TW202413982A - Calculation method of total loss of single-phase induction motor - Google Patents

Abstract

A method for calculating the total loss of a single-phase induction motor includes: calculating stator copper loss 𝑷𝒔; calculating the sum of iron loss and mechanical loss, the formula for the sum of iron loss and mechanical loss is: no-load input power 𝑷𝟎 - no-load stator copper loss 𝑷𝒔𝟎; calculating rotor copper loss, the formula for rotor copper loss is: (input power 𝑷𝟏-stator copper loss 𝑷𝒔-no-load input power 𝑷𝟎 + no-load stator copper loss 𝑷𝒔𝟎) × Slip S; calculate stray loss 𝑷𝑳𝑳; and calculate total loss. The formula for total loss is: stator copper loss 𝑷𝒔 + (no-load input power 𝑷𝟎 – no-load stator copper loss 𝑷𝒔𝟎) + (input power 𝑷𝟏-stator copper loss 𝑷𝒔-no-load input power 𝑷𝟎 + no-load stator copper loss 𝑷𝒔𝟎) × slip S + stray loss 𝑷𝑳𝑳; Among them, when the input voltage of a single-phase induction motor remains unchanged, the iron loss is negatively correlated with the load rate of the single-phase induction motor.

Description

Calculation method of total loss of single-phase induction motor

The present invention is a method for calculating motor energy loss, and in particular, a method for calculating various energy losses and total energy losses of a single-phase induction motor.

Induction motors use a rotating magnetic field to induce current in the rotor, thereby generating torque and rotating. In a single-phase induction motor, the rotor is a squirrel cage type. In order to generate a rotating magnetic field during starting, the stator windings of a single-phase induction motor include two types of windings: the run winding or main winding and the start winding or auxiliary winding. The two windings are arranged at a 90-degree motor angle difference.

According to the IEEE (Institute of Electrical and Electronic Engineers, IEEE) Standard (Std) 114, the loss of single-phase induction motors can be divided into five categories, including 1. Stator copper loss 2. Rotor copper damage 3. Iron damage 4. Mechanical damage and 5. Dissipation Among them, stator copper loss is the loss of current flowing through the stator coil and the rotor copper loss It is the loss caused by the rotor current passing through the rotor resistance. It refers to the energy lost in the iron core due to the influence of the changing magnetic field on the magnetic conductor. In the conventional technology, iron loss is For a certain value, mechanical damage Usually refers to the energy loss caused by the fan in a single-phase induction motor. Losses that do not fall into the above four categories are classified as stray losses. In the conventional art, the total loss of a single-phase induction motor is Stator copper loss + Rotor copper loss +Iron damage +Mechanical damage +Miscellaneous loss Among them, the basic assumption of known technology and known measurement regulations for iron loss is that iron loss is proportional to the square of the input voltage and has nothing to do with the load.

On the other hand, if the dynamometer method is used to calculate the total loss, the total loss of a single-phase induction motor under each load is the input electrical power minus the mechanical output power. The input electrical power - Mechanical output power .

However, after actual measurement, it was found that the total motor loss calculated by the conventional method (IEEE Std 114) was not equal to the total loss measured by the dynamometer. The actual measured values are shown in Table 1 below. Load factor % 0% 25% 50% 75% 100% 115% Voltage(V) Main Story 115.13 115.09 115.13 115.14 115.10 115.13 Auxiliary line 141.64 139.48 135.92 132.75 129.18 126.93 Capacitance 192.62 189.95 184.52 179.09 174.08 171.25 Current(A) Input 1.34 1.68 2.20 2.86 3.67 4.16 Main Story 2.99 2.58 2.40 2.54 2.98 3.34 Auxiliary line 2.61 2.57 2.49 2.42 2.35 2.31 Input power Watt 88.55 161.83 236.98 316.85 410.57 466.78 Cause % 57.57 83.62 93.57 96.06 97.22 97.56 Torque Kg-cm 0.00 2.29 4.55 6.74 9.18 10.60 Speed RPM 3600 3564 3531 3496 3453 3425 Motor efficiency % 0.00 51.89 69.60 76.38 79.27 79.91 Main line resistance Ohm 2.05 2.05 2.05 2.05 2.05 2.05 Auxiliary line resistance + capacitor equivalent resistance 2.96 2.96 2.96 2.96 2.96 2.96 No-load stator copper loss Watt 38.54 Iron damage Watt 50.01 50.01 50.01 50.01 50.01 50.01 Stator copper loss Watt 33.23 30.22 30.58 34.57 38.67 Rotor copper loss Watt 0.79 3.00 6.83 13.31 18.28 Total loss calculated according to IEEE 114 (known method) (excluding scattered loss) Watt 84.02 83.23 87.41 97.89 106.96 Total loss of actual measurement of dynamometer (including scattered loss) Watt 77.85 72.04 74.83 85.12 93.78 Table I

From Table 1 above, we can see that at load rates of 25%, 50%, 75%, 100% and 115%, the total motor losses calculated according to IEEE Std 114 are 84.02W, 83.23W, 87.41W, 97.89W and 106.96W respectively. At load rates of 25%, 50%, 75%, 100% and 115%, the total losses actually measured by the dynamometer are 77.85W, 72.04W, 74.83W, 85.12W and 93.78W respectively. Therefore, the total loss calculated by the known method (IEEE Std 114) is greater than the total loss actually measured by the dynamometer, indicating that the calculation method of the known method (IEEE Std 114) has room for improvement. This problem has always existed in the industry and needs to be solved.

[Problem to be solved by the invention] From the above-mentioned prior art, it can be seen that the current method for calculating the total loss of a single-phase induction motor has the problem of not being able to reflect the actual loss. Therefore, it is necessary to provide a new calculation method that can accurately calculate the total loss of a single-phase induction motor.

[Technical means to solve the problem] A method for calculating the total loss of a single-phase induction motor, including: calculating a stator copper loss 𝑷𝒔; calculating the sum of an iron loss and a mechanical loss, the formula for the sum of the iron loss and the mechanical loss is: no-load input power 𝑷𝟎 - no-load stator copper loss 𝑷𝒔𝟎; calculating a rotor copper loss, the formula for the rotor copper loss is: (input power 𝑷𝟏-the stator copper loss 𝑷𝒔-the no-load input power 𝑷𝟎 + the no-load stator copper loss 𝑷𝒔𝟎) × slip S; calculate a stray loss 𝑷𝑳𝑳; and calculate the total loss, the total loss formula is: the stator copper loss 𝑷𝒔 + (the no-load input power 𝑷𝟎 – the no-load stator copper loss 𝑷𝒔𝟎) + (the input power 𝑷𝟏-the stator copper loss 𝑷𝒔-the no-load input power 𝑷𝟎 + the no-load stator copper loss 𝑷𝒔𝟎) × the slip S + The stray loss 𝑷𝑳𝑳; wherein, when the input voltage of the single-phase induction motor remains unchanged, the iron loss is negatively correlated with a load rate of the single-phase induction motor.

Preferably, the negative correlation coefficient is between 0.8 and 1.

Preferably, in a phase relationship of an equivalent circuit of the single-phase induction motor, the sum of the current angles of a main line and an auxiliary line of the single-phase induction motor is further measured, the current angle of the main line being the angle between a line voltage and a main winding current in the phase relationship of the equivalent circuit, the current angle of the auxiliary line being the angle between the line voltage and an auxiliary winding current in the phase relationship of the equivalent circuit, and the iron loss is positively correlated with the sum of the current angles of the main line and the auxiliary line.

Preferably, the positive correlation coefficient is between 0.8 and 1.

Preferably, in an equivalent circuit of the single-phase induction motor, an auxiliary line voltage of the single-phase induction motor is further measured, and the iron loss is positively correlated with the square of the auxiliary line voltage.

Preferably, the calculation method is based on the specification of IEEE (Institute of Electrical and Electronic Engineers) Standard 114.

Preferably, the spurious loss 𝑷𝑳𝑳 is calculated according to the formula suggested by the patent, which is: the spurious loss 𝑷𝑳𝑳 = spurious factor × .

[Effect of the invention] From the above content, it can be seen that the present invention provides a new calculation method that can more accurately analyze the values and proportions of various losses in a single-phase induction motor at different load points. Furthermore, the present invention further discovered that iron loss is closely related to the load rate, the phase difference between the main and auxiliary line currents, and the square of the auxiliary line voltage, including that iron loss is negatively correlated with the load rate, iron loss is positively correlated with the sum of the angles between the main and auxiliary line currents, and iron loss is positively correlated with the square of the auxiliary line voltage. The calculation method of the present invention and the correlation between iron loss and load factor, main-auxiliary line current phase difference and auxiliary line voltage square effectively assist designers and manufacturers to more accurately measure the various losses of single-phase induction motors (motors), and further serve as a basis for further design optimization and improvement.

The following is a more detailed description of the implementation of the present invention with reference to the drawings and component symbols, so that those skilled in the art can implement the invention accordingly after reading this specification.

FIG. 1 is a flow chart for illustrating a method for calculating the total loss of a single-phase induction motor according to an embodiment of the present invention. Referring to FIG. 1 , the method for calculating the total loss of a single-phase induction motor of the present invention includes steps S10 to S50. Step S10 is to calculate a stator copper loss 𝑷𝒔; Step S20 is to calculate the sum of an iron loss and a mechanical loss, the sum of which is calculated as follows: no-load input power 𝑷𝟎 - no-load stator copper loss 𝑷𝒔𝟎; Step S30 is to calculate a rotor copper loss, the rotor copper loss is calculated as follows: (input power 𝑷𝟏 - the stator copper loss 𝑷𝒔 - the no-load input power 𝑷𝟎 + The no-load stator copper loss 𝑷𝒔𝟎) × slip S; step S40 is to calculate a stray loss 𝑷𝑳𝑳; and step S50 is to calculate the total loss, the total loss formula is: the stator copper loss 𝑷𝒔 + (the no-load input power 𝑷𝟎 – the no-load stator copper loss 𝑷𝒔𝟎) + (the input power 𝑷𝟏-the stator copper loss 𝑷𝒔-the no-load input power 𝑷𝟎 + the no-load stator copper loss 𝑷𝒔𝟎) × the slip S + The stray loss 𝑷𝑳𝑳; wherein, when the input voltage of the single-phase induction motor remains unchanged, the iron loss is negatively correlated with a load rate of the single-phase induction motor.

The calculation implementation of each step will now be described in detail, wherein the calculation method of the present invention is further calculated based on the background of the known method (IEEE Std 114). In step S10, the stator copper loss 𝑷𝒔 is calculated, and its formula is = ,in, = Mains current, = Mains resistance, = Auxiliary current, = Auxiliary line resistance.

In step S20, the sum of an iron loss and a mechanical loss is calculated. The formula is: = - - , will damage the iron After adjusting the formula, we can get = – ,in, = no-load input power, = No-load stator copper loss, = Mechanical damage, therefore iron damage and mechanical damage The formula for the sum of is: = – It is worth mentioning that, in order to further discover the relationship between iron loss and total loss of single-phase induction motor, the heat dissipation fan in the single-phase induction motor is removed, and the heat dissipation fan is the main source of mechanical loss in the single-phase induction motor. Therefore, after the heat dissipation fan is removed, the mechanical loss can be ignored, and iron loss and mechanical damage The formula for the sum of the above is: no-load input power 𝑷𝟎 - no-load stator copper loss 𝑷𝒔𝟎. In other embodiments of the present invention, a heat dissipation fan may be installed and the mechanical loss may be taken into account.

In step S30, the rotor copper loss is calculated. The calculation formula has been changed. In the conventional technology, the rotor copper loss The formula is: = - - - ) ,in, = Input power, = stator copper loss, = Iron loss, = Mechanical damage, = slip. In the present invention, the above formula is further = – Bringing in knowledge and technology to rotor copper loss Formula, thus the rotor copper loss of the present invention can be obtained formula: = ( - ) , that is, (input power 𝑷𝟏-stator copper loss 𝑷𝒔-no-load input power 𝑷𝟎 + no-load stator copper loss 𝑷𝒔𝟎) × slip S.

In step S40, a stray loss 𝑷𝑳𝑳 is calculated, wherein the stray loss 𝑷𝑳𝑳 can be estimated from the following Table 2. Among them, those that are basically not copper loss, iron loss and mechanical loss are all classified as stray losses, and the stray factor is determined by the load loss generated by the high-order harmonics of the air gap magnetic field in the single-phase induction motor, including surface loss, lateral current loss, pulse loss, high-frequency loss, leakage flux loss, etc. = Scattering factor =Input Power Table II

In step S50, the total loss of the single-phase induction motor is calculated. , and the total loss in learning technology The formula is + + + + , and after the recalculation of the present invention, the above formula (iron loss + mechanical loss) is = – And the formula for rotor copper loss = ( - ) Total loss of knowledge technology The total loss of the present invention can be obtained by using the formula The formula is: - + ( - ) + , that is, stator copper loss 𝑷𝒔 + (no-load input power 𝑷𝟎 – no-load stator copper loss 𝑷𝒔𝟎) + (input power 𝑷𝟏-stator copper loss 𝑷𝒔-no-load input power 𝑷𝟎 + no-load stator copper loss 𝑷𝒔𝟎) × slip S + stray loss 𝑷𝑳𝑳, that is, total loss = stator copper loss + (iron loss + mechanical loss) + (rotor copper loss) + stray loss. Furthermore, as described above, the present invention eliminates mechanical losses, so the total loss = stator copper loss + (iron loss) + (rotor copper loss) + stray loss.

In the present invention, the total loss of a single-phase induction motor is further calculated by the formula of the present invention, and the calculated total loss is compared with the total loss actually measured by the dynamometer. The comparison table is shown in Table 3 below. Load factor % 0% 25% 50% 75% 100% 115% Voltage(V) Main Story 115.13 115.09 115.13 115.14 115.10 115.13 Auxiliary line 141.64 139.48 135.92 132.75 129.18 126.93 Capacitance 192.62 189.95 184.52 179.09 174.08 171.25 Current(A) Input 1.34 1.68 2.20 2.86 3.67 4.16 Main Story 2.99 2.58 2.40 2.54 2.98 3.34 Auxiliary line 2.61 2.57 2.49 2.42 2.35 2.31 Input power Watt 88.55 161.83 236.98 316.85 410.57 466.78 Cause % 57.57 83.62 93.57 96.06 97.22 97.56 Torque Kg-cm 0.00 2.29 4.55 6.74 9.18 10.60 Speed RPM 3600 3564 3531 3496 3453 3425 Motor efficiency % 0.00 51.89 69.60 76.38 79.27 79.91 Main line resistance Ohm 2.05 2.05 2.05 2.05 2.05 2.05 Auxiliary line resistance + capacitor equivalent resistance 2.96 2.96 2.96 2.96 2.96 2.96 No-load stator copper loss Watt 38.54 Iron damage Watt 50.01 39.68 32.55 28.89 26.00 23.90 Stator copper loss Watt 33.23 30.22 30.58 34.57 38.67 Rotor copper loss Watt 0.89 3.34 7.44 14.29 19.54 Dispersion loss Watt 4.05 5.92 7.92 10.26 11.67 Total losses calculated according to this invention Watt 77.85 72.04 74.83 85.12 93.78 Actual measured total loss Watt 77.85 72.04 74.83 85.12 93.78 Table 3

As can be seen from Table 3 above, compared with the calculation method of the prior art, the calculation method of the present invention can more accurately calculate the actual total loss of the single-phase induction motor, thus avoiding the problem that the calculated value is inconsistent with the actual loss.

FIG2 is a schematic diagram for explaining the relationship between iron loss and load rate of an embodiment of the present invention. Please refer to FIG2 and Table 3 above. It can be further known from Table 3 above that the iron loss of a single-phase induction motor is not a fixed value as described in Table 1 in the prior art of the present invention. According to the iron loss formula of the present invention, = – Calculations show that the iron loss is 39.68W, 32.55W, 28.89W, 26.00W and 23.90W at load rates of 25%, 50%, 75%, 100% and 115% respectively. From the relationship diagram in Figure 2, it can be seen that when the input voltage of a single-phase induction motor remains unchanged, the iron loss is negatively correlated with the load rate. At this value, the correlation coefficient falls between 0.8-1, and the best value is 0.9618.

FIG3 is a circuit diagram for illustrating an equivalent circuit of a single-phase induction motor of an embodiment of the present invention. Referring to FIG3, in an embodiment of the calculation method of the present invention, a main line current angle and an auxiliary line current angle of the single-phase induction motor are further measured and calculated, and in the present invention, the angles of these angles are measured and calculated by using an equivalent circuit and a phase angle relationship diagram. The equivalent circuit 1 of the single-phase induction motor includes a rotor 10, a line voltage 101, a main winding inductance 201, a main winding resistance 203, an auxiliary winding inductance 301, an auxiliary winding resistance 303, and an auxiliary winding capacitance 401. Among them, the line voltage 101 is the input voltage, the input current Will be split into a main winding current and an auxiliary winding current There is no series capacitor in the main winding circuit, so the main winding current will lag behind the line voltage 101. The auxiliary winding has an auxiliary winding capacitor 401, so the auxiliary winding current flowing through the auxiliary winding will lead the line voltage 101. In addition, the line voltage 101, the main winding inductance 201, the main winding resistance 203, the auxiliary winding inductance 301, the auxiliary winding resistance 303 and the auxiliary winding capacitance 401 can also be expressed as the line voltage , Main Winding Inductive Reactance , Main Winding Resistance , Auxiliary Winding Inductive Reactance , Auxiliary Winding Resistance And auxiliary winding capacitance .

FIG4 is a schematic diagram for explaining the phase angle relationship in the equivalent circuit of an embodiment of the present invention. Please refer to FIG3 and FIG4, FIG4 is a diagram showing the relationship between the magnitude and phase of each branch current of the equivalent circuit 1. and auxiliary winding current From the analysis, we can see that the main winding current Will lag behind the line voltage , so the main line current angle Line voltage and main winding current The angle between the auxiliary winding current Will lead the line voltage , so the auxiliary line current angle Line voltage Auxiliary winding current In addition, the input current angle Line voltage and input current The phase angle of each current can be measured by a power meter.

Furthermore, the main line current angle and auxiliary line current angle The relationship between the sum of and iron loss is shown in Table 4 below. The sum of the main and auxiliary line current angles deg 141.92 126.56 109.62 93.82 86.97 Iron damage Watt 39.68 32.55 28.89 26.00 23.90 Table 4

FIG5 is a schematic diagram for explaining the relationship between the iron loss and the sum of the main and auxiliary line current angles of an embodiment of the present invention. Please refer to FIG5 and Table 4 above. In an embodiment of the present invention, when the iron loss is 39.68W, 32.55W, 28.89W, 26.00W and 23.90W, the sum of the main and auxiliary line current angles ( ) are 141.92 degrees, 126.56 degrees, 109.62 degrees, 93.82 degrees and 86.97 degrees. In other words, when the input voltage of a single-phase induction motor remains unchanged, the iron loss is positively correlated with the sum of the main and auxiliary line current angles. Under this value, the correlation coefficient falls between 0.8-1, and the best is 0.9638.

On the other hand, the relationship between the square of the auxiliary line voltage and the iron loss is shown in Table 5 below: Mains voltage Volt 115.09 115.13 115.14 115.10 115.13 Auxiliary line voltage Volt 139.48 135.92 132.75 129.18 126.93 Auxiliary line voltage square Volt 19454.67 18474.25 17622.56 16687.47 16111.22 Iron damage Watt 39.68 32.55 28.89 26.00 23.90 Table 5

FIG6 is a relationship diagram for illustrating the relationship between iron loss and auxiliary line voltage square of an embodiment of the present invention. Referring to FIG6 and Table 5 above, in an embodiment of the present invention, the auxiliary line voltage of the single-phase induction motor is further measured to find the relationship between the auxiliary line voltage square and iron loss. When the iron loss is 39.68W, 32.55W, 28.89W, 26.00W and 23.90W, the auxiliary line voltage square is 19454.67V, 18474.25V, 17622.56V, 16687.47V and 16111.22V respectively. In other words, when the input voltage of a single-phase induction motor remains constant, the iron loss is positively correlated with the square of the auxiliary line voltage.

From the above description, it can be seen that the present invention solves the contradiction that the sum of the losses in the current regulations is greater than the input power minus the output power. For the loss measurement of single-phase induction motors, the present invention provides a new calculation method, which can more accurately analyze the value and proportion of each loss at different load points.

Furthermore, the present invention further proposes three measurement calculation methods for iron loss for more accurate measurement, and finds that iron loss is closely related to load factor, main-auxiliary current phase difference, and auxiliary voltage square, including that iron loss is negatively correlated with load factor, iron loss is positively correlated with the sum of main-auxiliary current angles, and iron loss is positively correlated with auxiliary voltage square. The calculation method of the present invention and the correlation between iron loss and load factor, main-auxiliary current phase difference, and auxiliary voltage square can effectively assist designers and manufacturers to more accurately measure various losses of single-phase induction motors (motors), and further serve as a basis for further design optimization and improvement.

1: Equivalent circuit 10: Rotor 101: Line voltage 201: Main winding inductance 203: Main winding resistance 301: Auxiliary winding inductance 303: Auxiliary winding resistance 401: Auxiliary winding capacitance :Input current :Main winding current :Auxiliary winding current :Line voltage :Main Winding Inductive Reactance :Main winding resistance :Auxiliary winding inductive reactance :Auxiliary Winding Resistance :Auxiliary winding capacitance :Main line current angle :Auxiliary line current angle : Input current angle S10-S50: Step

After reading the detailed description below with reference to the attached figures, a person with ordinary knowledge in the field can have a better understanding of the various aspects of the present invention and its specific features and advantages, wherein the attached figures include: FIG. 1 is a flow chart of a method for calculating the total loss of a single-phase induction motor of an embodiment of the present invention. FIG. 2 is a schematic diagram of the relationship between iron loss and load rate of an embodiment of the present invention. FIG. 3 is an equivalent circuit diagram of a single-phase induction motor of an embodiment of the present invention. FIG. 4 is a schematic diagram of the phase angle relationship in the equivalent circuit of an embodiment of the present invention. FIG. 5 is a schematic diagram of the relationship between iron loss and the sum of the main and auxiliary line current angles of an embodiment of the present invention. Figure 6 is a schematic diagram showing the relationship between iron loss and the square of the auxiliary line voltage in an embodiment of the present invention.

S10-S50: Steps

Claims (7)

A method for calculating the total loss of a single-phase induction motor includes: Calculating a stator copper loss 𝑷𝒔; Calculating the sum of an iron loss and a mechanical loss, the formula for the sum of the iron loss and the mechanical loss is: no-load input power 𝑷𝟎 - no-load stator copper loss 𝑷𝒔𝟎; Calculating a rotor copper loss, the formula for the rotor copper loss is: (input power 𝑷𝟏-the stator copper loss 𝑷𝒔-the no-load input power 𝑷𝟎 + the no-load stator copper loss 𝑷𝒔𝟎)× slip S; Calculate a stray loss 𝑷𝑳𝑳; and Calculate the total loss, the total loss formula is: the stator copper loss 𝑷𝒔 + (the no-load input power 𝑷𝟎 – the no-load stator copper loss 𝑷𝒔𝟎) + (the input power 𝑷𝟏-the stator copper loss 𝑷𝒔-the no-load input power 𝑷𝟎 + the no-load stator copper loss 𝑷𝒔𝟎) × the slip S + the stray loss 𝑷𝑳𝑳; Among them, when the input voltage of the single-phase induction motor remains unchanged, the iron loss is negatively correlated with a load rate of the single-phase induction motor. As in the calculation method of claim 1, wherein the negative correlation coefficient is between 0.8 and 1. As in the calculation method of claim 1, in the phase relationship of an equivalent circuit of the single-phase induction motor, the sum of the current angles of a main line and an auxiliary line of the single-phase induction motor is further measured, the current angle of the main line is the angle between a line voltage and a main winding current in the phase relationship of the equivalent circuit, the current angle of the auxiliary line is the angle between the line voltage and an auxiliary winding current in the phase relationship of the equivalent circuit, and the iron loss is positively correlated with the sum of the current angles of the main line and the auxiliary line. As in the calculation method of claim 3, wherein the positive correlation coefficient falls between 0.8 and 1. As in the calculation method of claim 1, in an equivalent circuit of the single-phase induction motor, an auxiliary line voltage of the single-phase induction motor is further measured, and the iron loss is positively correlated with the square of the auxiliary line voltage. The calculation method of claim 1, wherein the calculation method is based on the specification of IEEE (Institute of Electrical and Electronic Engineers) standard 114. For example, the calculation method of item 1, where the calculation formula of the spurious loss 𝑷𝑳𝑳 is: the spurious loss 𝑷𝑳𝑳 = spurious factor × .

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