Initial position estimation method of multi-stage motor based on low-frequency rotation signal injection

Abstract

The present invention relates to a multi-stage motor initial position estimation method based on low-frequency rotating signal injection. By injecting low-frequency voltage signals rotating in the forward and reverse directions into the stator windings of the main motor, and collecting the stator winding current of the two-phase exciter in real time, the main motor excitation current is estimated and the estimated values ​​of four points within a cycle with intervals of 1 / 4 cycle are saved. Then, the sine and cosine signals containing the main motor rotor position information are extracted. The sine and cosine signals obtained by the forward and reverse injections are respectively subjected to arc tangent and compensated according to the positive and negative value relationship of the sine and cosine signals. The two estimated values ​​are added and averaged to uniquely estimate the initial position of the main motor rotor. The method proposed by the present invention is not affected by the salient polarity of the main motor and the initial position of the exciter rotor, has high estimation accuracy, and the signal extraction and position estimation methods are simple, with low requirements on processor performance.

Description

Technical Field

[0001] The present invention belongs to the field of motor technology and relates to a multi-stage motor initial position estimation method based on low-frequency rotation signal injection, and specifically relates to a multi-stage brushless electrically excited synchronous motor rotor initial position estimation method based on low-frequency rotation signal injection and independent of motor salient polarity and without the need for secondary magnetic pole identification. Background Art

[0002] Three-stage brushless synchronous motors offer excellent power generation quality and high reliability, and are widely used as generators in aircraft power systems. This allows the motor to operate in a motoring mode to start the aircraft engine. Once started, the engine then drives the motor in a generating mode to power onboard electrical equipment. This achieves integrated starting and power generation for the three-stage brushless synchronous motor, eliminating the need for a dedicated engine starter, reducing system size and weight, and improving system integration. This is of great significance to aircraft power systems.

[0003] Three-stage brushless synchronous motors require accurate rotor position information when operating in electric mode to start aircraft engines. Traditional mechanical position sensors for acquiring rotor position suffer from low reliability and increased system size and weight. Online rotor position estimation for three-stage brushless synchronous motors eliminates the need for mechanical position sensors, enabling sensorless starting control. This improves system reliability and reduces system size and weight.

[0004] The three-stage brushless synchronous motor consists of a coaxially mounted permanent magnet auxiliary exciter, an exciter and a main motor. The structural diagram is shown in the figure. Figure 1 As shown in Figure 2, in some applications, the permanent magnet auxiliary exciter can be omitted, resulting in a two-stage brushless synchronous motor. Because the core components and operating principles are essentially the same, three-stage and two-stage brushless synchronous motors are collectively referred to as multi-stage brushless synchronous motors.

[0005] Traditional methods for estimating the initial rotor position at zero speed primarily utilize the motor's saliency or magnetic saturation characteristics, inject an auxiliary voltage signal, and extract the response signal containing rotor position information to estimate the rotor position. Methods utilizing motor saliency also require identifying the rotor's magnetic pole direction during zero speed. The steps include: 1. Injecting a rotating or high-frequency signal; 2. Using a bandpass filter to extract the response signal; 3. Signal demodulation; 4. Using a low-pass filter to obtain the signal envelope; 5. Using a phase-locked loop or inverse tangent method to estimate the rotor position; and 6. Initial rotor position estimation requires secondary identification of the magnetic pole polarity. Methods utilizing magnetic saturation characteristics primarily include: 1. Injecting pulse voltages into the main stator winding at fixed intervals within the range of 0-2π, collecting and storing the response current at the end of the pulse voltage injection; 2. Fitting and smoothing the stored data; and 3. Selecting the angular position corresponding to the maximum value as the rotor's initial position. This method processes a large amount of data, and the estimation accuracy is significantly affected by the arc interval between pulse injections and the accuracy of the current pulse response detection.

[0006] As can be seen from the above, the traditional method of identifying the initial position of the rotor has the following disadvantages: 1. The method used requires large amounts of data calculation and storage, and has high requirements for the processor; 2. The magnetic pole direction needs to be identified twice in the zero-speed static state; 3. The estimation accuracy is easily affected. Summary of the Invention

[0007] Technical problems to be solved

[0008] In order to avoid the shortcomings of the existing technology, the present invention proposes a multi-stage motor initial position estimation method based on low-frequency rotation signal injection, which overcomes the shortcomings of the existing rotor initial position estimation technology, such as reliance on salient polarity, large data processing volume, and the need for secondary identification of the magnetic poles.

[0009] Technical Solution

[0010] A method for estimating the initial position of a multi-stage motor based on low-frequency rotation signal injection is provided, wherein the rotor position of the multi-stage brushless electrically excited synchronous motor refers to the rotor position of the main motor in the multi-stage brushless electrically excited synchronous motor, and the estimation steps are as follows:

[0011] Step 1: Apply two-phase symmetrical voltages to the stator windings of the two-phase exciter and collect the stator currents of the two-phase exciter to estimate the excitation current of the main motor in real time. The real-time estimated current is recorded as I f_est ;

[0012] Step 2: After the main motor excitation current is stable, a forward rotating low-frequency voltage is applied to the stator winding of the main motor. Within a low-frequency voltage cycle, the main motor excitation current is sequentially collected and estimated at intervals of 1 / 4 cycle, and recorded as I f_est_f0 , If_est_f1 , I f_est_f2 , I f_est_f3 ;

[0013] Step 3: Apply a counter-rotating low-frequency voltage to the stator winding of the main motor. Within a low-frequency voltage cycle, ensure that the low-frequency phase corresponding to the first sampling point is the same. At intervals of 1 / 4 cycle, sequentially collect and estimate the main motor excitation current, which are recorded as I f_est_r0 , I f_est_r1 , I f_est_r2 , I f_est_r3 ;

[0014] Step 4: Based on the above estimated value of the main motor excitation current, let:

[0015]

[0016]

[0017] Step 5: Calculate the initial position without magnetic pole polarity:

[0018]

[0019] Step 6: Compensate the initial position without magnetic polarity in step 5 according to the following rules:

[0020] If θ f0 <0, and A f <0, B f >0, then θ f1 =θ f0 +π,

[0021] If θ f0 <0, and A f >0, B f <0, then θ f1 =θ f0 +2π,

[0022] If θ f0 >0, and A f <0, B f <0, then θ f1 =θ f0 ,

[0023] If θ f0 >0, and A f >0, B f >0, then θ f1 =θ f0 +π,

[0024] If θ r0 <0, and A r <0, Br >0, then θ r1 =θ r0 +2π,

[0025] If θ r0 <0, and A r >0, B r <0, then θ r1 =θ r0 +π,

[0026] If θ r0 >0, and A r <0, B r <0, then θ r1 =θ r0 ,

[0027] If θ r0 >0, and A r <0, B r <0, then θ r1 =θ r0 +π;

[0028] Step 7: Based on the compensated rotor initial position, the final estimated rotor initial position is obtained:

[0029]

[0030] The multi-stage brushless electric excitation synchronous motor comprises a main motor and a two-phase exciter which are coaxially mounted.

[0031] The two-phase voltage of the exciter stator in step 1 is:

[0032]

[0033] Among them, u esα and u esβ is the stator winding voltage of the two-phase exciter, U es is the voltage amplitude, ω esf is the voltage fundamental angular velocity, and t is the time.

[0034] The main motor excitation current estimated in step 1 is:

[0035]

[0036] in, and are the estimated three-phase currents of the two-phase exciter rotor, and:

[0037]

[0038] Among them, θ er∈[0,2π) and is selected as any fixed value, M em is the mutual inductance of the stator and rotor of the exciter, R es is the stator winding resistance, dt is the time differential, i esα and i esβ is the stator current of the two-phase exciter collected in real time in step 1, L es is the stator inductance of the exciter.

[0039] The expressions of the forward and reverse rotating low-frequency voltages applied to the stator windings of the main motor in steps 2 and 3 on the αβ axes are respectively:

[0040]

[0041]

[0042] Among them, U L is the voltage amplitude, t is the time, ω L is the voltage angular velocity, and the low-frequency voltage period is And satisfy:

[0043]

[0044] During one cycle of steps 2 and 3, the four time points at which the estimated excitation current of the main motor is collected and saved at intervals of 1 / 4 cycle are:

[0045]

[0046] Among them, t r is the random sampling time of the first point.

[0047] In step 3, the low-frequency phase corresponding to the first sampling point in step 2 is ensured to be the same, which means that the phase ω corresponding to the first point is collected during forward rotation and reverse rotation respectively. L t r same.

[0048] The multi-stage brushless electric excitation synchronous motor also includes a coaxially mounted main motor and a three-phase exciter. The three-phase voltage or the three-phase current is subjected to Clark transformation to obtain an equivalent two-phase exciter as described in 2. esα and u esβ ,i esα and i esβ .

[0049] Beneficial effects

[0050] The present invention proposes a multi-stage motor initial position estimation method based on low-frequency rotating signal injection. By injecting forward and reverse rotating low-frequency voltage signals into the stator winding of the main motor, respectively, and collecting the stator winding current of the two-phase exciter in real time, the main motor excitation current is estimated and the estimated values ​​are saved at four points within a cycle, spaced 1 / 4 of the cycle. The sinusoidal and cosine signals containing the main motor rotor position information are then extracted. The sinusoidal and cosine signals obtained by the forward and reverse injections are respectively inverse tangent and compensated according to the positive and negative value relationship of the sinusoidal and cosine signals. The two estimated values ​​are then added and averaged to uniquely estimate the initial position of the main motor rotor. The method proposed by the present invention is not affected by the saliency of the main motor and the initial position of the exciter rotor, has high estimation accuracy, and the signal extraction and position estimation methods are simple, with low processor performance requirements.

[0051] The beneficial effects of the present invention include:

[0052] 1) The traditional method for estimating the initial position of the rotor that relies on the salient polarity of the main motor requires injecting a rotating high-frequency signal on the stator side of the main motor, extracting the signal using a filter, multiplying it with a signal of the same injection frequency for demodulation, and then sending it to a phase-locked loop to obtain the initial position of the rotor without the magnetic pole polarity. Finally, an additional pulse is required for secondary identification of the magnetic pole polarity. This process not only has complex parameter matching but also has high requirements on controller performance. The present invention only needs to inject a low-frequency rotating signal on the stator side of the main motor, collect it on the stator side of the exciter, perform simple addition and subtraction operations, and then use the inverse tangent to obtain the initial position of the main motor rotor based on the positive and negative value relationship of the collected signal. This does not require complex parameter matching and has lower requirements on processor performance.

[0053] 2) The traditional method for estimating the rotor's initial position based on magnetic saturation characteristics requires injecting signals into the stator winding of the main motor at fixed angles and storing the response current. The stored data is then fitted and the rotor's initial position is estimated by finding the maximum value. This method places high demands on processor memory and computing power, and the estimation accuracy is affected by the interval angle of the injected signal. The method shown in the present invention only requires injecting the rotation signal and collecting the values ​​at four moments for processing, thus reducing the storage requirements.

[0054] 3) The present invention adopts the method of injecting forward and reverse rotation signals to perform error compensation from the perspective of mathematical theory, which helps to improve the estimation accuracy;

[0055] 4) In the actual measurement, the main motor rotor is adjusted every 10° and estimated using the method proposed in the present invention. The estimation error under different actual positions is as follows: Figure 9 As shown, the estimated errors are all within 7°, which can meet the requirement of the error within 10° in this field;

[0056] 5) The method proposed in the present invention is also applicable to single-unit electromagnetic excitation motors. In this case, the same method can be used to collect and process the excitation current. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a schematic diagram of the structure of a three-stage brushless synchronous motor.

[0058] Figure 2 This is a flow chart of the method for estimating the initial position of the rotor of a multi-stage brushless synchronous motor proposed in the present invention.

[0059] Figure 3 The waveforms of the actual and estimated steady-state excitation currents are shown when there is no injection signal into the stator winding of the main motor of the present invention and the exciter has an ideal error.

[0060] Figure 4 The waveforms are the actual value and estimated value of the steady-state excitation current when there is no injection signal in the stator winding of the main motor of the present invention and the exciter has non-ideal errors.

[0061] Figure 5 This is the forward and reverse rotating low-frequency voltage signal waveform injected into the stator winding of the main motor of the present invention.

[0062] Figure 6 The stator current waveform of the exciter after the rotating low-frequency voltage is injected into the present invention.

[0063] Figure 7 The actual value and estimated value waveforms of the excitation current of the main motor rotor in different sectors at the initial position of the present invention.

[0064] Figure 8 These are the estimation results of the main motor of the present invention under different actual rotor initial positions.

[0065] Figure 9 It is the estimated error of the main motor rotor at different positions in the actual measurement of the present invention. DETAILED DESCRIPTION

[0066] The present invention will now be further described with reference to the embodiments and accompanying drawings:

[0067] A method for estimating the initial position of a multi-stage motor based on low-frequency rotating signal injection is applied to a multi-stage brushless electric excitation synchronous motor, wherein the multi-stage brushless electric excitation synchronous motor includes a coaxially mounted main motor and a two-phase exciter; the multi-stage brushless electric excitation synchronous motor also includes a coaxially mounted main motor and a three-phase exciter, and the three-phase voltage or the three-phase current is subjected to Clark transformation to obtain an equivalent two-phase exciter as described in 2 esα and u esβ ,i esα and i esβ .

[0068] The rotor position of the multi-stage brushless electric excitation synchronous motor refers to the rotor position of the main motor in the multi-stage brushless electric excitation synchronous motor. In the embodiment, the exciter of the multi-stage brushless synchronous motor is a two-phase exciter, that is, the stator excitation winding of the exciter is a two-phase winding with a 90 electrical angle difference. The exciter has 6 pairs of poles, and the main motor has 3 pairs of poles. In the following, the actual position of the main motor is θ 0real =120° and θ 0real =210° is used as an example for detailed explanation.

[0069] The method comprises the following steps:

[0070] Step 1: Apply two-phase symmetrical voltages to the stator windings of the two-phase exciter, and collect the stator current of the two-phase exciter to estimate the excitation current of the main motor in real time. The real-time estimated current is recorded as I f_est ;

[0071] The two-phase voltage of the exciter stator is:

[0072]

[0073] Among them, u esα and u esβ is the stator winding voltage of the two-phase exciter, U es is the voltage amplitude, ω esf is the voltage fundamental angular velocity, t is the time, and the estimated main motor excitation current is:

[0074]

[0075] in, and are the estimated three-phase currents of the two-phase exciter rotor, and:

[0076]

[0077] Among them, θ er ∈[0,2π) and can be selected as any fixed value, M em is the mutual inductance of the stator and rotor of the exciter, R es is the stator winding resistance, dt is the time differential, i esα and i esβ is the stator current of the two-phase exciter collected in real time in step 1, L es is the stator inductance of the exciter;

[0078] In the embodiment:

[0079] A two-phase symmetrical voltage is applied to the two-phase windings of the exciter stator (respectively denoted as α-phase winding and β-phase winding), with an excitation voltage amplitude of 50V and an excitation frequency of 200Hz. The two-phase currents of the stator of the two-phase exciter are collected and denoted as i esαand i esβ , then:

[0080]

[0081] Arbitrarily choose θ er =π / 12, the main motor excitation current can be estimated according to equations (2) and (3). er The error between the actual position of the exciter and When the excitation machine ideal error is abbreviated, the estimated steady-state excitation current of the main motor contains only DC quantity, which can be expressed as I f_dc ,like Figure 3 As shown. When θ er When the error between the actual position of the exciter and the exciter is other values, it is referred to as the exciter non-ideal error. The estimated steady-state excitation current of the main motor contains DC and periodic AC quantities, and the frequency of the periodic AC quantity is 6 times the frequency of the exciter stator voltage. The estimated excitation current can be expressed as I f_dc +I(6ω esf t), such as Figure 4 As shown;

[0082] Step 2: After the main motor excitation current is stable, a forward rotating low-frequency voltage is applied to the stator winding of the main motor. Within a low-frequency voltage cycle, the estimated main motor excitation current is sequentially collected and saved at intervals of 1 / 4 cycle, and recorded as I f_est_f0 , I f_est_f1 , I f_est_f2 , I f_est_f3 ;

[0083] The expressions of the forward and reverse rotating low-frequency voltages applied to the stator winding of the main motor on the αβ axis are respectively:

[0084]

[0085]

[0086] Among them, U L is the voltage amplitude, t is the time, ω L is the voltage angular velocity, and the low-frequency voltage period is And satisfy:

[0087]

[0088] In this embodiment, the injected low-frequency voltage amplitude U L =3V,ω L =100*2π, that is Then the injected positive rotating low frequency signal is as follows Figure 5 As shown, it can be expressed as:

[0089]

[0090] The stator current of the exciter is as follows Figure 6 As shown, under the more complex non-ideal error conditions of the exciter, the estimated current expressions corresponding to t0, t1, t2 and t3 are:

[0091]

[0092] Among them I fL is the low-frequency current amplitude induced by low-frequency injection, θ 0real is the actual value of the rotor position, Phase delay caused by signal transmission;

[0093] Step 3: Apply a reverse rotating low-frequency voltage to the stator winding of the main motor. Within a low-frequency voltage cycle, ensure that the low-frequency phase corresponding to the first sampling point is the same. Sequentially collect and save the estimated main motor excitation current at intervals of 1 / 4 cycle, and record them as I f_est_r0 , I f_est_r1 , I f_est_r2 , I f_est_r3 ;

[0094] In one cycle, the four time points at which the estimated excitation current of the main motor is collected and saved sequentially at intervals of 1 / 4 cycle are:

[0095]

[0096] Among them, t r is the random sampling time of the first point;

[0097] In step 3, the low-frequency phase corresponding to the first sampling point in step 2 is guaranteed to be the same, which means that the phase ω corresponding to the first point is collected during forward rotation and reverse rotation respectively. L t r same;

[0098] In the embodiment, the injected counter-rotating low frequency signal is as follows Figure 5 As shown, it can be expressed as:

[0099]

[0100] Under the more complex non-ideal error conditions of the exciter, the estimated current expressions corresponding to t0, t1, t2 and t3 are:

[0101]

[0102] Step 4: Based on the estimated value of the main motor excitation current saved above, let:

[0103]

[0104]

[0105] In the embodiment, A can be obtained from formula (13) and (14): f , B f , A r and B r The expression is as follows:

[0106]

[0107]

[0108] Step 5: According to equations (1) and (2), the following initial position without magnetic polarity is obtained:

[0109]

[0110] In the embodiment, the position information without the magnetic polarity can be obtained from formula (17), which can be expressed as follows:

[0111]

[0112]

[0113] Step 6: Compensate the initial position without magnetic polarity in equation (3) according to the following rules:

[0114] If θ f0 <0, and A f <0, B f >0, then θ f1 =θ f0 +π,

[0115] If θ f0 <0, and A f >0, B f <0, then θ f1 =θ f0 +2π,

[0116] If θ f0 >0, and A f <0, B f <0, then θ f1 =θ f0 ,

[0117] If θ f0 >0, and A f >0, B f >0, then θ f1 =θ f0 +π,

[0118] If θ r0<0, and A r <0, B r >0, then θ r1 =θ r0 +2π,

[0119] If θ r0 <0, and A r >0, B r <0, then θ r1 =θ r0 +π,

[0120] If θ r0 >0, and A r <0, B r <0, then θ r1 =θ r0 ,

[0121] If θ r0 >0, and A r <0, B r <0, then θ r1 =θ r0 +π;

[0122] In the embodiment, according to the compensation rules, and Perform phase compensation to obtain θ f1 and θ r1 ;

[0123] Step 7: The final estimated rotor initial position can be obtained from the compensated rotor initial position in step 6, which is expressed as:

[0124]

[0125] In this embodiment, the actual position of the main motor is θ 0real =120° and θ 0real =210° when the estimated result is as follows Figure 7 shown.

[0126] When the present invention estimates the excitation current of the main motor, if the exciter is in the ideal error state, I(6ω esf t) is always 0.

[0127] The actual value and estimated value waveforms of the excitation current of the main motor rotor at the initial position in different sectors are as follows: Figure 8 As shown, the estimation process is as follows Figure 2 shown.

Claims

1. A method for estimating the initial position of a multi-stage motor based on low-frequency rotation signal injection, characterized in that The rotor position of a multi-stage brushless electrically excited synchronous motor refers to the rotor position of the main motor in the multi-stage brushless electrically excited synchronous motor. The estimation steps are as follows: Step 1: Apply two-phase symmetrical voltages to the stator windings of the two-phase exciter and collect the stator currents of the two-phase exciter to estimate the excitation current of the main motor in real time. The real-time estimated current is recorded as I f_est ; Step 2: After the main motor excitation current is stable, a forward rotating low-frequency voltage is applied to the stator winding of the main motor. Within a low-frequency voltage cycle, the main motor excitation current is sequentially collected and estimated at intervals of 1 / 4 cycle, and recorded as I f_est_f0 , I f_est_f1 , I f_est_f2 , I f_est_f3 ; Step 3: Apply a counter-rotating low-frequency voltage to the stator winding of the main motor. Within a low-frequency voltage cycle, ensure that the low-frequency phase corresponding to the first sampling point is the same. At intervals of 1 / 4 cycle, sequentially collect and estimate the main motor excitation current, which are recorded as I f_est_r0 , I f_est_r1 , I f_est_r2 , I f_est_r3 ; Step 4: Based on the above estimated value of the main motor excitation current, let: Step 5: Calculate the initial position without magnetic pole polarity: Step 6: Compensate the initial position without magnetic polarity in step 5 according to the following rules: If θ f0 <0, and A f <0, B f >0, then θ f1 =θ f0 +π, If θ f0 <0, and A f >0, B f <0, then θ f1 =θ f0 +2π, If θ f0 >0, and A f <0, B f <0, then θ f1 =θ f0 , If θ f0 >0, and A f >0, B f >0, then θ f1 =θ f0 +π, If θ r0 <0, and A r <0, B r >0, then θ r1 =θ r0 +2π, If θ r0 <0, and A r >0, B r <0, then θ r1 =θ r0 +π, If θ r0 >0, and A r <0, B r <0, then θ r1 =θ r0 , If θ r0 >0, and A r <0, B r <0, then θ r1 =θ r0 +π; Step 7: Based on the compensated rotor initial position, the final estimated rotor initial position is obtained:

2. The method for estimating the initial position of a multi-stage motor based on low-frequency rotation signal injection according to claim 1, characterized in that: The multi-stage brushless electric excitation synchronous motor comprises a main motor and a two-phase exciter which are coaxially mounted.

3. The method for estimating the initial position of a multi-stage motor based on low-frequency rotation signal injection according to claim 1, characterized in that: The two-phase voltage of the exciter stator in step 1 is: Among them, u esα and u esβ is the stator winding voltage of the two-phase exciter, U es is the voltage amplitude, ω esf is the voltage fundamental angular velocity, and t is the time.

4. The method for estimating the initial position of a multi-stage motor based on low-frequency rotation signal injection according to claim 1, wherein: The main motor excitation current estimated in step 1 is: in, and are the estimated three-phase currents of the two-phase exciter rotor, and: Among them, θ er ∈[0,2π) and is selected as any fixed value, M em is the mutual inductance of the stator and rotor of the exciter, R es is the stator winding resistance, dt is the time differential, i esα and i esβ is the stator current of the two-phase exciter collected in real time in step 1, L es is the stator inductance of the exciter, u esα and u esβ is the stator winding voltage of the two-phase exciter.

5. The method for estimating the initial position of a multi-stage motor based on low-frequency rotation signal injection according to claim 1, characterized in that: The expressions of the forward and reverse rotating low-frequency voltages applied to the stator windings of the main motor in steps 2 and 3 on the αβ axes are respectively: Among them, U L is the voltage amplitude, t is the time, ω L is the voltage angular velocity, and the low-frequency voltage period is And satisfy: Where: esf is the voltage fundamental angular velocity.

6. The method for estimating the initial position of a multi-stage motor based on low-frequency rotation signal injection according to claim 1, characterized in that: During one cycle of steps 2 and 3, the four time points at which the estimated excitation current of the main motor is collected and saved at intervals of 1 / 4 cycle are: Among them, t r is the random sampling time of the first point.

7. The method for estimating the initial position of a multi-stage motor based on low-frequency rotation signal injection according to claim 1, characterized in that: In step 3, the low-frequency phase corresponding to the first sampling point in step 2 is ensured to be the same, which means that the phase ω corresponding to the first point is collected during forward rotation and reverse rotation respectively. L t r Same, where: ω L is the voltage angular velocity, t r is the random sampling time of the first point.

8. The method for estimating the initial position of a multi-stage motor based on low-frequency rotation signal injection according to claim 1, characterized in that: The multi-stage brushless electric excitation synchronous motor also includes a coaxially mounted main motor and a three-phase exciter. The three-phase voltage or the three-phase current is subjected to Clark transformation to obtain the u of the equivalent two-phase exciter. esα and u esβ ,i esα and i esβ , where: u esα and u esβ is the stator winding voltage of the two-phase exciter, i esα and i esβ It is the stator current of the two-phase exciter collected in real time in step 1.

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