The integral is graphically represented by the difference between areas and A£ on Figure 2.3. — will be zero when = A^. At this point, where the electrical power is greater than the mechanical power, and the rate of change of 6 reverses, the rotor swings back towards angle 6^. Because there are always losses to damp a real system, the rotor will eventually stabilize at a new equilibrium angle $2* Generator instabilities can occur because there is a critical value 6^ for 6. If the rotor exceeds this critical power angle, the generator cannot regain equilibrium. This critical power angle exists because, as shown on the figure, has a maximum value equal to the area between curve II and the line P = P . If A- is larger than this maximum, the rate of change of 6 never reaches zero, and the power balance tends further to increase the machine's angle. Thus, there are certain critical machine angles which must not be exceeded during a switching operation or else some of the machines will not be able to reestablish equilibrium states. If the power network is subjected to frequent changes in generation capacity, the power distribution over the lines of the network will be changing often. It is not inconceivable that redistribution of power over a network due to generation fluctuation could cause the power on some line to exceed the setting of its protective device, causing the line to be disconnected, creating the sort of transient problem described above in addition to the frequency transient set up by the loss of generation. Since the switching of the line again redistributes the power flow, a chain reaction could occur, magnifying the stability problem. The magnitudes and frequencies of fluctuations likely to initiate a chain reaction of this sort are difficult to forecast; the sort of system breakup just discussed is a line-by-line and machine-bymachine process which does not lend itself to description by average characteristics. It is more than a simple cascade of analyses like that
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