# Heating

This maintains constant resistance with voltage change and hence the power varies with (voltage)^{2}.

The above loads may be described as static.

# Synchronous Motors

The power consumed is approximately constant with the applied voltage. For a given excitation the VArs change in a leading direction (i.e. reactive power is generated) with network voltage reduction. The P-V, Q-V, generalized characteristics are shown in Figure 3.37.

# Induction Motors

The P-V, Q-V characteristics may be determined by the use of the simplified circuit shown in Figure 3.38. It is assumed that the mechanical load on the shaft is constant.

The electrical power

The reactive power consumed Also, from Figure 3.38

The well-known power-slip curves for an induction motor are shown in Figure 3.39. It is seen that for a given mechanical torque there is a critical voltage and a corresponding critical slip scr. If the voltage is reduced further the motor becomes unstable and stalls. This critical point occurs when

**Figure 3.39 **Power-slip curves for an induction motor. If voltage falls to 0.6p.u. at full load P = 1, the condition is critical (slip s_{cr}) that is when
so that

Alternatively, for a given output power, P