The IEEE Standard provides other control elements for the system. Whether stator current limiters, power stabilizers, or reactive power controllers. However, as seen in Figure 5.1, they configure these control loops as inputs to the voltage regulator, adding their outputs to the pre-established fixed reference. So, at the last moment, it all comes down to a voltage regulation loop, which limits the dynamics of the system’s excitation.
Previously, it was also presented that the power and frequency grids are a function of the primary control (gas turbine). And these are the two control loops provided and used in the case study. Thus, the complete control dynamics is summarized by these two systems.
Now assume a short-circuit at the stator’s terminals. Be it a short-circuit inside the machine or closer to the load. Maintenance of the stator’s voltage no longer makes sense.
After all, for adjusting the three-phase voltages to the levels previously desired, it would require high levels of current, inconsistent with the delivered mechanical power. In this situation, the system is generally considered uncontrollable and inoperable until normal operating conditions are restored. In other words, until the protection system acts, the short-circuit is finished, the current arc has vanished, then it might be possible to start the machines again.
Based on this condition assumed above, some simulation results are obtained. Note that, apart from the failure, no changes are made to the system here. It continues to operate with conventional excitation and primary control. That is, with the AVR under a fixed reference amplitude voltage of 1 p.u. at the generator terminals. The system is subject to a short-circuit within a restricted time window. Then, after that period, the protection works, and it interrupts the short-circuit. This work will not go into detail in the analysis of the short-circuits. Only in terms of observing the behavior of the system under these conditions.
5.2.1 Two-phase short-circuit fault
Figure 5.2 shows the results of the simulations under a two-phase short-circuit fault condition. From the figure, some characteristics of the system are perceived after the short-circuit. The electrical fault immediately results in an over-current peak followed by a fluctuation and a transition period until reaching a constant stage. According to the nomenclature used by Kundur[16], he names these phases. The first phase, the peak of over-current and undulation, is called the sub-transient period. The second, longer, transitional phase is called a transient period. And, the third is the steady-state period of the current in short-circuit.
The two-phase short-circuit, therefore, has a high instantaneous over-current char-acteristic and an even higher fault current during steady-state. Also noteworthy is the
0 2 4 6 8 10
Time (seconds)
-2 -1 0 1 2 3
Electric Torque (p.u.) 0.5
1 1.5
Frequency (p.u.)
-4 -2 0 2 4
Current (p.u.)
5 5.05 5.1
-4 -2 0 2 4
-1 0 1 2 3
Voltage (p.u.)
5 5.05 5.1
-1 0 1
2.7 2.75 2.8
Two-phase short circuit fault
a)
b)
c)
Figure 5.2 – Results with regular excitation control during two-phase short-circuit - a) Sta-tor’s terminal (a,b,c) current; b) Stator’s terminal (a,b,c) voltage; c)Rotor’s mechanical frequency ωm (in green) and electrical torqueTe (in gray).
resulting electric torque, with high and oscillating amplitude in Figure 5.2.c). If the frequency does not change so much, then its oscillatory characteristic results from the instantaneous power of the system during the fault. In fact, the transient current response has a sinusoidal component as much as a DC component. This last component has an accommodation time which is directly related to the R/L characteristic of the system [16].
Since no active power is delivered to the load through the two shorted phases at the stator’s terminals, all of this power is concentrated in the operating phase. Also, forasmuch
Chapter 5. The Control Strategy 74
as the synchronous frequency is a fixed reference, the primary control should produce a counter torque on the turbine rotor.
5.2.2 Three-phase short-circuit fault
Figure 5.3 shows the system in a three-phase short-circuit condition. In the first moment, it can be observed that the steady-state’s current amplitude in the fault condition is pretty similar to the amplitude in the short-circuit after the transient response. Saving
0 2 4 6 8 10
Three-phase short circuit fault
a)
b)
c)
Figure 5.3 – Results with regular excitation control during three-phase short-circuit - a) Stator’s terminal (a,b,c) current; b)Stator’s terminal(a,b,c)voltage; c)Rotor’s mechanical frequency ωm (in green) and electrical torqueTe (in gray).
the amplitude difference between the phases in the two-phase short-circuit. However, the energy conservation law explains why the over-current reaches its highest value at the instant that the three-phase voltage at the terminals reaches practically zero. The amplitude of this over-current reaches almost 10 times its nominal value and is much higher than the two-phase short-circuited over-current amplitude. Moreover, the electric torque decreases substantially, since there is no active power supplied to the terminals.
This last-mentioned behavior is an important difference between the three-phase and two-phase fault.
It is noticeable that the voltage regulator control is inoperative during the fault, be it two-phase or three-phase short-circuit. Or, at least, it does not produce the expected result. Besides, the current reaches chief amplitude values in the transient period and steady-state. And it will not be easily extinguished except by protection fully designed to break its arc.