Variable Voltage and Frequency Conversion Speed Regulation Based on Steady State Model of Induction Motor

In the induction motor, only the stator winding is connected to the power supply, the rotor winding is short-circuited, and the rotor winding receives the energy of the stator winding through the electromagnetic induction theorem. The induction motor can be regarded as a kind of rotary transformer. After the rotor winding is equivalent to the stator side, the steady-state T-shaped equivalent circuit of the induction motor can be obtained, as shown in Figure 1.

In the figure, Rs and Xsσ are the stator phase windings and leakage reactance values, Xm is the three-phase equivalent excitation reactance, Rr is the rotor resistance, and Xrσ is the rotor leakage reactance.

Thanks to Rs and Xsσ Are very small, there are

In the formula, N is the number of turns in series per phase; ks is the fundamental winding coefficient; Φm is the air gap flux.

In the motor design, Φm is determined under the rated voltage and rated speed, and the magnetic circuit of the motor is designed close to the saturation point, so that the motor materials can be fully utilized. In the process of speed regulation, if the frequency is reduced while keeping Ès unchanged, the air gap flux will increase, which will cause the excitation current to increase, the power factor to decrease, the stator core loss to increase, and the efficiency to decrease, so in practical applications At the same time as the medium frequency modulation, the voltage should be adjusted proportionally, that is, the variable voltage and frequency conversion speed regulation (VVVF). When the speed is below the rated speed, keep Es/fs=const (constant)

At this time, the corresponding electromagnetic torque is:

Let ωf=ωs﹣ωr

Then the slip ratio is s=(ωs-ωr)/ωs, and both ends of the above formula are multiplied by Xrσ to obtain:

sX_{rσ}= ω_{f}L_{rσ}

Both ends of the slip are multiplied by Es to get

sEs= ω_{f}L_{m}I_{m}

In the formula, ωs is the synchronous angular velocity; ωr is the rotor angular velocity; ωf is the slip angular velocity; Im is the excitation current; Lrσ is the rotor leakage inductance; Lm is the stator and rotor mutual inductance.

Then the electromagnetic torque can be written as:

Keeping Es/fs constant is essentially keeping the excitation current Im unchanged, that is, the air gap flux Φm. At this time, the electromagnetic torque is only related to the slip angle frequency ωf, and has nothing to do with the stator current frequency. The shape of the torque-speed external characteristic curve under different power supply frequencies does not change, but it shifts along the speed axis, as shown in Figure 2.

Let (dTe/dfs)=0, the slip angle frequency at the maximum electromagnetic torque ωfmax=Rr/Lsσ, at this time, the maximum electromagnetic torque is Temax=(3/2)ρnI²m(L²m/Lrσ), in In actual control, if the slip angle frequency is kept constant, a constant electromagnetic torque can be obtained, as shown by the dotted line in Figure 2.

Below the rated speed, the motor can work in the constant torque mode. During the speed adjustment process, the slip frequency must be limited to prevent the motor torque from exceeding the maximum torque, otherwise the system will be unstable.

Due to the limited amplitude of the motor power supply voltage, when the motor speed exceeds the rated speed, the voltage can no longer increase proportionally with the frequency, and can only be maintained near the maximum voltage. From (1), when Es is constant, fsΦm=const (constant ), the air gap flux of the motor decreases with the increase of frequency, and from the electromagnetic torque formula (2), the electromagnetic torque is proportional to the square of the air gap flux, so the electromagnetic torque also increases with the frequency And decrease, by the torque formula (3)

Can be deduced

The product of torque and frequency is approximately a constant. At this time, the induction motor runs in an approximately constant power mode. To sum up, the external characteristic curve of the motor based on the variable voltage and frequency conversion speed regulation (VVVF) is shown in Figure 3. Below the rated speed, the motor torque is kept constant, and above the rated speed, the motor runs at a constant power. In driving, it is also required that the speed regulation range in the constant power zone is as wide as possible.

It can be seen from formula (2) that when the slip rate is small, the electromagnetic torque of the motor is proportional to the slip rate, so that the torque can be controlled by controlling the slip rate. This control method is called slip frequency control This algorithm is also often used in asynchronous motor control.