Reduced-order model and electromagnetic parameter design method of brushless doubly-fed induction machine with concentric cages

Abstract

The application discloses a kind of concentric cage brushless doubly-fed induction motor reduced-order model and electromagnetic parameter design method, belong to motor design field, method includes: using primary and secondary inductance variation coefficient and primary-secondary mutual inductance variation coefficient respectively simplifies primary winding inductance matrix, secondary concentric cage inductance matrix, primary-secondary mutual inductance matrix;First equation represented by voltage vector, current vector, resistance matrix and simplified inductance matrix is constructed;Using voltage variable ratio matrix and current variable ratio matrix, secondary resistance matrix and secondary concentric cage inductance matrix in first equation are transformed;Primary-secondary mutual inductance matrix in first equation is replaced by newly set primary-secondary mutual inductance matrix, and reduced-order model is obtained, to be used for motor electromagnetic parameter design or optimization.The reduced-order model and electromagnetic parameter design method proposed in the application are more accurate, and the transformation method is simple and practical.

Description

Technical Field

[0001] This invention belongs to the field of motor design, and more specifically, relates to a reduced-order model and electromagnetic parameter design method for a concentric cage brushless doubly fed induction motor. Background Technology

[0002] Concentric cage brushless doubly-fed induction motors have attracted widespread attention due to their simple structure, easy manufacturing process, and good starting and asynchronous operation capabilities. However, because each cage loop in a concentric cage has an independent induced electromotive force and induced current, the winding calculation cannot be performed using the methods for induction motors. If each cage loop is considered as a separate winding, it will be coupled not only to the primary power winding and control winding but also to other cage loops, resulting in an excessively high order of the impedance matrix and making calculation difficult. To address this issue, it is necessary to study the calculation of the equivalent parameters of the concentric cage.

[0003] In existing technologies, the following four methods are commonly used to calculate the equivalent parameters of concentric cages. The first method treats M cage loops within the same cell as a single equivalent loop, then uses winding functions to obtain the inductance matrix. This method neglects secondary resistance. The second method considers N cage loops with the same span in different cells as a subsystem, using winding functions to obtain the inductance matrix between each subsystem. The third method uses mathematical transformation matrices to establish a first-order equivalent model of the cage secondary. The fourth method uses transformer modeling methods, defining the secondary turns ratio based on the principle of secondary magnetomotive force balance, and converting the cage secondary impedance to a single equivalent circuit.

[0004] The first type of method assumes that the secondary resistance is negligible compared to the inductance. However, when the secondary resistance is not negligible, the equivalent result obtained by this method is not accurate enough. The second and fourth types of methods only require considering M cage loops to determine the state of all cage loops; however, when the number of cage loops is large, it still leads to an excessively high matrix order, making calculation difficult. The third type of method lacks a corresponding physical interpretation in the resulting model, making it difficult to guide motor design. Therefore, a new reduced-order model and electromagnetic parameter design method are needed to solve the problems of low accuracy, complex transformations, and ambiguous physical meaning of the above methods. Summary of the Invention

[0005] To address the shortcomings and improvement needs of existing technologies, this invention provides a reduced-order model and electromagnetic parameter design method for a concentric cage brushless doubly fed induction motor. The purpose is to solve the problems of low accuracy, complex transformation, and ambiguous physical meaning in existing concentric cage brushless doubly fed induction motor design methods.

[0006] To achieve the above objectives, according to one aspect of the present invention, a reduced-order model and electromagnetic parameter design method for a concentric cage brushless doubly-fed induction motor are provided, comprising: S1, establishing the inductance matrix of the concentric cage brushless doubly-fed induction motor, and simplifying the primary winding inductance matrix, secondary concentric cage inductance matrix, and primary-secondary mutual inductance matrix in the inductance matrix using the primary inductance variation coefficient, secondary inductance variation coefficient, and primary-secondary mutual inductance variation coefficient, respectively; S2, constructing a first equation characterized by the current vector, resistance matrix, simplified inductance matrix, and voltage equation of any phase primary winding of the concentric cage brushless doubly-fed induction motor; S3, transforming the secondary resistance matrix and secondary concentric cage inductance matrix in the first equation using the voltage ratio matrix and current ratio matrix; S4, replacing the primary-secondary mutual inductance matrix in the first equation with a newly set primary-secondary mutual inductance matrix to perform a reduced-order transformation on the first equation, obtaining a reduced-order model; S5, designing or optimizing the electromagnetic parameters of the concentric cage brushless doubly-fed induction motor using the reduced-order model.

[0007] Furthermore, the primary inductance variation coefficient includes m pw / 2 and m cw / 2, where m pw m is the number of phases of the power winding. cw To control the number of winding phases, step S1 simplifies the primary winding inductance matrix using the primary inductance variation coefficient, including: using the constraint that the sum of the currents in each phase of the primary winding equals 0, and simplifies the primary winding inductance matrix using the primary inductance variation coefficient.

[0008] Furthermore, in S1, the secondary winding inductance matrix is ​​simplified using the secondary inductance variation coefficient, including: using the current pair constraint condition of the i-th cage loop of all nests in the secondary concentric cage during steady-state operation, the secondary winding inductance matrix is ​​simplified using the secondary inductance variation coefficient, i∈(1,M), where M is the number of cage loops in a nest.

[0009] Furthermore, the primary and secondary mutual inductance variation coefficients are (p pw +p cw ) / 2, where p pw p is the number of pole pairs of the power winding. cw To control the number of pole pairs of the winding; in S1, the primary and secondary mutual inductance matrix is ​​simplified using the primary and secondary mutual inductance variation coefficients, including: using the current pair symmetry of the i-th cage ring of all nests in the secondary concentric cage during steady-state operation as a constraint condition, the primary and secondary mutual inductance matrix is ​​simplified using the primary and secondary mutual inductance variation coefficients, i∈(1,M), where M is the number of cage rings in a nest.

[0010] Furthermore, the reset primary and secondary mutual inductance matrices are as follows:

[0011]

[0012] in, The mutual inductance matrix is ​​the result of resetting the effect of the primary current on the secondary flux linkage. The mutual inductance matrix is ​​the result of resetting the effect of the secondary current on the primary flux linkage. and Together they form the reset primary and secondary mutual inductance matrix, m pw m is the number of phases of the power winding. cw To control the number of winding phases, For the conjugate phasor of the power winding and the secondary winding's reduced mutual inductance, To control the reduced mutual inductance between the winding and the secondary winding, The phase is the same as the phase of the first cage ring and the first mutual inductance of the power winding, and the amplitude is the same as the self-inductance of the power winding. The phase of the first ring of the first nest and the first mutual inductance of the control winding are the same, and the amplitude is the same as the self-inductance of the control winding.

[0013] Furthermore, the voltage transformation matrix is:

[0014]

[0015] K E_pw_sec_i =k pw1 N pw T sec_pw_i

[0016] K E_cw_sec_i =k cw1 N cw T sec_cw_i

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] Among them, K E Let K be the voltage transformation matrix. E_pw_sec_i K represents the voltage transformation ratio of the power winding to the i-th ring of each cage in the concentric cage. E_cw_sec_i To control the voltage transformation ratio of the winding to the i-th cage loop in each cell of the concentric cage, i∈(1,M), k pw1 k is the fundamental winding coefficient of the power winding. cw1 To control the fundamental winding factor of the winding, Npw N represents the number of series turns per phase of the power winding. cw To control the number of turns in series per phase of the winding, T sec_pw_i For the i-th cage ring p pw The reciprocal of the equivalent series number of turns, T sec_cw_i For the i-th cage ring p cw The reciprocal of the equivalent series number of turns, C sec_cw For each nest, all cage rings p cw Sum of squares of pole winding coefficients, C sec_pw For each nest, all cage rings p pw Sum of squares of pole winding coefficients, C sec_pw_cw For each nest, all cage rings p pw The pole and p cw The sum of the products of the pole winding coefficients, k sec_pw_i Let k be the fundamental winding coefficient of the power winding of the i-th ring from the outside to the inside of each cage. sec_cw_i Let M be the fundamental winding coefficient of the control winding of the i-th cage loop from the outside to the inside of each nest, and M be the number of cage loops in a nest.

[0023] Furthermore, the current transformation ratio matrix is:

[0024]

[0025]

[0026]

[0027] Among them, K I Let K be the current transformation ratio matrix. I_pw_sec_i K represents the current transformation ratio of the power winding to the i-th ring of each cage in the concentric cage. I_cw_sec_i To control the current ratio of the winding to the i-th cage loop in each cell of the concentric cage, i∈(1,M), m pw m is the number of phases of the power winding. cw To control the number of winding phases, N is the number of concentric cages, and k pw1 k is the fundamental winding coefficient of the power winding. cw1 To control the fundamental winding factor of the winding, N pw N represents the number of series turns per phase of the power winding. cw To control the number of turns in series per phase of the winding, T sec_pw_i For the i-th cage ring p pw The reciprocal of the equivalent series number of turns, T sec_cw_i For the i-th cage ring p cw The reciprocal of the equivalent series number of turns, M is the number of cage loops in a nest.

[0028] Furthermore, the reduced-order model is as follows:

[0029]

[0030] in, Let x be the phase voltage of the x-th phase of the power winding. To control the conjugate of the phase voltage of phase x of the winding, R pwx R is the phase resistance of the x-th phase of the power winding. cwx To control the phase resistance of the x-th phase of the winding, R s ′ ec1 R s ′ ec2 R s ′ ec1,2 and R s ′ ec2，1 For different secondary cage-like resistors, Let x be the phase current of the x-th phase of the power winding. To control the conjugate of the phase current of the x-th phase of the winding, and For different secondary cage-like currents, ω pw ω is the angular frequency of the power winding current. cw To control the angular frequency of the winding current, ω sec The angular frequency of the secondary current, m pw m is the number of phases of the power winding. cw To control the number of winding phases, L p For the fundamental self-inductance of each phase winding of the power winding, L c To control the fundamental self-inductance of each phase winding of the winding, L pσ For the leakage inductance of the power winding, L cσ To control the leakage inductance of the winding, The mutual inductance is calculated for the power winding and the secondary winding. The phase is the same as the phase of the first cage ring and the first mutual inductance of the power winding, and the amplitude is the same as the self-inductance of the power winding. To control the reduced mutual inductance between the winding and the secondary winding; The phase of the first ring of the first cage and the first mutual inductance of the control winding are the same, and the amplitude is the same as the self-inductance of the power winding; L s " ec1 L s " ec2 L s " ec1,2 L s " ec2,1 These are different secondary cage-to-ring inductances.

[0031] Furthermore, S5 specifically includes: designing the electromagnetic parameters using the reduced-order model based on the electromagnetic thrust, efficiency, and power factor performance indicators of the concentric cage brushless doubly fed induction motor; or, optimizing the existing electromagnetic parameters using the reduced-order model with the goal of outputting maximum electromagnetic thrust, efficiency, and power factor performance.

[0032] According to another aspect of the present invention, a concentric cage brushless doubly fed induction motor is provided, which is obtained by using the reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly fed induction motor as described above.

[0033] In summary, the above-described technical solutions of this invention achieve the following beneficial effects: A design method for a concentric cage brushless doubly-fed induction motor is provided. This method simplifies the primary and secondary inductance matrices using primary and secondary inductance variation coefficients, respectively; it also simplifies the primary and secondary mutual inductance matrices using primary and secondary mutual inductance variation coefficients; finally, based on the transformation results, the primary and secondary mutual inductance matrices are reset, and the secondary resistance and inductance matrices are transformed using voltage and current ratio matrices. This ensures that the magnetic flux linkage between the magnetic field established by the primary current and itself remains unchanged after being acted upon by the secondary induced magnetic field, thus achieving order reduction of the secondary inductance matrix. Compared with traditional order reduction models and parameter calculation methods, the order reduction model and parameters in this embodiment are more accurate, and the transformation method is simple and practical. Attached Figure Description

[0034] Figure 1 A flowchart of the reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly fed induction motor provided in an embodiment of the present invention;

[0035] Figure 2 This is a schematic diagram of the structure of the concentric cage secondary in a concentric cage brushless doubly fed induction motor provided in an embodiment of the present invention;

[0036] Figure 3 A comparison chart is provided to illustrate the electromagnetic thrust simulation results of the reduced-order model, the electromagnetic thrust simulation results of the existing original-order model, and the finite element analysis (FEA) simulation results for implementation examples of the present invention. Detailed Implementation

[0037] 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. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0038] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0039] Figure 1 This is a flowchart illustrating the design method of a concentric cage brushless doubly-fed induction motor provided in an embodiment of the present invention. (See also...) Figure 1 , combined Figures 2-3 The design method of the concentric cage brushless doubly fed induction motor in this embodiment is described in detail. The method includes operations S1-S5.

[0040] Operation S1 establishes the inductance matrix of the concentric cage brushless doubly fed induction motor. The primary winding inductance matrix, the secondary concentric cage inductance matrix, and the primary-secondary mutual inductance matrix are simplified using the primary inductance variation coefficient, the secondary inductance variation coefficient, and the primary-secondary mutual inductance variation coefficient.

[0041] 1) The voltage vector U of the concentric cage brushless doubly-fed induction motor is:

[0042]

[0043] Where, m pw m is the number of phases of the power winding. cw To control the number of winding phases; u pw1 u pw2 ... These are the 1st, 2nd, ..., mth windings in the power winding. pw Voltage of phase winding; u cw1 u cw2 ... These are the 1st, 2nd, ..., mth windings in the control winding. cw Voltage of the phase winding.

[0044] 2) The current vector I of the concentric cage brushless doubly fed induction motor is:

[0045]

[0046] in, These are the 1st, 2nd, ..., mth windings in the power winding. pw Current in the phase winding; These are the 1st, 2nd, ..., mth windings in the control winding. cw Phase winding current; i sec_j,i Let be the current in the i-th cage ring within the j-th concentric cage, where j∈(1,N) and i∈(1,M). A concentric cage brushless doubly-fed induction motor has N concentric cages, each containing M cage rings, ordered from the outside in as 1, 2, ..., M, as shown below. Figure 2 As shown, the concentric cage brushless doubly fed induction motor has a total of N×M cage rings.

[0047] 3) The resistance matrix R of the concentric cage brushless doubly fed induction motor is:

[0048]

[0049] Among them, R pri For the primary resistor matrix of a concentric cage brushless doubly fed induction motor, R sec This is the secondary N-cell ring resistor matrix for a concentric cage brushless doubly fed induction motor.

[0050] R pri It can be represented as:

[0051]

[0052] in, These are the 1st, 2nd, ..., mth windings in the power winding. pw Resistance of the phase winding; These are the 1st, 2nd, ..., mth windings in the control winding. cw Resistance of the phase winding.

[0053] R sec It can be represented as:

[0054]

[0055]

[0056] Among them, R sec_i Let R be the resistance matrix of the i-th cage ring of different secondary nests. 1i R 2i ... R Ni These are the resistances of the i-th cage loop from the outside to the inside of the 1st, 2nd, ..., Nth nests, respectively.

[0057] 4) The inductance matrix L of the concentric cage brushless doubly fed induction motor is:

[0058]

[0059] Among them, L pri M is the primary winding inductance matrix. pri_sec M is the mutual inductance matrix representing the effect of the secondary current on the primary flux linkage. sec_pri M is the mutual inductance matrix representing the effect of the primary current on the secondary flux linkage. pri_sec and M sec_pri Together they form the primary and secondary mutual inductance matrices, L sec This is the secondary concentric cage inductor matrix.

[0060] L pri It can be represented as:

[0061]

[0062]

[0063] Among them, L p For the fundamental self-inductance of each phase winding of the power winding, L c To control the fundamental self-inductance of each phase winding of the winding, L pσ For the leakage inductance of the power winding, L cσ To control the leakage inductance of the winding, α p α is the electrical difference angle between the phases of the power winding. c To control the phase-to-phase electrical differential angle of the windings, μ0 is the free permeability, δ ef D is the equivalent air gap length of the motor. ef τ is the equivalent lateral length of the motor. pw1 τ is the fundamental pole pitch of the power winding. cw1 To control the fundamental pole pitch of the winding, k pw1 k is the fundamental winding coefficient of the power winding. cw1 To control the fundamental winding factor of the winding, N pw N represents the number of series turns per phase of the power winding. cw To control the number of turns in series per phase of the winding.

[0064] L sec It can be represented as:

[0065]

[0066]

[0067]

[0068]

[0069] Among them, L sec_i For a concentric cage brushless doubly fed induction motor, the secondary winding consists of an inductance matrix of N different cage rings, arranged from the outermost to the innermost i-th cage ring. M sec_i,j For the i-th and j-th cage rings of a concentric cage brushless doubly fed induction motor ( i The mutual inductance matrix composed of ≠j) For the mutual inductance of the i-th and j-th cage rings of the same nest, For the mutual inductance of the i-th and j-th cage rings in different nests, L i For the self-induction of the i-th cage ring in each nest, L σi Let i be the leakage inductance of the i-th cage ring in each nest. Let L be the mutual inductance between the i-th cage links of different nests, and L be the length of the secondary link, τ be the mutual inductance between the i-th cage links of different nests. i Let be the span of the i-th cage ring in each nest.

[0070] M pri_sec It can be represented as:

[0071] M pri_sec =[M pri_sec_1 M pri_sec_2… M pri_sec_M (14)

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] Among them, M pri_sec_i Let M be the mutual inductance matrix between the i-th cage ring (outermost from the innermost) and the primary winding of N different secondary nests. pwx_n,i M is the mutual inductance between the i-th cage ring of the n-th nest and the x-th phase of the power winding. cwx_n,i Let v be the mutual inductance between the i-th cage ring of the n-th nest and the x-th phase of the control winding, and v be the secondary running speed. Let the initial phase difference between the fundamental electromagnetic phase of the first cage ring (from left to right, along the direction of motion) and the fundamental electromagnetic phase of the first phase winding of both the power winding and the control winding be respectively... Let the position of the spatial mechanical axis of the first cage ring be x. nl0 The spatial mechanical axis positions of the first phase windings of the power winding and the control winding are x and x, respectively. pm and x cm .

[0078] M sec_pri It can be represented as:

[0079]

[0080]

[0081] Among them, M sec_pri_i Let N be the mutual inductance matrices between the i-th cage ring (outermost from the innermost) and the primary winding, representing different secondary nests. M is the mutual inductance between the i-th cage ring of the n-th nest and the x-th phase of the power winding. cwx_n,i Let i be the mutual inductance between the i-th cage ring of the n-th nest and the x-th phase of the control winding.

[0082] The original-order mathematical equations constructed based on the voltage vector U, current vector I, resistance matrix R, and inductance matrix L are as follows:

[0083]

[0084] According to an embodiment of the present invention, the primary inductance variation coefficient includes m pw / 2 and m cw / 2. In operation S1, the sum of the currents in each phase of the primary winding is equal to 0 as a constraint. The primary winding inductance matrix is ​​simplified using the primary inductance variation coefficient. Formula (8) can be simplified as follows:

[0085]

[0086] According to an embodiment of the present invention, the current pair of the i-th cage loop in all nests of the secondary concentric cage during steady-state operation in operation S1 is called the constraint condition. The secondary winding inductance matrix is ​​simplified using the secondary inductance variation coefficient, i∈(1,M), where M is the number of cage loops in a nest.

[0087] Formula (11) can be simplified to:

[0088]

[0089] Formula (12) can be simplified to:

[0090]

[0091] Finally, formula (10) is simplified to:

[0092]

[0093] Where, ε i,j ε is the single-phase reduction factor for the mutual inductance between the i-th cage ring and the j-th cage ring. i is the single-phase conversion factor for the i-th cage ring.

[0094] According to an embodiment of the present invention, the mutual inductance variation coefficient of the primary and secondary windings is (p pw +p cw ) / 2. In operation S1, the current pair of the i-th cage loop in all nests of the secondary concentric cages during steady-state operation is called the constraint condition. The primary and secondary mutual inductance matrices are simplified using the primary and secondary mutual inductance variation coefficients, i∈(1,M), where M is the number of cage loops in a nest.

[0095] Formula (15) can be simplified to:

[0096]

[0097] Finally, formula (14) is simplified to:

[0098] M p ′ ri_sec =[M p ′ ri_sec_1 M p ′ ri_sec_2 M p ′ ri_sec_M (28)

[0099] Formula (21) can be simplified to:

[0100]

[0101] Finally, formula (20) is simplified to:

[0102]

[0103] in, Let i be the mutual inductance between the i-th cage ring of the n-th nest and the x-th phase of the power winding. Let i be the mutual inductance between the i-th cage ring of the n-th nest and the x-th phase of the control winding.

[0104] In this embodiment, the number of power / control winding phases in the primary inductance variation coefficient is a positive integer, and the secondary length and span in the secondary inductance variation coefficient can be represented by angle or length, and the secondary length is an integer multiple of the pole pitch of the power winding and the control winding.

[0105] The primary and secondary mutual inductance coefficients can be converted to any row or column of mutual inductance parameters without affecting the final simplification result.

[0106] Operation S2 constructs the first equation, characterized by the current vector, resistance matrix, simplified inductance matrix, and voltage equation of any phase primary winding of the concentric cage brushless doubly fed induction motor.

[0107] Specifically, the inductance matrix L in the original mathematical equation of formula (22) is replaced with the simplified inductance matrix, that is, replaced with the matrix composed of formulas (23), (26), (28) and (30). Then, the voltage equation of the primary winding of the x-th phase is retained, and the first equation can be obtained.

[0108]

[0109] Operation S3 transforms the secondary resistance matrix and secondary concentric cage inductor matrix in the first equation using the voltage ratio matrix and current ratio matrix.

[0110] According to an embodiment of the present invention, the voltage transformation matrix is:

[0111]

[0112] K E_pw_sec_i =k pw1 N pw T sec_pw_i (33)

[0113] K E_cw_sec_i =k cw1 N cw T sec_cw_i (34)

[0114]

[0115]

[0116]

[0117]

[0118]

[0119] Among them, K E Let K be the voltage transformation matrix. E_pw_sec_i K represents the voltage transformation ratio of the power winding to the i-th ring of each cage in the concentric cage. E_cw_sec_i To control the voltage transformation ratio of the winding to the i-th cage loop in each cell of the concentric cage, i∈(1,M), k pw1 k is the fundamental winding coefficient of the power winding. cw1 To control the fundamental winding factor of the winding, N pw N represents the number of series turns per phase of the power winding. cw To control the number of turns in series per phase of the winding, T sec_pw_i For the i-th cage ring p pw The reciprocal of the equivalent series number of turns, T sec_cw_i For the i-th cage ring p cw The reciprocal of the equivalent series number of turns, C sec_cw For each nest, all cage rings p cw Sum of squares of pole winding coefficients, C sec_pw For each nest, all cage rings p pw Sum of squares of pole winding coefficients, C sec_pw_cw For each nest, all cage rings p pw The pole and p cw The sum of the products of the pole winding coefficients, k sec_pw_i Let k be the fundamental winding coefficient of the power winding of the i-th ring from the outside to the inside of each cage. sec_cw_i Let M be the fundamental winding coefficient of the control winding of the i-th cage loop from the outside to the inside of each nest, and M be the number of cage loops in a nest.

[0120] According to an embodiment of the present invention, the current transformation ratio matrix is:

[0121]

[0122]

[0123]

[0124] Among them, K I Let K be the current transformation matrix. I_pw_sec_i K represents the current transformation ratio of the power winding to the i-th ring of each cage in the concentric cage. I_cw_sec_iTo control the current ratio of the winding to the i-th cage loop in each cell of the concentric cage, i∈(1,M), m pw m is the number of winding phases of the power winding in the primary winding. cw N is the number of winding phases of the control winding in the primary winding, N is the number of nests in the concentric cage, and k is the number of phases of the control winding in the primary winding. pw1 k is the fundamental winding coefficient of the power winding. cw1 To control the fundamental winding factor of the winding, N pw N represents the number of series turns per phase of the power winding. cw To control the number of turns in series per phase of the winding, T sec_pw_i For the i-th cage ring p pw The reciprocal of the equivalent series number of turns, T sec_cw_i For the i-th cage ring p cw The reciprocal of the equivalent series number of turns, M is the number of cage loops in a nest.

[0125] The transformed matrix is:

[0126]

[0127]

[0128]

[0129] Operation S4 replaces the primary and secondary mutual inductance matrices in the first equation with newly set primary and secondary mutual inductance matrices to perform a reduction transformation on the first equation, resulting in a reduced-order model.

[0130] According to an embodiment of the present invention, the reset primary and secondary mutual inductance matrices are as follows:

[0131]

[0132] in, The mutual inductance matrix is ​​the result of resetting the effect of the primary current on the secondary flux linkage. The mutual inductance matrix is ​​the result of resetting the effect of the secondary current on the primary flux linkage. and Together they form the reset primary and secondary mutual inductance matrix, m pw m is the number of phases of the power winding. cw To control the number of winding phases, For the mutual inductance of the power winding and the secondary winding, To control the mutual inductance of the winding and secondary winding; The phase is the same as the phase of the first cage ring and the first mutual inductance of the power winding, and the amplitude is the same as the self-inductance of the power winding. The phase of the first ring of the first nest and the first mutual inductance of the control winding are the same, and the amplitude is the same as the self-inductance of the control winding.

[0133] The reduced-order model of the fourth-order concentric cage brushless doubly-fed induction motor obtained after the transformation is as follows:

[0134]

[0135] in, Let x be the phase voltage of the x-th phase of the power winding. To control the conjugate of the phase voltage of phase x of the winding, R pwx R is the phase resistance of the x-th phase of the power winding. cwx To control the phase resistance of the x-th phase of the winding, R s ′ ec1 R s ′ ec2 R s ′ ec1,2 and R s ′ ec2，1 For different secondary cage-like resistors, Let x be the phase current of the x-th phase of the power winding. To control the conjugate of the phase current of the x-th phase of the winding, and For different secondary cage-like currents, ω pw ω is the angular frequency of the power winding current. cw To control the angular frequency of the winding current, ω sec L is the angular frequency of the secondary current. s " ec1 L s " ec2 L s " ec1,2 L s " ec2,1 These are different secondary cage-to-ring inductances.

[0136] Operate S5 to design or optimize the electromagnetic parameters of a concentric cage brushless doubly fed induction motor using a reduced-order model.

[0137] According to an embodiment of the present invention, operation S5 specifically includes: designing electromagnetic parameters using a reduced-order model based on the electromagnetic thrust, efficiency, and power factor performance indicators of the concentric cage brushless doubly fed induction motor; or, optimizing existing electromagnetic parameters using a reduced-order model with the goal of outputting maximum electromagnetic thrust, efficiency, and power factor performance.

[0138] In this embodiment, the parameters shown in Table 1 are used as an example to illustrate the effect of optimizing existing electromagnetic parameters using a reduced-order model.

[0139] Table 1

[0140]

[0141] First, the primary order mathematical equations of the concentric cage brushless doubly-fed induction motor are written based on the motor's electromagnetic parameters. Then, the motor's electromagnetic parameters are substituted into the above steps to obtain the primary and secondary inductance transformation coefficients, the primary and secondary mutual inductance transformation coefficients, the voltage transformation matrix, and the current transformation matrix, as follows.

[0142] Primary inductance transformation coefficient: m pw / 2 = 1.5, m cw / 2=1.5. Inductance transformation coefficient: ε1=ε 1,2 =ε 1,3 =1.171, ε2=ε 2，3 =1.1292, ε3=1.0896. Primary and secondary mutual inductance transformation coefficients: (p pw +p cw ) / 2 = 3. Voltage transformation matrix: Current transformation matrix:

[0143] Finally, the inductance matrix is ​​simplified based on the obtained transformation coefficients and matrix. The electromagnetic thrust of the motor is calculated and analyzed under cascade asynchronous operation (control winding short-circuited, power winding connected to 180V AC power). Figure 3 The simulation results of the original order model, the reduced order model, and the FEA model shown are basically consistent.

[0144] This invention also provides a concentric cage brushless doubly fed induction motor, which is obtained by using the reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly fed induction motor described above.

[0145] 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 reduced-order model and electromagnetic parameter design method for a concentric cage brushless doubly-fed induction motor, characterized in that, include: S1. Establish the inductance matrix of the concentric cage brushless doubly fed induction motor. Use the primary inductance variation coefficient, secondary inductance variation coefficient, and primary-secondary mutual inductance variation coefficient to simplify the primary winding inductance matrix, secondary concentric cage inductance matrix, and primary-secondary mutual inductance matrix in the inductance matrix, respectively. S2, construct the first equation characterized by the current vector, resistance matrix, simplified inductance matrix, and voltage equation of any phase primary winding of the concentric cage brushless doubly fed induction motor. S3, use the voltage ratio matrix and current ratio matrix to transform the secondary resistance matrix and secondary concentric cage inductor matrix in the first equation; S4, replace the primary and secondary mutual inductance matrices in the first equation with newly set primary and secondary mutual inductance matrices to perform a reduction transformation on the first equation, and obtain a reduced-order model; S5. The electromagnetic parameters of the concentric cage brushless doubly fed induction motor are designed or optimized using the reduced-order model.

2. The reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly-fed induction motor as described in claim 1, characterized in that, The primary inductance variation coefficient includes m pw / 2 and m cw / 2, where m pw m is the number of phases of the power winding. cw To control the number of winding phases; The simplification of the primary winding inductance matrix using the primary inductance variation coefficient in step S1 includes: using the constraint that the sum of the phase currents in the primary winding is equal to 0, and simplifying the primary winding inductance matrix using the primary inductance variation coefficient.

3. The reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly-fed induction motor as described in claim 1, characterized in that, The simplification of the secondary winding inductance matrix in S1 using the secondary inductance variation coefficient includes: using the current pair constraint of the i-th cage loop of all nests in the secondary concentric cage during steady-state operation, the secondary winding inductance matrix is ​​simplified using the secondary inductance variation coefficient, i∈(1,M), where M is the number of cage loops in a nest.

4. The reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly-fed induction motor as described in claim 1, characterized in that, The primary and secondary mutual inductance variation coefficients are (p) pw +p cw ) / 2, where p pw p is the number of pole pairs of the power winding. cw To control the number of pole pairs in the winding; The simplification of the primary and secondary mutual inductance matrix in S1 using the primary and secondary mutual inductance variation coefficients includes: using the current pair of the i-th cage ring in all nests in the secondary concentric cage during steady-state operation as a constraint condition, and simplifying the primary and secondary mutual inductance matrix using the primary and secondary mutual inductance variation coefficients, i∈(1,M), where M is the number of cage rings in a nest.

5. The reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly-fed induction motor as described in claim 1, characterized in that, The reset primary and secondary mutual inductance matrices are as follows: in, The mutual inductance matrix is ​​the result of resetting the effect of the primary current on the secondary flux linkage. The mutual inductance matrix is ​​the result of resetting the effect of the secondary current on the primary flux linkage. and Together they form the reset primary and secondary mutual inductance matrix, m pw m is the number of phases of the power winding. cw To control the number of winding phases, For the conjugate phasor of the power winding and the secondary winding's reduced mutual inductance, To control the reduced mutual inductance between the winding and the secondary winding, The phase is the same as the phase of the first cage ring and the first mutual inductance of the power winding, and the amplitude is the same as the self-inductance of the power winding. The phase of the first ring of the first nest and the first mutual inductance of the control winding are the same, and the amplitude is the same as the self-inductance of the control winding.

6. The reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly-fed induction motor as described in claim 1, characterized in that, The voltage transformation matrix is ​​as follows: K E_pw_sec_i =k pw1 N pw T sec_pw_i K E_cw_sec_i =k cw1 N cw T sec_cw_i Among them, K E Let K be the voltage transformation matrix. E_pw_sec_i K represents the voltage transformation ratio of the power winding to the i-th ring of each cage in the concentric cage. E_cw_sec_i To control the voltage transformation ratio of the winding to the i-th cage loop in each cell of the concentric cage, i∈(1,M), k pw1 k is the fundamental winding coefficient of the power winding. cw1 To control the fundamental winding factor of the winding, N pw N represents the number of series turns per phase of the power winding. cw To control the number of turns in series per phase of the winding, T sec_pw_i For the i-th cage ring p pw The reciprocal of the equivalent series number of turns, T sec_cw_i For the i-th cage ring p cw The reciprocal of the equivalent series number of turns, C sec_cw For each nest, all cage rings p cw Sum of squares of pole winding coefficients, C sec_pw For each nest, all cage rings p pw Sum of squares of pole winding coefficients, C sec_pw_cw For each nest, all cage rings p pw The pole and p cw The sum of the products of the pole winding coefficients, k sec_pw_i Let k be the fundamental winding coefficient of the power winding of the i-th ring from the outside to the inside of each cage. sec_cw_i Let M be the fundamental winding coefficient of the control winding of the i-th cage loop from the outside to the inside of each nest, and M be the number of cage loops in a nest.

7. The reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly-fed induction motor as described in claim 1, characterized in that, The current ratio matrix is: Among them, K I Let K be the current transformation ratio matrix. I_pw_sec_i K represents the current transformation ratio of the power winding to the i-th ring of each cage in the concentric cage. I_cw_sec_i To control the current ratio of the winding to the i-th ring of each cage in the concentric cage, i∈(1,M), m pw m is the number of phases of the power winding. cw To control the number of winding phases, N is the number of concentric cages, and k pw1 k is the fundamental winding coefficient of the power winding. cw1 To control the fundamental winding factor of the winding, N pw N represents the number of series turns per phase of the power winding. cw To control the number of turns in series per phase of the winding, T sec_pw_i For the i-th cage ring p pw The reciprocal of the equivalent series number of turns, T sec_cw_i For the i-th cage ring p cw The reciprocal of the equivalent series number of turns, M is the number of cage loops in a nest.

8. The reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly-fed induction motor as described in claim 1, characterized in that, The order reduction model is as follows: in, Let x be the phase voltage of the x-th phase of the power winding. To control the conjugate of the phase voltage of phase x of the winding, R pwx R is the phase resistance of the x-th phase of the power winding. cwx To control the phase resistance of the x-th phase of the winding, R′ sec1 、R′ sec2 、R′ sec1,2 and R′ sec2，1 For different secondary cage-like resistors, Let x be the phase current of the x-th phase of the power winding. To control the conjugate of the phase current of the x-th phase of the winding, and For different secondary cage-like currents, ω pw ω is the angular frequency of the power winding current. cw To control the angular frequency of the winding current, ω sec The angular frequency of the secondary current, m pw m is the number of phases of the power winding. cw To control the number of winding phases, L p For the fundamental self-inductance of each phase winding of the power winding, L c To control the fundamental self-inductance of each phase winding of the winding, L pσ For the leakage inductance of the power winding, L cσ To control the leakage inductance of the winding, The mutual inductance is calculated for the power winding and the secondary winding. The phase is the same as the phase of the first cage ring and the first mutual inductance of the power winding, and the amplitude is the same as the self-inductance of the power winding. To control the reduced mutual inductance between the winding and the secondary winding; The phase of the first ring of the first cage and the first mutual inductance of the control winding are the same, and the amplitude is the same as the self-inductance of the power winding; L″ sec1 、L″ sec2 、L″ sec1,2 、L″ sec2,1 These are different secondary cage-to-ring inductances.

9. The reduced-order model and electromagnetic parameter design method of the concentric cage brushless doubly-fed induction motor as described in any one of claims 1-8, characterized in that, S5 specifically includes: Based on the electromagnetic thrust, efficiency, and power factor performance indicators of the concentric cage brushless doubly fed induction motor, the electromagnetic parameters are designed using the reduced-order model; or, with the goal of maximizing output electromagnetic thrust, efficiency, and power factor performance, the existing electromagnetic parameters are optimized using the reduced-order model.

10. A concentric cage brushless doubly-fed induction motor, characterized in that, The model and electromagnetic parameter design method of the concentric cage brushless doubly fed induction motor as described in any one of claims 1-9 are used to obtain the model.

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