Handbook of Electrical Engineering For Practitioners in the Oil, Gas ...

302 HANDBOOK OF ELECTRICAL ENGINEERINGA more detailed treatment of this aspect is given in sub-section 3.5, however, (11.10) will beused to illustrate the stability problem.11.11.1.1 Steady state stability of a generator or motorEquation (11.10) applies to any simple form of synchronous source and sink where E R and E S andthe voltages at either side of the linking reactance X. δ is the phase angle between E R and E S .Forthe generator case, E R and E S may be replaced by V and E g and X by X sg . (For the synchronousmotor case E R and E S may be replaced by E m and V and X by X sm .)Hence, for the generator:P = VE gsin δ gX sgNow V is usually kept close to the system rated voltage, i.e. 1.0 pu± 0.05 pu and X gs ,thesynchronous reactance of the generator may be assumed constant i.e. typically 1.8 pu to 2.9 pu(depending on the generator rating).E qis the internal emf produced by the field winding on the rotor. Hence, for any givenvalue of power P supplied by the generator there will be a wide range of E g and rotor angle δ gvalues.Example:LetV = 1.0 pu,X sg = 2.5 pu and P = 1.0 pu (full load).P = 1.0 = 1.0E g sin δ g2.5sin δ g = 2.5E g≤ 1.0It can be seen that the larger the value of E g the smaller will be the value of δ g .For full-load normal operation δ g is about 50 degrees, which would require E g to be 3.264 pu.Suppose E g is reduced to 2.51 pu, then δ g would be 85 degrees.If E g is reduced again, to 2.5 pu, then δ g wouldbe90degrees.If E g is reduced below 2.5 pu then there is not a value of δ g to satisfy the equation and thismeans that the power cannot be transferred if δ g is caused to exceed 90 degrees. The generator rotorcan no longer be kept in synchronism with the terminal voltage to which it is connected. δ g canbe caused to exceed 90 degrees by either reducing the field excitation, as described above, or byallowing more power to be applied to the generator from its prime-mover, e.g. gas turbine. This canhappen at any level of power loading on the generator (above zero power). When the rotor angleδ g exceeds 90 degrees, and the generator rotor pulls out of synchronism, the condition is unstablewhich means the limit of steady state stability has been exceeded.