**4. Case study**

In order to assess the impacts on the steam turbine blades of a thermal unit, which steam is originated by the burning of bagasse and cane sugar straw, it is used the electrical system depicted in Figure 12 below.

Figure 12 illustrates the single line diagram of the electrical system to be used as reference for the study to be conducted. This single line diagram is very representative of the typical condition of independent generation interconnected with a larger electrical system. It is an

Thus, we can define three characteristic zones of frequency for operation of turbines, as

OPERATION ZONE FREQUENCY - f (Hz)

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

Figure 11 shows the characteristic ranges or zones of frequencies (based on Table 2) and the

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

In order to assess the impacts on the steam turbine blades of a thermal unit, which steam is originated by the burning of bagasse and cane sugar straw, it is used the electrical system

Figure 12 illustrates the single line diagram of the electrical system to be used as reference for the study to be conducted. This single line diagram is very representative of the typical condition of independent generation interconnected with a larger electrical system. It is an

Table 2. Characteristic zones of frequency for operation of turbines

this requires a prior knowledge of the system behavior.

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

minimum values that can cause damage in the operation of steam turbines.

Favorable *fn – 0.17% < fn < fn + 0.17%*  Tolerable *fn – 1% < fn < fn + 1%*  Extreme *fn – 6% < fn < fn + 1.7%* 

shown in table 2.

order of (60+0.05) Hz.

**4. Case study** 

depicted in Figure 12 below.

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.

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 from manufacturers.

Steam Turbines Under Abnormal Frequency Conditions in Distributed Generation Systems 393

**Source PG [MW] QG [MVAr]**  G1 0.7 0.25 G2 0.7 0.25

It is worth clarifying to the reader the pre-established conditions to the speed governors of the IPP machines, these where adjusted to operate with a 5% slope, in order to better meet the interconnection. Therefore, no machine installed in the IPP generation, has the characteristic to ensure that frequency oscillations will be inside the favorable frequency

Faced by the sudden opening of the interconnection circuit breaker there is a considerable fluctuation in the speed of the electric machine G2, Figure 14(a). Such transient oscillation immediately affects the frequency in the electrical system belonging to the IPP, burdening strongly the quality of electricity, especially with regard to the efficiency of micro-

However, slight changes in the operating speed of the machines originate variations in power demand, since the active and reactive powers, required by electrical loads vary dynamically with system frequency. Nevertheless, there is clearly and strongly the tendency of the synchronous machine speed G2 to stabilize, as shown in Figure 14(a) in the period after contingency, thus indicating the influence of the IPP generation penetration in the

As for the speed regulator, Figure 14(b) convincingly portrays the attempt of that regulator

(a) (b) Fig. 14. Response of the mechanical variables of the generator G3 (a): Operating frequency;

In the moment immediately after the opening of the interconnection breaker, the machine is subjected to an immediate rejection of load. Thus, the operating speed rises gently to 189.63 rad/s (f = 60.4 Hz). However, at this moment the lower inertia machine G1 is taken out of the system, in order to restore the load-generation balance. It is worth mentioning the

Table 4. Active and reactive power generated by the independent power sources

range, i.e., there is no need for the presence of an isochronous generator.

computerized devices (Dugan et al., 2002).

transient stability of its own machines.

(b) Action of the speed governor

to meet the new situation imposed on the system.


Table 3. Synchronous machine parameters for the independent generator

It is highlighted that this independent generator is driven by a steam turbine with regulators and governors modeled in "ATP-Alternative Transients Program", through the use of TACS subroutines. Thus we adopted here the block diagram shown in Figure 8 in order to assess the dynamic response of the system of Figure 12, towards the contingency to be applied. Similar works using ATP were developed like (Saldaña et al., 2006) and an important work about distributed generation can be found in through (Freitas et al. 2006).

However, it is necessary the modeling of the voltage regulator to obtain a better and more reliable response from the model. In this way, it is presented through Figure 13 the block diagram used to represent the excitation regulator. This is the IEEE type I model (Guimarães, 1990).

Fig. 13. Voltage regulator model

### **4.1 Sudden opening of the interconnection breaker**

With the purpose of evaluating the influence of penetration of the independent power producer in the largest network and its close correlation with the inertia moment of the generator, with regard to the maintenance of transient stability was established the power flow illustrated in Table 4.

The machines of the IPP generate a total of 4.2 MW and 1.5 MVAr respectively of active and reactive three-phase power. Thus, the total of active power generated 1.7 MW is designed to the grid of the local electricity authority.

**Data needed for G1 (G1 = G2)**  *Sn = 5MVA x0=0.046pu*  Un= 6.6kV *T'd0=1.754s RA= 0.004pu T'q0=0s xL= 0.1pu T"d0=0.019s xd= 1.8pu T"q0=0.164s xq=1.793pu H1=1s ;H2=2s x'd=0.166pu P=4 poles x'q=0.98pu f=60 Hz x"d=0.119pu ωs = 188.5 rad/s x"q=0.17pu ---* 

It is highlighted that this independent generator is driven by a steam turbine with regulators and governors modeled in "ATP-Alternative Transients Program", through the use of TACS subroutines. Thus we adopted here the block diagram shown in Figure 8 in order to assess the dynamic response of the system of Figure 12, towards the contingency to be applied. Similar works using ATP were developed like (Saldaña et al., 2006) and an important work

However, it is necessary the modeling of the voltage regulator to obtain a better and more reliable response from the model. In this way, it is presented through Figure 13 the block diagram used to represent the excitation regulator. This is the IEEE type I model

With the purpose of evaluating the influence of penetration of the independent power producer in the largest network and its close correlation with the inertia moment of the generator, with regard to the maintenance of transient stability was established the power

The machines of the IPP generate a total of 4.2 MW and 1.5 MVAr respectively of active and reactive three-phase power. Thus, the total of active power generated 1.7 MW is designed to

Table 3. Synchronous machine parameters for the independent generator

about distributed generation can be found in through (Freitas et al. 2006).

(Guimarães, 1990).

Fig. 13. Voltage regulator model

flow illustrated in Table 4.

the grid of the local electricity authority.

**4.1 Sudden opening of the interconnection breaker** 


Table 4. Active and reactive power generated by the independent power sources

It is worth clarifying to the reader the pre-established conditions to the speed governors of the IPP machines, these where adjusted to operate with a 5% slope, in order to better meet the interconnection. Therefore, no machine installed in the IPP generation, has the characteristic to ensure that frequency oscillations will be inside the favorable frequency range, i.e., there is no need for the presence of an isochronous generator.

Faced by the sudden opening of the interconnection circuit breaker there is a considerable fluctuation in the speed of the electric machine G2, Figure 14(a). Such transient oscillation immediately affects the frequency in the electrical system belonging to the IPP, burdening strongly the quality of electricity, especially with regard to the efficiency of microcomputerized devices (Dugan et al., 2002).

However, slight changes in the operating speed of the machines originate variations in power demand, since the active and reactive powers, required by electrical loads vary dynamically with system frequency. Nevertheless, there is clearly and strongly the tendency of the synchronous machine speed G2 to stabilize, as shown in Figure 14(a) in the period after contingency, thus indicating the influence of the IPP generation penetration in the transient stability of its own machines.

As for the speed regulator, Figure 14(b) convincingly portrays the attempt of that regulator to meet the new situation imposed on the system.

Fig. 14. Response of the mechanical variables of the generator G3 (a): Operating frequency; (b) Action of the speed governor

In the moment immediately after the opening of the interconnection breaker, the machine is subjected to an immediate rejection of load. Thus, the operating speed rises gently to 189.63 rad/s (f = 60.4 Hz). However, at this moment the lower inertia machine G1 is taken out of the system, in order to restore the load-generation balance. It is worth mentioning the

Steam Turbines Under Abnormal Frequency Conditions in Distributed Generation Systems 395

An increase in angular speed greatly increases the energy stored in the flywheel, and the energy density of the KESS – Kinetic Energy Storage System. However, the no-load losses, viscous friction with air and by contact and friction in mechanical bearings, will be higher, hurting the efficiency of the system. In addition, the rotating parts of the system must support high mechanical stresses due to high speed at which they are submitted. These

the use of vacuum systems, which reduce the losses by viscous friction with the air;

the evolution of microelectronics, that allowed more sophisticated and less expensive

These factors enable the development and implementation of a new generation of KESSs, with superior performance, whose speed can reach tens of thousands of rpm (approximately 60,000 rpm). Thus, increases the number of possibilities for the use of flywheels, since this

The moment of inertia is a measure of resistance to the applied torques in a rotating object, i.e., the higher the moment of inertia, the slower the wheel will spin after applying a certain

<sup>1</sup> <sup>2</sup> I .m.r

However, for an empty cylinder with thin walls, one must employ the equation (8) detailed

However, in the case of an empty cylinder with thick walls, one should use the equation 9

It is worth to present equation (10) used to obtain the constant of inertia of a generator.

H 2

2 2 1 2 <sup>1</sup> I .m.(r r ) <sup>2</sup>

> 2 s n

<sup>1</sup> . .I

S 

<sup>2</sup> (7)

<sup>2</sup> I m.r (8)

(9)

(10)

It is presented here the main ways to obtain the moment of inertia for a solid cylinder:

the advancement of power electronics, which improved signal conditioning;

limitations found in KESS can now be properly solved because:

the development of new materials such as fiberglass and carbon;

the use of magnetic bearings that eliminate friction by contact;

generation presents high energy density and power.

uninterruptible power supply (UPS systems);

Where m is the mass and r is the radius of gyration.

compensation of voltage dips.

force on its axis.

below:

below:

Among the applications for this equipment, we can mention:

provision of extra energy in case of increased demand;

control systems.

performance of the machine G2 speed regulator in Figure 14(b) to reduce the steam consumption to ensure the G2 synchronous speed.

With the withdrawal of G1, a new scenario is presented with respect to the power flow in the system. The machine G2 becomes responsible for all the electrical loads at the IPP. Thus, according to equation (5), the balancing equation, the electrical power becomes greater than the mechanical power, which leads to deceleration of the generator, taking the angular speed to = 184.45 rad/s (f = 58.71 Hz). At this moment, the speed governor acts to increase the steam consumption to restore the load-generation balance. However, the frequency of operation of the machine oscillates in a damped transient between f1 = 59.6 Hz ( = 187.15 rad/s) and f2 = 59.33 Hz ( = 186.42 rad/s), and tends to stabilize at a frequency f = 59.4 Hz, i.e., = 186.74 rad/s.

$$\frac{2.41.d^2\delta}{\alpha\_\text{R}.d\text{t}^2} = \mathbf{P\_m} - \mathbf{P\_e} = \mathbf{P\_a} \tag{5}$$

As for the speed governor, it follows the oscillations observed in the operating speed of the machine G2, tending to stabilize around 1.17 pu, in other words, it is necessary the production by the boilers of 17% more steam, to be supplied to the generators turbine to meet the new request of active power, as can be observed in Figure 14(b).

The moment immediately after the withdrawal of the machine G1, the remaining generator G2 reaches the frequency f = 58.71 Hz. That is classified as extreme in Table 2, burdening sharply the impeller blades of this generating set. However, during the damped transient period, G2 oscillates within the tolerable region of Table 2. The observation of such limits ensures the life time of the equipment, thus reducing the mechanical wear of turbine blades and reduces the number of stoppages for maintenance of this generating set.

In order to get a better response in operation for the IPP electrical system after the opening of the interconnection circuit breaker, it is possible the insertion of a flywheel in the axis of G2, in order to rise the generating set equivalent inertia.

However, it is necessary to reject the generating unit G1 inside the 100 ms after the application of contingency.

#### **4.2 Application of a flywheel**

The flywheel is a mechanical device with significant moment of inertia used for storing rotational energy. Has high resistance to variations in speed, which helps to ensure a small variation in rotation speed of the shaft (Kundur, 1994).

The energy is stored in the rotor as kinetic energy, or more specifically, rotational energy:

$$\mathbf{E}\_{\mathbf{k}} = \frac{1}{2} \mathbf{I}.\text{o}\mathbf{o}^{2} \tag{6}$$

where:


An increase in angular speed greatly increases the energy stored in the flywheel, and the energy density of the KESS – Kinetic Energy Storage System. However, the no-load losses, viscous friction with air and by contact and friction in mechanical bearings, will be higher, hurting the efficiency of the system. In addition, the rotating parts of the system must support high mechanical stresses due to high speed at which they are submitted. These limitations found in KESS can now be properly solved because:


These factors enable the development and implementation of a new generation of KESSs, with superior performance, whose speed can reach tens of thousands of rpm (approximately 60,000 rpm). Thus, increases the number of possibilities for the use of flywheels, since this generation presents high energy density and power.

Among the applications for this equipment, we can mention:


394 Mechanical Engineering

performance of the machine G2 speed regulator in Figure 14(b) to reduce the steam

With the withdrawal of G1, a new scenario is presented with respect to the power flow in the system. The machine G2 becomes responsible for all the electrical loads at the IPP. Thus, according to equation (5), the balancing equation, the electrical power becomes greater than the mechanical power, which leads to deceleration of the generator, taking the angular speed to = 184.45 rad/s (f = 58.71 Hz). At this moment, the speed governor acts to increase the steam consumption to restore the load-generation balance. However, the frequency of operation of the machine oscillates in a damped transient between f1 = 59.6 Hz ( = 187.15 rad/s) and f2 = 59.33 Hz ( = 186.42 rad/s), and tends to stabilize at a

2

.dt

R

meet the new request of active power, as can be observed in Figure 14(b).

and reduces the number of stoppages for maintenance of this generating set.

G2, in order to rise the generating set equivalent inertia.

variation in rotation speed of the shaft (Kundur, 1994).

*I* is the mass moment of inertia about the center of rotation.

application of contingency.

where:

**4.2 Application of a flywheel** 

is the angular speed, and

2 mea

(5)

2.H.d P PP

As for the speed governor, it follows the oscillations observed in the operating speed of the machine G2, tending to stabilize around 1.17 pu, in other words, it is necessary the production by the boilers of 17% more steam, to be supplied to the generators turbine to

The moment immediately after the withdrawal of the machine G1, the remaining generator G2 reaches the frequency f = 58.71 Hz. That is classified as extreme in Table 2, burdening sharply the impeller blades of this generating set. However, during the damped transient period, G2 oscillates within the tolerable region of Table 2. The observation of such limits ensures the life time of the equipment, thus reducing the mechanical wear of turbine blades

In order to get a better response in operation for the IPP electrical system after the opening of the interconnection circuit breaker, it is possible the insertion of a flywheel in the axis of

However, it is necessary to reject the generating unit G1 inside the 100 ms after the

The flywheel is a mechanical device with significant moment of inertia used for storing rotational energy. Has high resistance to variations in speed, which helps to ensure a small

The energy is stored in the rotor as kinetic energy, or more specifically, rotational energy:

k <sup>1</sup> E .I.

2

<sup>2</sup> (6)

consumption to ensure the G2 synchronous speed.

frequency f = 59.4 Hz, i.e., = 186.74 rad/s.

The moment of inertia is a measure of resistance to the applied torques in a rotating object, i.e., the higher the moment of inertia, the slower the wheel will spin after applying a certain force on its axis.

It is presented here the main ways to obtain the moment of inertia for a solid cylinder:

$$\mathbf{I} = \frac{1}{2}\mathbf{m}\mathbf{r}\mathbf{r}^2\tag{7}$$

However, for an empty cylinder with thin walls, one must employ the equation (8) detailed below:

$$\mathbf{I} = \mathbf{m} . \mathbf{r}^2\tag{8}$$

However, in the case of an empty cylinder with thick walls, one should use the equation 9 below:

$$\mathbf{I} = \frac{1}{2}\text{.m.} (\mathbf{r\_1}^2 + \mathbf{r\_2}^2) \tag{9}$$

Where m is the mass and r is the radius of gyration.

It is worth to present equation (10) used to obtain the constant of inertia of a generator.

2 s n <sup>1</sup> . .I H 2 S (10)

Steam Turbines Under Abnormal Frequency Conditions in Distributed Generation Systems 397

(a)

(b)

(c)

Fig. 16. Frequency response of machine G2 for different inertia moments (a): I = 600 kgm2;

(b): I = 700 kgm2; (c): I = 800 kgm2

In a simplified perspective, the procedure is the analysis of the flywheel shown in Figure 15.

Fig. 15. Simplified representation of a flywheel.

Where:


i angular speed at the angular position i ; . 0 angular speed at the angular position 0 .

Taking, arbitrarily, the torques Ti and T0 as a positive and negative, respectively, we get the equation for the motion of the wheel:

$$\mathbf{M} = \mathbf{T}\_{\dot{\mathbf{i}}} (\boldsymbol{\theta}\_{\dot{\mathbf{i}}}, \dot{\boldsymbol{\theta}}\_{\dot{\mathbf{i}}}) - \mathbf{T}\_{\mathbf{0}} (\boldsymbol{\theta}\_{0\prime} \dot{\boldsymbol{\theta}}\_{0}) - \mathbf{I}\_{\cdot} \ddot{\boldsymbol{\theta}} = \mathbf{0} \tag{11}$$

It is presented here different situations for three specific inertia moments, and their corresponding implications on the speed response of the IPP generator G2 in Figure 16.

With the increase in the synchronous machine G2 equivalent moment of inertia, due to the insertion of a wheel, in Figure 16(a) for I = 600 kgm2, there is the stabilization of the operating speed of the generator for the considered time period in the simulation at t = 40s. However, at the moment immediately after the untimely opening of the interconnection breaker, the operating speed of machine G2 reaches = 189.5 rad/s (f = 60.3 Hz). This is due to the instantaneous rejection of the applied load. Nevertheless, due to the withdrawal of machine G1, G2 provides a considerable reduction in its speed of operation due to the increase in electric power demand. The frequency reduces to 184.93 rad/s (f = 58.9 Hz), the extreme region of operation according Table 2. However, the machine varies in speed within the range between 186.53 187.07 rad/s, or 59.4 f 59.5 Hz. Note that, observing Table 2, the oscillation frequency remains within the favorable zone of operation, ensuring the life time of steam turbine blades.

In a simplified perspective, the procedure is the analysis of the flywheel shown in Figure 15.

Taking, arbitrarily, the torques Ti and T0 as a positive and negative, respectively, we get

It is presented here different situations for three specific inertia moments, and their corresponding implications on the speed response of the IPP generator G2 in Figure 16.

With the increase in the synchronous machine G2 equivalent moment of inertia, due to the insertion of a wheel, in Figure 16(a) for I = 600 kgm2, there is the stabilization of the operating speed of the generator for the considered time period in the simulation at t = 40s. However, at the moment immediately after the untimely opening of the interconnection breaker, the operating speed of machine G2 reaches = 189.5 rad/s (f = 60.3 Hz). This is due to the instantaneous rejection of the applied load. Nevertheless, due to the withdrawal of machine G1, G2 provides a considerable reduction in its speed of operation due to the increase in electric power demand. The frequency reduces to 184.93 rad/s (f = 58.9 Hz), the extreme region of operation according Table 2. However, the machine varies in speed within the range between 186.53 187.07 rad/s, or 59.4 f 59.5 Hz. Note that, observing Table 2, the oscillation frequency remains within the favorable zone of operation, ensuring

. . ..

i 0 M T ( , ) T ( , ) I. 0 ii 00 (11)

Fig. 15. Simplified representation of a flywheel.

I is the inertia moment of the wheel; is the wheel angular position;

the equation for the motion of the wheel:

the life time of steam turbine blades.

Ti corresponding torque to an angular position i ; T0 corresponding torque to an angular position 0 ; .

i angular speed at the angular position i ; . 0 angular speed at the angular position 0 .

Where:

Fig. 16. Frequency response of machine G2 for different inertia moments (a): I = 600 kgm2; (b): I = 700 kgm2; (c): I = 800 kgm2

Steam Turbines Under Abnormal Frequency Conditions in Distributed Generation Systems 399

The answers regarding the performance of the speed governor, for the transfer function shown here, respond faithfully and reliably to dynamical requests imposed to the electrical

Due to untimely performance by interconnection break, the IPP machines face an immediate rejection of load, which burdens the system frequency, thereby compromising the integrity of turbine blades. However, it appears that even without the application of mitigation measures the system tends to stabilize. Nevertheless, the responses refer to a system such that the penetration of IPP does not take place significantly. The literature shows that higher levels of active power exported by the IPP mean larger damage to the turbines due to higher frequency oscillations. Thus, the use of the flywheel is shown as an effective alternative, since it damps transient oscillations, thys contributing to ensuring the life time of the

In short, it is extremely important the correct modeling and use of speed governors in studies relevant to the dynamic stability of power system analysis in terms of commitment

Moura, F. A. M. ; Camacho, J. R. ; Chaves, M. L. R. & Guimarães, G. C. *"The Dynamic* 

Moura, F. A. M. ; Camacho, J. R. ; Chaves, M. L. R. & Guimarães, G. C. *"Independent Power* 

Kundur, P. *Power Systems Stability and Control*, McGraw-Hill, EPRI Power Systems

IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems, IEEE

LIPA-Long Island Power Authority, *Control and Protection Requirements for Independent Power* 

Saldaña, C. ; Calzolari, G. & Cerecetto, G. *"ATP modeling and field tests of the ac voltage* 

Freitas, W. ; França, A. M.; Vieira Jr., J. C. M. & Silva, L. C. P. *"Comparative Analysis Between* 

*Applications"*. IEEE Trans. Power Systems, vol. 21,NO.1, FEBRUARY 2006. Guimarães, G. C. *Computer Methods for Transient Stability Analysis of Isolated Power Generation* 

*Producers, Transmission Interconnections*, found at the internet in 22/11/2007, at

*regulator in the Palmar hydroelectric power plant"*, Electric Power Systems Research,

*Synchronous and Squirrel Cage Induction Generators for Distributed Generation* 

*Systems with Special Reference to Prime Mover and Induction Motor Modelling*, PhD

Elsevier, Article in Press, (2009),doi:10.1016/j.epsr.2009.08.016. Anderson , P. M. & Fouad , A. A. *Power System Control and Stability*, vol. I. Iowa, 1977.

Electrical Machines, Rome, Italy, September 2010.

Engineering Series, New York, 1994.

Std. 1547, New York, USA, 2003.

http://tinyurl.com/33clq4.

Elsevier, 76 (2006), pp.681-687.

Thesis, University of Aberdeen, 1990.

*Interaction of Independent Power Producer Synchronous Machines Connected to a Distribution Network in ATP-EMTP"*, ICEM2010 – XIX International Conference on

*Producer Parallel Operation Modeling in Transient Network Simulations for Interconnected Distributed Generation Studies"*, Electric Power Systems Research,

system under analysis.

impeller blades.

**6. References** 

to the life time of the blades of steam turbines.

Figure 16(b) shows the response to an equivalent moment of inertia I = 700 kgm2. The system has more damping, reducing the time required to reach a new steady state speed at = 186.77 rad/s (f = 59.5 Hz). Therefore, according Table 2, the industrial frequency falls in the tolerable operating zone, contributing not only to maintain the transient stability of the system, but also ensures the integrity of the steam turbine blades, as well as presenting a significant contribution in terms of the quality of electric power. As for the oscillations of frequency in the transient period, it is verified a maximum speed of = 189.4 rad/s (f = 60.3 Hz), at the moment immediately after the contingency. Nevertheless, with the removal from operation of G1, machine G2 reaches a minimum speed of = 185.28 rad/s (f = 59.0 Hz) at the extreme operation zone.

However, the machine G2 varies in speed within the range between 186.61 187.01 rad/s or 59.4 f 59.5 Hz. It can be noticed that the frequency oscillation, according Table 2, remains in the favorable zone of operation, ensuring the expected life time for blades of the steam turbine.

With the main objective to reduce the oscillations, evident in the speed of operation, of the remaining synchronous generator (G2) it was applied an equivalent moment of inertia I = 800 kgm2, the result can be seen in Figure 16(c). There, the damping obtained allows reaching the new steady state more efficiently. This helps to mitigate the harmful effects to the quality of electric power to ensure better response of electrical parameters of the system.

With regard to changes in speed, the maximum reaches the magnitude =189.3 rad/s (f = 60.3 Hz) at the tolerable zone of operation, but the minimum is settled at = 185.55 rad/s (f = 59.06 Hz) at the extreme operation zone. Thus, one can conclude here and for the other equivalent inertia moments simulated that, at the instant immediately after the removal of generator G1, the synchronous machine G2 presents a significant reduction in its operating speed. In this way, it is generated a sub-frequency costly to the physical and mechanical integrity of the turbine blades, since the obtained frequency, at this instant, fits the extreme region of operation at Table 2. However, oscillations in the transient period do not affect the impeller blades, as they pass inside the tolerable zone. Nevertheless, after the damped transient period, the machine reaches the new steady-state and stabilizes at a speed = 186.77 rad/s (f = 59.5 Hz), similar to that obtained for the case illustrated in Figure 16(b).

### **5. Conclusion**

Through the discussions presented along this chapter, there is the need to make the correct and effective study of the synchronous machine speed governors, in order to obtain better dynamic response of the system. However, this goal is achieved from te transfer function of these governors, so it is essential to be aware of the topology of the turbine used, i.e., whether or not this is reheating . It shows that before the model transfer function, yet it is necessary to choose an appropriate software to implement the model. In this way, it can be seen that ATP, through TACS subroutines allows the correct and efficient computational modeling of both the speed governor and voltage regulator.

The answers regarding the performance of the speed governor, for the transfer function shown here, respond faithfully and reliably to dynamical requests imposed to the electrical system under analysis.

Due to untimely performance by interconnection break, the IPP machines face an immediate rejection of load, which burdens the system frequency, thereby compromising the integrity of turbine blades. However, it appears that even without the application of mitigation measures the system tends to stabilize. Nevertheless, the responses refer to a system such that the penetration of IPP does not take place significantly. The literature shows that higher levels of active power exported by the IPP mean larger damage to the turbines due to higher frequency oscillations. Thus, the use of the flywheel is shown as an effective alternative, since it damps transient oscillations, thys contributing to ensuring the life time of the impeller blades.

In short, it is extremely important the correct modeling and use of speed governors in studies relevant to the dynamic stability of power system analysis in terms of commitment to the life time of the blades of steam turbines.
