Abstract : This paper analyzes in detail the variation of starting torque and starting current of a PWM voltage-type variable frequency speed control motor under different starting frequencies, and the impact of the skin effect caused by higher harmonics on the starting characteristics of the motor due to the significant increase in the resistance of the stator and rotor conductors. The optimal starting frequency range that satisfies both the starting torque requirements of the motor and the current requirements of the frequency converter is found, which has certain engineering reference value. Keywords: PWM variable frequency speed regulation; starting characteristics; Discussion on the best start-up frequency of conversion [align=center][b] regulating speed motor YANG Yu-ting[/b] (Shengyang Aluminum and Magnesium Engineering and Research Institute, Liaoning g,1 10001, China)[/align] Abstract: The PWM voltagec onversionr egulatings peedm otorw asa nalyzedi nt hep aper.I ncludingt hev ariationalru lefo rs start-up orsiona nds start-up current of motor under different start-up frequencies, and the influence to start-up characters of motors because of remarkable increase of the rotor conductor resistance caused by higher harmonic. This paper was very useful in finding the best start-up frequency range which fulfills the demands of motor start-up torque and bearable current of transducer. KeyWords： PWM conversionr eregulatings peed, start-upc haracte, start-upf Frequency-type variable frequency drives have advantages such as soft start, smooth speed regulation, and good energy saving in practical applications. However, due to the parasitic capacitance between the motor windings, instantaneous overcurrent of the power switch often occurs, causing the inverter protection to operate and resulting in motor starting failure. Therefore, it is very important to reasonably select the motor starting frequency. Only in this way can the starting torque be guaranteed to meet the requirements of the motor's rated torque, and the starting current not exceed 1.5 times the inverter's withstand current (1), thus fundamentally eliminating the phenomenon of motor starting failure. This is very important for optimizing the combination of inverter and motor, improving the motor's starting characteristics, reducing costs, and increasing productivity. 1 Starting characteristics of variable frequency speed control motors 1.1 Relationship between starting current and starting frequency of variable frequency speed control motors For functional variable frequency drives, the voltage-frequency relationship of their output variable frequency voltage is generally linear or piecewise linear, as shown in Figure 1. Line segment 1 represents the constant torque load characteristic, i.e., E1/f1 = C; line segment 2 represents the curve characteristic where the basic voltage-frequency ratio is constant, i.e., U1/f1 = C; line segment 3 is applicable to the load characteristics of fans and pumps. In the figure, U_a refers to the rated voltage of the power grid, in V; U_a refers to the torque boost voltage near zero frequency, and the value of U_a varies depending on the different torque loads, in V; f_f refers to the fundamental frequency of the inverter output voltage, in Hz. This article only uses the load characteristic of line segment 2 as an example. Assuming the voltage supplied to the motor by the PWM inverter is close to the standard sinusoidal inverter voltage, and ignoring the influence of higher harmonic voltages, based on the T-type equivalent circuit of the asynchronous motor, the fundamental voltage U1 and starting torque Tst of the motor are: In the above formulas, R1 is the stator resistance; R'2 is the rotor conductor resistance referred to the stator side; R is the sum of R1 and R'2; L1 is the stator leakage inductance; L'2 is the rotor leakage inductance referred to the stator side; X1 is the stator leakage reactance; X'2 is the rotor leakage reactance referred to the stator side; X is the sum of Xi and X'2; M1 is the number of phases of the motor input voltage; P is the number of pole pairs of the motor. From equation (4), it can be seen by taking the derivative with respect to fl that no matter what value U0 takes, its derivative result is greater than zero, indicating that in the range from zero frequency to power frequency, the starting current I is an increasing function of the starting frequency fl, that is, the lower the starting frequency, the smaller the starting current; the higher the starting frequency, the larger the starting current. 1.2 Relationship between starting torque and starting frequency of variable frequency speed control motor For a load curve characteristic with a basic voltage-frequency ratio of constant, i.e., Ui/fl = C, the torque boost voltage U0 = 0V. Substituting U0 = OV into equations (3) and (4), and letting k1 = Ue/50, the starting torque T"o and starting current I510 are only functions of the starting frequency fl. See equations (5) and (6) respectively: From equation (7), it can be seen that in the higher frequency stage, the starting torque Ts is inversely proportional to the starting frequency fl. In the medium frequency stage, when R and X are equal, according to equation (5), after differentiation with respect to fl, it can be seen that the derivative result is equal to zero. At this time, the starting torque reaches its maximum value, and the corresponding starting frequency is flmax. When starting at a lower frequency, according to equation (5), the derivative result with fl is greater than zero, and the starting torque increases with the increase of the starting frequency. It can be seen that the starting torque has a maximum value in the range from zero frequency to power frequency. When the starting frequency is equal to fl, the starting torque is the maximum starting torque; when the starting frequency is less than flmax, the starting torque is an increasing function of the starting frequency; when the starting frequency is greater than fl, the starting torque is a decreasing function of the starting frequency. 2 The Influence of Skin Effect on Motor Starting Characteristics At the moment of motor starting, the high-order harmonics generated by the PWM voltage output by the inverter will cause the skin effect of the stator and rotor of the motor, which will greatly increase the AC resistance of the stator and rotor and have a significant impact on the starting characteristics of the motor. According to equations (2) and (3), when the stator resistance R1 increases, the starting torque will decrease. According to equation (4), when the stator resistance Rr and the rotor resistance R' increases, the starting current will decrease, and the starting frequency f1max at the maximum starting torque will shift backward. According to equation (2), for a certain starting frequency, the starting torque is less than the starting torque without the skin effect only when (R'2)2>R2f(X fl/ 50)2. Although the skin effect of the rotor conductor is stronger than that of the stator conductor, this condition is not easy to achieve. Therefore, in general, the skin effect will not reduce the starting torque of the motor. 3 Determination of the Optimal Starting Frequency Range 3.1 Results Analysis This paper takes the starting characteristics of a squirrel-cage motor J0241-4 as an example. Given the starting torque and stator and rotor parameters of the motor at the power frequency, according to equation (5), the ratio curve of the starting torque TS to the load torque TLD of the motor when the starting frequency f changes from 0 to 50 Hz is plotted, as shown in curve 1 of Figure 2; then according to equation (6), the ratio curve of the starting current I to the rated current I when the starting frequency fl changes from 0 to 50 Hz is plotted, as shown in curve 2 of Figure 2. As can be seen from Figure 2, the variation law of starting torque and starting current with starting frequency is the same as the theoretical analysis results. Within the power frequency range, the starting torque does have a maximum value, as shown in curve 1 of Figure 2. The starting frequency fl corresponding to the maximum starting torque is about 23 Hz. When the starting frequency is less than flmax, the starting torque increases with the increase of starting frequency. When the starting frequency is greater than flmax, the starting torque decreases with the increase of starting frequency. For the starting current, within the power frequency range, the starting current is an increasing function of the starting frequency, as shown in curve 2 of Figure 2. Before the maximum starting torque occurs, the starting torque is an increasing function of the starting frequency, and the starting current is also an increasing function of the starting frequency. Therefore, the starting frequency range that satisfies the starting torque requirement and the starting frequency range that the inverter power switch requires for the starting current can be plotted separately in the figure. The common part of the two is the optimal starting frequency range of the variable frequency speed control motor. 3.2 Determination of the Optimal Starting Frequency According to the variation law of starting torque and starting current relative to the starting frequency, the optimal starting frequency range should be the starting frequency range that simultaneously satisfies the motor's requirements for starting torque and the inverter's requirements for starting current. The determination method is as follows: First, plot the starting frequency range where the ratio of starting torque Ts to load torque TLD is greater than 1.2; then, plot the starting frequency range where the ratio of starting current Isc to rated current I is less than 1.5 in the same figure; finally, plot the common part of the above two frequency ranges, which is the desired value. Taking Figure 2 as an example, when the starting torque is greater than 120% of the load torque, the starting frequency should be greater than 10. Hz, when the starting current is less than 150% of the rated current, the starting frequency should be less than 16Hz, so 10-16Hz should be the optimal starting frequency range for this variable frequency speed control motor. 4 Conclusion For variable frequency speed control motors, based on the variation law of their starting torque and starting current relative to the starting frequency, the ratio curves of starting torque and load torque, starting current and rated current of the motor at different starting frequencies are plotted in the same figure. Then, based on the requirements of the starting torque and the starting current of the inverter power switch during the starting process, the optimal starting frequency range can be determined. In addition, the skin effect caused by higher harmonics greatly increases the resistance of the stator and rotor of the motor, which reduces the starting current, but is not enough to reduce the starting torque. Therefore, the starting of a variable frequency speed control motor does not need to start from zero frequency, but should be started within the optimal starting frequency range. This can reduce the starting acceleration time of the motor, improve the starting characteristics of the motor, reduce costs, and increase productivity. References : (1) Wang Jian, et al. The influence of power filter on the power performance index of inverter-motor system (J). Basic Automation, 1998, 5: 29-32. (2) Chen Boshi. Automatic Control System for Electric Drive [M]. Machinery Industry Press (Second Edition), 1992.