**3. Steam turbine operation under abnormal conditions of frequency**

Special attention has been given to the operation of turbo-generators under abnormal system operating conditions concerning the frequency (over or under frequency). In particular, more research efforts have been made to analyze the possible damage the steam turbines are the subject when operating in conditions of prolonged under frequency, during a severe overload imposed on the system with the occurrence of a generation deficit.

To avoid a total collapse of the system and minimize the damage to the equipment during such disturbances, considerable effort has been expended in the development and implementation of automatic load shedding. These load shedding programs are idealized to reject just enough loads to lighten the remaining generation system from overload to restore as soon as possible the system frequency close to nominal.

Both the turbines and generators have operational restrictions, to different degrees, under abnormal frequency conditions. On the other hand, steam turbines are more sensitive to the under frequency phenomena when compared with the attached generators. For this reason, the following discussion is related to the steam turbines (Anderson & Fouad, 2003).

### **3.1 Turbine limits**

The steam turbine consists of a sequence of stages of increasing dimensions with each stage having more complicated geometry of stator and rotor blades. Each blade row has its own natural frequency. The turbines are carefully designed so that the resonance frequencies of the blades to the rated speed are sufficiently out of phase, to avoid vibration and excessive "stress" or fatigue.

Steam Turbines Under Abnormal Frequency Conditions in Distributed Generation Systems 389

From figure 10, we can build table 1 that shows the maximum time values of operating a

The condition most often found corresponds to the turbine over-frequency, resulting in sudden shutdown of the generator by the action of the breaker. Under these conditions the characteristic of the speed governor will allow an over speed of around 5% and from there take immediate action to reduce the speed to close to the nominal (Anderson & Fouad, 2003).

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

**Frequency at full load (Hz) Maximum operating time**  *fn – 1%* Continuously *fn – 2%* 100 minutes *fn – 3%* 10 minutes *fn – 4%* 1 minute *fn – 5%* 0.1 minute *fn – 6%* 1 second Table 1. Maximum operating time of a steam turbine according to its frequency of operation

Fig. 10. Frequency limits of the operation of a steam turbine

system enters a cascade process until it comes to the collapse.

steam turbine according to its frequency.

at full load

**3.2 Cascading shots** 

Must be highlighted that here will be presented a discussion for systems operating in a nominal frequency of 60 Hz, like in Brazil.

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" increases and some damage can be cumulative.

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 cycles (Kundur, 1994).

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

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 are represented in figure 10.

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

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

Fig. 10. Frequency limits of the operation of a steam turbine

From figure 10, we can build table 1 that shows the maximum time values of operating a steam turbine according to its frequency.


Table 1. Maximum operating time of a steam turbine according to its frequency of operation at full load

The condition most often found corresponds to the turbine over-frequency, resulting in sudden shutdown of the generator by the action of the breaker. Under these conditions the characteristic of the speed governor will allow an over speed of around 5% and from there take immediate action to reduce the speed to close to the nominal (Anderson & Fouad, 2003).
