**3.2 Cascading shots**

388 Mechanical Engineering

Must be highlighted that here will be presented a discussion for systems operating in a

Figure 9 illustrates the phenomenon that involves operations of the turbines under offnominal frequency ("off-frequency operation"), showing the amplitude of vibrations fatigue for a number of stages of a turbine vane according to the nominal frequency. It is observed that when the turbine operates out of its nominal frequency, the amplitude of "stress"

The Campbell diagram, illustrates how a change in turbine speed can provide steam excitation frequencies that coincide with the natural frequencies of a blade, how can be seen in the reference cited at final of this paragraph. At the figure 9 is demonstrated the relationship between blade failure due to fatigue and off-frequency operation. Below stress level A, the vibration stress amplitude is low enough that no damage results. Operation at stress level B would produce a failure at 104 cycles, and at level C failure would occur at 103

(a) (b)

Research for a large amount of vibration frequency data leads to the time limits suggested for operations outside of the nominal frequency range and for different steam turbines that

The diagram of figure 10 represents the estimated minimum time to the failure of some part of the structure of the blades, illustrating the limits of time for operation of steam turbines for both the under-frequency and for over-frequency. It is observed for a frequency deviation of 5% or more, the damage time becomes very small and it is not practical to

As can be seen, for the lower limit frequency, i.e., approximately *fn- 6%* Hz (see figure 10), the permissible minimum time is one second for frequencies near the nominal time is undefined so that a variation frequency of 1%, will have no harmful effect on the blades. It is important to note that the effect of operation outside the nominal frequency is cumulative, i.e., half a minute of operation under full load at *fn–4%* Hz now leaves only

Fig. 9. Frequency x *stress* (fatigue) range for steam turbines (a) Increase in vibration amplitude with off-frequency operation; (b) Stress *x* number of cycles to failure

operate a system more than a few seconds in this frequency range.

approximately another half a minute of *fn–4%* Hz for operation in the unit life.

nominal frequency of 60 Hz, like in Brazil.

increases and some damage can be cumulative.

cycles (Kundur, 1994).

are represented in figure 10.

If a limit is reached for operating a turbine, it will be disconnected from the system by actions of its protection. This exacerbates the problem, since the power imbalance increases (greater deficit of generation), and consequently, the frequency drops quickly and the system enters a cascade process until it comes to the collapse.

Steam Turbines Under Abnormal Frequency Conditions in Distributed Generation Systems 391

Fig. 12. Single line diagram for the electrical system in the case considered

electricity distribution network, connected to the busbar number 3 (Point of Common Coupling - PCC), through a transformer, the independent producer electrical system. The representation of the (IPP) Independent Power Producer consists of two synchronous generators (whose primary machines are steam turbines), a static electrical load as well as an electric motor, internal to this "independent" system. In addition to meeting its domestic demand for energy, these generators also provides power to the distribution network.

The three-phase distribution network has an ideal voltage source (infinite bus), connected to transformer T1, through busbar 1. This transformer T1 is connected to two power distribution lines of 13.8 kV through busbar 2. This busbar has a capacitor bank and load. The two referred distribution lines end at busbar 3, where it is connected to transformer T2. At busbar 3, there is a bank of capacitors and load. Transformer T2 is used to make the connection between the power utility and the independent power producer. The transformer T2 is also connected to busbar 4, where are connected the generators of the independent power producer (IEEE Std. 1547, 2003). These generators have the nominal values of 5 MVA, 6.6 kV. At busbar 4 there is also another transformer T3, which is

connected to busbar 5, where we have the loads of the independent power producer.

from manufacturers.

The voltage source, which is the mains of the distribution system, was implemented as na ideal three-phase source. Therefore, the short-circuit level at busbar 1 is considered infinite. The data needed for modeling the independent power producers generators (among others, the sub-transient, transient, synchronous reactance and time constants) are listed in Table 3. The rated parameters obtained for the machine voltage and speed regulators, as well as data referred to the independent power producer synchronous generator, were obtained directly

Thus, we can define three characteristic zones of frequency for operation of turbines, as shown in table 2.


Table 2. Characteristic zones of frequency for operation of turbines

The zone limits are practical, because they were obtained empirically. Table 2 indicates a favorable frequency zone of (600.1) Hz. As a reference, in the USA the limits are of the order of (60+0.05) Hz.

Figure 11 shows the characteristic ranges or zones of frequencies (based on Table 2) and the minimum values that can cause damage in the operation of steam turbines.

For this reason, emphasis is given to methods to protect the turbine under-frequency conditions, and to this end, a system must be equipped with a load shedding program, and this requires a prior knowledge of the system behavior.

Fig. 11. Effect of frequency on the operation of the turbines
