Demonstrative Video
Effect of parameters on Torque and speed
\(T\) at any \(N_r\) is proportional to \(V^2\)
If \(V\) decreases by 10%, then \(T\) decreases by 19% at fixed slip and frequency, since \(0.9^2=0.81\)
Changes in \(V\) not only affect\(T_{st}\) but torque under running conditions also
If \(V\) decreases, then \(T\) also decreases
Hence, for maintaining same \(T\), \(s\) increases i.e. \(N_r\) falls
- and , Let\[\dfrac{T}{T'}=\dfrac{sV^{2}}{s^{'}V^{'2}}\]
Hardly any important changes in \(f\) take place on a large distribution system except during a major disturbance
However, large frequency changes often take place on isolated, low-power systems in which electrical energy is generated by means of diesel engine or gas turbines
Example of such systems are: emergency supply in hospital and the electrical system on a ship etc.
The major effect of change in \(f\) is on motor speed
If the supply frequency falls by 10%, synchronous speed falls by 10%. Rotor speed also depends on the operating slip, which can change with load and voltage.
At 60 Hz the synchronous speed of a 50 Hz motor is 20% higher. The actual rotor speed is \(N_r=N_s(1-s)\).
Raising voltage to 120% while raising frequency from 50 Hz to 60 Hz maintains nominal V/f and approximately maintains flux in the ideal model. Actual use requires manufacturer approval of insulation voltage, mechanical speed, cooling and load capability.
In that case, the new breakdown torque becomes equal to the original breakdown torque and the starting torque is only slightly reduced
Power factor, efficiency and temperature rise cannot be guaranteed from V/f alone. They depend on motor design, load and cooling at the new speed.
For 60 Hz to 50 Hz, reducing voltage to \(5/6=83.33\%\) maintains nominal V/f. The lower speed can reduce shaft-driven cooling; permissible torque and power must be checked.
Full-load Torque and Maximum Torque
- be the slip corresponding to the full-load torque Let\[\begin{aligned} T_{f} & \propto\dfrac{s_{f}R_{2}}{R_{2}^{2}+\left(s_{f}X_{2}\right)^{2}}~\mbox{and}~T_{max}\propto\dfrac{1}{2X_{2}}\\ \therefore\dfrac{T_{f}}{T_{max}} & =\dfrac{2s_{f}R_{2}X_{2}}{R_{2}^{2}+\left(s_{f}X_{2}\right)^{2}}\\ \Rightarrow & \dfrac{T_{f}}{T_{max}}=\dfrac{2s_{f}\cdot R_{2}/X_{2}}{\left(R_{2}/X_{2}\right)^{2}+s_{f}^{2}}=\dfrac{2s_{m}s_{f}}{s_{m}^{2}+s_{f}^{2}} \end{aligned}\]
- At any slip in the reduced model neglecting stator impedance.\[\dfrac{\mbox{operating torque at any slip s}}{\mbox{maximum torque}} = \dfrac{2s_ms}{s_m^2+s^2}\]