Method and system for determining asymmetric current of linear induction motor

Abstract

The invention discloses a method and a system for determining asymmetric current of a linear induction motor, and belongs to the technical field of linear motors. The method comprises the following steps: obtaining electromotive force vectors of the linear induction motor under the excitation of positive sequence current and negative sequence current, calculating the positive sequence current and the negative sequence current according to the given phase voltage of the linear induction motor and the electromotive force vectors by adopting the value constraints of the positive sequence current and the negative sequence current, and calculating the positive sequence current and the negative sequence current according to the positive sequence current and the negative sequence current. And taking the sum of the positive sequence current and the negative sequence current which conform to the constraint as the asymmetric current of the linear induction motor. According to the method, the asymmetric current of the linear induction motor can be accurately calculated, the asymmetry of the linear induction motor under different operation conditions is analyzed, and the method is a basis for further refined modeling and analysis.

Description

Technical Field

[0001] The present invention belongs to the technical field of linear motors, and more specifically, relates to a method and system for determining an asymmetric current of a linear induction motor. Background Art

[0002] The linear induction motor can be regarded as a rotary induction motor that has been flattened along the radial direction. Its thrust is generated directly by the primary and secondary electromagnetic fields. Because there is no intermediate conversion and transmission device, the linear induction motor system has the advantages of simple structure, fast acceleration and deceleration, small size and low noise. In recent years, it has been applied in many fields such as rail transportation, servo systems, electromagnetic catapults, electromagnetic induction pumps, etc., and has gradually become an important choice for linear drive occasions.

[0003] Short primary linear induction motors are often used in applications with longer travels, such as in the field of urban rail transit. Affected by the disconnected primary structure of the linear induction motor, the instantaneous values ​​of the magnetic field at the input and output ends remain constant, and the secondary induction plate will induce eddy currents that hinder the change of the magnetic field, namely the end effect. The corresponding magnetic fields are called dynamic end effect input wave magnetic field and dynamic end effect output wave magnetic field. Under normal circumstances, the dynamic end effect input wave magnetic field decays slowly and can cover the entire primary area, which will weaken the normal traveling wave magnetic field and distort the air gap magnetic field. The dynamic end effect output wave magnetic field decays quickly and its influence can be ignored. Furthermore, due to the different longitudinal arrangement positions of the windings of each phase, the electromotive force generated by the cutting of the air gap magnetic field is also different, and the symmetrical phase current will generate asymmetrical electromotive force. However, rail transit linear induction motors are generally powered by a converter controlled by variable voltage and frequency, that is, the current of each phase is not symmetrical. Rail transit linear induction motors often use star wiring, which has no neutral line and cannot provide a channel for zero-sequence current. The direction of the magnetic field generated by the negative-sequence current is opposite to that of the positive-sequence current, which will hinder the movement of the motor and affect output characteristics such as thrust and efficiency.

[0004] At present, the current calculation of linear induction motors is based on the assumption of symmetry of each phase, solving the equivalent circuit parameters and equivalent circuit impedance, and then obtaining the calculated value of the current. However, as the motor speed increases, the slip rate changes, and the end effect becomes more serious and complex, resulting in an increase in the difference in current between phases, that is, there is a large negative sequence current component. If it is still based on the assumption of symmetrical current, the calculation error of the motor output characteristics will inevitably increase. Therefore, determining the accurate current is the key. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a method and system for determining the asymmetric current of a linear induction motor, aiming to solve the technical problem that the prior art cannot accurately determine the asymmetric current of a linear induction motor.

[0006] To achieve the above object, the present invention provides a method for determining an asymmetric current of a linear induction motor, comprising the following steps:

[0007] The electromotive force vector of the linear induction motor under the excitation of the positive sequence current and the negative sequence current is obtained, and the positive sequence current and the negative sequence current are calculated according to the given phase voltage of the linear induction motor and the electromotive force vector, and the value constraints of the positive sequence current and the negative sequence current are adopted, and the sum of the positive sequence current and the negative sequence current that meet the constraints is used as the asymmetric current of the linear induction motor; wherein the value constraints of the positive sequence current and the negative sequence current are:

[0008]

[0009] in, is the given phase voltage, M is the number of any phase of A, B, C, R s is the primary phase resistance, X s is the primary leakage reactance, is the positive sequence current, is the negative sequence current, is the positive-sequence electromotive force vector under the positive-sequence current excitation, is the negative sequence electromotive force vector under the positive sequence current excitation, is the positive sequence electromotive force vector under the excitation of negative sequence current, is the negative-sequence electromotive force vector under negative-sequence current excitation.

[0010] Furthermore, the positive-sequence and negative-sequence electromotive force vectors of phase A are decomposed from the electromotive force vectors of each phase winding, and the positive-sequence and negative-sequence electromotive force vectors of phases B and C are obtained based on the relationship between the electromotive force vectors of each phase;

[0011] The positive and negative sequence electromotive force vectors of phase A are:

[0012]

[0013] The relationship between the electromotive force vectors of each phase is:

[0014]

[0015] In the formula, the subscripts (m,1) and (m,2) represent the positive-sequence and negative-sequence electromotive force vectors generated by the m-sequence current, and m=1 or 2 represents the positive-sequence and negative-sequence, respectively.

[0016] Furthermore, the electromotive force vector of each phase winding under the excitation of positive sequence current and negative sequence current is obtained by adding the single-turn coil electromotive force vectors of all coils in each phase winding, and the expression is:

[0017]

[0018] In the formula, N = w1 / (2pq), w1 is the number of series turns per phase, p is the number of pole pairs, q is the number of slots per pole per phase, A, B, C represent phase A, phase B, and phase C respectively. is the single-turn coil electromotive force vector of the i-th coil under the excitation of the m-sequence current.

[0019] Further, and The electromotive force vector of the single-turn coil under the positive sequence current excitation is obtained by making a difference. and The electromotive force vector of a single-turn coil under negative sequence current excitation is obtained by making a difference, which is expressed as:

[0020]

[0021] Where y1 is the winding pitch, is the slot electromotive force vector under the excitation of m-sequence current.

[0022] Furthermore, the expression of the slot electromotive force vector under the excitation of positive sequence current and negative sequence current is:

[0023]

[0024] In the formula, 2a is the motor width, ω is the current angular frequency, B s(1) , B s(2) are the amplitudes of the air gap magnetic field density under the excitation of positive sequence current and negative sequence current, τ is the pole distance, x is the position, i is the slot number where the upper side of the coil is located, L is the length of the primary core, S is the number of slots,

[0025] C=(σ s V) 2 , V is the running speed of the linear induction motor, σ s is the conductivity of the secondary conductive plate, δ e is the equivalent electromagnetic air gap length, μ0 is the air magnetic permeability.

[0026] Furthermore, the air gap magnetic field density distribution under the positive sequence current and negative sequence current excitation is expressed as:

[0027]

[0028]

[0029] Where, the subscripts (1) and (2) represent the quantities generated by the positive sequence current and negative sequence current excitation, s (1) =1-V / V s(1) , V s(1) =2τf,δ s(1)=tan -1 [1 / (s (1) G)], V s(2) =-2τf,s (2) =1-V / V s(2) , δ s(2) =tan -1 [1 / (s (2) G)];

[0030] In the formula, I m(1) and I m(2) are the amplitudes of positive and negative sequence currents, and are the initial angles of positive sequence current and negative sequence current respectively, m1 is the phase number, k p and k y are the winding distribution coefficient and short-distance coefficient, V is the operating speed of the linear induction motor, and f is the current frequency.

[0031] The present invention also provides a linear induction motor asymmetric current determination system, comprising: a computer readable storage medium and a processor;

[0032] The computer-readable storage medium is used to store executable instructions;

[0033] The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the above-mentioned method for determining the asymmetric current of the linear induction motor.

[0034] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0035] 1. The present invention fully considers that the direction of the magnetic field generated by the negative-sequence current component is opposite to that of the positive-sequence current, which will hinder the movement of the motor, and thus proposes that the asymmetric current consists of two parts: the positive-sequence current and the negative-sequence current. In the specific implementation determination, according to the given phase voltage of the linear induction motor and the electromotive force vector of each phase winding under the excitation of the positive-sequence current and the negative-sequence current respectively determined by parameter collection, the positive-sequence current and the negative-sequence current are correspondingly adopted to calculate the positive-sequence current and the negative-sequence current; the sum of the positive-sequence current and the negative-sequence current that meet the constraints is used as the asymmetric current of the linear induction motor, and the determined current takes into account the negative-sequence current component, thereby solving the technical problem that the prior art cannot accurately calculate the current.

[0036] 2. The present invention fully considers the end effect and the longitudinal arrangement characteristics of each phase winding, assumes that the asymmetric current is composed of a set of symmetrical positive-sequence current and negative-sequence current, solves the air gap magnetic field density generated by the positive-sequence current and negative-sequence current excitation, obtains the electromotive force vector of each slot, and then synthesizes the single-turn coil electromotive force vector, which is multiplied by the number of turns to obtain the coil electromotive force vector. The electromotive force vector is solved according to the spatial position and arrangement law of each phase winding, and the positive-sequence and negative-sequence currents are solved according to the voltage constraint equation to obtain the asymmetric current. The present invention adds the corresponding single-turn coil electromotive force vectors according to the longitudinal arrangement of the primary winding to obtain the electromotive force vector of each phase winding, can accurately calculate the asymmetric current of the linear induction motor, and analyze the asymmetry of the linear induction motor under different operating conditions. It is the basis for further refined modeling and analysis, and solves the technical problem that the existing technology cannot accurately calculate the current.

[0037] 3. The method of adding an induction-type compensation winding proposed in the present invention is applicable to all types of short primary linear induction motors, including single-sided short primary linear induction motors, double-sided short primary linear induction motors, cylindrical short primary linear induction motors, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is a flow chart of a method for determining asymmetric current of a linear induction motor provided by the present invention;

[0039] Figure 2 It is a diagram of the spatial motion law of the air gap magnetic field provided by the present invention;

[0040] Figure 3 is a primary equivalent circuit diagram of a linear induction motor provided by the present invention;

[0041] Figure 4 is a schematic diagram of the structure of a short primary linear induction motor;

[0042] Figure 5 It is a comparison diagram of the asymmetric current calculation value of the linear induction motor provided by an embodiment of the present invention and the current simulation value using the finite element method. DETAILED DESCRIPTION

[0043] In order to make the purpose and technical solution of the present invention clearer, the embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in each embodiment of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0044] like Figure 1 As shown, the present invention provides a method for determining the asymmetric current of a linear induction motor, comprising the following steps:

[0045] The electromotive force vector of the linear induction motor under the excitation of positive-sequence current and negative-sequence current is obtained respectively, the given phase voltage of the linear induction motor and the electromotive force vector are used, and the value constraints of the positive-sequence current and the negative-sequence current are used to calculate the positive-sequence current and the negative-sequence current, and the sum of the positive-sequence current and the negative-sequence current that meet the constraints is used as the asymmetric current of the linear induction motor.

[0046] The application principle of the present invention is further described below in conjunction with specific embodiments.

[0047] The expression of the traveling wave current layer generated by the positive sequence current and the negative sequence current is:

[0048]

[0049] In the formula, the subscripts (1) and (2) represent the quantities generated by the positive sequence current and negative sequence current excitation, ω is the current angular frequency, τ is the pole pitch, x is the position, I m(1) and I m(2) are the amplitudes of positive and negative sequence currents, and are the initial angles of positive sequence current and negative sequence current respectively, m1 is the number of phases, w1 is the number of series turns per phase, p is the number of pole pairs, k p and k y are the winding distribution coefficient and short-distance coefficient, and L is the primary core length.

[0050] As a preferred embodiment, within the length range of the primary core, the air gap magnetic field density distribution under positive sequence current excitation is expressed as:

[0051]

[0052] On this basis, if the assumption of symmetrical current is still used, the calculation error of the motor output characteristics will inevitably increase. Considering that the direction of the magnetic field generated by the negative sequence current is opposite to that of the positive sequence current, the air gap magnetic field density distribution under the excitation of the negative sequence current is obtained by combining the preset relationship between the phase and amplitude of the negative sequence current and the positive sequence current, which is expressed as:

[0053]

[0054] in, s (1) =1-V / V s(1) , V s(1) =2τf,δ s(1) =tan -1 [1 / (s (1) G)], C=(σ s V) 2 , V s(2) =-2τf,s (2) =1-V / V s(2) , δ s(2) =tan -1 [1 / (s (2) G)];

[0055] Where V is the speed of the linear induction motor, σ s is the conductivity of the secondary conductive plate, f is the current frequency, δ e is the equivalent electromagnetic air gap length, μ0 is the air magnetic permeability.

[0056] As a preferred embodiment, Figure 2 As shown, the magnetic fields generated by the positive-sequence current and the negative-sequence current have different directions of travel. For example, when the linear induction motor is in electrodynamic operation, the magnetic field generated by the positive-sequence current is in the same direction as the secondary motion, providing thrust, while the negative-sequence current is the opposite, providing braking force.

[0057] As a preferred embodiment, the expression of the slot electromotive force vector under the excitation of positive sequence current and negative sequence current is:

[0058]

[0059] In the formula, i is the slot number, L is the primary core length, and S is the number of slots.

[0060] As a preferred implementation, the slot electromotive force vectors corresponding to the upper and lower layers of the coil are subtracted to obtain the electromotive force vector of the single-turn coil, which is expressed as:

[0061]

[0062] Where the subscript (m) represents 1 or 2, which are the amount produced by positive or negative sequence current excitation, respectively, and y1 is the winding pitch.

[0063] As a preferred embodiment, the electromotive force vectors of the corresponding single-turn coils are added according to the primary winding arrangement, and the electromotive force expression of each phase winding is:

[0064]

[0065] Where q is the number of slots per pole per phase, N = w1 / (2pq).

[0066] As a preferred embodiment, according to the symmetrical component method, the asymmetrical electromotive force can be decomposed into symmetrical positive sequence, negative sequence and zero sequence electromotive force, such as Figure 3 As shown, the expression is:

[0067]

[0068] The relationship between the electromotive force vectors of each phase is expressed as:

[0069]

[0070] Where the subscripts (m,1), (m,2) and (m,0) represent the positive-sequence, negative-sequence and zero-sequence electromotive forces generated by the m-sequence current.

[0071] As a preferred embodiment, since the winding adopts a star connection method, the zero-sequence electromotive force is offset, and the electromotive force vector of each phase winding under the excitation of the positive-sequence current and the negative-sequence current and the given phase voltage respectively construct the constraints of the positive-sequence current and the negative-sequence current, and the sum of the positive-sequence current and the negative-sequence current that satisfy the constraints is used as the asymmetric current of the linear induction motor. The difference between the positive-sequence voltage and the positive-sequence electromotive force vector is the given phase voltage, and the difference between the negative-sequence voltage and the negative-sequence electromotive force vector is zero, which is expressed by the formula:

[0072]

[0073] In the formula, is the given phase voltage, M is the number of any phase, R s is the primary phase resistance, X s is the primary leakage reactance.

[0074] As a preferred implementation, the positive sequence and negative sequence components of the current are added together to obtain an asymmetric current, which is expressed as:

[0075]

[0076] This embodiment is applied to a 79-slot 8-pole double-layer short-pitch winding linear induction motor with half-filled slots. The motor is 2.476 m long and 0.3 m wide. The motor structure is as follows: Figure 4 As shown, sequence 1 is the winding, with a pitch y1 of 7, a phase number m1 of 3, a slot number q of 3 per pole per phase, a pole number 2p of 8, a pole pitch τ of 0.2808m, and a series number of turns w1 of 216 per phase; sequence 2 is the stator core, made of 50WW470 silicon steel sheet, with a slot pitch of 0.0312m, a slot width of 0.02m, and a total of 79 slots; sequence 3 is the secondary conductive plate, made of Cu, with a thickness of 0.005m; sequence 4 is the secondary back iron, made of No. 10 steel, with a thickness of 0.025m. At a speed V of 40km / h, the phase voltage amplitude is 635V, the initial electrical angle of phase A is 0, the frequency is 22.5Hz, and the primary phase resistance R s is 0.1382Ω, the primary leakage reactance is 6.6mH, and the current calculation value of the method of the present invention is compared with the current simulation value of the finite element method, as shown in FIG. Figure 5 shown.

[0077] The present invention can accurately calculate the asymmetric current of the linear induction motor and analyze the asymmetry of the linear induction motor under different operating conditions, which is the basis for further refined modeling and analysis and solves the technical problem that the prior art cannot accurately calculate the current.

[0078] It will be easily understood by those skilled in the art that the above description is only 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 in the protection scope of the present invention.

Claims

1. A method for determining asymmetric current of a linear induction motor, characterized in that: The following steps are involved: The electromotive force vector of the linear induction motor under the excitation of the positive sequence current and the negative sequence current is obtained, and the positive sequence current and the negative sequence current are calculated according to the given phase voltage of the linear induction motor and the electromotive force vector, and the value constraints of the positive sequence current and the negative sequence current are adopted, and the sum of the positive sequence current and the negative sequence current that meet the constraints is used as the asymmetric current of the linear induction motor; wherein the value constraints of the positive sequence current and the negative sequence current are: in, is the given phase voltage, M is the number of any phase of A, B, C, R s is the primary phase resistance, X s is the primary leakage reactance, is the positive sequence current, is the negative sequence current, is the positive-sequence electromotive force vector under the positive-sequence current excitation, is the negative sequence electromotive force vector under the positive sequence current excitation, is the positive sequence electromotive force vector under the excitation of negative sequence current, is the negative-sequence electromotive force vector under negative-sequence current excitation.

2. The method for determining the asymmetric current of a linear induction motor according to claim 1, characterized in that: The positive-sequence and negative-sequence electromotive force vectors of phase A are decomposed from the electromotive force vectors of each phase winding, and the positive-sequence and negative-sequence electromotive force vectors of phases B and C are obtained based on the relationship between the electromotive force vectors of each phase; The positive and negative sequence electromotive force vectors of phase A are: The relationship between the electromotive force vectors of each phase is: In the formula, the subscripts (m,1) and (m,2) represent the positive-sequence and negative-sequence electromotive force vectors generated by the m-sequence current, and m=1 or 2 represents the positive-sequence and negative-sequence, respectively.

3. The method for determining the asymmetric current of a linear induction motor according to claim 2, characterized in that: The electromotive force vector of each phase winding under the excitation of positive sequence current and negative sequence current is obtained by adding the single-turn coil electromotive force vectors of all coils in each phase winding, and the expression is: In the formula, N = w1 / (2pq), w1 is the number of series turns per phase, p is the number of pole pairs, q is the number of slots per pole per phase, A, B, C represent phase A, phase B, and phase C respectively. is the single-turn coil electromotive force vector of the i-th coil under the excitation of the m-sequence current.

4. The method for determining the asymmetric current of a linear induction motor according to claim 3, characterized in that: Will and The electromotive force vector of the single-turn coil under the positive sequence current excitation is obtained by making a difference. and The electromotive force vector of a single-turn coil under negative sequence current excitation is obtained by making a difference, which is expressed as: Where y1 is the winding pitch, is the slot electromotive force vector under the excitation of m-sequence current.

5. The method for determining the asymmetric current of a linear induction motor according to claim 4, characterized in that: The expression of the slot electromotive force vector under the excitation of positive sequence current and negative sequence current is: In the formula, 2a is the motor width, ω is the current angular frequency, B s(1) , B s(2) are the amplitudes of the air gap magnetic field density under the excitation of positive sequence current and negative sequence current, τ is the pole distance, x is the position, i is the slot number where the upper side of the coil is located, L is the length of the primary core, S is the number of slots, C=(σ s V) 2 , V is the running speed of the linear induction motor, σ s is the conductivity of the secondary conductive plate, δ e is the equivalent electromagnetic air gap length, μ0 is the air magnetic permeability.

6. The method for determining the asymmetric current of a linear induction motor according to claim 5, characterized in that: The air gap magnetic field density distribution under the positive sequence current and negative sequence current excitation is expressed as: Where, the subscripts (1) and (2) represent the quantities generated by the positive sequence current and negative sequence current excitation, s (1) =1-V / V s(1) , V s(1) =2τf, V s(2) =-2τf,s (2) =1-V / V s(2) , δ s(2) =tan -1 [1 / (s (2) G)]; In the formula, I m(1) and I m(2) are the amplitudes of positive and negative sequence currents, and are the initial angles of positive sequence current and negative sequence current respectively, m1 is the phase number, k p and k y are the winding distribution coefficient and short-distance coefficient, V is the operating speed of the linear induction motor, and f is the current frequency.

7. A linear induction motor asymmetric current determination system, characterized in that: include: A computer readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the method for determining the asymmetric current of the linear induction motor according to any one of claims 1 to 6.

Images