What is Generator Capability Curve?

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The generator operating point limits are stated and visualized in the form of the generator capability curve. The generator load capability curve and generator operating capability include active power (MW), reactive power (MVAr), and apparent power (MVA).

The capability curve is drawn on the PQ axis. Where P is in MW and Q is in MVAr.

Information derived from the Generator Capability Curve:

  1. Maximum generation limit.
  2. Determine the operating limit of the generator’s steady-state stability.
  3. Limitation of the constraints on the various elements of the generator.
  4. To improve the active power pricing mechanism by considering the reactive power component.
  5. Determine the settings of the protection system by knowing the safe operating limits of the generator.
  6. Minimum limit in under-excitation conditions.

Generator Characteristics:

  • Synchronous generators are rated in terms of the maximum MVA at a specified voltage and power factor (usually 0.85 or 0.9 lagging).
  •  The active power output is limited by the prime mover.
  •  The continuous reactive power output capability is limited by three considerations: Armature current limit, Field current limit, and End region heating limit.

A Synchronous machine cannot be operated at all points inside the region bounded by the circle shown in the below figure without exceeding the machine rating.

Generator Capability Curve with Limits
Generator Capability Curve

Generator Limitations:

There are 6 principal limitations on the generator operation.

1. Stator winding heating limit.                                  

2. MW limit.                                                   

3. Rotor heating limit.                                      

4. Steady-state Stability limit.                                           

5. Stator core end heating limit.

6. VOLTAGE Instability at Leading Power factors.

1. Stator Winding Heating Limit:

The generator stator conductors are operating at their thermal limit. This limit is due to I square R heating in the stator conductors.

If the generator power factor is altered to a value nearer to UPF, then due to the lower stator current, the generator stator conductors would be operating well within their thermal limit. 

One of the limitations of generator rating is the maximum current that can be carried by the armature without exceeding the heating limitations.  Therefore, in the P-Q plane the armature current limit, as shown in Figure, appears as a circle with a center at the origin and a radius equal to the MVA rating.

Synchronous Machine Capability Curves
Synchronous Machine Capability Curves
  • The circle with center at the origin O and radius S= Vt*Ia defines the region of operation for which armature heating will not exceed a specified limit.

2. MW Limit:                                                   

MW output is limited by turbine output and stator conductor heating. The real power output of the generator is usually limited to a value within the apparent power rating by the capability of its prime mover. Maximum prime mover capability is generally smaller than the maximum active power that is limited by the generator stator current.

3. Rotor Heating Limit:

Rotor currents caused heat resulting from I square R losses, the field current imposes a second limit on the operation of the generator. Due to this limitation rotor conductors are unable to carry larger currents to the rotor. This limit affects the capability of the machine in over-excited conditions.

4. Steady-state Stability Limit:

The steady-state stability limit is the maximum power that can be transferred without the system becoming unstable when the load is increased gradually, under steady-state conditions.

In the case of a generator operating with a leading power factor, the excitation and hence flux produced by the rotor is weak. Consequently, the magnetic coupling between the rotor and stator rotating magnetic fields is also weak. If the generator is loaded under this condition, a large load angle (rotor angle) is produced.

When this load angle reaches 90°, the generator is producing the maximum amount of power for the excitation being used and is said to be operating at its steady-state stability limit.

Generator Power Angle Curve
Generator Power Angle Curve

Any further increase in load will cause the magnetic fluxes to stretch further and the load angle to increase further. A point is reached when the rotor is at the 180 Deg position, where there is no magnetic coupling between the rotor and stator. When this occurs, the rotor will speed up and the generator, instead of giving a steady output, will only give surges of power as the rotor N pole passes the stator S pole. This effect is known as “pole slipping” and the generator is now unstable.

The large surges of power, from a mechanical point of view, puts great strain on the generator to turbine coupling, the bearings, and foundations. From an electrical point of view, the surges of power will cause current surges and hence magnetic stresses to all load-carrying components. These surges of power will also cause the voltages to fluctuate rapidly and cause lights to flash.

To make sure that the generator will remain stable, it must not be operated with more leading vars than is shown by the stability limit line.

  • The horizontal line XYZ specifies the steady-state stability limit.

5. Stator Core End Heating Limit:

When a generator is operating at unity or lagging power factor, a strong flux is produced by the rotor. Under this condition, little flux is able to leak out from the ends of the stator -core and there is no excessive heating at the core ends.

Generator Stator Core End Region Heating
Stator Core End Region Heating

When the generator is operating at a leading power factor, the flux produced by the rotor is weaker and more flux is able to leak out from the ends of the stator core. When this flux leaks out from the ends of the stator core, it passes through the face of each lamination and causes large eddy currents to flow in these laminations. These eddy currents can cause excessive heating.

6. Voltage Instability at Leading Power Factors:

Terminal voltage output is limited by the heating of the stator iron core, as distinct from the core end heating.


Therefore, for a generator operating at its rated speed (frequency) the:

  • MW output is limited by turbine output and stator conductor heating.
  • Mvar output (lag) is limited by the rotor heating.
  • Mvar output (lead) is limited by stator core end heating and also by stability considerations.
  • Terminal voltage output is limited by the heating of the stator iron core.

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