Abstract: This paper briefly discusses the composition, control principle, traction and electric braking characteristic curves of the AC drive system of subway vehicles. A brief description of the subway vehicle's system circuit is provided, and the advantages and disadvantages of DC and AC drives are analyzed. Keywords : Subway vehicle; AC drive; VVVF inverter; Electrical system Early subway trains in China were mostly domestically produced DC drive electric multiple units (EMUs), employing cam-based or chopper-based traction control methods, with DC traction motors. However, subway projects built in recent years have adopted imported AC drive EMUs, using VVVF inverter control for traction, and asynchronous traction motors. Compared with DC drive systems, AC drive systems have advantages such as a wider constant power speed range, higher power factor and viscosity coefficient, simpler traction motor structure, and easier maintenance. 1. Composition of AC Drive Systems Metro vehicles differ significantly from railway locomotives in structure and system integration. Locomotives are complete traction systems, relatively independent of the passenger (or freight) cars connected to them; while metro vehicles are assembled in groups, consisting of motor cars and trailer cars, all of which are passenger cars, with the power system distributed under the floor of each car (distributed power). An AC drive system is an electric drive system centered on a VVVF (Variable Voltage Variable Frequency) inverter. It mainly consists of high-speed circuit breakers, filter reactors, VVVF inverters, and asynchronous motors. The composition of the AC drive system in metro vehicles varies depending on the manufacturer and user requirements. Here, we briefly discuss the composition of an AC drive system using a six-car, four-motor, two-trailer (Tc+M+M+M+M+Tc) metro vehicle as an example. The following diagram is a simplified schematic of the traction power supply system in a subway transportation system. Electrical energy is filtered and transformed into a stable 1500V DC power at the traction substation, then led to the main traction inverter via the contact network and current collector. The main traction inverter converts the 1500V DC power into AC power with adjustable voltage and frequency to power the asynchronous motors. The following diagram shows an example of the main circuit of a "two-motor-one-trailer (2M1T)" unit. The power grid supplies power to the inverter via the high-speed switches of the two motor cars (car B and car C) after passing through the pantograph. The auxiliary inverter on the trailer car (car A) is powered through isolation diodes. [img=519,249]http://hnzmedia.com/upload/20070809135415701.gif[/img] The following diagram is a schematic circuit diagram of the main drive system of the 1C4M unit. 1C4M refers to a method where one VVVF inverter supplies power to four asynchronous motors connected in parallel on the same car, also called the "car control" method. The filter reactor and filter capacitor constitute the line filter. The VVVF inverter includes a chopper, which consists of T7 and T8. The chopper's main function is for resistance braking, which is used to adjust the braking current. Another function is overvoltage protection. [img=498,340]http://hnzmedia.com/upload/20070809135811304.gif[/img] [b]2 Control Principle of AC Drive System[/b] The basic principle of VVVF control is to change the load voltage by changing the turn-on time of each IGBT element of the VVVF inverter, and to change the output frequency by changing the turn-on period of each IGBT element of the VVVF inverter. The torque formula for an asynchronous motor is: T = K1·φ·Ir = K2·（V/fi）²·fs, where T is the torque, φ is the magnetic flux, Ir is the rotor current, V is the motor voltage, fi is the power supply frequency, fs is the slip frequency, and K1 and K2 are proportionality coefficients. From the above formula, it can be seen that the torque T is directly proportional to the square of the ratio of the motor voltage to the power supply frequency (V/fi) and directly proportional to the slip frequency fs. It also shows that when the slip frequency fs is negative, the torque T is negative, generating braking force. Therefore, in electric vehicles using VVVF inverters, traction and regenerative braking force can be freely controlled simply by controlling the voltage-to-frequency ratio (V/fi) and the slip frequency (fs). That is, only three factors need to be controlled: the inverter output voltage V, the inverter frequency fi, and the slip frequency fs. [b]3 Traction and Electric Braking Characteristics of AC Drive System[/b] 3.1 Traction Condition During traction, the asynchronous motor acts as a motor, converting the electrical energy provided by the inverter into kinetic energy, with a slip frequency (fs) greater than zero. The control of vehicle starting and accelerating from a standstill can generally go through three modes: constant torque control, constant power control, and natural characteristic zone. Mode 1 (Constant Torque Control) Constant torque control gradually increases the inverter frequency fi while controlling the slip frequency, making its value match the speed. As the speed gradually increases, the actual rotational frequency fm of the asynchronous motor rotor increases accordingly. To keep the slip frequency fs constant, the inverter frequency fi must be increased. Keeping the voltage-to-frequency ratio (V/fi) constant, the magnetic flux φ of the asynchronous motor is constant, keeping the slip frequency fs constant, the rotor current Ir of the asynchronous motor is constant, resulting in constant torque. Keeping the voltage-to-frequency ratio (V/fi) constant, the asynchronous motor voltage V increases proportionally with the inverter frequency fi, and the voltage control is PWM control. When the inverter output voltage reaches its upper limit, it switches to constant power control. For example, under a grid voltage of 1500V, according to the formula Vimax=VC·61/2/π, the upper limit of the output voltage of the VVVF inverter is 1170V. Mode Two (Constant Power Control Region): After the inverter voltage V reaches its upper limit, it remains constant. The slip frequency fs increases with speed to keep the motor current Ir constant. Since both voltage and current remain constant, it is constant power control. As the slip frequency fs increases, the inverter frequency fi increases accordingly, and the torque T decreases, T∝1/fi. Constant power operation continues until the slip frequency fs reaches its maximum value, then transitions to the natural characteristic region. If the inverter capacity has a large margin, after the motor voltage reaches its maximum value, the slip frequency can be increased for a period of time to increase with speed (frequency), thereby increasing the current and extending the constant torque operation time until the current reaches the maximum allowable value of the inverter or motor, and then it enters constant power operation. Mode Three (Natural Characteristic Region): The inverter voltage V remains at its constant maximum value, and the slip frequency fs remains at its constant maximum value. As speed increases, the inverter frequency fi continues to increase. The motor current Ir∝1/fi decreases, the torque T decreases, and T∝1/fi². 3.2 Braking Condition During braking, the asynchronous motor acts as a generator to convert the vehicle's kinetic energy into electrical energy, and the slip frequency (fs) is less than zero. The control of the vehicle gradually decelerating from motion to a stop can generally go through three modes: constant slip control, constant torque 1 (constant voltage), and constant torque 2 (constant flux). During braking, the vehicle mainly uses regenerative braking, and the generated electrical energy is directly fed back into the power grid and absorbed by adjacent vehicles. When the power grid is unable to absorb all the energy of regenerative braking, regenerative braking switches to resistive braking, which is consumed in the braking resistor. The conversion between regenerative braking and resistive braking is automatically completed by the control unit based on the voltage across the line filter capacitor and the control brake chopper. When the voltage across the filter capacitor exceeds 1800V, resistive braking completely replaces regenerative braking. Mode 4 (Constant Voltage, Constant Slip) Braking begins at high speed. At this time, the inverter voltage V remains at a constant maximum value, and the slip frequency fs remains at a constant maximum value. As vehicle speed decreases, the inverter frequency fi decreases. The motor current Ir increases inversely proportional to the inverter frequency, and the braking force increases inversely proportional to the square of the inverter frequency. When the motor current Ir increases to a value consistent with constant torque, constant torque control is initiated. However, when the motor current Ir increases to the inverter's maximum allowable value, the motor current must be kept constant from the moment Ir reaches this maximum value. Constant current control is then performed within a small segment by controlling the slip frequency. In this case, the braking force increases inversely proportionally with the inverter frequency. Mode 5 (Constant Torque 1, Constant Voltage): The inverter voltage V remains at a constant maximum value. While controlling the slip frequency fs to be inversely proportional to the square of the inverter frequency fi, the inverter frequency fi decreases as speed decreases, causing the slip frequency fs value to decrease until it reaches its minimum value. The motor current Ir decreases proportionally to the inverter frequency, and the braking force remains constant. Mode 6 (Constant Torque 2, Constant Flux): The slip frequency fs remains at a constant minimum value, and the motor current Ir is also constant. The inverter frequency fi decreases as vehicle speed decreases. By using PWM control to decrease the motor voltage V, i.e., keeping (V/fi) constant, the magnetic flux and braking force remain constant. The curves showing the relationship between motor voltage V, slip frequency fs, motor current Ir, traction/braking force, and speed v in the six modes are shown in the following figure: 3.3 Traction/braking force relative to speed characteristic curves. Because the characteristic curves of subway vehicles vary depending on the vehicle type, this figure is for reference only. As shown in the figure, when the subway car is in traction mode, it is in the constant torque control zone from starting to 37.5 km/h; from 37.5 km/h to 75 km/h, it is in the constant power control zone; and from 75 km/h to 80 km/h, it is in the natural characteristic zone. When the subway car is in braking mode, it is in the constant pressure and constant slip zone from high speed to 50 km/h. Theoretically, the subway car is in the constant torque control zone from 50 km/h to a stop. However, in actual operation, the regenerative braking force will drop rapidly at a certain point below 10 km/h. Therefore, after the subway car decelerates to below 10 km/h, air braking should be supplemented to maintain constant braking force. 4. Conclusion Compared to DC drive systems, AC drive systems utilize asynchronous motors and VVVF contactless control, eliminating the need for forward/reverse switching and traction/brake switching required by DC drives. This results in miniaturization and weight reduction of the traction system, significantly reducing maintenance workload; the energy regeneration rate reaches approximately 35%, demonstrating significant energy savings. Therefore, VVVF AC drive systems have become a trend in subway vehicle development. This paper only provides a preliminary discussion of AC drive systems for subway vehicles. After decades of practice, and with the continuous maturation and improvement of VVVF AC drive system technology, future development of new subway vehicle electric drive systems should be based on VVVF AC drive system technology. References: [1] Changchun Railway Vehicles Factory Senior Science and Technology Workers Association (ed.). Urban Rail Vehicle Technology and Application. China Railway Publishing House, 2005.10. [2] Gao Shuang (ed.). Subway Vehicle Structure and Maintenance Management. China Railway Publishing House, 2003.12. [3] Rong Zhilin. DC1500V IGBT Traction Inverter for TGN10 Subway Vehicles [J]. Locomotive Electric Transmission, 2004 (4). [4] Zhuzhou Times Group Co., Ltd. Technical Specifications of Traction System for Beijing Subway Electric Passenger Cars. [5] Yu Qingsong, Wen Longxian. Tianjin Light Rail Electrical System. Changchun Railway Vehicles Technology. [6] Hu Jisheng, Miao Yanying. 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