Method for extracting fundamental back emf estimation value in case of inter-turn short circuit fault of permanent magnet synchronous motor

Abstract

The application discloses a method for extracting the fundamental back electromotive force estimation value of a permanent magnet synchronous motor under a turn-to-turn short circuit fault, and specifically comprises the following steps: transforming three-phase voltages to a rotating coordinate system to obtain the dq-axis voltage of the motor; calculating the d q-axis current according to the voltage equation and the flux linkage equation of the permanent magnet synchronous motor under the synchronous rotating coordinate system to obtain the current of the motor under the natural coordinate system, i.e. three-phase current; filtering the three-phase current and voltage after Clark transformation through a low-pass filter after inputting the current and voltage into a sliding mode observer to obtain the back electromotive force extracted based on the sliding mode observer; extracting the positive sequence component of the back electromotive force from the back electromotive force extracted based on the sliding mode observer through second-order generalized integration to obtain the effective fundamental back electromotive force, and accurate rotor position information can be estimated by using the back electromotive force. According to the method, the position of the rotor can be accurately estimated by the fundamental back electromotive force after the effective fundamental back electromotive force is extracted, and the reliable diagnosis of the turn-to-turn short circuit fault of the motor is ensured.

Description

Technical Field

[0001] This invention belongs to the field of AC motor drive control technology, specifically relating to a method for extracting the estimated value of the fundamental back EMF during inter-turn short-circuit faults in permanent magnet synchronous motors. Background Technology

[0002] With the rapid development of high-speed rail trains, permanent magnet synchronous traction motors (PMSMs), characterized by wide speed range, high power density, and low energy consumption, have become a research hotspot in the rail transit field. However, in actual operation, existing EMU traction systems face complex electromagnetic environments and severe vibrations. PMSMs are prone to mechanical, electrical, and permanent magnet failures during long-term operation, with electrical failures being the most frequent, particularly inter-turn short circuits. Inter-turn short circuits are highly destructive, generating significant eddy currents in the short-circuit loop. If the fault is not detected and addressed, it can lead to permanent magnet demagnetization, single-phase grounding, or phase-to-phase short circuits, causing the motor temperature to rise continuously and ultimately resulting in complete motor failure, jeopardizing train operation safety. Furthermore, the application of sensorless technology in high-speed rail PMSMs is becoming a trend. Inter-turn short circuits directly degrade the input current signal of the position observer, causing rotor position estimation errors and resulting in magnetic field orientation deviations, thus reducing the accuracy of inter-turn short circuit fault diagnosis. Therefore, if the fundamental back EMF estimate can be accurately extracted when the train is running at high speed, the rotor position of the motor can be accurately estimated, ensuring reliable diagnosis of inter-turn short circuit faults in the motor.

[0003] Currently, fault diagnosis methods for inter-turn short circuits in high-speed sensorless permanent magnet synchronous motors (PMSMs) fall into three categories: methods based on mathematical model analysis, methods based on signal transformation, and methods based on intelligent algorithms. Compared to signal transformation and intelligent algorithms, methods based on mathematical model analysis offer advantages such as achieving high-precision fault detection, lower requirements for mechanical sensors, and lower design complexity. The mathematical model for an inter-turn short-circuit PMSM is constructed based on voltage, current, and torque equations; therefore, the accuracy of rotor position estimation largely depends on the accuracy of the command voltage, feedback current, and motor parameters. By extracting the effective fundamental back electromotive force (EMF) of the faulty motor, the actual rotor position is estimated using this EMF. Comparing this estimate with the rotor position obtained from mechanical sensors effectively determines the correctness of the back EMF estimate under inter-turn short circuit conditions. Therefore, a precise method for extracting the back EMF estimate of a PMSM under inter-turn short-circuit fault conditions is crucial for maintaining the stability of sensorless closed-loop control during the initial inter-turn short circuit phase. Summary of the Invention

[0004] The purpose of this invention is to provide a method for extracting the fundamental back EMF estimate during inter-turn short circuit faults in permanent magnet synchronous motors. The method can accurately extract the fundamental back EMF estimate, accurately estimate the rotor position of the motor, and ensure reliable diagnosis of inter-turn short circuit faults in the motor.

[0005] The technical solution adopted in this invention is a method for extracting the estimated value of the fundamental back EMF during inter-turn short-circuit faults in permanent magnet synchronous motors, which is implemented according to the following steps:

[0006] Step 1: Transform the three-phase voltage in the natural coordinate system to the rotating coordinate system to obtain the d-axis voltage u of the motor. d and q-axis voltage u q ;

[0007] Step 2: Calculate the d-axis current i based on the voltage equation and flux linkage equation of the permanent magnet synchronous motor in the synchronous rotating coordinate system. d and q-axis current i q ;

[0008] Step 3: Obtain the motor current in the natural coordinate system under fault conditions, i.e., the three-phase current input to the sliding mode observer;

[0009] Step 4: Input the three-phase current and three-phase voltage into the sliding mode observer after Clark transformation to obtain the back electromotive force under the α and β axes;

[0010] Step 5: Filter the back EMF obtained in Step 4 using a low-pass filter to obtain the back EMF. and

[0011] Step 6: The positive-sequence component of the back electromotive force is converted from the second-order generalized integral SOGI. and Extracted, the fundamental back electromotive force e is obtained. α+ and e β+ The accurate rotor position information can be estimated using this fundamental back EMF information.

[0012] The invention is further characterized in that,

[0013] In step 1, the d-axis voltage u d and q-axis voltage u q As shown in equation (1);

[0014]

[0015] In the formula, u a u b and u c These are the three-phase voltages input to the motor; θ is the electrical angle.

[0016] In step 2, the d-axis current id q-axis current i q The magnetic flux linkage equations are shown in equations (2) and (3);

[0017]

[0018]

[0019] In the formula: u d For the d-axis voltage, u q L is the q-axis voltage. d For the d-axis inductance, L q For q-axis inductance, ψ d Let ψ be the d-axis flux linkage. q R is the q-axis flux linkage; s Stator resistance; ψ f For permanent magnet flux linkage, ω e This is the actual electric angular velocity.

[0020] Step 3 specifically involves:

[0021] When one of the phases of the permanent magnet synchronous motor is a faulty phase, the motor experiences an inter-turn short circuit fault. The faulty phase in the simulation is set as phase A. The current amplitude of phase A increases significantly. The current formula in the stationary coordinate system is shown in equation (4).

[0022]

[0023] In the formula, i′ d and i′ q This represents the current along the d and q axes of the motor under fault conditions, i d and i q This represents the d-axis and q-axis currents under normal motor operation, where μ is the short-circuit turns ratio and i f It is short-circuit current. and These are the current fault phase components of the d and q axes after an inter-turn short circuit;

[0024] i f The calculation formula is shown in equation (5):

[0025]

[0026] In the formula, u n The neutral point voltage is given, L0 is the stator inductance per phase, and R is the stator voltage. f For short-circuit resistance;

[0027] will i′ d and i′ q Performing the Park transformation yields the three-phase currents of the sliding mode observer, as shown in equation (6):

[0028]

[0029] i a ′、i b ′ and i c ′ represents the current in the natural coordinate system of the motor under fault conditions, that is, the three-phase current input to the sliding mode observer.

[0030] Step 4 specifically involves:

[0031] The output three-phase current and three-phase voltage are subjected to Clark transformation to obtain the α-axis current i′. α and voltage u α and the current i′ under the β axis β and voltage u β As shown in equations (7) and (8);

[0032]

[0033]

[0034] The obtained u α u β 、i′ α 、i′ β After inputting the sliding mode observer, the back electromotive force under the α and β axes is obtained. and The equations for the sliding mode observer are constructed as shown in equation (9):

[0035]

[0036]

[0037] in, and These are the stator α-axis and β-axis current observations, h is the sliding mode gain, sgn is the sign function, and L... d and L q These are the d-axis and q-axis inductances, i α and i β These are the α-axis and β-axis currents, respectively. It is the estimated electric angular velocity, R s It is the stator resistance;

[0038] The error equation for current observation is shown in equation (10):

[0039]

[0040] The current is estimated using a sliding mode observer, and the selection of its sliding mode hyperplane is shown in Equation (11):

[0041]

[0042] Based on this, the back electromotive force along the α and β axes can be obtained. and As shown in equation (12):

[0043]

[0044] In step 6, the positive-sequence component in the back potential extracted based on the sliding mode observer is the fundamental back potential e. α+ and e β+ ;

[0045] e αd and e αq e α In the back electromotive force components along the d-axis and q-axis, e βd and e βq e β The back electromotive force components on the d-axis and q-axis, For the estimated electric angular velocity, the transfer function of SOGI is shown in equation (13):

[0046]

[0047] Fundamental back electromotive force e α+ and e β+ The calculation formula is shown in equation (15):

[0048]

[0049] In the formula, e αd and e αq Therefore The output of SOGI is the input signal; e βd and e βq Therefore The output of SOGI is the input signal.

[0050] The beneficial effects of this invention are:

[0051] The method of this invention extracts an effective fundamental back electromotive force and then uses the fundamental back electromotive force to accurately estimate the rotor position. It applies the principle of control variables to determine whether the motor has a fault, and can provide a technical basis for reliable diagnosis of inter-turn short circuit faults in motor systems operating without position sensors. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the principle of the method for extracting the estimated value of the fundamental back EMF during inter-turn short-circuit faults in permanent magnet synchronous motors according to the present invention.

[0053] Figure 2 This is the SOGI structure diagram;

[0054] Figure 3 This is a flowchart of the method for extracting the positive-sequence component of the back potential estimate based on SOGI;

[0055] Figure 4 These are the waveforms of the three-phase current and the short-circuit current under inter-turn short circuit conditions.

[0056] Figure 5 It is a graph of the fundamental component of the back electromotive force;

[0057] Figure 6 It is a comparison between the back potential extracted by the sliding mode observer and the fundamental back potential extracted by SOGI;

[0058] Figure 7 It is an FFT analysis diagram of the back EMF extracted based on the sliding mode observer before the inter-turn short circuit;

[0059] Figure 8 It is an FFT analysis diagram of the back EMF extracted based on a sliding mode observer after an inter-turn short circuit;

[0060] Figure 9 It is an FFT analysis diagram of the fundamental back EMF waveform extracted by SOGI before the inter-turn short circuit.

[0061] Figure 10 This is an FFT analysis diagram of the fundamental back EMF waveform extracted by SOGI after an inter-turn short circuit. Detailed Implementation

[0062] The present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0063] Example 1

[0064] This invention relates to a method for extracting the estimated fundamental back EMF value during inter-turn short-circuit faults in permanent magnet synchronous motors, such as... Figure 1 As shown, please follow these steps:

[0065] Step 1: Transform the three-phase voltages in the natural coordinate system to the rotating coordinate system to obtain the d-axis and q-axis voltages of the motor, denoted as u. d and u q As shown in equation (1);

[0066]

[0067] In the formula, u a u b and u c These are the three-phase voltages input to the motor; θ is the electrical angle.

[0068] Step 2: Calculate the d-axis current i based on the voltage equation and flux linkage equation of the permanent magnet synchronous motor in the synchronous rotating coordinate system. d and q-axis current i q As shown in equations (2) and (3);

[0069]

[0070]

[0071] In the formula: u d For the d-axis voltage, u q Let i be the q-axis voltage. d Let i be the d-axis current. q Let L be the q-axis current. d For the d-axis inductance, L q For q-axis inductance, ψ d For d-axis flux linkage, ψ q R is the q-axis flux linkage; s Stator resistance; ψ f For permanent magnet flux linkage, ω e It is the actual electric angular velocity.

[0072] Step 3: When one of the phases of the permanent magnet synchronous motor is a faulty phase, the motor experiences an inter-turn short circuit fault, and the current amplitude of that phase increases significantly. The current formula in the stationary coordinate system is shown in equation (4).

[0073]

[0074] In the formula, i′ d and i′ q This represents the current along the d and q axes of the motor under fault conditions, i d and i q This represents the d-axis and q-axis currents under normal motor operation, where μ is the short-circuit turns ratio and i f It is short-circuit current. and These are the current fault phase components of the d and q axes after an inter-turn short circuit;

[0075] i f The calculation formula is shown in equation (5):

[0076]

[0077] In the formula, u n The neutral point voltage is given, L0 is the stator inductance per phase, and R is the stator voltage. f For short-circuit resistance;

[0078] will i′ d and i′ qPerforming the Park transformation yields the three-phase currents of the sliding mode observer, as shown in equation (6):

[0079]

[0080] i′ a 、i′ b and i′ c This represents the current in the natural coordinate system of the motor under fault conditions, i.e., the three-phase current input to the sliding mode observer;

[0081] Step 4: Perform Clark transformation on the output three-phase current and three-phase voltage to obtain the α-axis current i′. α and voltage u α and the current i′ under the β axis β and voltage u β As shown in equations (7) and (8);

[0082]

[0083]

[0084] The obtained u α u β 、i′ α 、i′ β After inputting the sliding mode observer (SMO), the back electromotive force under the α and β axes is obtained. and The equations for the sliding mode observer are constructed as shown in equation (9):

[0085]

[0086]

[0087] in, and These are the stator α-axis and β-axis current observations, h is the sliding mode gain, sgn is the sign function, and L... d and L q These are the d-axis and q-axis inductances, i α and i β These are the α-axis and β-axis currents, respectively. It is the estimated electric angular velocity, R s It is the stator resistance;

[0088] The error equation for current observation is shown in equation (10):

[0089]

[0090] The current is estimated using a sliding mode observer, and the selection of its sliding mode hyperplane is shown in Equation (11):

[0091]

[0092] Based on this, the back electromotive force along the α and β axes can be obtained. and As shown in equation (12):

[0093]

[0094] Step 5: Convert the back electromotive force and After passing through a low-pass filter, the back electromotive forces at the α and β axes extracted based on the sliding mode observer are obtained. and

[0095] Step 6: Transform the positive-sequence component of the back electromotive force from the second-order generalized integral (SOGI) to... and Separating from the middle, we obtain the fundamental back electromotive force e. α+ and e β+ After inputting it into the PLL phase-locked loop, the output angle can estimate the accurate rotor position information. Obtaining the accurate rotor position can effectively ensure the diagnosis of inter-turn short circuit faults in the motor.

[0096] From and Extract the positive sequence component, which is the fundamental back electromotive force e. α+ and e β+ ;

[0097] e αd and e αq They are respectively The back electromotive force components along the d-axis and q-axis, e βd and e βq They are respectively The back electromotive force components along the d-axis and q-axis, Let be the estimated electric angular velocity, and k be the SOGI filtering parameter. The transfer function is shown in equation (13):

[0098]

[0099] In the formula, D1(s) is e αd (s) The transfer function, Q1(s), is e αq (s) The transfer function, D2(s), is e βd (s) The transfer function, Q2(s), is e βq (s) The transfer function.

[0100] The structural block diagram of SOGI is as follows: Figure 2 As shown, the original waveform signal and estimated electric angular velocity As input to SOGI, after processing by SOGI, two mutually orthogonal sinusoidal output signals e are finally output. αd and e αq Among them, e αd track The fundamental frequency signal, while e αq It is phase-shifted by 90°, forming an orthogonal output. αd and e αq The transfer function is shown in equation (14):

[0101]

[0102] In the formula, s is the independent variable of the transfer function, and D1(s) is the expression for e. αd (s) The transfer function, Q1(s), is e αq (s) The transfer function is given, where k is the filtering parameter of SOGI, and the filtering coefficient depends on the magnitude of the fundamental back electromotive force frequency. Generally speaking, the positive parameter k is less than 1. The role of k determines the filtering performance of SOGI; the smaller k is, the stronger the filtering capability of SOGI, but the SOGI response time will be longer. SOGI has a certain suppression effect on harmonics, so it can be used for filtering.

[0103] Fundamental back electromotive force e α+ and e β+ The calculation formula is shown in equation (15):

[0104]

[0105] In the formula, e αd and e αq Therefore The output of SOGI is the input signal; e βd and e βq Therefore The positive-sequence component extraction method based on the back potential estimate of SOGI is as follows, given the SOGI output of the input signal. Figure 3 As shown.

[0106] This invention provides a method for accurately extracting the back EMF estimate of a permanent magnet synchronous motor under inter-turn short circuit conditions. After obtaining the current characteristics of the motor when an inter-turn short circuit fault occurs, the back EMF information of the faulty motor in the rotating coordinate system is obtained by combining a sliding mode observer and a low-pass filter. The fundamental back EMF of the faulty motor is extracted by second-order generalized integral to estimate the accurate rotor position, thereby determining whether the motor needs to be diagnosed for inter-turn short circuit faults.

[0107] Example 2

[0108] First, in a built-in permanent magnet synchronous motor (PMSM) experiencing an inter-turn short-circuit fault, a partial inter-turn short-circuit fault is simulated in the A-phase stator winding. The B-phase and C-phase stator windings are in a healthy state. When an inter-turn short circuit occurs in the A-phase stator winding of the PMSM, a fault loop is added to the A-phase winding. Therefore, the voltage expression equation for the PMSM also needs to include a fault loop voltage equation. Two parameters μ and R are introduced. f μ is the ratio of the number of short-circuit turns n1 to the total number of turns n in phase A, R f It is the resistance of the short-circuited branch. The magnitude of μ can characterize the degree of inter-turn short circuit, R f Size and I f The number of turns in a turn is closely related to the severity of the inter-turn short circuit. Because the inter-turn short circuit fault occurs in phase A, the short-circuit turns ratio μ affects the phase A current I. a However, it has little impact on the currents of the other two phases, so it will cause a difference with I. a I b I c The imbalance of current waveform peak values, i.e., the fluctuation of current peak values ​​between phases caused by inter-turn short circuit faults, is shown in the following current waveform after an inter-turn short circuit fault occurs in the motor: Figure 4 As shown, the current amplitude of phase A increases, while the current amplitudes of phases B and C are not significantly affected.

[0109] Using phase current as a characteristic quantity of motor faults, the three-phase current output by the faulty motor is input into a sliding mode observer and a low-pass filter to obtain the back electromotive force (EMF) extracted from the sliding mode observer along the α and β axes. A second-order generalized integrator is used to extract the fundamental back EMF of the faulty motor from this back EMF, resulting in a healthy fundamental back EMF waveform. The fundamental back EMF along the α and β axes is then input into a phase-locked loop to obtain the accurate rotor position. The rotor position extracted from the healthy fundamental back EMF of the faulty motor is compared with the rotor position extracted during normal motor operation to determine whether the motor needs fault diagnosis. This method provides reliable technical support for the diagnosis of inter-turn short-circuit faults in motor systems operating without position sensors.

[0110] The waveform of the fundamental back electromotive force is as follows Figure 5 As shown, the back electromotive forces along the α and β axes are output as sinusoidal waveforms with the same amplitude, indicating that the effective fundamental back electromotive force has been extracted. The waveform of the harmonic back electromotive force is as follows: Figure 6As shown, the back electromotive forces (EMFs) of the α and β axes are output as sinusoidal waveforms with the same amplitude, indicating that effective harmonic back EMFs have been extracted. By filtering out the fault back EMF and extracting the fundamental back EMF, and inputting it into the PLL phase-locked loop, accurate rotor position information can be estimated. Obtaining accurate rotor position can effectively ensure reliable diagnosis of inter-turn short-circuit faults in the motor.

[0111] Example 3

[0112] Before and after a short circuit fault occurs between turns in the motor, such as Figure 6 The image shows a comparison between the back EMF extracted using a sliding mode observer and the fundamental back EMF extracted using SOGI. From 0.1 to 0.2 s, the motor is in normal operation. At 0.2 s, an inter-turn short circuit fault occurs. The short circuit severity is set to 12%, the motor speed is set to 1500 r / min, and the number of pole pairs is 2, therefore the frequency is 50 Hz. Figure 7 and 8 This is an FFT harmonic analysis diagram of the back EMF waveform extracted based on a sliding mode observer before and after the inter-turn short circuit. Compare the back EMF extracted based on the sliding mode observer before and after the inter-turn short circuit. Figure 9 and 10 This is an FFT harmonic analysis plot of the fundamental back EMF waveform extracted using SOGI. After an inter-turn short circuit, the third harmonic in the back EMF extracted using the sliding mode observer increases significantly, and the introduced component causes a significant increase in its amplitude; the third and fifth harmonics in the fundamental back EMF also increase, and the introduced components cause an increase in the amplitude of the fundamental back EMF. The back EMF waveform extracted using the sliding mode observer contains many harmonic interferences, resulting in severe waveform distortion; the harmonic interference in the fundamental back EMF is very small, and its waveform is smooth. After an inter-turn short circuit, the third harmonic component introduced into the back EMF extracted using the sliding mode observer is significantly higher than that of the third harmonic component in the fundamental back EMF, resulting in its amplitude being higher than that of the fundamental back EMF. Both waveforms maintain good sinusoidal characteristics.

Claims

1. A method for extracting the estimated value of the fundamental back EMF during an inter-turn short-circuit fault in a permanent magnet synchronous motor, characterized in that, The specific steps are as follows: Step 1: Transform the three-phase voltage from the natural coordinate system to the rotating coordinate system to obtain the motor's... shaft voltage and shaft voltage ; Step 2: Based on the voltage equation and flux linkage equation of the permanent magnet synchronous motor in the synchronous rotating coordinate system, calculate the... shaft current and shaft current ; Step 3: Obtain the motor current in the natural coordinate system under fault conditions, i.e., the three-phase current input to the sliding mode observer; specifically: When one phase of a permanent magnet synchronous motor is a faulty phase, the motor experiences an inter-turn short circuit fault, and the current amplitude of that phase increases significantly. The current formula in the stationary coordinate system is shown in equation (4). （4）； In the formula, and Indicates the motor is in a faulty condition. and shaft current, and Indicates the normal operating condition of the motor and shaft current, It is the short-circuit turns ratio. It is short-circuit current. and After the inter-turn short circuit and Current fault phase component of the shaft; The calculation formula is shown in equation (5): （5）； In the formula, The neutral point voltage, It is the stator phase inductance. For short-circuit resistance; Will and Performing the Park transformation, the three-phase currents of the sliding mode observer are obtained, as shown in equation (6): （6）； , and This represents the current in the natural coordinate system of the motor under fault conditions, i.e., the three-phase current input to the sliding mode observer; Step 4: After Clark transformation, the three-phase current and three-phase voltage are input into the sliding mode observer to obtain... and The back electromotive force under the axis; specifically: The output three-phase current and three-phase voltage are transformed by Clark transformation to obtain Under-shaft current and voltage ,as well as Under-shaft current and voltage As shown in equations (7) and (8); （7）； （8）； The result , , , After inputting the sliding mode observer, the following is obtained: and Back EMF under the axis and The equations for the sliding mode observer are constructed as shown in equation (9): （9）； in, and It is a stator and Axis current observations For sliding mode gain, It is a symbolic function. and They are shaft and Shaft inductor, and They are shaft and shaft current, It is the estimated electric angular velocity; The error equation for current observation is shown in equation (10): （10）； The current is estimated using a sliding mode observer, and the selection of its sliding mode hyperplane is shown in equation (11): （11）； Based on this, we can obtain and Back EMF under the axis and As shown in equation (12): （12）； Step 5: Use a low-pass filter to filter and obtain the back electromotive force. and ; Step 6: Separate the positive sequence component of the back electromotive force using the second-order generalized integral SOGI, input it to the PLL phase-locked loop, and the output angle can estimate the accurate rotor position information. The positive-sequence component can be extracted from the back potential based on the sliding mode observer; the positive-sequence component is the fundamental back potential. and ; and They are respectively exist shaft and The back electromotive force component of the axis, and They are respectively exist shaft and The back electromotive force component of the axis, The filtering parameters for SOGI are given, and the transfer function of SOGI is shown in equation (13): （13）； In the formula It is the argument of the transfer function. yes right The transfer function, yes right The transfer function, yes right The transfer function, yes right The transfer function; Fundamental back electromotive force and The calculation formula is shown in equation (15): （15）； In the formula, and Therefore The output of SOGI is the input signal; and Therefore The output of SOGI is the input signal.

2. The method for extracting the estimated fundamental back EMF during inter-turn short-circuit faults in permanent magnet synchronous motors according to claim 1, characterized in that, In step 1, shaft voltage and shaft voltage As shown in equation (1); （1）； In the formula, , and These are the three-phase voltages input to the motor; It is an electrical angle.

3. The method for extracting the estimated value of the fundamental back EMF during inter-turn short-circuit faults in permanent magnet synchronous motors according to claim 2, characterized in that, In step 2, shaft current , shaft current The magnetic flux linkage equations are shown in equations (2) and (3); （2）； （3）； In the formula: for shaft voltage, for shaft voltage, for Shaft inductor, for Shaft inductor, for Axial magnetic flux, for Axial magnetic flux; Stator resistance; It is a permanent magnet flux linkage. This is the actual electric angular velocity.

Images