Unified equivalent magnetic circuit analysis and calculation method for transformers and asynchronous machines based on magnetic induction

Abstract

The application discloses a unified equivalent magnetic circuit analysis and calculation method for transformers and asynchronous motors based on magnetic induction, and belongs to the field of motors and transformers. In the method, the equivalent magnetic circuits of the transformers and the asynchronous motors are composed of magnetic resistance, core loss equivalent magnetic induction and secondary phase winding (rotor squirrel cage winding in the asynchronous motor) equivalent magnetic induction. The application can intuitively and effectively reflect the fact that the primary and secondary phase windings of the transformers and the asynchronous motors are connected in the circuit insulation and the magnetic circuit, can clearly qualitatively and quantitatively represent the influence of the core loss equivalent magnetic induction of the transformers and the asynchronous motors on the magnetic flux and the phase difference, can directly calculate the parameter variables, and can draw the transformer and asynchronous motor phasor diagram based on the vector equivalent magnetic circuit.

Description

Technical Field

[0001] This invention relates to the field of asynchronous motor and transformer technology, and specifically to a unified equivalent magnetic circuit analysis and calculation method for transformers and asynchronous motors based on magnetic induction. Background Technology

[0002] Existing analyses of transformers and asynchronous motors largely rely on equivalent circuits. Equivalent circuit analysis equates actual magnetic physical quantities to electrical quantities. Compared to equivalent magnetic circuits, this conceptual understanding is less clear and fails to reflect the fact that transformers and asynchronous motors are electrically insulated but magnetically connected. Furthermore, traditional magnetic circuit theory uses only a single reluctance element, which not only fails to characterize the phase difference between magnetic flux and magnetomotive force but also cannot characterize losses in the iron core, becoming a bottleneck in the analysis. Summary of the Invention

[0003] The technical problem to be solved by this invention is to address the shortcomings of the prior art by proposing a unified equivalent magnetic circuit analysis and calculation method for transformers and asynchronous motors based on magnetic induction.

[0004] To solve the above technical problems, the present invention employs the following technical means:

[0005] This invention proposes a unified equivalent magnetic circuit analysis and calculation method for transformers and asynchronous motors based on magnetic induction. The equivalent magnetic circuits of both transformers and asynchronous motors are composed of magnetic reluctance. Core loss equivalent magnetic inductance Equivalent magnetic induction of the secondary winding (or rotor squirrel-cage winding in an asynchronous motor) The system is composed of the following components: Based on the equivalent magnetic circuit, the performance parameters of the transformer under no-load and load conditions can be calculated; Based on the equivalent magnetic circuit, the performance parameters of the asynchronous motor under any operating condition can be calculated; Based on the equivalent magnetic circuit, the phasor diagrams of the transformer and the asynchronous motor can be drawn.

[0006] Furthermore, in transformers, magnetic reluctance Equal to its core magnetic reluctance In asynchronous motors in, The reluctance of the core of the asynchronous motor; It is a single-sided air gap magnetoresistive.

[0007] Furthermore, the external loads of the transformer and the asynchronous motor are directly considered in the equivalent magnetic induction. Inside, among which:

[0008] Equivalent magnetic induction of a transformer Where, N 2T R is the number of turns in the secondary winding of the transformer. 2T R is the resistance of the secondary winding of the transformer. LT L is the external load resistance of the transformer. LTω is the external load inductance of the transformer; j is the imaginary number; T This is the excitation frequency of the primary winding of the transformer.

[0009] Equivalent magnetic induction of an asynchronous motor Where, N 2I R is the effective number of turns of the rotor squirrel-cage winding of the asynchronous motor; 2I R is the equivalent resistance of the rotor squirrel cage winding of the asynchronous motor; LI =R 2I (1-s) / s is the simulated load resistance of the rotor mechanical output power, and s is the slip.

[0010] Furthermore, on the transformer, the electrical frequency ω T It is the excitation frequency of the primary winding; in an asynchronous motor, the electrical frequency sω I It is the slip frequency of the rotor relative to the rotating magnetic field of the stator, ω. I It is the alternating frequency of the magnetic flux in the stator core of the asynchronous motor, and corresponds to the angular frequency at the synchronous speed of the rotor.

[0011] Furthermore, the magnetomotive force balance equation of the transformer under no-load conditions is as follows:

[0012]

[0013] Where, N 1T I is the number of turns in the primary winding of the transformer. 0T The effective value of the input excitation current of the primary winding of the transformer; Ф mT This represents the effective value of the magnetic flux flowing through the transformer's magnetic circuit.

[0014] According to the transformer no-load magnetomotive force balance equation, I 0T The calculation formula is:

[0015]

[0016] According to the transformer no-load magnetomotive force balance equation, Ф mT Lag I 0T The formula for calculating the iron loss angle is:

[0017]

[0018] Furthermore, the magnetomotive force balance equation for the magnetic circuit under transformer load conditions is as follows:

[0019]

[0020] Among them, I 1T This represents the effective value of the input current of the primary winding under load.

[0021] According to the transformer load magnetomotive force balance equation, I 1T The calculation formula is:

[0022]

[0023] According to the transformer load magnetomotive force balance equation, the magnetic flux Ф mT The lagging transformer primary winding generates magnetomotive force N. 1T I 1T phase angle θ T The calculation formula is:

[0024]

[0025] The formula for calculating the input power on the primary winding side is:

[0026]

[0027] Furthermore, the magnetomotive force balance equation of the asynchronous motor under no-load conditions is as follows:

[0028]

[0029] Where, N 1I I is the number of turns in the primary winding of the asynchronous motor. 0I This represents the effective value of the input current of the primary winding of the asynchronous motor under no-load conditions; Ф mI This represents the effective value of the magnetic flux flowing through the magnetic circuit of the asynchronous motor.

[0030] The magnetomotive force balance equation for the asynchronous motor under load conditions is:

[0031]

[0032] Among them, I 1I This represents the effective value of the input current to the primary winding of the asynchronous motor.

[0033] According to the magnetomotive force balance equation under asynchronous motor load conditions, I 1I The calculation formula is:

[0034]

[0035] According to the magnetomotive force balance equation under asynchronous motor load conditions, the magnetic flux Ф mI The magnetomotive force N generated by the primary winding of the lagging asynchronous motor 1I I 1I phase angle θ I The calculation formula is:

[0036]

[0037] The formula for calculating the electromagnetic power of an asynchronous motor is:

[0038]

[0039] Where m is the number of phases of the asynchronous motor. The formula for calculating the output mechanical power of an asynchronous motor is:

[0040]

[0041] The formula for calculating the electromagnetic torque of an asynchronous motor is:

[0042]

[0043] Where Ω is the rotor mechanical angular velocity of the asynchronous motor.

[0044] The formula for calculating the output mechanical torque of an asynchronous motor is:

[0045] T2 = TT mech

[0046] Among them, T mech This refers to the mechanical loss torque.

[0047] Furthermore, the phasor diagrams of the transformer and the asynchronous motor are drawn using the aforementioned magnetomotive force balance equations.

[0048] The steps for drawing a transformer phasor diagram are as follows:

[0049] (1) With the main magnetic flux Ф mT For public reference phasor;

[0050] (2) Draw the no-load phasor diagram of the transformer based on the triangle corresponding to the no-load magnetomotive force balance equation.

[0051] (3) Based on the no-load phasor diagram, the equivalent magnetic induction of the secondary winding under load is calculated. The magnetic potential drop is used to obtain the load magnetomotive force triangle, and the load phasor diagram of the transformer is drawn.

[0052] (4) The voltage and current phasors of the primary winding and the secondary winding are drawn independently according to their respective voltage equations and superimposed on the phasor diagram.

[0053] The steps for drawing a phasor diagram of an asynchronous motor are as follows:

[0054] (1) With the main magnetic flux Ф mI For public reference phasor;

[0055] (2) Draw the no-load phasor diagram of the asynchronous motor based on the triangle corresponding to the no-load magnetomotive force balance equation;

[0056] (3) Based on the no-load phasor diagram, the equivalent magnetic induction of the rotor squirrel cage winding under load is calculated. The magnetic potential drop is used to obtain the load magnetomotive force triangle, and the load phasor diagram of the asynchronous motor is drawn.

[0057] (4) The voltage and current phasors of the primary winding are drawn independently according to its voltage equation and superimposed on the phasor diagram.

[0058] The present invention adopts the above technical solution and has the following beneficial effects compared with the prior art:

[0059] (1) Based on magnetic induction, this invention proposes a unified equivalent magnetic circuit analysis and calculation method applicable to transformers and asynchronous motors under any working conditions; it eliminates the work of turning number reduction and frequency reduction that are indispensable in the original analysis of transformers and asynchronous motors, and the physical concepts are clear and the calculation process is concise.

[0060] (2) This invention intuitively and effectively demonstrates the fact that the primary and secondary windings of transformers and asynchronous motors are insulated in the circuit and connected in the magnetic circuit. The drawing process is simple and the principle is easy to understand. This invention shows that the vector equivalent magnetic circuit of transformers and asynchronous motors is a series circuit composed of magnetic reluctance and magnetic induction elements. From the magnetic circuit, it helps to understand the phase difference between magnetomotive force and magnetic flux under any working condition.

[0061] (3) This invention can clearly characterize the influence of the equivalent magnetic induction of core loss on magnetic flux and phase difference in transformers and asynchronous motors in terms of qualitative and quantitative analysis. It can also directly calculate their parameter variables. Based on the equivalent magnetic circuit, it can calculate the performance parameters of transformers under no-load and load conditions, the performance parameters of asynchronous motors under any conditions, and draw phasor diagrams of transformers and asynchronous motors based on vector equivalent magnetic circuits. Attached Figure Description

[0062] Figure 1 This invention presents a unified equivalent magnetic circuit diagram for transformers and asynchronous motors based on magnetic induction.

[0063] Figure 2 It is a transformer no-load magnetic circuit diagram obtained based on a unified equivalent magnetic circuit.

[0064] Figure 3 It is a transformer load magnetic circuit diagram obtained based on a unified equivalent magnetic circuit.

[0065] Figure 4 It is a magnetic circuit diagram of an asynchronous motor obtained based on a unified equivalent magnetic circuit.

[0066] Figure 5 This is a comparison chart of the torque slip rate curves of asynchronous motors.

[0067] Figure 6 It is a transformer global phasor diagram drawn based on a unified equivalent magnetic circuit.

[0068] Figure 7The transformer is based on the main magnetic flux Ф mT A diagram serving as a public reference phasor.

[0069] Figure 8 It is a transformer no-load phasor diagram drawn based on a unified equivalent magnetic circuit.

[0070] Figure 9 It is a transformer load phasor diagram drawn based on a unified equivalent magnetic circuit.

[0071] Figure 10 It is a global phasor diagram of an asynchronous motor drawn based on a unified equivalent magnetic circuit.

[0072] Figure 11 An asynchronous motor uses the main magnetic flux Ф mI A diagram serving as a public reference phasor.

[0073] Figure 12 It is an unloaded phasor diagram of an asynchronous motor drawn based on a unified equivalent magnetic circuit.

[0074] Figure 13 It is a load phasor diagram of an asynchronous motor drawn based on a unified equivalent magnetic circuit. Detailed Implementation

[0075] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] This invention proposes a unified equivalent magnetic circuit analysis and calculation method for transformers and asynchronous motors based on magnetic induction. The unified equivalent magnetic circuit is as follows: Figure 1 As shown, by magnetic reluctance Core loss equivalent magnetic inductance Equivalent magnetic induction of the secondary winding (or rotor squirrel-cage winding in an asynchronous motor) Composition. In a transformer, magnetic reluctance... Equal to its core magnetic reluctance Electrical frequency ω T This is the excitation frequency of the primary winding. Under no-load conditions, the secondary winding is inactive, and the equivalent magnetic induction... The value is 0. The transformer no-load magnetic circuit obtained based on the unified equivalent magnetic circuit is as follows: Figure 2 As shown, the corresponding magnetomotive force balance equation is:

[0077]

[0078] Where, N 1T I is the number of turns in the primary winding of the transformer.0T The effective value of the input excitation current of the primary winding of the transformer; Ф mT is the effective value of the magnetic flux flowing through the transformer's magnetic circuit; j is the imaginary number.

[0079] According to the transformer no-load magnetomotive force balance equation, I 0T The calculation formula is:

[0080]

[0081] According to the transformer no-load magnetomotive force balance equation, Ф mT Lag I 0T The formula for calculating the iron loss angle is:

[0082]

[0083] The specifications of the single-phase transformer in this implementation case are shown in Table 1. A no-load test was conducted on the transformer, and the measurement data are shown in Table 2. Based on the above formula, the parameters of the transformer under no-load conditions were calculated as shown in Table 2. It can be seen that the measured values ​​and the calculated values ​​are in good agreement.

[0084] Table 1 Specifications of Single-Phase Transformers in Implementation Cases

[0085] Transformer specifications numerical values Transformer model JR / C–3264100 Rated capacity 1kVA Original rated voltage 220V Secondary rated voltage 110V Number of turns of primary winding 340 Number of turns of secondary winding 172

[0086] Table 2 Comparison of Transformer Parameters under No-Load Conditions

[0087]

[0088] Under transformer load, the equivalent magnetic flux density of the secondary winding Begin adjusting the amplitude and phase of the magnetic flux, with a magnitude of... Where, N 2T R is the number of turns in the secondary winding of the transformer. 2T R is the resistance of the secondary winding of the transformer. LT L is the external load resistance of the transformer. LT This refers to the external load inductance of the transformer. The transformer load magnetic circuit, obtained based on the unified equivalent magnetic circuit, is as follows: Figure 3 As shown, the corresponding magnetomotive force balance equation is:

[0089]

[0090] Among them, I 1T This represents the effective value of the input current of the primary winding under load.

[0091] According to the transformer load magnetomotive force balance equation, I 1T The calculation formula is:

[0092]

[0093] According to the transformer load magnetomotive force balance equation, the magnetic flux Ф mT The lagging transformer primary winding generates magnetomotive force N. 1T I 1T phase angle θ T The calculation formula is:

[0094]

[0095] The formula for calculating the input power on the primary winding side is:

[0096]

[0097] Based on the above formula, the parameters of the transformer under load were calculated, and experimental data were measured. The comparison between the two is shown in Table 3. Under varying voltage and varying load resistance conditions, the equivalent magnetic circuit calculation results based on magnetic induction agree well with the experimental results and meet the calculation requirements under different load conditions.

[0098] Table 3 Comparison of Transformer Parameters under Load

[0099]

[0100] In an asynchronous motor, magnetic reluctance in, The core magnet of the asynchronous motor; It is a single-sided air gap magnetoresistive circuit; the electrical frequency is sω. I It is the slip frequency of the rotor relative to the rotating magnetic field of the stator; ω I It is the alternating frequency of the magnetic flux in the stator core of the asynchronous motor, and corresponds to the angular frequency at the rotor synchronous speed; equivalent magnetic induction. Where, N 2I R is the effective number of turns of the rotor squirrel-cage winding of the asynchronous motor; 2I R is the equivalent resistance of the rotor squirrel cage winding of the asynchronous motor; LI =R 2I (1-s) / s represents the simulated load resistance of the rotor's mechanical output power, and s represents the slip. The magnetic circuit of the asynchronous motor, based on the unified equivalent magnetic circuit, is as follows: Figure 4 As shown, the corresponding magnetomotive force balance equation is:

[0101]

[0102] Where, N 1I I is the number of turns in the primary winding of the asynchronous motor. 1I This represents the effective value of the input current to the primary winding of the asynchronous motor; Ф mI This represents the effective value of the magnetic flux flowing through the magnetic circuit of the asynchronous motor.

[0103] The formula for calculating the electromagnetic power of an asynchronous motor is:

[0104]

[0105] Where m is the number of phases of the asynchronous motor. The formula for calculating the output mechanical power of an asynchronous motor is:

[0106]

[0107] The formula for calculating the electromagnetic torque of an asynchronous motor is:

[0108]

[0109] Where Ω is the rotor mechanical angular velocity of the asynchronous motor.

[0110] The formula for calculating the output mechanical torque of an asynchronous motor is:

[0111] T2 = TT mech

[0112] Among them, T mech This refers to the mechanical loss torque.

[0113] The specifications of the asynchronous motor in this implementation case are shown in Table 4. The output mechanical torque of the motor was measured at 0–3000 r / min and compared with the theoretical mechanical torque calculated according to the above formula. Figure 5 As shown, the theoretical and experimental results agree well across the entire slip range, validating the effectiveness of the equivalent magnetic circuit calculation for asynchronous motor performance.

[0114] Table 4 Asynchronous Motor Specifications

[0115] Parameter name numerical values Motor model Y132S2–2 <![CDATA[Rated voltage U N / V]]> 380 <![CDATA[Rated current I N / A]]> 15 <![CDATA[Rated speed n N / (r / min)]]> 2900

[0116] The general phasor diagram of the transformer is as follows Figure 6 As shown, the steps are as follows:

[0117] Step 1: Using the main magnetic flux Ф mT As a common reference phasor during drawing, such as Figure 7 As shown;

[0118] Step 2: Based on the no-load magnetomotive force triangle, draw the no-load phasor diagram of the transformer:

[0119] The magnetic circuit balance equation corresponding to the no-load magnetomotive force triangle of the transformer is:

[0120]

[0121] The no-load phasor diagram of the transformer is drawn as follows: Figure 8 As shown.

[0122] Step 3: Based on the no-load magnetomotive force triangle, add the equivalent magnetic induction of the secondary winding under load. The magnetic potential drop is used to obtain the load magnetomotive force triangle, and the load phasor diagram is then drawn:

[0123] The equivalent magnetic flux density of the secondary winding under transformer load is:

[0124]

[0125] Based on the transformer no-load phasor diagram, the equivalent magnetic induction of the secondary winding under load is added. The magnetic potential drop above the load yields a magnetomotive force triangle, and the corresponding magnetic circuit balance equation is:

[0126]

[0127] Based on the above equations, the load phasor diagram of the transformer is drawn, as follows: Figure 9 As shown.

[0128] Step 4: After independently plotting the voltage and current phasors of the primary and secondary windings according to their respective voltage equations, they are added to the phasor diagram without needing to perform turns reduction. Furthermore, the induced electromotive force E of the primary and secondary windings... 1T E 2T The average lag of the main magnetic flux Ф m The angle is 90°, and its magnitude is proportional to the number of turns in each winding. This results in the final transformer global phasor diagram as shown below. Figure 6 As shown. Where, U 1T U 2T These are the terminal voltages of the primary and secondary windings of the transformer, respectively; E 1T E 2T These are the induced electromotive forces of the primary and secondary windings of the transformer, respectively; R 1T R 2T These are the resistances of the primary and secondary windings of the transformer, respectively; L 1σT L 2σT These are the leakage inductances of the primary and secondary windings of the transformer, respectively.

[0129] The global phasor diagram of the asynchronous motor is as follows: Figure 10 As shown, the steps are as follows:

[0130] Step 1: Using the main magnetic flux Ф mT As a common reference phasor during drawing, such as Figure 11 As shown;

[0131] Step 2: Based on the no-load magnetomotive force triangle, draw the no-load phasor diagram of the transformer:

[0132] The magnetic circuit balance equation corresponding to the no-load magnetomotive force triangle of the asynchronous motor is:

[0133]

[0134] Among them, I 0I This represents the effective value of the input current of the primary winding of the asynchronous motor under no-load conditions.

[0135] The no-load phasor diagram of the asynchronous motor is drawn as follows: Figure 12 As shown.

[0136] Step 3: Based on the no-load magnetomotive force triangle, add the equivalent magnetic induction of the rotor squirrel cage winding. The magnetic potential drop is used to obtain the load magnetomotive force triangle, and the load phasor diagram is then drawn:

[0137] The equivalent magnetic induction of the rotor squirrel-cage winding of the asynchronous motor is:

[0138]

[0139] Based on the no-load phasor diagram of the asynchronous motor, the equivalent magnetic induction of the rotor squirrel-cage winding under load is added. The magnetic potential drop yields the load magnetomotive force triangle, and the corresponding magnetic circuit balance equation is:

[0140]

[0141] Based on the above equations, the load phasor diagram of the asynchronous motor is drawn as follows: Figure 13 As shown.

[0142] Step 4: After independently plotting the voltage and current phasors of the primary winding of the asynchronous motor according to its voltage equation, they are added to the phasor diagram without needing to perform turns reduction. Furthermore, the induced electromotive force E of the primary winding... 1I Lag main flux Ф m The angle is 90°, and its magnitude is proportional to the number of turns in its winding. The final global phasor diagram of the asynchronous motor is shown below. Figure 10 As shown. Where, U 1I E is the terminal voltage of the primary winding of the asynchronous motor. 1I R is the induced electromotive force of the primary winding of the asynchronous motor; 1I L is the resistance of the primary winding of the asynchronous motor; 1σI This is the leakage inductance of the primary winding of the asynchronous motor.

[0143] The above description is only a partial embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A unified equivalent magnetic circuit analysis and calculation method for transformers and asynchronous motors based on magnetic induction, characterized in that, include: Design an equivalent magnetic circuit for a transformer and an asynchronous motor. The equivalent magnetic circuit of the transformer consists of magnetic reluctance R, equivalent magnetic induction L0 of core loss, and equivalent magnetic induction L2 of secondary winding. The equivalent magnetic circuit of the asynchronous motor consists of magnetic reluctance R, equivalent magnetic induction L0 of core loss, and equivalent magnetic induction L2 of rotor squirrel cage winding. In a transformer, the magnetic reluctance R is equal to the magnetic reluctance R of its core. FeT In an asynchronous motor, the magnetic reluctance R = R FeI +2R g , where R FeI R is the core reluctance of the asynchronous motor; g It is a single-sided air gap magnetoresistive; The external loads of the transformer and the asynchronous motor are included in the equivalent magnetic induction L2, where: The equivalent magnetic induction of the transformer is L2 = (N 2T ) 2 / [(R 2T +R LT )+jω T L LT ], where N 2T R is the number of turns in the secondary winding of the transformer. 2T R is the resistance of the secondary winding of the transformer. LT L is the external load resistance of the transformer. LT ω is the external load inductance of the transformer; j is the imaginary number; T This is the excitation frequency of the primary winding of the transformer. The equivalent magnetic induction L2 of an asynchronous motor is (N 2I ) 2 / (R 2I +R LI ), where N 2I R is the effective number of turns of the rotor squirrel-cage winding of the asynchronous motor; 2I R is the equivalent resistance of the squirrel cage winding of the asynchronous motor rotor; LI R is the simulated load resistance for the rotor's mechanical output power. LI =R 2I (1−s) / s, where s is the slip ratio.

2. The method according to claim 1, characterized in that, On the transformer, the electrical frequency ω T It is the excitation frequency of the primary winding; in an asynchronous motor, the electrical frequency sω I It is the slip frequency of the rotor relative to the rotating magnetic field of the stator, ω. I It is the alternating frequency of the magnetic flux in the stator core of the asynchronous motor, and corresponds to the angular frequency at the synchronous speed of the rotor.

3. The method according to claim 1, characterized in that, The magnetomotive force balance equation of the transformer under no-load conditions is: ， According to the transformer no-load magnetomotive force balance equation, I 0T The calculation formula is: ， According to the transformer no-load magnetomotive force balance equation, Ф mT Lag I 0T The formula for calculating the iron loss angle is: ， Where, N 1T I is the number of turns in the primary winding of the transformer. 0T The effective value of the input excitation current of the primary winding of the transformer; Ф mT This represents the effective value of the magnetic flux flowing through the transformer's magnetic circuit.

4. The method according to claim 3, characterized in that, The magnetomotive force balance equation for the transformer under load conditions is: ， Among them, I 1T This represents the effective value of the input current of the primary winding under load. According to the transformer load magnetomotive force balance equation, I 1T The calculation formula is: ， According to the transformer load magnetomotive force balance equation, the magnetic flux Ф mT The lagging transformer primary winding generates a magnetomotive force N. 1T I 1T phase angle θ T The calculation formula is: ， The formula for calculating the input power P on the primary winding side is: 。 5. The method according to claim 2, characterized in that, The magnetomotive force balance equation of the asynchronous motor under no-load conditions is: ， Where, N 1I I is the number of turns in the primary winding of the asynchronous motor. 0I This represents the effective value of the input current of the primary winding of the asynchronous motor under no-load conditions; Ф mI This represents the effective value of the magnetic flux flowing through the magnetic circuit of the asynchronous motor. The magnetomotive force balance equation for the asynchronous motor under load conditions is: ， Among them, I 1I This represents the effective value of the input current to the primary winding of the asynchronous motor. According to the magnetomotive force balance equation under asynchronous motor load conditions, I 1I The calculation formula is: ， According to the magnetomotive force balance equation under asynchronous motor load conditions, the magnetic flux Ф mI The magnetomotive force N generated by the primary winding of the lagging asynchronous motor 1I I 1I phase angle θ I The calculation formula is: ， The formula for calculating the electromagnetic power of an asynchronous motor is: ， Where m is the number of phases of the asynchronous motor, and P is the output mechanical power of the asynchronous motor. i The calculation formula is: ， The formula for calculating the electromagnetic torque T of an asynchronous motor is: ， Where Ω is the rotor mechanical angular velocity of the asynchronous motor; The formula for calculating the output mechanical torque T2 of an asynchronous motor is: ， Among them, T mech This refers to the mechanical loss torque.

6. A method for drawing a transformer phasor diagram, characterized in that, The magnetic circuit magnetomotive force balance equation under no-load conditions of the transformer as described in claim 3 and the magnetic circuit magnetomotive force balance equation under load conditions of the transformer as described in claim 4 are used to draw the equation. The drawing steps are as follows: (1) With the main magnetic flux Ф mT For public reference phasor; (2) Draw the no-load phasor diagram of the transformer based on the triangle corresponding to the no-load magnetomotive force balance equation; (3) Based on the no-load phasor diagram, add the magnetic potential drop on the equivalent magnetic induction L2 of the secondary winding under load to obtain the load magnetomotive force triangle, and draw the load phasor diagram of the transformer. (4) The voltage and current phasors of the primary winding and the secondary winding are drawn independently according to their respective voltage equations and then superimposed on the phasor diagram.

7. A method for drawing a phasor diagram of an asynchronous motor, characterized in that, The magnetomotive force balance equations for the asynchronous motor under no-load and load conditions in claim 5 are used to draw the equations. The drawing steps are as follows: (1) With the main magnetic flux Ф mI For public reference phasor; (2) Draw the no-load phasor diagram of the asynchronous motor based on the triangle corresponding to the no-load magnetomotive force balance equation; (3) Based on the no-load phasor diagram, add the magnetic potential drop on the equivalent magnetic induction L2 of the rotor squirrel cage winding under load to obtain the load magnetomotive force triangle, and draw the load phasor diagram of the asynchronous motor. (4) The voltage and current phasors of the primary winding are drawn independently according to its voltage equation and then superimposed on the phasor diagram.

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