1. Introduction To save energy and improve process control, more and more industrial processes are using frequency converters (VDCs) to improve the overall efficiency of production systems. The PWM pulse voltage output by a VDC has rich harmonic components, high pulse frequency, and a steep rise edge. This is very different from driving a motor with a 50Hz AC sine wave. During energy conversion, losses inevitably occur inside the motor, causing its temperature to rise. When the temperature rise exceeds the maximum allowable operating temperature, the motor's lifespan will be significantly shortened. Therefore, studying the temperature rise problem of motors and its mitigation strategies is very important. Furthermore, due to the complex structure of motors and different heat dissipation conditions, the temperature distribution and temperature rise of various parts inside the motor are not entirely the same; however, there is currently very little specific data available for reference. This paper first introduces the temperature rise limit of motors, then explains the temperature rise problem of motors under VDC power supply conditions through a combination of experimental data and principle analysis, and finally introduces strategies to mitigate the temperature rise. 2. Temperature Rise Limit of Motors The commonly used insulation materials in motors are classified into five levels according to their heat resistance: A, E, B, F, and H. Class A insulation uses organic materials such as cotton yarn, silk, and paper that have been impregnated or immersed in oil during use. Class E insulation is an insulating film made of polyester resin, epoxy resin, and triacetate fiber. The basic materials for Class B, F, and H insulation are mica, asbestos, and glass fiber, but the heat resistance of the impregnating varnish varies. Table 1 lists the maximum permissible operating temperatures for each class of insulation. The above heat resistance refers to the ability to operate at that temperature for an extended period. When the operating temperature exceeds the maximum permissible operating temperature, the service life will be rapidly shortened. Tests show that for Class A insulation, if it is consistently maintained at 90–95℃, its service life can reach 20 years; when the operating temperature is above 95℃, for every 8℃ increase in temperature, the service life of the insulation will be reduced by half (commonly known as the 8℃ rule); for example, if it is consistently operating at 110℃, the service life will only be 4–5 years. General electric motors mostly use Class E and Class B insulation. Electric motors required for use in high-temperature environments, such as hoisting and metallurgical motors, often use Class F and Class H insulation. The temperature difference between a certain part of an electric motor and the temperature of the surrounding cooling medium is called the temperature rise of that part, generally denoted by θ. Once the insulation material used for that part is determined, the maximum allowable operating temperature of the part is also determined. At this point, the temperature rise limit depends on the temperature of the cooling medium. The higher the temperature of the cooling medium, the lower the allowable temperature rise. Considering the significant variations in ambient temperature across different regions and seasons in China, the national standard GB755-87 (Basic Technical Requirements for Electric Motors) clearly stipulates that, at altitudes below 1000m, the ambient air temperature is specified as 40℃. When the highest ambient temperature exceeds 40℃ by δt0 (δt0 not exceeding 20℃), the temperature rise limit should be reduced accordingly by δt0; if it is below 40℃, the temperature rise limit generally remains unchanged. When the altitude is above 1000m but not exceeding 4000m, the temperature rise limit is corrected according to the altitude difference between the test and usage locations. After the electric motor is trial-produced, a temperature rise test must be conducted to determine its actual temperature rise. Because different measurement methods yield different results, the temperature rise limit should be specified along with the measurement method. There are three commonly used methods: thermometer method, resistance method, and embedded thermometer method. The maximum allowable temperature of components specified in national standards also varies depending on the measurement method. For example, when the ambient air temperature is 40℃, the temperature rise limit for the AC winding of an AC motor below 5000kW using Class B insulation is specified as follows: resistance method—80℃; thermometer method—90℃; after adding the ambient temperature, the value is lower than or equal to the allowable operating temperature of Class B materials. 3. Temperature Rise of Motors under Variable Frequency Power Supply For motors powered by variable frequency drives, the presence of high-order harmonics will cause the following additional losses inside the motor: (1) Additional copper losses in the stator and rotor caused by high-order harmonics; (2) Additional iron losses in the stator caused by high-order harmonics; (3) Additional stray losses caused by high-order harmonics; (4) When a three-phase asynchronous motor runs at high frequency, the skin effect increases the rotor resistance, leading to a significant increase in slip copper losses. These additional losses caused by high-order harmonic voltage and current result in an increase in motor temperature rise. On the other hand, for ordinary standard motors, the cooling fan is directly mounted on the rotor shaft. When the motor runs at low frequency, the cooling effect decreases significantly, which will further exacerbate the increase in motor temperature rise. The relationship between motor temperature rise and the cooling effect produced by the cooling airflow is usually: where q is the cooling airflow and n is the motor speed. If the losses generated by the motor remain unchanged, the temperature rise is inversely proportional to the 0.4 to 0.5 power of the speed. In summary, when motors, especially ordinary motors, are powered by variable frequency drives, the temperature rise of the motor will increase due to both heat generation and heat dissipation. Increased temperature rise in electric motors affects the lifespan of the windings, limits the motor's output, and can even burn out the motor in severe cases. Experimental results of actual temperature rise measurements are very useful for understanding the temperature distribution patterns of electric motors, especially the impact of frequency converters on temperature rise. Using a three-phase, four-pole, 230V, 2.2kW squirrel-cage induction motor as the experimental object, the temperature rise was compared using a typical SPWM frequency converter (operating at 50Hz) and a mains frequency sinusoidal power supply. Using specialized design and manufacturing methods, 20 thermistor sensors (stable and high-precision) were placed or embedded within the motor body (stator, rotor, air gap, and housing), with three sensors placed in the rotor. The stator end winding sensors are located at the radial center of the stator windings (positions 1 and 10). Generally, the average temperature of the two sensors at the shaft extension end and the fan end is taken as the final temperature. The temperature sensor layout is shown in Figure 1. Figure 1. Temperature Sensor Distribution Diagram. Sensor Installation Location Description: Rotor: 13 (shaft center), 14 (shaft extension side surface), 15 (fan side surface); Stator winding end: 1 (shaft extension side), 10 (fan side); Stator core slot: 17 (shaft extension side), 4 (fan side); Air gap in the housing: 8 (shaft extension side), 19 (shaft extension side near stator winding), 20 (fan side); Motor housing: 6. Under both mains frequency sinusoidal and variable frequency power supply conditions, a large amount of data is measured at each temperature point, and the temperature curve for that point is obtained using the least squares method. Figure 2 shows the temperature curves at each measurement point under full load conditions when powered by both the variable frequency drive and the sinusoidal power supply. Figure 3 shows the temperature curves of the motor powered by the variable frequency drive under different load conditions (operating frequency 50 Hz). Figure 4 shows the temperature curves under different load conditions when powered by a sinusoidal wave. Figure 2 shows the temperature curve under full load. Figure 3 shows the temperature curve under different load conditions. Figure 4 shows the temperature curves under different load conditions with sinusoidal power supply. It is evident that the temperature curves show the same upward trend under both inverter and sinusoidal power supply conditions. The additional temperature rise caused by inverter harmonics is relatively large, around 7°C on the stator side (position 1) and approximately 15°C on the rotor side (position 13). The above results also apply to induction motors of other capacities with similar structural materials. Furthermore, the temperature distribution varies greatly across different parts of the motor. The temperature of the stator end winding (position 1) is lower than that of the stator center (position 17) because the cooling conditions of the stator end winding are better. Simultaneously, due to the cooling effect of the fan, the temperature of the stator end winding (position 10) and the air gap temperature (position 20) on the fan side are both lower than those on the corresponding shaft extension side (position 1) and the air gap temperature (position 8). Due to the complexity of heat transfer and the inconsistency of cooling conditions, the relationship between temperature and losses is non-linear. For square torque loads, the load torque decreases at low speeds, reducing motor copper losses and heat generation. Although cooling capacity decreases at low speeds (e.g., with self-cooling or self-ventilated motors), the increase in motor temperature rise is not significant. For constant torque loads, the load torque remains constant at low speeds, and motor copper losses and heat generation are not less than at high speeds, but cooling capacity decreases, resulting in a substantial increase in motor temperature rise. Special attention must be paid during use. Table 2 shows the measured data on the effect of speed on temperature rise of a Y100i2-4 self-ventilated motor under inverter power supply conditions. Table 2: Measured data on the effect of speed on temperature rise of a self-ventilated motor. As can be seen from the table, although the motor torque and output power decrease with decreasing frequency (i.e., heat generation decreases), the motor temperature increases, especially when the motor operates below 30Hz. Therefore, it is almost inevitable that the temperature rise of a motor will increase after frequency conversion, especially for ordinary motors operating at low speeds, where overheating is highly likely. Therefore, understanding methods to mitigate motor temperature rise is crucial. 4. Countermeasures to alleviate motor temperature rise Temperature rise is a key factor affecting the service life of motors, and the "8℃ theorem" of motor temperature rise is evidence of this view. As mentioned above, the temperature rise of motors when powered by frequency converters will be significantly higher than that when powered by power frequency. Generally, the lower the operating frequency of the motor, the higher the temperature rise. It is necessary to take measures to limit or alleviate the increase in motor temperature rise and ensure the safe operation of equipment. Under the selected conditions of motor, limiting or alleviating motor temperature rise is nothing more than two aspects: one is to reasonably reduce losses, that is, reduce heat generation; the other is to improve cooling conditions so that heat energy can be effectively dissipated. The fundamental measures to reduce losses are to suppress harmonics and limit load torque. The specific measures are as follows: (1) Take various measures to suppress harmonics, such as adding filters on the output side of the frequency converter to improve the output harmonic performance and reduce the additional losses caused by high-order harmonics. (2) Adjust the "carrier frequency" parameter reasonably to improve harmonic performance and reduce various losses of motors. It is generally believed that if the carrier frequency is moderately increased, the content of high-order harmonics will be reduced and the motor loss will be small. However, it must be noted that: an excessively high carrier frequency will exacerbate the impact voltage of the motor, which is detrimental to the motor insulation, and the losses of the inverter itself will increase. Therefore, the carrier frequency setting should not be too high. (3) For situations where the load is reduced or the motor is running under light load, the inverter output voltage should be reduced appropriately, i.e., the u/f given value should be reduced. (4) For situations where the load is reduced, the maximum operating frequency limit should be appropriately reduced to reduce the motor output. (5) The capacity of the motor and the inverter should be appropriately increased to reduce their load factor. In addition, if the production process allows, using the motor under light load is also a simple and effective method. Figure 5 shows an example of the permissible continuous operating torque and short-time maximum torque characteristics of the motor when the inverter capacity and the motor capacity are combined in a 1:1 ratio. These characteristics vary depending on the type and structure of the motor, and detailed information needs to be studied based on the data provided by each manufacturer. Figure 5 Permissible continuous operating torque and maximum torque In Figure 5, the permissible continuous operating torque represents the permissible torque value that can limit the motor temperature rise to within the specified value when the general motor is running continuously. If a motor is continuously operated at 20Hz using a 220V, 60Hz power supply, and the load torque is within 80% of the motor's rated value, the motor's temperature rise will not exceed the specified value. The maximum torque represents the maximum torque value that a general-purpose motor can generate when driven by a frequency converter. This torque value cannot be used for continuous operation, so it is a short-time rating. Specific measures to improve heat dissipation capacity: (1) Select a frequency converter-specific motor or use a forced-ventilation motor. (2) Modify the existing equipment and install a dedicated cooling fan. In addition, if the production process allows, limiting the minimum operating frequency of the motor to ensure the cooling capacity of the self-ventilated motor at low speed is also a simple and effective method. It is worth noting that most of the commonly used small and medium-sized AC motors are designed for constant frequency/constant voltage (50Hz/380V). In order to reduce costs, these motors are all equipped with fan-type cooling, and the cooling air volume is basically designed according to the rated speed of the motor. The problem of the heat dissipation capacity of the self-ventilated motor is rarely considered after the motor speed is adjusted (reduced). With the widespread use of frequency converters today, this type of motor is actually no longer suitable for the requirements of variable frequency speed control, making variable frequency motors one of the ideal choices. Compared to ordinary AC motors, variable frequency motors are currently expensive, making them unaffordable for many companies. Upgrading the cooling method of small and medium-sized motors, specifically adopting a fan-cooled system—a cooling method previously used primarily for large motors—is a simple, effective, and cost-efficient solution. When upgrading an old ordinary asynchronous motor constant speed system using a general-purpose frequency converter, the following points should be particularly noted: For square torque loads (such as fans and water pumps), a frequency converter of appropriate capacity can generally be selected directly; however, for constant torque loads, it is important to measure or estimate the long-term operating frequency of the motor to determine its actual power consumption and margin. For motors with a wide speed range, especially those with both constant torque and constant power speed control, fan-cooled motors should not be used. This method is detrimental to both high and low speeds; the cooling effect is poor at low speeds, and the excessive cooling capacity at high speeds reduces system efficiency. 4. Conclusion This paper studies the temperature rise of induction motors under inverter power supply conditions, analyzes the reasons for the increased temperature rise caused by motor losses and heat dissipation problems, and uses experimental data to illustrate the temperature distribution law of the motor and the influence of the inverter power supply on the motor temperature rise. Specific measures to reduce losses and improve heat dissipation are proposed, providing a reference for solving the problem of motor temperature rise.