A method for compensating static end effects of a concentric cage secondary linear doubly fed motor

Abstract

This invention discloses a method for compensating for the static end effect of a concentric cage secondary linear doubly-fed induction generator (DFIG). The method includes the following steps: acquiring and extracting the fundamental negative-sequence current and directly coupled positive and negative-sequence currents from the primary three-phase windings based on the three-phase current of the primary coil, and transforming them into their respective synchronous rotating coordinate systems for closed-loop control, thereby suppressing the negative-sequence current and DC-coupled current to compensate for the static end effect of the DFIG; deriving the expression for the pulsating back electromotive force based on the mechanism of the static end effect, and synthesizing it as a voltage reference vector feedforward to compensate the primary winding, further offsetting the negative-sequence current and directly coupled current generated by the static end effect, thus improving its dynamic response speed. This invention can effectively suppress the negative-sequence current and directly coupled current generated in the primary winding due to the static end effect, improving motor performance.

Description

Technical Field

[0001] This invention belongs to the field of linear doubly fed motor control technology, and more specifically, relates to a method for compensating for static end effects in a concentric cage secondary linear doubly fed motor. Background Technology

[0002] The linear motor traction system for urban rail transit trains does not require a mechanical transmission device and can directly generate electromagnetic thrust along the direction of motion. It has advantages such as small turning radius, strong climbing ability, small tunnel shield face, low noise, and low maintenance cost, and has been widely used in urban subways, light rails, and maglev trains both domestically and internationally.

[0003] Linear Doubly-Fed Machine (LDFM) drive systems have gradually attracted attention from scholars both domestically and internationally due to their advantages such as adjustable power factor and flexible operation. Depending on the location of the two sets of feed windings, LDFMs can be divided into two types: bilaterally excited and single-sided excited. Bilaterally excited LDFMs have windings embedded in both the primary and secondary windings, allowing independent adjustment of the secondary current; this type has been extensively studied by scholars worldwide. The working principle of a single-sided excited LDFM is similar to that of a brushless doubly-fed induction motor. The primary winding has two sets of three-phase windings with different pole pairs, referred to as the power winding and the control winding, respectively. The secondary winding can have various structures, including squirrel-cage, reluctance, and wound-rotor types, among which the squirrel-cage secondary structure is simple and has lower track construction costs.

[0004] Nest-loop secondary linear dobly-fed machines (NLS-LDFMs) suffer from significant static end effects, generating both negative-sequence current and direct-coupled current in both primary windings. The negative-sequence current component generates reverse thrust, weakening the motor's average thrust. Direct-coupled energy transfer occurs between the two primary windings and does not produce effective thrust or active power, thus leading to a decrease in the motor's power factor and efficiency, negatively impacting its operation.

[0005] Therefore, it is urgent to study static end effect compensation strategies to suppress negative sequence current and direct coupling current, thereby improving the thrust, power factor and efficiency of NLS-LDFM. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the present invention aims to provide a method for compensating for static end effects in a concentric cage secondary linear doubly fed motor, which effectively suppresses negative sequence current and direct coupling current generated in the primary winding due to static end effects, thereby improving motor performance.

[0007] To achieve the above objectives, the present invention provides a static end-effect compensation method for a concentric cage secondary linear doubly-fed induction generator, comprising static end-effect compensation steps for two sets of primary windings, namely a control winding and a power winding, wherein the static end-effect compensation steps for each set of primary windings include the following steps:

[0008] (1) Obtain the three-phase currents ABC of the primary winding, extract the fundamental current and direct coupling current, and perform positive and negative sequence decomposition on the fundamental current and direct coupling current to obtain the positive and negative sequence components of the fundamental current and direct coupling current.

[0009] (2) Perform a rotation coordinate transformation on the positive and negative sequence components of the fundamental current and the direct coupling current to obtain the positive and negative sequence d and q axis components of the fundamental current and the direct coupling current;

[0010] (3) The given values ​​of the positive and negative sequence d and q axis components of the fundamental current and the direct coupling current are compared with the positive and negative sequence d and q axis components of the fundamental current and the direct coupling current obtained in step (2), and each difference is controlled by PI to obtain the given values ​​of the positive and negative sequence d and q axis components of the fundamental voltage and the direct coupling voltage; wherein, the given values ​​of the negative sequence d and q axis components of the fundamental current and the positive and negative sequence of the direct coupling current are both zero, and the given values ​​of the positive sequence d and q axis components of the fundamental current are determined according to the motor load conditions;

[0011] (4) Transform the positive and negative sequence d and q axis components of the fundamental voltage and the direct coupling voltage to the αβ coordinate system, and add the positive and negative sequence α and β axis components of the fundamental voltage and the direct coupling voltage to obtain the voltage setpoints for suppressing negative sequence current and direct coupling current of the primary winding.

[0012] (5) Based on the given voltage value and the DC bus voltage, the actual required voltage is generated by SVPWM modulation and applied to the primary winding to drive the motor and compensate for static end effects.

[0013] The static end effect compensation method for concentric cage secondary linear doubly fed motors provided by this invention does not require an accurate mathematical model of the motor and only requires a few motor parameters to obtain the voltage setpoint for compensating the static end effect. It can extract and suppress the negative sequence current and direct coupling current generated by the static end effect in the power winding (control winding), and effectively improve key performance indicators such as motor thrust.

[0014] In one embodiment, the method further includes the following steps:

[0015] (6) Based on the short primary linear motor winding theory, the expression of the pulsating back electromotive force is derived for the static end effect generation mechanism of the concentric cage secondary linear doubly fed motor, and it is synthesized as a voltage reference vector feedforward compensation to the two primary windings to offset the fundamental negative sequence current and direct coupling current generated by the static end effect.

[0016] In one embodiment, step (6) specifically involves:

[0017] (a) Obtain the C-phase current of the power winding and the control winding, and use a second-order linear tracking differentiator to calculate the derivative of the C-phase current of the power winding and the control winding with respect to time.

[0018] (b) Calculate the pulsating back electromotive force of the power winding and control winding based on the derivatives of the C-phase currents of the power winding and control winding with respect to time. The calculation formula is as follows:

[0019]

[0020]

[0021] In the formula, e p2A e p2B and e p2C e represents the three-phase pulsating back electromotive force of the power winding. c2A e c2B and e c2C pi represents the three-phase pulsating back electromotive force of the control winding. pC pi represents the time derivative of the C-phase current of the power winding. cC L represents the time derivative of the C-phase current of the control winding; pp and L cc These are the pulsating self-inductances of the power winding and the control winding, respectively; L pc For direct coupling mutual inductance between the power winding and the control winding; i pC and i cC , respectively, are the C-phase currents of the power winding and the control winding; p is the differential operator;

[0022] (c) Based on the phase relationship of the three-phase pulsating back electromotive force, the three-phase pulsating back electromotive forces of the power winding and the control winding are synthesized accordingly, and used as the pulsating voltage reference vector u of the power winding and the control winding. p2M and u c2M The formula for its calculation is:

[0023] u p2M =-4(L) pp pi pC +L pc pi cC )

[0024] uc2M =-4(L) cc pi cC +L pc pi pC );

[0025] (d) The pulse voltage reference vector u of the power winding and control winding p2M and u c2M By decomposing these components onto the αβ coordinate axis, the αβ-axis components of the feedforward voltage compensation for the static end effect of the power winding and the control winding are obtained, and their calculation formulas are as follows:

[0026]

[0027]

[0028] In the formula, u * p2α and u * p2β The αβ-axis component represents the feedforward voltage compensation for the static end effect of the power winding; u * c2α and u * c2β The αβ-axis component represents the feedforward voltage compensation amount for the static end effect of the control winding.

[0029] (e) The αβ axis component of the feedforward voltage compensation amount of the static end effect of each primary winding and the DC bus voltage are modulated by SVPWM to generate the required voltage and apply it to the corresponding primary winding end of the motor to cancel the fundamental negative sequence current and direct coupling current generated by the static end effect.

[0030] In one embodiment, in step (a), the transfer function G(s) of the second-order linear tracking differentiator is:

[0031]

[0032] In the formula, s represents the sign of the Laplace transform; r is the damping coefficient of the system.

[0033] In one embodiment, in step (c), the phase relationship of the three-phase pulsating back electromotive force is as follows:

[0034] The amplitudes of the three-phase pulsating back electromotive forces are the same. The phases of the pulsating back electromotive forces of the AB phase windings near the two ends of the primary are the same, and the phases are opposite to those of the pulsating back electromotive forces of the C phase winding of the primary.

[0035] In one embodiment, step (1) specifically involves:

[0036] (A) Obtain the three-phase currents ABC of the primary winding, and transform them from the ABC coordinate system to the αβ coordinate system through Clark transformation to obtain the current in the αβ coordinate system.

[0037] (B) The current in the αβ coordinate system is decoupled by harmonics to obtain the pre-extracted fundamental current and direct coupling current;

[0038] (C) For the power winding, the pre-extracted fundamental current and direct coupling current are respectively fed into the center frequency f. p1 and f p2 A dual-hybrid second- to third-order generalized integrator; for the control winding, the pre-extracted fundamental current and the directly coupled current are fed into the center frequency f. c1 and f c2 A dual-hybrid second- to third-order generalized integrator; where the frequency f p1 f p2 f c1 and f c2 The relationship is:

[0039]

[0040] f p1 =f c2

[0041] f c1 =f p2

[0042] In the formula, f p1 f represents the fundamental current frequency in the power winding. p2 f represents the frequency of the directly coupled current in the power winding; c1 f represents the fundamental current frequency in the control winding. c2 Indicates the frequency of the direct-coupled current in the control winding; v n p represents the secondary mechanical operating speed; p and p c The corresponding numbers represent the number of pole pairs in the power winding and the control winding; L represents the longitudinal length of the primary core.

[0043] (D) The output of the dual-hybrid second-order to third-order generalized integrator is used to obtain the fundamental current and direct coupling current of the primary winding and their orthogonal current signals with a lag of 90 degrees. Then, the positive and negative sequence components of the fundamental current and direct coupling current are extracted using the positive and negative sequence component calculation method in the αβ coordinate system to obtain the positive and negative sequence components of the fundamental current and direct coupling current of the primary winding.

[0044] In one embodiment, the dual-hybrid second- to third-order generalized integrator is a structure of two parallel MSTOGIs, with the transfer functions G1(s) and G2(s) of the in-phase and quadrature signals of the MSTOGIs being:

[0045]

[0046]

[0047] In the formula, s represents the symbol of the Laplace transform; k represents the gain coefficient; ω0 is the center frequency; u(s) represents the input signal; u1(s) is the filtered signal with the same phase as u(s); and u2(s) is the signal with a phase lag of 90 degrees over u1(s).

[0048] In one embodiment, step (4) specifically involves:

[0049] For the power winding, the coordinate transformation angle of the fundamental current and the positive and negative sequence components of the direct coupling current is used to transform the given values ​​of the fundamental voltage and the positive and negative sequence d-axis components of the direct coupling voltage to the αβ coordinate system; for the control winding, the coordinate transformation angle of the fundamental current and the positive and negative sequence components of the direct coupling current is used to transform the given values ​​of the fundamental voltage and the positive and negative sequence d-axis components of the direct coupling voltage to the αβ coordinate system.

[0050] Among them, the transformation angle θ of the fundamental current and the positive sequence component of the direct coupling current of each primary winding + p1 and θ + p2 The fundamental current frequency f of this winding p1 and the frequency f of the directly coupled current p2 The transformation angle θ of its negative-order component is obtained by integration. - p1 and θ - p2 It is obtained by integrating the negative numbers of the fundamental current and the direct coupling current frequency of the winding. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating a method for compensating for static end effects in a concentric cage secondary linear doubly fed motor according to an embodiment of the present invention.

[0052] Figure 2 This is a block diagram of static end effect compensation for a concentric cage secondary linear doubly fed motor provided by the present invention;

[0053] Figure 3 This is a block diagram of the dual-hybrid second- to third-order generalized integrator structure provided by the present invention;

[0054] Figure 4 This is a principle block diagram of the positive and negative order component calculation method provided by the present invention;

[0055] Figure 5 This is a schematic diagram of the space vector of the three-phase synthesized pulsating electromotive force provided by the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0057] The following explains the relevant concepts in this invention:

[0058] ABC coordinate system: Corresponding to the three-phase symmetrical stationary winding of an AC motor, it has three coordinate axes A, B and C that intersect at the origin. The three coordinate axes are stationary in space and symmetrically distributed with a difference of 120 degrees between them. In a clockwise direction, they are A, B and C axes respectively.

[0059] αβ coordinate system: Corresponds to the virtual two-phase orthogonal stationary windings of an AC motor. It has two coordinate axes, α and β, which intersect at the origin. The two coordinate axes are stationary in space and differ from each other by 90 degrees. They are the α axis and β axis in the counterclockwise direction.

[0060] SVPWM generator: Using the ideal flux linkage circle of the stator of a three-phase symmetrical motor when powered by a three-phase symmetrical sinusoidal voltage as a reference standard, and making appropriate switching of different switching modes of the three-phase inverter, a PWM wave is formed, and the actual flux linkage vector formed is used to track its accurate flux linkage circle.

[0061] To suppress the negative sequence current and DC coupling current generated by the static end effect in the two primary windings of a concentric cage secondary linear doubly fed motor, this invention provides a static end effect compensation method for a concentric cage secondary linear doubly fed motor. This method is applicable to all operating modes of the power winding and control winding, including cascaded asynchronous operating mode, synchronous operating mode, and doubly fed operating mode. Furthermore, the method for suppressing negative sequence current is also applicable to other types of asymmetrical motors.

[0062] The static end-effect compensation method for a concentric cage secondary linear doubly-fed induction generator provided by this invention includes static end-effect compensation steps for two sets of primary windings (power winding and control winding). The static end-effect compensation steps for the two sets of primary windings are the same, both including steps S10 to S50, as follows: Figure 1 As shown, the details are as follows:

[0063] S10: Obtain the three-phase currents (A, B, C) of the power winding (control winding), extract the fundamental current and direct coupling current, and perform positive and negative sequence decomposition on the fundamental current and direct coupling current to obtain the positive and negative sequence components of the fundamental current and direct coupling current of the power winding (control winding).

[0064] In this embodiment, step S10 can be implemented using steps S101 to S104, as follows:

[0065] S101: Obtain the three-phase currents (A, B, and C) of the power winding (control winding), and transform them from the ABC coordinate system to the αβ coordinate system using Clark transformation to obtain the current i of the power winding (control winding) in the αβ coordinate system. pαβ (i cαβ ).

[0066] S102, the current i in the power winding (control winding) αβ coordinate system. pαβ (i cαβ After harmonic decoupling, the pre-extracted fundamental current i' of the power winding (control winding) is obtained. p1αβ (i' c1αβ ) and direct coupling current i' p2αβ (i' c2αβ ).

[0067] Harmonic decoupling involves subtracting currents of other frequencies from the obtained power winding (control winding) current to obtain the current of the desired extraction frequency. This reduces the interference of currents of different frequencies on harmonic current extraction.

[0068] S103, the pre-extracted fundamental current i' of the power winding (control winding) p1αβ (i' c1αβ The input center frequency is f p1 (f c1 The Dual Mixed Second-and Third-Order Generalized Integrator (DMSTOGI) directly couples the pre-extracted power winding (control winding) current i' p2αβ (i' c2αβ The input center frequency is f p2 (f c2 ) of DMSTOGI.

[0069] Among them, f p1 (f c1 f is the fundamental current frequency of the power winding (control winding). p2 (f c2The direct coupling current frequency f in the power winding (control winding) is the frequency of the current directly coupled to the winding. p2 With the fundamental current frequency f of the control winding c1 Equal, controlling the frequency f of the direct coupling current in the winding. c2 With the fundamental current frequency f of the power winding p1 Equal, i.e., f p1 =f c2 f c1 =f p2 The fundamental current frequencies of the power winding and the control winding satisfy the following relationship:

[0070]

[0071] In the above formula, v n For the secondary mechanical operating speed, f p1 and f c1 These are the fundamental current frequencies of the power winding and the control winding, respectively, p p and p c These represent the number of pole pairs for the power winding and the control winding, respectively, and L is the longitudinal length of the primary core.

[0072] Specifically, the DMSTOGI provided in this embodiment is a combination structure of two MSTOGIs connected in parallel, used to extract the α and β axis components of the fundamental current or directly coupled current of the power winding (control winding), respectively. The transfer functions of the in-phase and quadrature signals of the MSTOGI are as follows:

[0073]

[0074]

[0075] Where s is the symbol for the Laplace transform, k is the gain coefficient, ω0 is the center frequency, u(s) is the input signal, u1(s) is the filtered signal with the same phase as u(s), and u2(s) is the signal with a phase lag of 90 degrees over u1(s).

[0076] S104, the output of the dual hybrid second- to third-order generalized integrator yields the fundamental current i of the power winding (control winding). p1αβ (i c1αβ ) and direct coupling current i p2αβ (i c2αβ ), and the orthogonal current signal qi with a 90-degree lag. p1αβ (qi c1αβ ) and qi p2αβ (qi c2αβThen, using the positive and negative sequence component calculation method in the αβ coordinate system, the positive and negative sequence components of the fundamental current and the directly coupled current are extracted to obtain the positive and negative sequence components i of the fundamental current of the power winding (control winding). + p1αβ i - p1αβ (i + c1αβ i - c1αβ ) and the positive and negative sequence components i of the directly coupled current + p2αβ i - p2αβ (i + c2αβ i - c2αβ ).

[0077] The positive and negative sequence components of the power winding fundamental current and the direct coupling current can be calculated by the following formulas. Similarly, the calculation method of the positive and negative sequence components of the control winding fundamental current and the direct coupling current is not repeated in this embodiment.

[0078]

[0079]

[0080]

[0081]

[0082] S20, converts the positive and negative sequence components i of the fundamental current of the power winding (control winding) + p1αβ i - p1αβ (i + c1αβ i - c1αβ ) and the positive and negative sequence components i of the directly coupled current + p2αβ i - p2αβ (i + c2αβ i - c2αβ Perform a multi-synchronous rotating coordinate transformation from the αβ coordinate system to the dq coordinate system to obtain the positive and negative sequence components i of the current in the dq coordinate system of the power winding (control winding). + p1dq i - p1dq (i + c1dq i -c1dq ) and i + p2dq i - p2dq (i + c2dq i - c2dq ).

[0083] Among them, the transformation angle θ of the fundamental current and the positive sequence component of the directly coupled current of the power winding (control winding) is... + p1 (θ + c1 ) and θ + p2 (θ + c2 The transformation angle θ of the negative sequence component is obtained by integrating the fundamental current and the directly coupled current of the winding. - p1 (θ - c1 ) and θ - p2 (θ - c2 The value is obtained by integrating the negative numbers of the fundamental current and the direct coupling current frequency of the winding.

[0084] S30, perform PI control on the difference between the given values ​​of the positive and negative sequence d-axis components of the fundamental current and direct coupling current of the power winding (control winding) and the given values ​​of the positive and negative sequence d-axis components of the fundamental current and direct coupling current obtained in step 6, to obtain the given values ​​u of the positive and negative sequence d-axis components of the fundamental voltage and direct coupling voltage of the power winding (control winding). + p1dq u - p1dq (u + c1dq u - c1dq ) and u + p2dq u - p2dq (u + c2dq u - c2dq ).

[0085] The given value of the positive sequence component of the fundamental current of the power winding (control winding) can be given according to the load conditions, and the given values ​​of the negative sequence component of the fundamental current and the positive and negative sequence components of the direct coupling current of the power winding (control winding) are all set to 0.

[0086] S40 utilizes the coordinate transformation angle θ of the fundamental current and the positive and negative sequence components of the direct coupling current in the power winding (control winding). + p1 θ - p1 (θ + c1 θ - c1 ) and θ + p2 θ - p2 (θ + c2 θ - c2 The fundamental voltage of the power winding (control winding) and the positive and negative sequence d-axis and q-axis components of the direct coupling voltage are given by the value u. + p1dq u - p1dq (u + c1dq u - c1dq ) and u + p2dq u - p2dq (u + c2dq u - c2dq Transform to the αβ coordinate system, and add the fundamental voltage of the power winding (control winding) and the positive and negative sequence α and β axis components of the direct coupling voltage to obtain the voltage setpoint u of the power winding (control winding) that suppresses negative sequence current and direct coupling current. * p1αβ (u * c1αβ ).

[0087] S50, based on the voltage setpoint u of the power winding (control winding) * p1αβ (u * c1αβ ) and DC bus voltage U dc The required voltage is modulated by an SVPWM generator and applied to the primary winding to drive the motor and compensate for static end effects.

[0088] The static end effect compensation method for concentric cage secondary linear doubly fed motors provided in this embodiment does not require an accurate mathematical model of the motor and only requires a few motor parameters to obtain the voltage setpoint for compensating the static end effect. It can extract and suppress the negative sequence current and direct coupling current generated by the static end effect in the power winding (control winding), and effectively improve key performance indicators such as motor thrust.

[0089] In one embodiment, the static end effect compensation method provided by the present invention further includes step S60, which is detailed below:

[0090] S60, based on the short primary linear motor winding theory, derives the expression for the pulsating back electromotive force (EMF) of a concentric cage secondary linear doubly fed motor, taking into account the static end effect generation mechanism. This expression is then synthesized and used as a voltage reference vector feedforward compensation to the primary winding, further effectively suppressing negative sequence and direct coupling currents generated by the static end effect. More importantly, the pulsating back EMF feedforward compensation provided in this embodiment is an open-loop compensation, which can more effectively improve its dynamic response speed.

[0091] Specifically, step S60 is divided into a pulse voltage vector feedforward step for the power winding and a pulse voltage vector feedforward step for the control winding. The pulse voltage vector feedforward steps for both windings are the same, both including S601 to S605, as detailed below:

[0092] S601, obtains the C-phase current i of the power winding and control winding. pC and i cC The time derivatives pi of the C-phase currents of the power winding and control winding are calculated using a second-order linear tracking differentiator. pC and pi cC .

[0093] The transfer function G(s) of the second-order linear tracking differentiator is:

[0094]

[0095] In the formula, s represents the sign of the Laplace transform; r is the damping coefficient of the system.

[0096] S602, based on the time derivative pi of the C-phase (intermediate phase) current of the power winding and control winding. pC and pi cC Calculate the pulsating back electromotive force (EMF) of the power winding (control winding). The formulas for calculating the pulsating back EMF of the power winding and the control winding are as follows:

[0097]

[0098]

[0099] In the formula, e p2A e p2B and e p2c e represents the three-phase pulsating back electromotive force of the power winding. p2A e p2B and e p2c pi represents the three-phase pulsating back electromotive force of the control winding. pCpi represents the time derivative of the C-phase current of the power winding. cC L represents the time derivative of the C-phase current of the control winding; pp and L cc These are the pulsating self-inductances of the power winding and the control winding, respectively; L pc For direct coupling mutual inductance between the power winding and the control winding; i pC and i cC , respectively, are the C-phase currents of the power winding and the control winding; p is the differential operator.

[0100] S603, based on the phase relationship of the three-phase pulsating back electromotive force, synthesizes the three-phase pulsating back electromotive force of the power winding (control winding) accordingly, and uses it as the pulsating voltage reference vector u of the power winding (control winding). p2M (u c2M The formula for its calculation is:

[0101] u p2M =-4(L) pp pi pC +L pc pi cC )

[0102] u c2M =-4(L) cc pi cC +L pc pi pC )

[0103] The phase relationship of the three-phase pulsating back electromotive force is as follows: the amplitude of the three-phase pulsating back electromotive force is the same, the phase of the pulsating back electromotive force of the two phases (A and B phases) windings near the two ends of the primary is the same, and the phase of the pulsating back electromotive force of the winding of the primary middle phase (C phase) is opposite.

[0104] S604, uses the pulsating voltage reference vector u of the power winding (control winding) as an example. p2M (u c2M The static end effect feedforward voltage compensation of the power winding (control winding) is decomposed onto the αβ coordinate axis to obtain the αβ axis component u. * p2αβ (u * c2αβ ).

[0105] Among them, the static end effect feedforward voltage compensation amount u of the power winding (control winding) p2 (u c2 αβ axis components u * p2αβ (u * c2αβ The formula for calculating ) is:

[0106]

[0107]

[0108] S605 feeds forward the αβ-axis component u of the static end effect compensation amount of the power winding (control winding). * p2αβ (u * c2αβ According to the voltage setpoint u of the power winding (control winding) in step S50 above. * p1αβ (u * c1αβ The compensation method is applied to the corresponding winding end, which is to obtain the αβ axis component u of the static end effect feedforward voltage compensation. * p2αβ (u * c2αβ ) and DC bus voltage U dc The required voltage is generated by modulation through an SVPWM generator and applied to the corresponding winding terminals of the motor to further drive the motor and compensate for static end effects.

[0109] To more clearly illustrate the present invention, the following provides a detailed description of the static end-effect compensation method in the asynchronous operation mode of a concentric cage secondary linear doubly fed motor, with its control block diagram as follows: Figure 2 As shown.

[0110] Step 1: Detect the three-phase current of the power winding, and transform the three-phase current from the ABC coordinate system to the αβ coordinate system using Clark transformation to obtain the current i in the αβ coordinate system of the power winding. pαβ .

[0111] Step 2, convert the power winding current i in the αβ coordinate system pαβ After harmonic decoupling, the pre-extracted power winding fundamental current i' is obtained. p1αβ and direct coupling current i' p2αβ .

[0112] Harmonic decoupling involves subtracting currents of other frequencies from the measured power winding current to obtain the current at the desired extraction frequency. This reduces the interference of currents of different frequencies on harmonic current extraction. That is, i' p1αβ =i pαβ -i p2αβ , i' p2αβ =i pαβ -i p1αβ i p1αβ and i p2αβ These are the fundamental current and the direct coupling current of the power winding after harmonic decoupling, respectively.

[0113] Step 3: The fundamental currents and directly coupled currents of different frequencies, after harmonic decoupling, are fed into a dual mixed second-and-third-order generalized integrator (DMSTOGI). The mixed second-and-third-order generalized integrator is composed of a second-order generalized integrator (SOGI) and a third-order generalized integrator (TOGI), as shown in the block diagram below. Figure 3 As shown. The pre-extracted power winding fundamental current i' p1αβ The input center frequency is f p1 DMSTOGI directly couples the pre-extracted power winding current i' p2αβ The input center frequency is f p2 DMSTOGI.

[0114] Among them, f p1 f is the fundamental current frequency of the power winding. p2 Let be the frequency of the direct coupling current in the power winding. The frequency of the direct coupling current in the power winding (control winding) is equal to the fundamental current frequency of the control winding (power winding), satisfying the following relationship:

[0115]

[0116] f p1 =f c2

[0117] f c1 =f p2

[0118] In the above formula, v n For the secondary mechanical operating speed, p p and p c These represent the number of pole pairs for the power winding and the control winding, respectively, and L is the longitudinal length of the primary core of the motor.

[0119] DMSTOGI is a parallel structure of two MSTOGIs, used to extract the α and β axis components of the fundamental current or directly coupled current of the power winding, respectively. The transfer functions of the in-phase and quadrature signals of MSTOGI are as follows:

[0120]

[0121]

[0122] Where s is the symbol for the Laplace transform, k is the gain coefficient, and ω0 is the center frequency. u(s) is the input signal, u1(s) is the filtered signal with the same phase as u(s), and u2(s) is the signal with a phase lag of 90 degrees over u1(s).

[0123] Step 4: The fundamental current i of the power winding is obtained from the output of the dual hybrid second-order to third-order generalized integrator. p1αβ and direct coupling current i p2αβ and the current signal qi that lags by 90 degrees p1αβ and qi p2αβ Then, using the positive and negative sequence component calculation method in the αβ coordinate system, the positive and negative sequence components of the fundamental current and the directly coupled current are extracted to obtain the positive and negative sequence components i of the fundamental current of the power winding. + p1αβ i - p1αβ and the positive and negative sequence components i of the directly coupled current + p2αβ i - p2αβ ,like Figure 4 As shown.

[0124] The positive and negative sequence components of the power winding fundamental current and the direct coupling current can be calculated by the following formulas, and the calculation methods for the positive and negative sequence components of the control winding fundamental current and the direct coupling current are the same.

[0125]

[0126]

[0127]

[0128]

[0129] Step 5, convert the positive and negative sequence components i of the fundamental current of the power winding. + p1αβ i - p1αβ and the positive and negative sequence components of the directly coupled current i + p2αβ i - p2αβ By transforming the αβ coordinate system into the synchronously rotating dq coordinate system corresponding to their respective frequencies, the positive and negative sequence components of the current in the dq coordinate system are obtained. + p1dq i - p1dq and i + p2dq i - p2dq .

[0130] Among them, the transformation angle θ of the fundamental current and the positive sequence component of the directly coupled current of the power winding is... + p1 and θ + p2 The fundamental current frequency f of this winding p1 and the frequency f of the directly coupled current p2 The transformation angle θ of its negative-order component is obtained by integration. - p1 and θ - p2 It is obtained by integrating the negative numbers of the fundamental current and the directly coupled current frequencies of this winding. That is, θ + p1 =∫f p1 dt, θ + p2 =∫f p2 dt, θ - p1 =-θ + p1 θ - p2 =-θ + p2 .

[0131] Step 6: Perform PI control on the difference between the given values ​​of the fundamental current and the positive and negative sequence d-axis components of the direct coupling current and the feedback values ​​of the fundamental current and the positive and negative sequence d-axis components of the direct coupling current and the direct coupling current, to obtain the given values ​​u of the fundamental voltage and the positive and negative sequence d-axis components of the direct coupling voltage. + p1dq u - p1dq and u + p2dq u - p2dq .

[0132] The given value for the positive sequence component of the fundamental current can be manually set according to the load conditions. The given values ​​for the negative sequence of the power winding fundamental current and the positive and negative sequence d-axis components of the direct coupling current are both 0.

[0133] Step 7: Transform the coordinates of the fundamental current of the power winding and the positive and negative sequence components of the direct coupling current by angle θ. + p1 θ - p1 and θ + p2 θ - p2 The positive and negative sequence d-axis and q-axis components of the power winding fundamental voltage and the direct coupling voltage are given by the value u. + p1dq u- p1dq and u + p2dq u - p2dq Transform to the αβ coordinate system and add the positive and negative sequence α and β axis components of the power winding fundamental voltage and the direct coupling voltage to obtain the power winding voltage setpoint u that suppresses negative sequence current and direct coupling current. * p1αβ .

[0134] Step 8: Detect the C-phase (intermediate phase) current i of the power winding and control winding. pC and i cC The derivatives pi of the C-phase currents of the power winding and control winding with respect to time are calculated using a second-order linear tracking differentiator. pC and pi cC ;

[0135] The transfer function of the second-order linear tracking differentiator is:

[0136]

[0137] Where r is the damping coefficient of the system.

[0138] Step 9, the phase relationship of the pulsating back electromotive force, as follows: Figure 5 As shown. Based on the time derivatives pi of the C-phase currents of the power winding and control winding. pC and pi cC Calculate the power winding pulsating voltage reference vector u p2M The formula for its calculation is:

[0139] u p2M =-4(L) pp pi pC +L pc pi cC )

[0140] Among them, L pp and L cc The pulsating inductances L for the power winding and control winding are respectively. pc This refers to the direct coupling mutual inductance between the power winding and the control winding.

[0141] Step 10, set the power winding pulsating voltage reference vector u p2M Decomposed onto the αβ coordinate axis, the αβ-axis component u of the power winding static end effect feedforward voltage compensation is obtained. * p2αβ .

[0142] Among them, the αβ-axis component u of the power winding static end effect feedforward voltage compensation amount p2αβ The formula for calculation is:

[0143]

[0144] Step 11, set the power winding voltage setpoint u to suppress negative sequence current and direct coupling current. * p1αβ Compensation amount u for feedforward voltage of static end effect of power winding * p2αβ The α and β axis components are added together to obtain the power winding voltage setpoint u. * pαβ .

[0145] Step 12, based on the power winding voltage setpoint u * pαβ and DC bus voltage U dc The required voltage is generated by modulating the SVPWM generator and applied to the motor power winding. At the same time, the winding is controlled to keep the three phases short-circuited so that the motor runs in a cascaded asynchronous operation mode.

[0146] One method to short-circuit the three phases of the motor control winding using the converter on the control winding side without changing the motor wiring is as follows: keep the upper bridge arm switch of the converter off, and at the same time turn on the lower bridge arm switch.

[0147] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for compensating for static end effects in a concentric cage secondary linear doubly-fed induction generator, characterized in that, The static end-effect compensation steps include two sets of primary windings: a control winding and a power winding. Each set of primary windings includes the following steps: (1) Obtain the three-phase currents ABC of the primary winding, extract the fundamental current and direct coupling current, and perform positive and negative sequence decomposition on the fundamental current and direct coupling current to obtain the positive and negative sequence components of the fundamental current and direct coupling current. (2) Perform a rotation coordinate transformation on the positive and negative sequence components of the fundamental current and the direct coupling current to obtain the positive and negative sequence d and q axis components of the fundamental current and the direct coupling current; (3) The given values ​​of the positive and negative sequence d and q axis components of the fundamental current and the direct coupling current are compared with the positive and negative sequence d and q axis components of the fundamental current and the direct coupling current obtained in step (2), and each difference is controlled by PI to obtain the given values ​​of the positive and negative sequence d and q axis components of the fundamental voltage and the direct coupling voltage; wherein, the given values ​​of the negative sequence d and q axis components of the fundamental current and the positive and negative sequence of the direct coupling current are both zero, and the given values ​​of the positive sequence d and q axis components of the fundamental current are determined according to the motor load conditions; (4) Transform the given values ​​of the positive and negative sequence d-axis components of the fundamental voltage and the direct coupling voltage to... A coordinate system is used to determine the positive and negative order of the obtained fundamental voltage and directly coupled voltage. , The axial components are added together to obtain the voltage setpoint values ​​for suppressing negative sequence current and direct coupling current in the primary winding; (5) Based on the given voltage value and the DC bus voltage, the actual required voltage is generated by SVPWM modulation and applied to the primary winding to drive the motor and compensate for static end effects; Step (1) is as follows: (A) Obtain the three-phase currents (A, B, C) of the primary winding, and transform them from the ABC coordinate system to the Clark coordinate system using the Clark transformation. coordinate system, to obtain Current in a coordinate system; (B) will The current in the coordinate system is decoupled by harmonics to obtain the pre-extracted fundamental current and the direct coupling current; (C) For the power winding, the pre-extracted fundamental current and the direct coupling current are respectively fed into the center frequency. and A dual-hybrid second- to third-order generalized integrator; for the control winding, the pre-extracted fundamental current and the directly coupled current are fed into the center frequency. and A dual-hybrid second- to third-order generalized integrator; where the frequency , , and The relationship is: In the formula, This indicates the frequency of the fundamental current in the power winding. Indicates the frequency of the directly coupled current in the power winding; This indicates the frequency of the fundamental current in the control winding. Indicates the frequency of the direct coupling current in the control winding; Indicates the secondary mechanical operating speed; p p and p c This corresponds to the number of pole pairs in the power winding and the control winding; Indicates the longitudinal length of the primary iron core; (D) The output of the dual-hybrid second-order to third-order generalized integrator is used to obtain the fundamental current and direct coupling current of the primary winding, as well as the orthogonal current signal with a 90-degree lag. Then, the signal is used... The positive and negative sequence components calculation method in the coordinate system extracts the positive and negative sequence components of the fundamental current and the direct coupling current, and obtains the positive and negative sequence components of the fundamental current and the direct coupling current of the primary winding. The dual-hybrid second- to third-order generalized integrator is a structure of two parallel MSTOGIs, and the transfer functions of the in-phase and quadrature signals of the MSTOGIs are... and They are respectively: In the formula, Symbols representing Laplace transforms; Indicates the gain coefficient; The center frequency; Indicates the input signal; The filtered result is... Signals with the same phase For phase lag A signal at 90 degrees.

2. The static end effect compensation method for a concentric cage secondary linear doubly fed motor according to claim 1, characterized in that, The method further includes the following steps: (6) Based on the short primary linear motor winding theory, the expression of the pulsating back electromotive force is derived for the static end effect generation mechanism of the concentric cage secondary linear doubly fed motor, and it is synthesized as a voltage reference vector feedforward compensation to the two primary windings to offset the fundamental negative sequence current and direct coupling current generated by the static end effect.

3. The static end effect compensation method for a concentric cage secondary linear doubly fed motor according to claim 2, characterized in that, Step (6) specifically involves: (a) Obtain the C-phase current of the power winding and the control winding, and use a second-order linear tracking differentiator to calculate the derivative of the C-phase current of the power winding and the control winding with respect to time; (b) Calculate the pulsating back electromotive force of the power winding and control winding based on the derivatives of the C-phase currents of the power winding and control winding with respect to time. The calculation formula is as follows: In the formula, , and This represents the three-phase pulsating back electromotive force of the power winding. , and This indicates the three-phase pulsating back electromotive force of the control winding; This represents the time derivative of the C-phase current of the power winding. This represents the time derivative of the C-phase current of the control winding; and These are the pulsating self-inductances of the power winding and the control winding, respectively. This is the direct coupling mutual inductance between the power winding and the control winding; and , respectively, are the C-phase currents of the power winding and the control winding; p is the differential operator; (c) Based on the phase relationship of the three-phase pulsating back electromotive force, the three-phase pulsating back electromotive forces of the power winding and the control winding are synthesized accordingly, and used as the pulsating voltage reference vector of the power winding and the control winding. and The formula for its calculation is: ； (d) The pulsating voltage reference vector of the power winding and control winding and Decomposed into On the coordinate axis, the feedforward voltage compensation amounts for the static end effects of the power winding and control winding are obtained. The axial component is calculated using the following formula: In the formula, and This indicates the amount of feedforward voltage compensation for the static end effect of the power winding. Axial components; and This indicates the amount of feedforward voltage compensation for the static end effect of the control winding. Axial components; (e) The feedforward voltage compensation amount of the static end effect of each primary winding The shaft component and DC bus voltage are modulated by SVPWM to generate the required voltage and apply it to the corresponding primary winding terminal of the motor to counteract the fundamental negative sequence current and direct coupling current generated by the static end effect.

4. The static end effect compensation method for a concentric cage secondary linear doubly fed motor according to claim 3, characterized in that, In step (a), the transfer function of the second-order linear tracking differentiator for: In the formula, Symbols representing Laplace transforms; is the damping coefficient of the system.

5. The static end effect compensation method for a concentric cage secondary linear doubly fed motor according to claim 3, characterized in that, In step (c), the phase relationship of the three-phase pulsating back electromotive force is as follows: The amplitudes of the three-phase pulsating back electromotive forces are the same. The phases of the pulsating back electromotive forces of the AB phase windings near the two ends of the primary are the same, and the phases are opposite to those of the pulsating back electromotive forces of the C phase winding of the primary.

6. The static end effect compensation method for a concentric cage secondary linear doubly fed motor according to claim 1, characterized in that, Step (4) is as follows: For the power winding, the coordinate transformation angles of the fundamental current and the positive and negative sequence components of the direct coupling current are used to transform the given values ​​of the fundamental voltage and the positive and negative sequence d-axis components of the direct coupling voltage to... Coordinate system; for the control winding, the coordinate transformation angle of the fundamental current and the positive and negative sequence components of the direct coupling current of the control winding is used to transform the given values ​​of the fundamental voltage and the positive and negative sequence d-axis components of the direct coupling voltage of the control winding to a coordinate system. Coordinate system; Among them, the transformation angle of the fundamental current and the positive sequence component of the directly coupled current of each primary winding. and The fundamental current frequency of this winding f p1 and direct coupling current frequency f p2 The transformation angle of its negative-order component is obtained by integration. and It is obtained by integrating the negative numbers of the fundamental current and the direct coupling current frequency of the winding.

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