Speed and torque control  (Page 5/19)

Control of synchronous motors

Speed control

• Synchronous motors are essentially constant-speed machines, with their speed being determined by the frequency of the armature currents. The synchronous angular velocity ${\omega }_s=\left[\frac{2}{\text{poles}}\right]{\omega }_e$ (10.10)

where

${\omega }_s=$ synchronous spatial angular velocity of the air-gap mmf wave [rad/sec]

${\omega }_e={\mathrm{2\pi f}}_e=$ angular frequency of the applied electrical excitation [rad/sec]

$f_e=$ applied electrical frequency [Hz]

• The simplest means of synchronous motor control is speed control via control of the frequency of the applied armature voltage, driving the motor by a polyphase voltage-source inverter shown in Fig. 10.10. This inverter can either be used to supply stepped ac voltage waveforms of amplitude $V_{\text{dc}}$ or the switches can be controlled to produce pulse-widthmodulated ac voltage waveforms of variable amplitude. The dc-link voltage $V_{\text{dc}}$ can itself be varied, for example, through the use of a phase-controlled rectifier.

Figure 10.10 Three-phase voltage-source inverter.

• The frequency of the inverter output waveforms can of course be varied by controlling the switching frequency of the inverter switches. For ac-machine applications, coupled with this frequency control must be control of the amplitude of the applied voltage.
• The air-gap component of the armature voltage in an ac machine is proportional to the peak flux density in the machine and the electrical frequency. If we neglect the voltage drop across the armature resistance and leakage reactance,

$V_a=\left[\frac{f_e}{f_{\text{rated}}}\right]\left[\frac{B_{\text{peak}}}{B_{\text{rated}}}\right]V_{\text{rated}}$ (10.11)

where $V_a$ is the amplitude of the armature voltage, $f_e$ is the operating frequency, and $B_{\text{peak}}$ is the peak air-gap flux density. $V_{\text{rated}}$ , $f_{\text{rated}}$ , and $B_{\text{rated}}$ are the corresponding rated-operating-point values.

• Consider a situation in which the frequency of the armature voltage is varied while its amplitude is maintained at its rated value ( $V_a=V_{\text{rated}}$ ). Under these conditions,

$B_{\text{peak}}=\left[\frac{f_{\text{rated}}}{f_e}\right]B_{\text{rated}}$ (10.12)

For a given armature voltage, the machine flux density is inversely proportional to frequency and thus as the frequency is reduced, the flux density will increase. A significant drop in frequency will increase the flux density to the point of potential machine damage due both to increased core loss and to the increased machine currents required to support the higher flux density.

• As a result, for frequencies less than or equal to rated frequency, it is typical to operate a machine at constant flux density. From Eq. 10.11, with $B_{\text{peak}}=B_{\text{rated}}$

$V_a=\left[\frac{f_e}{f_{\text{rated}}}\right]V_{\text{rated}}$ (10.13)

$\frac{V_a}{f_e}=\frac{V_{\text{rated}}}{f_{\text{rated}}}$ (10.14)

• From Eq. 10.14, constant-flux operation can be achieved by maintaining a constant ratio of armature voltage to frequency. This is referred to as constant volts- per-hertz (constant V/Hz) operation. It is typically maintained from rated frequency down to the low frequency at which the armature resistance voltage drop becomes a significant component of the applied voltage.
• If the machine is operated at frequencies in excess of rated frequency with the voltage at its rated value, the air-gap flux density will drop below its rated value. In order to maintain the flux density at its rated value, it would be necessary to increase the terminal voltage for frequencies in excess of rated frequency. In order to avoid insulation damage, it is common to maintain the machine terminal voltage at its rated value for frequencies in excess of rated frequency.
• Figure 10.11 shows a plot of maximum power and maximum torque versus speed for a synchronous motor under variable-frequency operation. The operating regime below rated frequency and speed is referred to as the constant-torque regime and that above rated speed is referred to as the constant-power regime.