Method for calculating instantaneous stator iron loss of doubly salient electro-magnetic motor

Abstract

The invention discloses an electro-magnetic doubly salient motor instantaneous stator iron loss calculation method, which comprises the following steps of: replacing a flux linkage generated by exciting current with a flux linkage generated by each phase current according to an equivalent current principle, obtaining data of a phase equivalent flux linkage, a rotor angle and a phase equivalent current by utilizing finite element simulation, and combining magnetic circuit analysis to calculate the instantaneous stator iron loss of an electro-magnetic doubly salient motor. A flux density solving module of each region of the stator yoke is built by using a phase flux linkage look-up table model, and the data dimension is reduced. The method comprises the following steps: dividing stator pole regions according to the magnitude of the flux density of a stator pole, directly solving the data of the flux density, the rotor angle and the phase current of each region by finite element simulation, and constructing an instantaneous iron loss calculation model of the doubly salient electro-magnetic motor stator in combination with a time domain iron loss calculation formula. According to the modeling method, the used data amount is small, the time consumed in the modeling process is short, model calculation is accurate, the modeling method can operate along with a motor control model, the required operation time is greatly shortened compared with finite element joint simulation, and research on motor stator iron loss and control strategy optimization can be rapidly carried out.

Description

Technical Field

[0001] The present invention relates to the technical field of motor iron loss calculation and modeling, and in particular to a method for calculating the instantaneous stator iron loss of an electrically excited double-salient-pole motor. Background Art

[0002] The modeling method of the present invention is applicable to an electrically excited double-salient-pole motor (DSEM), the rotor of which is made of laminated silicon steel sheets only, and has a solid and reliable structure and can work in harsh environments. The stator has an independent DC excitation winding, and the power generation control is simple. It can be used as an aircraft starter generator, especially in the application of multi-electric engine built-in high-speed starter generator system, which has unique competitive advantages and application prospects.

[0003] Since the stator and rotor of the DSEM present a salient pole structure, there is severe local saturation in the stator magnetic field when the motor is running, and the magnetic flux density at each position of the stator is affected by both the phase current and the excitation current, making it difficult to calculate the instantaneous iron loss under different conditions.

[0004] Chen Hao et al. disclosed a method for quickly calculating the iron loss of a switched reluctance motor (patent publication number CN106339563B), which divides the switched reluctance motor into regions, solves the radial and tangential magnetic flux waveforms of the characteristic points of each region under each phase current through finite element method as a lookup model, obtains the real magnetic flux waveform of each region by superimposing the magnetic flux of each current in each region, and establishes a model for solving the instantaneous iron loss of the motor. This method simulates the magnetic flux waveform of each current acting alone in each region, and is suitable for switched reluctance motors with single-phase or two-phase energized at the same time. For electrically excited double-pole motors, the excitation current and multi-phase current are simultaneously used during operation. Modeling using this method requires a large amount of finite element simulation, which results in a large amount of data and difficult data processing. Summary of the invention

[0005] The technical problem to be solved by the present invention is to address the defects involved in the background technology and provide a method for calculating the instantaneous stator iron loss of an electrically excited double-pole motor. The instantaneous iron loss modeling of an N-phase electrically excited double-pole motor is realized based on the equivalent current and magnetic circuit analysis method. The model can obtain the magnetic density of each region of the stator only through two-dimensional table lookup and calculation, thereby quickly and accurately calculating the instantaneous iron loss of the stator.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] A method for calculating the instantaneous stator iron loss of an electrically excited double-salient-pole motor comprises the following method:

[0008] Step 1), analyzing the stator magnetic field distribution when the phase winding of the electrically excited double-pole motor is subjected to current, dividing the stator pole characteristic area according to the saturation condition, and dividing the stator yoke characteristic area according to the yoke magnetic flux path; for each stator pole characteristic area, selecting its center point as its characteristic point;

[0009] Step 2), using finite element simulation to obtain a data table of flux linkage, mechanical angle, and equivalent phase current of each phase winding of the electrically excited double-pole motor, and establishing a motor equivalent flux linkage lookup model;

[0010] Step 2.1), according to the minimum current i allowed to pass through the armature winding and the excitation winding kmin 、i fmin and the maximum current i kmax 、i fmax , calculate the minimum equivalent current required by the motor equivalent flux lookup model using the following formula: and the maximum equivalent current

[0011] Where N is the number of phases of the electrically excited doubly salient-pole motor, N a is the number of turns of the phase winding, N f is the number of turns of the excitation winding, i k is the kth phase current, i f is the excitation current, is the kth phase equivalent current;

[0012] Step 2.2), perform finite element simulation and set the step size of the phase winding current to The rotor mechanical angle range is set to one electrical cycle, n is the preset equal division threshold, and the flux linkage ψ of each phase winding is obtained respectively. k , rotor mechanical angle θ, equivalent phase current i k * Data table;

[0013] Step 2.3), use the model fitting tool to fit the data table obtained in step 2.2) into the table lookup model data, establish the equivalent flux table lookup model of the motor from the first phase to the Nth phase, and the equivalent phase current of each phase The current value is used as the table input, the rotor mechanical angle θ is taken as the table input angle by taking the remainder, and the equivalent flux linkage of each phase is the table output result;

[0014] Step 3), the equivalent flux of each phase output by the equivalent flux table lookup model is calculated by the following formula to obtain the magnetic flux of each stator yoke characteristic area:

[0015] φ sp1 (t) = ψ1(t) / N a

[0016] φsp2 (t) = ψ2(t) / N a ...

[0018] φ spN (t) = ψ N (t) / N a

[0019]

[0020] In the formula, ψ1(t_~ψ N (t) are the equivalent flux linkages from the 1st phase to the Nth phase obtained by looking up the table at time t, φ sp1 (t)~φ spN (t) are the magnetic fluxes of the 1st to Nth stator poles, φ sy1 (t)~φ syN (t) are the magnetic fluxes of the characteristic regions of the stator yoke from the 1st to the Nth, respectively;

[0021] The magnetic flux density of each stator yoke characteristic area is calculated according to the following formula:

[0022] B sy1 =φ sy1 (t) / S sy1

[0023] B sy2 =φ sy2 (t) / S sy2 ...

[0025] B syN =φ syN (t) / S syN

[0026] In the formula, S sy1 ~S syN are the longitudinal cross-sectional areas of the characteristic regions of the stator yoke from the 1st to the Nth, B sy1 ~B syN are the magnetic flux densities of the characteristic regions of the stator yoke from the 1st to the Nth respectively;

[0027] Step 4), through finite element simulation, obtain the data of magnetic flux density, rotor mechanical angle, and equivalent phase current of the characteristic points of each stator pole characteristic area; establish a stator pole two-dimensional magnetic flux lookup table model, and combine the magnetic flux and magnetic flux of each stator yoke characteristic area to form a complete motor stator instantaneous magnetic flux acquisition model for each area;

[0028] Step 5), determine the hysteresis loss coefficient k of the stator core material of the electrically excited double-pole motor h , eddy current loss coefficient k c, estimating the volume of each stator pole characteristic area and each stator yoke characteristic area;

[0029] Step 6), according to the instantaneous magnetic flux density of each region of the motor stator, the instantaneous magnetic flux density output by the model is obtained, and the instantaneous hysteresis loss P of each stator pole characteristic region and each stator yoke characteristic region is calculated respectively. h (t) and instantaneous eddy current loss P c (t):

[0030]

[0031] In the formula, B max , B min are the current maximum and minimum magnetic density values, B s+1 is the current magnetic density value, B s is the magnetic density value of the last calculation, and T is the calculation step length;

[0032] Step 7), for each stator pole characteristic region and each stator yoke characteristic region, calculate its instantaneous hysteresis loss P h (t), instantaneous eddy current loss P c (t) are multiplied by their regional volumes and then added together to obtain their instantaneous iron losses. Then, the instantaneous iron losses of each stator pole characteristic area and each stator yoke characteristic area are added together to obtain the stator instantaneous iron loss.

[0033] After the above steps, the instantaneous iron loss calculation model of the electrically excited double-pole motor is finally completed.

[0034] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0035] 1. Compared with the existing modeling method of instantaneous iron loss of motor, this modeling method reduces the finite element data required to generate the stator yoke flux density. Based on the characteristics of the electrically excited double-pole motor, the phase current is used as the equivalent excitation current, and then by analyzing the magnetic circuit, only the flux data of each phase is obtained to calculate the yoke flux density. Calculation of instantaneous iron loss of the stator of an electrically excited double-pole motor;

[0036] 2. The stator iron loss waveform can be generated at any time during the simulation process, without the need to perform other data operations after running the simulation. The instantaneous iron loss of each divided stator area, as well as the hysteresis loss and eddy current loss components in the instantaneous iron loss can be observed by changing the program output, which is convenient for conducting research on the stator iron loss distribution and the proportion of each loss component. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a cross-sectional view of a four-phase 8 / 6-pole electrically excited doubly salient motor;

[0038] Figure 2This is a schematic diagram of the division of stator iron loss calculation area for a four-phase 8 / 6-pole electrically excited doubly salient motor;

[0039] Figure 3 A flow chart of a modeling method for instantaneous iron loss of a stator of an electrically excited double-salient-pole motor according to the present invention;

[0040] Figure 4 This is a system structure diagram of the stator instantaneous iron loss calculation model and motor simulation model built by the present invention;

[0041] Figure 5 This is a comparison waveform of the stator instantaneous iron loss of the finite element and calculation models. DETAILED DESCRIPTION

[0042] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0043] The present invention can be implemented in many different forms and should not be considered to be limited to the embodiments described herein. On the contrary, these embodiments are provided to make this disclosure thorough and complete, and will fully express the scope of the present invention to those skilled in the art. In the accompanying drawings, components are enlarged for clarity.

[0044] The present invention is directed to an electrically excited double-salient-pole motor. Taking a four-phase 8 / 6-pole electrically excited double-salient-pole motor as an example, its cross section is as follows: Figure 1 As shown, it includes armature winding and excitation winding. The modeling method of the present invention is used to convert the excitation current into each phase current, so that the four-phase winding flux can replace the excitation winding flux, and the finite element simulation is used to obtain the flux-angle-current data of each phase. The phase flux can be used to calculate the stator magnetic circuit to obtain the stator yoke flux density. At the same time, the stator pole flux density is directly affected by the single-phase equivalent current. The flux density-angle-current data is directly simulated by dividing the area. According to the flux waveform of each region of the stator, combined with the time domain iron loss calculation program, the stator instantaneous iron loss model is established.

[0045] like Figure 3 As shown, the specific implementation steps are as follows:

[0046] Step 1) Analyze the stator magnetic field distribution when the phase winding of the electro-magnetic doubly salient motor is energized with current. Since the magnetic field saturation degree of the stator pole tip is high, while the saturation degree of other parts is relatively uniform, each stator pole is radially divided into two regions, and the center point is selected as the regional feature point, such as Figure 2 sp1A, sp2A; according to the closed path of the four-phase winding flux in the stator yoke, the stator yoke area is divided, such as Figure 2 middle sy1~sy4;

[0047] Step 2), using finite element simulation to obtain a data table of flux linkage, mechanical angle, and equivalent phase current of each phase winding of the electrically excited double-pole motor, and establishing a motor equivalent flux linkage lookup model;

[0048] Step 2.1), for a four-phase (N=4) electrically excited doubly salient motor, the maximum current allowed to flow through the armature winding and the field winding is i kmax =20A, i fmax =10A, minimum current i kmin =-20A, i fmin =0A. Armature winding turns N a =180, number of turns of excitation winding N f =220, calculate the minimum equivalent current required by the motor equivalent flux table model using the following formula and the maximum equivalent current

[0049]

[0050] The simulation range of equivalent current is calculated as Pick

[0051] For an N-phase electrically excited double-pole motor, the minimum current i allowed to flow through the armature winding and the excitation winding is kmin 、i fmin and the maximum current i kmax 、i fmax , calculate the minimum equivalent current required by the motor equivalent flux lookup model and the maximum equivalent current

[0052] Step 2.2), perform finite element simulation, set the phase winding current step size to 1A, and obtain the A phase winding flux ψ k , mechanical angle θ, equivalent phase current i k * The data table of phases B, C and D can be obtained by phase shifting the data table of phase A due to good symmetry.

[0053] For an N-phase motor, perform a finite element simulation and set the step size of the phase winding current to n is the preset equal division threshold, and the rotor mechanical angle range is set to one electrical cycle. If the flux symmetry of each phase of the N-phase motor is good, the finite element simulation is used to simulate the flux of the first phase winding ψ k , rotor mechanical angle θ, equivalent phase current i k * The data table of the first phase is obtained by using the phase offset of the first phase data to obtain the data table of the second phase to the Nth phase; if the phases are not symmetrical, the winding flux ψ of the first phase to the Nth phase is obtained respectively k , rotor mechanical angle θ, equivalent phase current i k * Data table;

[0054] Step 2.3), use the model fitting tool to fit the data obtained in step 2.2) into the table lookup model data, establish the equivalent flux linkage table lookup model of the four phases of the motor, and the equivalent phase current of each phase The current value used as the table input, the input angle is the rotor mechanical angle shifted by 0°, 15°, 30°, 45° and the modulo result of 60°, and the equivalent flux linkage of each phase is the table output result;

[0055] For an N-phase motor, the equivalent phase current of each phase The current value is the input value of the table, the mechanical angle of the rotor is shifted and the remainder of the mechanical angle corresponding to one electrical cycle is taken as the input angle of the table, and the N-phase equivalent flux is the output result of the table;

[0056] Step 3), the four-phase equivalent flux linkage output by the four-phase equivalent flux linkage table lookup model is used to calculate the tangential flux of each stator yoke characteristic area using the following formula:

[0057] φ spA (t) = ψ A (t) / N a

[0058] φ spB (t) = ψ B (t) / N a

[0059] φ spC (t) = ψ C (t) / N a

[0060] φ spD (t) = ψ D (t) / N a

[0061]

[0062] In the formula, ψ A (t)~ψ D (t) are the equivalent flux from phase A to phase D obtained by looking up the table at time t, φ spA (t)~φ spD (t) are the magnetic flux of the stator poles corresponding to phase A to phase D, φ sy1 (t)~φ syN (t) are the magnetic flux of the first to fourth stator yoke characteristic regions, respectively;

[0063] For an N-phase motor, the magnetic flux of the N stator yoke characteristic areas is calculated from the N-phase equivalent flux according to the following formula:

[0064] φ sp1 (t) = ψ1(t) / N a

[0065] φ sp2 (t) = ψ2(t) / N a ...

[0067] φ spN (t) = ψ N (t) / N a

[0068]

[0069] In the formula, ψ1(t_~ψ N (t) are the equivalent flux linkages from the 1st phase to the Nth phase obtained by looking up the table at time t, φ sp1 (t)~φ spN (t) are the magnetic fluxes of the 1st to Nth stator poles, φ sy1 (t)~φ syN (t) are the magnetic fluxes of the characteristic regions of the stator yoke from the 1st to the Nth, respectively;

[0070] The magnetic flux density of each stator yoke characteristic area is calculated according to the following formula:

[0071] B sy1 =φ sy1 (t) / S sy1

[0072] B sy2 =φ sy2 (t) / S sy2

[0073] B sy3 =φ sy3 (t) / S sy3

[0074] B sy4 =φ sy4 (t) / S sy4

[0075] In the formula, S sy1 ~S sy4 are the longitudinal cross-sectional areas of the 1st to 4th stator yoke characteristic regions, B sy1 ~B sy4 The magnetic flux density of the characteristic areas of the stator yoke from the 1st to the 4th respectively;

[0076] For an N-phase motor, the magnetic flux density of each stator yoke characteristic area is calculated according to the following formula:

[0077] B sy1 =φ sy1 (t) / S sy1

[0078] B sy2 =φ sy2 (t) / S sy2 ...

[0080] B syN =φ syN (t) / S syN

[0081] In the formula, S sy1 ~S syN are the longitudinal cross-sectional areas of the characteristic regions of the stator yoke from the 1st to the Nth, B sy1 ~B syN are the magnetic flux densities of the characteristic regions of the stator yoke from the 1st to the Nth respectively;

[0082] Step 4), by finite element simulation, when the current of phase A is passed alone, the magnetic flux density of the characteristic points sp1A and sp2A of the characteristic region of the stator pole corresponding to phase A, the rotor mechanical angle θ, and the equivalent phase current i k * Data, due to the good symmetry of the motor, the data of the remaining stator poles are obtained by phase shift of the A-phase data; a two-dimensional magnetic flux lookup table model for the stator pole is established, and a complete instantaneous magnetic flux acquisition model for each region of the motor stator is constructed by combining the magnetic flux and magnetic flux of each characteristic region of the stator yoke;

[0083] For an N-phase motor, if the symmetry of each phase is good, the magnetic flux density, rotor mechanical angle θ, and equivalent phase current i of the characteristic points of the stator pole characteristic area corresponding to the first phase are simulated using finite element method. k * Data, the magnetic flux density data of each characteristic point on the stator pole of the second phase to the Nth phase is obtained by phase shift; if there is no symmetry, the magnetic flux density, rotor mechanical angle θ, and equivalent phase current i of each stator pole characteristic area of ​​the first phase to the Nth phase are obtained respectively k * ; Establish a two-dimensional magnetic flux lookup table model for the stator pole, which together with the module obtained in step 3) constitutes a complete instantaneous magnetic flux acquisition model for each region of the motor stator;

[0084] Step 5), determine the hysteresis loss coefficient k of the stator material of the electrically excited double-pole motor h , eddy current loss coefficient k c , and estimate the volume of each characteristic area of ​​the stator pole and stator yoke;

[0085] Step 6), according to the instantaneous magnetic flux density of each region of the motor stator, the instantaneous magnetic flux density output by the model is obtained, and the instantaneous hysteresis loss P of each stator pole characteristic region and each stator yoke characteristic region is calculated respectively. h (t) and instantaneous eddy current loss P c (t):

[0086]

[0087] In the formula, B max , B min are the current maximum and minimum magnetic density values, B s+1 is the current magnetic density value, B s is the magnetic density value of the last calculation, and T is the calculation step length;

[0088] Step 7), for each stator pole characteristic region and each stator yoke characteristic region, calculate its instantaneous hysteresis loss P h (t), instantaneous eddy current loss P c (t) are multiplied by their regional volumes and then added together to obtain their instantaneous iron losses. Then, the instantaneous iron losses of each stator pole characteristic area and each stator yoke characteristic area are added together to obtain the stator instantaneous iron loss.

[0089] After the above steps, the modeling of the instantaneous iron loss calculation model of the stator of the electrically excited double-pole motor is completed.

[0090] The model is connected to the motor control model and run, such as Figure 4 , set the motor speed to 240rpm, the amplitude of each phase current in the forward conduction interval is 7.70A, the amplitude in the negative conduction interval is -2.42A, the excitation current is constant at 3.28A, and compare the stator instantaneous iron loss results of the finite element simulation and the established model within one electrical cycle. Figure 5 According to the comparison results, the proposed modeling method has a high degree of consistency with the finite element waveform; comparing the average value of iron loss in this electrical cycle, the proposed modeling method is 5.76W, and the finite element simulation result is 5.59W, with an error of about 3%. Through comparison, it is verified that the stator instantaneous iron loss calculation model established based on equivalent current and magnetic circuit analysis can achieve better results, is consistent with finite element simulation, and can be connected to different control model simulations, greatly saving simulation time and improving efficiency.

[0091] Through analysis, the accuracy, rapidity and practicality of the modeling method of the stator instantaneous iron loss of the electrically excited double-pole motor are verified, and it has great application value and prospects in the field of motor iron loss calculation and control modeling. The present invention can also be applied to the modeling of switched reluctance motors with DC bias windings, electrically excited flux switching motors, etc.

[0092] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0093] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the instantaneous stator iron loss of an electrically excited doubly salient pole motor, characterized in that: The following steps are involved: Step 1), analyzing the stator magnetic field distribution when the phase winding of the electrically excited double-pole motor is subjected to current, dividing the stator pole characteristic area according to the saturation condition, and dividing the stator yoke characteristic area according to the yoke magnetic flux path; for each stator pole characteristic area, selecting its center point as its characteristic point; Step 2), using finite element simulation to obtain a data table of flux linkage, mechanical angle, and equivalent phase current of each phase winding of the electrically excited double-pole motor, and establishing a motor equivalent flux linkage lookup model; Step 2.1), according to the minimum current i allowed to pass through the armature winding and the excitation winding kmin 、i fmin and the maximum current i kmax 、i fmax , calculate the minimum equivalent current required by the motor equivalent flux lookup model using the following formula: and the maximum equivalent current Where N is the number of phases of the electrically excited doubly salient-pole motor, N a is the number of turns of the phase winding, N f is the number of turns of the excitation winding, i k is the kth phase current, i f is the excitation current, is the kth phase equivalent current; Step 2.2), perform finite element simulation and set the step size of the phase winding current to The rotor mechanical angle range is set to one electrical cycle, n is the preset equal division threshold, and the flux linkage ψ of each phase winding is obtained respectively. k , rotor mechanical angle θ, equivalent phase current Data table; Step 2.3), use the model fitting tool to fit the data table obtained in step 2.2) into the table lookup model data, establish the equivalent flux table lookup model of the motor from the first phase to the Nth phase, and the equivalent phase current of each phase The current value is used as the table input, the rotor mechanical angle θ is taken as the table input angle by taking the remainder, and the equivalent flux linkage of each phase is the table output result; Step 3), the equivalent flux of each phase output by the equivalent flux table lookup model is calculated by the following formula to obtain the magnetic flux of each stator yoke characteristic area: φ sp1 (t)=ψ1(t) / N a φ sp2 (t)=ψ2(t) / N a ... f spN (t)=ψ N (t) / N a In the formula, ψ1(t)~ψ N (t) are the equivalent flux linkages from the 1st phase to the Nth phase obtained by looking up the table at time t, φ sp1 (t)~φ spN (t) are the magnetic fluxes of the 1st to Nth stator poles, φ sy1 (t)~φ syN (t) are the magnetic fluxes of the characteristic regions of the stator yoke from the 1st to the Nth, respectively; The magnetic flux density of each stator yoke characteristic area is calculated according to the following formula: B sy1 =φ sy1 (t) / S sy1 B sy2 =φ sy2 (t) / S sy2 ... B syN =φ syN (t) / S syN In the formula, S sy1 ~S syN are the longitudinal cross-sectional areas of the characteristic regions of the stator yoke from the 1st to the Nth, B sy1 ~B syN are the magnetic flux densities of the characteristic regions of the stator yoke from the 1st to the Nth respectively; Step 4), through finite element simulation, obtain the data of magnetic flux density, rotor mechanical angle, and equivalent phase current of the characteristic points of each stator pole characteristic area; establish a stator pole two-dimensional magnetic flux lookup table model, and combine the magnetic flux and magnetic flux of each stator yoke characteristic area to form a complete motor stator instantaneous magnetic flux acquisition model for each area; Step 5), determine the hysteresis loss coefficient k of the stator core material of the electrically excited double-pole motor h , eddy current loss coefficient k c , estimating the volume of each stator pole characteristic area and each stator yoke characteristic area; Step 6), according to the instantaneous magnetic flux density of each region of the motor stator, the instantaneous magnetic flux density output by the model is obtained, and the instantaneous hysteresis loss P of each stator pole characteristic region and each stator yoke characteristic region is calculated respectively. h (t) and instantaneous eddy current loss P c (t): In the formula, B max , B min are the current maximum and minimum magnetic density values, B s+1 is the current magnetic density value, B s is the magnetic density value of the last calculation, and T is the calculation step length; Step 7), for each stator pole characteristic region and each stator yoke characteristic region, calculate its instantaneous hysteresis loss P h (t), instantaneous eddy current loss P c (t) are multiplied by their regional volumes and then added together to obtain their instantaneous iron losses. Then, the instantaneous iron losses of each stator pole characteristic area and each stator yoke characteristic area are added together to obtain the stator instantaneous iron loss.

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