Control of electric machines
With the voltage proportional to the frequency, at 10 Hz the maximum torque of a motor falls from 191 to 86 N·m, because the stator drop is no longer negligible. A 15 V boost brings it back to 122 N·m.
01DC motors
The speed of a separately excited DC motor is proportional to the armature voltage, less the drop across its resistance, and the torque to the current. It is controlled with a controlled rectifier from the line or with a DC chopper; with two bridges in antiparallel, or with a transistor H-bridge, the drive works in the four quadrants: it turns in both directions and brakes by returning energy. Classical control has two cascaded loops: an inner current loop, which limits the torque, and an outer speed loop. The machines were described in DC machines.
02The induction motor with variable frequency
The speed of an induction motor is tied to the frequency: the synchronous speed is \( n_s = 60 f / p \), with \( p \) pole pairs, and the rotor turns slightly slower, with a slip \( s \). A variable-frequency drive —rectifier, DC bus and inverter— changes the frequency, and with it the speed. So that the flux does not change, the voltage is varied in proportion: this is scalar V/f control. The torque curves come from the equivalent circuit in AC machines:
A four-pole motor, 400 V and 50 Hz, of about 7.5 kW, with R1 = 0.5 Ω, R2' = 0.4 Ω, X1 = X2' = 1 Ω and Xm = 30 Ω at 50 Hz. The gray curves are 10, 25 and 50 Hz without boost; the blue one, the chosen frequency; the yellow line, the load torque.
03Vector control and synchronous motors
V/f control is simple and sufficient for pumps and fans, but slow. Vector control, or field-oriented control, transforms the three-phase currents to a system of axes that rotates with the rotor flux, where one component controls the flux and the other the torque, as in a DC motor; this achieves torque response in milliseconds and full torque at zero speed. Direct torque control chooses the inverter states according to the torque and flux error. Permanent-magnet synchronous motors, with high efficiency, dominate electric vehicles and robotics, and are controlled with the same methods based on the position of the rotor. When the motor brakes, the energy returns to the DC bus: it is dissipated in a braking resistor or, with an active rectifier, returned to the grid. The design of the loops relies on controller design.
04In the laboratory
Program a drive in V/f mode, and measure the speed and current of a motor with a brake at several frequencies, with and without voltage boost.
Control a DC motor with an H-bridge and PWM, close a speed loop with an encoder and measure the step response.
Brake a motor abruptly with a drive that has no braking resistor and observe the overvoltage of the DC bus.
05Common mistakes
- Using pure V/f at low speed. Without boost, the motor loses torque exactly where it is most needed for starting.
- Running a self-ventilated motor at low speed for a long time. Its fan turns slowly and the motor overheats.
- Braking fast without planning where the energy goes. The DC bus rises until it trips the protection.
- Exceeding the rated frequency expecting the same torque. With field weakening, the available torque drops.
06Self-assessment
At what synchronous speed does a four-pole motor fed at 25 Hz turn?
750 rpm.
With the lab data and 50 N·m, how many rpm does it turn at 50 Hz?
About 1466 rpm, with a slip of 2.2 %.
Why does the maximum torque fall at low frequency with constant V/f?
Because the drop across the stator resistance takes up an ever larger share of the voltage, which is already small.
What does vector control separate?
The component of the current that produces flux from the one that produces torque.
07Further reading
- Bimal K. Bose. Modern Power Electronics and AC Drives. Prentice Hall, 2002. Scalar and vector control of AC motors.
- R. Krishnan. Electric Motor Drives: Modeling, Analysis, and Control. Prentice Hall, 2001. The modeling of motors and of their DC and AC drives.
- Ned Mohan. Electric Drives: An Integrative Approach. MNPERE. An introduction to drives with vector control explained from scratch.