative virtual DC signals. The difference between these two signals is then used through PI control to determine the optimal current vector angle. Summary of the Invention

[0004] The purpose of this invention is to propose a dual virtual DC signal injection MTPA control method for interior permanent magnet synchronous motors (MTPAs). This method is applicable to a wider range of operating conditions and is less affected by load changes than traditional virtual DC signal injection methods. The specific scheme is as follows:

[0005] Injecting a pair of DC signals with opposite polarity, d1(t) = A and d2(t) = -A, into the stator current vector angle can effectively reduce β under all loads. mtpa The fluctuation of dq current and output torque is reduced. The high-order components ignored during the extraction process are fewer, and the control accuracy is higher. The details are as follows:

[0006] First, establish the stator voltage equation of the built-in permanent magnet synchronous motor in the dq coordinate system:

[0007]

[0008] Where u d 、u q is the dq axis component of the stator voltage; i d 、i q is the dq axis component of the stator current; L d 、L q is the direct-axis and quadrature-axis inductance; f is the permanent magnet flux; ω e is the electrical angular velocity.

[0009] The torque equation of the motor is:

[0010] T e =1.5p[Ψ f i q +(L d -L q )i d i q ] (2)

[0011] After the motor reaches steady state, i d and i q It does not change with time. The differential term L in the above stator voltage equation (1) d (di d / dt) and L q (di q The two terms ( / dt) can be ignored and the steady-state stator voltage equation can be rewritten for parameter decoupling:

[0012]

[0013] Substituting (3) into (1) yields:

[0014]

[0015] The relationship between the current vector and the stator current dq axis components and the current vector angle β is:

[0016]

[0017] Through mathematical operations, positive and negative DC signals are injected into the current vector angle. The current containing the DC signal is expressed as:

[0018]

[0019] Taking the injection of DC signal A as an example, the electromagnetic torque T containing the injected signal is obtained e d (β+A):

[0020]

[0021] Where i d (β+A), i q (β+A) is the dq axis current after injecting the DC signal into the stator current vector angle β, i d 、i q is the actual dq axis current.

[0022] T e d Taylor expansion of (β+A) at β yields:

[0023]

[0024] The same applies to T e d (β-A):

[0025]

[0026] Since the amplitude of the injected DC signal A is much smaller than 1 and has a small value, the odd-order terms of A are extremely small and can be ignored. Subtracting (9) from (8) yields:

[0027]

[0028] The current vector angle (denoted as β) output by the DVDSIC algorithm is introduced. do ) parameter σ d :

[0029]

[0030] DVDSIC through control Continuously approaching 0, β doContinuously approaching the optimal β mtpa , express β in integral form do We can get:

[0031]

[0032] Where k' is the integral coefficient. According to σ d Theoretically, the smaller the injection signal amplitude A is, the better the control effect is. However, a smaller A will slow down the convergence of the algorithm. Therefore, a variable amplitude dual virtual signal algorithm is used to take into account both steady-state performance and dynamic performance, making the injection signal A amplitude controllable.

[0033] Compared with the traditional VDSIC method, the DVDSIC proposed in this paper has smaller error and higher control accuracy when tracking the MTPA point. The algorithm structure is simple and the calculation amount is small. The β obtained by tracking the MTPA point under a large load is mtpa Smaller fluctuations. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 : MTPA curve

[0035] Figure 2 :Dual virtual DC signal injection MTPA control block diagram

[0036] Figure 3 :Block diagram of variable amplitude DVDSIC algorithm

[0037] Figure 4 :Relationship diagram of VDSIC torque and current vector angle under multiple load conditions

[0038] Figure 5 :Diagram showing the relationship between DVDSIC torque and current vector angle under multiple load conditions

[0039] Figure 6 :5Nm load VDSIC and DVDSIC current and β m Simulation Results

[0040] Figure 7 :10Nm load VDSIC and DVDSIC current and β m Simulation Results

[0041] Figure 8 :DVDSIC simulation results of variable amplitude when the load steps from 5Nm to 10Nm DETAILED DESCRIPTION

[0042] like Figure 1 As shown in the figure, when the built-in permanent magnet synchronous motor outputs constant torque, the corresponding input current has a minimum value, and the current vector angle corresponding to this minimum value is the optimal current vector angle, that is, β mtpaThis embodiment aims to identify β by a double virtual signal injection method. mtpa , thus realizing MTPA control, the control flow chart and principle diagram are as follows Figure 2 、 Figure 3 The following is the specific implementation method.

[0043] After Clark transformation and Park transformation, the abc three-phase permanent magnet synchronous motor will obtain the following voltage equation:

[0044]

[0045] The torque equation of the motor is:

[0046] T e =1.5p[Ψ f i q +(L d -L q )i d i q ] (2)

[0047] The relationship between the current vector and the stator current dq axis components and the current vector angle β is:

[0048]

[0049] where ω e is the electrical angular velocity; R s is the stator resistance; the orthogonal axis inductance is L d and L q Indicates; f is the permanent magnet flux. f Written about i d 、i q function, thereby compensating for the effects of load, temperature and other factors on Ψ f When the motor reaches steady state, the differential term L d (di d / dt) and L q (di q / dt) can be ignored, so Ψ f and i d 、i q The relationship can be expressed as follows:

[0050]

[0051] By injecting small-amplitude virtual DC signals d1(t)=A and d2(t)=-A with opposite polarities into the current vector angle β, two virtual current signals can be obtained:

[0052]

[0053] The electromagnetic torque T containing the injected DC signal is obtained e d (β+A) and T e d (β-A):

[0054]

[0055] Further get T e d (β+A) and T e d Taylor expansion of (β-A):

[0056]

[0057] Subtraction can produce the following results:

[0058]

[0059] The current vector angle β (denoted as β) output by the DVDSIC algorithm is introduced. do ) parameter σ d :

[0060]

[0061] DVDSIC through control Continuously approaching 0, β do Continuously approaching the optimal β mtpa , express β in integral form do We can get:

[0062]

[0063] Where k' is the integration coefficient.

[0064] like Figure 4 As shown, β mtpa β m .when When it is negative, T e (β) monotonically decreasing, β>β m , then the β value should be reduced to approach β m ;when When it is positive, T e (β) monotonically increasing, β<β m , then the β value should be increased to approach β m According to the above characteristics, when the signal σ d Input to the integral regulator to get the current vector angle β doWhen the output value of the differential regulator remains basically unchanged, it means that the value of the input quantity is close to 0, which means that σ d Approaching 0, the obtained β do Can be seen as and β m Approximately equal. β will be updated in real time do Substitute the value into formula (3) to obtain the reference current of the dq axis and complete the control closed loop.

[0065] Due to T e d (β+A) and T e d (β-A) cannot be equal in mathematical sense, σ d In fact, it is an approximate value of the subtraction between the two. Therefore, the signal input to the integral regulator is always changing and not 0, which will also lead to the identified β m There are fluctuations. The fluctuations generated when the VDSIC and DVDSIC algorithms reach steady state are compared and analyzed as follows:

[0066]

[0067] The parameter σ is introduced to calculate the output current vector angle β of the VDSIC algorithm, and its value is the same as ΔT e+ Equal, used to calculate the parameter σ of the current vector angle β output by the DVDSIC algorithm d Numerical and ΔT ed Equal. Figure 5 It can be seen that ΔT e+ >ΔT e- >ΔT ed , ΔT e+ Much larger than ΔT ed After the control system reaches a steady state, the fluctuation of σ in VDSIC is much greater than that in DVDSIC. d The fluctuation of DVDSIC is d After integration, β do The fluctuation value is naturally smaller. Under heavy load conditions, the suppression of this fluctuation is particularly obvious. The previous section has explained that when the motor is running under a large load, T e (β) as a convex function will be amplified, that is, in (0,β m ) and (β m ,π) two intervals T e The slope of (β) will increase accordingly. When the amplitude of the injected signal A remains unchanged, ΔT e+ will increase, and ΔT e+ and ΔT e- The values ​​are similar under any load, ΔT ed It basically does not change with load changes, so DVDSIC is more adaptable to large load conditions.

[0068] According to σ d Theoretically, the smaller the amplitude of the injected signal A is, the better the control effect will be. However, a smaller A will lead to slower convergence of the algorithm and a longer time for the system to reach steady state. Therefore, a variable amplitude dual virtual signal algorithm is used to balance steady-state performance and dynamic performance, making the amplitude of the injected signal A controllable. Based on the motor model used in this paper, a dual virtual DC signal with an amplitude of A = 0.05rad is injected when the DVDSIC control algorithm is started, and β do Rapidly approaching β m , reaching the MTPA operating point. The motor model used in this paper is under DVDSIC control at the maximum load steady state. m The fluctuation θ steady Less than 1°, so when Δβ is less than 1°, the control system has entered a steady state. At this time, the main purpose of the control algorithm is to reduce β m Fluctuation, so the injection signal amplitude A is changed from 0.05rad to 0.005rad, thereby further reducing β while ensuring the dynamic performance of the control system. m Fluctuations, improve control stability. When the load changes, β m Will track the new real β m This will cause a large change, and the control algorithm detects β m When the change Δβ exceeds 1°, the injection signal amplitude A is changed from 0.005 rad to 0.05 rad, thereby quickly tracking the MTPA operating point under the new load and completing the control process of the variable amplitude DVDSIC. The value of A is shown in Table 1:

[0069] Table 1 Variable amplitude DVDSIC algorithm parameters

[0070]

[0071] Finally, to verify the method proposed in this paper, a simulation based on the IPMSM model was built. The parameters of the motor used in the simulation are listed in Table 2:

[0072] Table 2 Motor parameters

[0073]

[0074] Figure 6 The β obtained by DVDSIC compared with VDSIC m From 94.2° to 94.4°, the control accuracy is improved, and β m The fluctuation amount is reduced from 0.9° to 0.5°, and the fluctuation amount is reduced by 0.4°. m The volatility is reduced, Figure 7 i in DVDSICd The fluctuation amount is reduced from 0.69A to 0.62A. Figure 8 in i q The fluctuation is reduced from 0.43A to 0.42A, and the current fluctuation is reduced, which verifies that DVDSIC can suppress β m Fluctuations, thereby reducing current and output torque fluctuations.

[0075] Then, under the given speed of 1000r / min and the maximum load of 10Nm, the VDSIC algorithm is used within 0-1s, and the DVDSIC algorithm is switched to after 1s to obtain β m The current simulation results are as follows Figure 7 shown.

[0076] Figure 7 DVDSIC compared to VDSIC β m From 98.05° to 98.5°, the control accuracy is improved, and β m The fluctuation is reduced from 1.2° to 0.6°, which is a significant decrease. m The volatility is reduced, and DVDSIC's i d The fluctuation is reduced from 0.86A to 0.69A, i q The fluctuation is reduced from 0.5A to 0.47A, and the current fluctuation is greatly reduced. Compared with the smaller load of 5Nm, the current fluctuation is significantly reduced. Figure 6 As a result, DVDSIC suppresses β at large loads m The effects are more pronounced with fluctuations and current fluctuations.

[0077] At the same time, when VDSIC increases from a small load of 5Nm to a large load of 10Nm, β m The fluctuation amount increased from 0.9° to 1.2°, an increase of 0.3°; i d The fluctuation amount increased from 0.69A to 0.86A, an increase of 0.17A; i q The fluctuation amount increased from 0.43A to 0.5A, an increase of 0.07A, β m The fluctuation and current fluctuation increase significantly with the increase of load. m The fluctuation amount increased from 0.5° to 0.6°, which is only 0.1°; i d The fluctuation amount increased from 0.62A to 0.69A, an increase of only 0.07A; i q The fluctuation amount increases from 0.42A to 0.47A, which is only 0.05A. When DVDISC is increased from a small load to a large load, β m The fluctuation and current fluctuation increase only slightly, which solves the problem of the VDSIC algorithm current and output torque fluctuation increasing with the increase of load.

[0078] The variable amplitude DVDSIC proposed in this paper injects a signal amplitude A of 0.05 rad when the motor starts and the load changes to quickly track the MTPA point. After entering the steady state, A is changed to 0.005 rad to reduce the current and torque fluctuations, and β m The change is the switching criterion. If it is less than 1°, it is considered as steady state, and if it is greater than 1°, it is considered as tracking state. The simulation results of the amplitude value DVDSIC at a given speed of 1000r / min and a load switching from 5Nm to 10Nm in 1s are as follows Figure 8 shown.

[0079] Figure 8 Medium amplitude DVDSIC β after load surge m The fluctuation amount increased from 0.15° to 0.2°, an increase of only 0.05°; i d The fluctuation amount increased from 0.55A to 0.61A, which is only 0.06A higher; q The fluctuation increased from 0.42A to 0.46A, a mere 0.04A increase. This results in smaller fluctuations and better steady-state control performance compared to DVDSIC. Furthermore, by using a larger injection signal amplitude A during MTPA tracking to quickly track the MTPA point, and then rationally selecting a smaller A to reduce fluctuations after entering steady state, the algorithm can complete MTPA tracking and fluctuation suppression after a sudden load change within 0.08s, significantly improving dynamic performance.

[0080] In summary, the DVDSIC proposed in this paper can be compared with VDSIC. q One-step inhibition of β m Fluctuations are minimized, thereby reducing current and output torque fluctuations, with a more pronounced suppression effect under heavy load conditions. Furthermore, the variable-amplitude DVDSIC, developed based on DVDSIC, achieves faster response and better dynamic performance to sudden load changes by rationally switching the injected signal amplitude A. Consequently, the variable-amplitude DVDSIC boasts improved steady-state and dynamic performance, resulting in superior overall control effectiveness.

Claims

1. A permanent magnet synchronous motor MTPA control method based on dual virtual DC signal injection is characterized in that: include: Define the stator current vector angle β is the angle between the stator current direction and the positive direction of the d-axis. β Inject a pair of fixed-value signals with the same amplitude and opposite signs d 1( t )= A and d 2( t )=- A (hereinafter referred to as DC signal), the electromagnetic torque containing these signals T e d ( β+A )and T e d ( β-A ) performs Taylor expansion, T e d ( β+A )and T e d ( β-A ) and do the subtraction to get ∂ T e ( β ) / ∂ β The approximate value is input to the integral regulator, and the output of the integral regulator is β The updated value of When controlling ∂ T e ( β ) / ∂ β When the value approaches 0, the output value of the integral regulator β That is, it converges to the optimal current vector angle β mtpa , thereby realizing MTPA control; The current vector angle β Set a non-zero initial value.

2. A dual virtual DC signal injection type permanent magnet synchronous motor MTPA control method according to claim 1, characterized in that: Building an interior permanent magnet synchronous motor dq Axis mathematical model: ； Transform the resulting equation to use the stator current d - q Axis component i d and i q Indicates magnetic linkage Ψ f : ； The electromagnetic torque equation of the motor is: ； Will Ψ f Replace with i d and i q The formula is: ； When the signal is subsequently injected into the current vector angle, the virtual signal only exists in the MTPA algorithm, and the motor is not actually injected with the real signal. Ψ f The parameter expression should remain unchanged, which is used to express Ψ f of dq Shaft current i d and i q Will not contain injected signal.

3. A dual virtual DC signal injection type permanent magnet synchronous motor MTPA control method according to claim 2, characterized in that: Directional current vector angle β Inject two virtual DC signals of opposite sign and equal amplitude: d 1( t )= A and d 2( t )=- A , and obtain the virtual dq Shaft current: ； The electromagnetic torque after injecting the virtual signal is obtained: ； In the formula i d ( β+A ), i q ( β+A ), i d ( β-A ), i q ( β-A ) is the stator current vector angle after the DC signal is injected d - q Shaft current; i d 、 i q For practical d - q Shaft current.

4. A dual virtual DC signal injection type permanent magnet synchronous motor MTPA control method according to claim 3, characterized in that: Will T e d ( β+A )and T e d ( β-A ) performs Taylor expansion: ； From the above formula we can see that T e d ( β+A )and T e d ( β-A ) can eliminate the even-order Taylor expansion term of the electromagnetic torque. A The amplitude is very small, and the odd-order Taylor expansion term can be ignored. The extracted signal is as follows: ； Introducing parameters σ d As the input of the integral regulator: 。 5. A dual virtual DC signal injection type permanent magnet synchronous motor MTPA control method according to claim 4, characterized in that: Will get σ d Input to the integral regulator can make β Continuously approaching the optimal β mtpa , expressed in integral form β We can get: ； in k ’ is the integral coefficient. β After the value stabilizes, σ d tends to 0, which means ∂ T e ( β ) / ∂ β tends to 0, at this time β Can be approximately regarded as β mtpa equal; according to σ d and A Proportional to the characteristic, theoretically the amplitude of the injected signal in the algorithm A The smaller the control effect, the better, but the smaller the A This will slow down the convergence of the algorithm, so the injected signal A The amplitude is controllable, and a variable amplitude dual virtual DC signal injection algorithm is used to take into account both steady-state performance and dynamic performance.

6. A dual virtual DC signal injection type permanent magnet synchronous motor MTPA control method according to claim 5, characterized in that: In order to take into account both the steady-state performance and dynamic performance of the motor during operation, the injection signal A Amplitude controllable. Based on the motor model used in this paper, a dual virtual DC signal with a large amplitude is injected when the control algorithm starts. A , quickly β Approach β mtpa , reaching near the MTPA working point. β When it is less than 1°, the control system is considered to have entered a steady state. At this time, the main purpose of the control algorithm is to reduce β mtpa Fluctuations, so the injected signal amplitude A Reduce, thereby further reducing the dynamic performance of the control system β mtpa Fluctuation, improve control stability; At the same time, when using this variable amplitude double virtual DC signal injection permanent magnet synchronous motor MTPA control method, β mtpa The fluctuation does not increase with the increase of load.

7. A dual virtual DC signal injection type permanent magnet synchronous motor MTPA control method according to claim 6, characterized in that: When the motor is in MTPA mode, β mtpa Expressed as β m , the stator current is expressed as: ； The electromagnetic torque is expressed as: ； ∂ T e ( β ) / ∂ β Expressed as: ； When the load increases, the magnetic saturation effect of the motor deepens. L d -L q |decreases. From the above formula, we can see that at this time T em and β m The slope of the curve increases, that is, T e ( β ) is further amplified as a convex function, so that at the identified angle β Converge to β m When the load changes, the angle fluctuation generated by the dual virtual DC signal injection permanent magnet synchronous motor MTPA control method does not change significantly.

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