**2.1 Isochronous governor**

382 Mechanical Engineering

For this it is essential to develop a computer model able to represent accurately the

The speed regulation system is the primary control loop of the Automatic Generation Control (*AGC*) of an electrical system. The control of active power in a power system is accomplished primarily by controlling the torque of the machines primary drive system

Figure 1 illustrates a system for regulating the speed of a steam turbine. By controlling the position xE of the control valve, a control can be exercised over the admission of steam (or water) at high pressure trough the turbine, and therefore the torque of the turbine. For a hydraulic amplifier, the input is the position of the pilot valve xD and the output is position xE of the main piston. A small downward movement of point E, the steam flow increases by an amount that, if measured in terms of power valve, represents an increment *Pv* . This

Fig. 1. Example illustrating the mechanical speed control system of a steam turbine

A ( *<sup>A</sup> x* ) corresponds to an increase in the reference power, Pr *ef* ;

main piston ( *<sup>E</sup> x* ), resulting from variations in steam pressure;

The pilot valve XD, still in figure 1, can have its position changed, through the links or arms

Directly, by the speed changer. A small downward movement of the connecting point

Indirectly, by feedback, due to changes in the position of the connection point E of the

phenomena experienced.

(Anderson & Fouad, 2003).

connection system, in three ways:

**2. Steam turbines control functions** 

increased flow is rendered by the increase in turbine power, *PT* .

Another simple mechanism of regulation is shown by figure 2. In this case, the deviation in speed, captured by the centrifugal body (*flyballs*), cause the displacement x in the pilot valve, which makes the oil to flow though the main servo motor. This servo motor, in turn, opens or closes the valve or turbine blades, depending on the direction of x.

It is important to observe that a displacement x in the pilot valve causes a rate of change of the servo piston, or a rate of change in the valve position.

Fig. 2. "Isochronous" type speed governor

With reference to figure 2, can be written for the position of pilot valve (x):

$$
\Delta \mathbf{x} = \mathbf{k}\_1 \Delta \mathbf{f} \tag{1}
$$

where: f = frequency deviation (f0 – f); k1 = proportionality constant.

Also, for the turbine valve position (y), we have:

$$\frac{d}{dt}(\Delta \mathbf{y}) = \mathbf{k}\_2 \Delta \mathbf{x} \tag{2}$$

Steam Turbines Under Abnormal Frequency Conditions in Distributed Generation Systems 385

With reference to the block diagram of the isochronous governor in figure 2, the effect of the feedback connection, figure 4, is represented by inserting a gain K3. This fact is illustrated in

Figure 6 shows the time response of the valves controlled by the speed governor to a step change in the frequency deviation. TG is known as a time constant of speed governor,

From the transfer function in figure 6, a function given by equation (4), one can notice that the value of the steady-state frequency shift f required to produce a variation of 1 p.u. at

> valve (p.u.) 1 frequency (p.u.) R(1 sT ) G

0 R N N R% 100% N 

(4)

the valve of the turbine V is R. This parameter is known as "speed control".

Fig. 4. Schematics of the *speed drop* governor

Fig. 5. Block diagram of the governor with speed drop

The parameter R can also be expressed in percentage as

N0 = speed in steady-state at no load (valves closed);

usually the order of a fraction of a second (0.5 s).

figure 5.

where:

where: k2 = proportionality constant.

$$
\frac{d}{dt}(\Delta \mathbf{y}) = \mathbf{k}\_1 \mathbf{k}\_2 \Delta \mathbf{f}
$$

$$
\Delta \mathbf{y} = \int \mathbf{k}\_1 \mathbf{k}\_2 \Delta \mathbf{f} \, d\mathbf{t}
\tag{3}
$$

These equations are described in the block diagram in figure 3.

Fig. 3. Block diagram of the isochronous type speed governor

Due to the integrative action of the main servo motor, it is evident that y reach a new equilibrium state only when f reaches zero.

The governor with the configuration of figure 2 will therefore reduce the frequency error to zero in steady state and move the valve position, within physical limits, to any position that is necessary to make such reduction. It is known as an isochronous governor.

Note that a frequency shift may occur either by variation of the actual frequency, or change in the reference value f0, which is accomplished through a change in the pivot point, usually via a screw mechanism, triggered by a "synchronization engine", or change of speed level motor.

Isochronous governors are not used in multiple machines systems, because of the need for appropriate division of load between the machines. The division itself is ensured by providing a regulation and speed decrease in the governor action or speed control (Kundur, 1994).

#### **2.2 Governor with speed drop**

Figure 4 shows the schematic of a governor with speed drop or adjustment of equilibrium. The characteristic drop is due to the connection between the pilot valve and the main servo motor

or

Fig. 4. Schematics of the *speed drop* governor

With reference to the block diagram of the isochronous governor in figure 2, the effect of the feedback connection, figure 4, is represented by inserting a gain K3. This fact is illustrated in figure 5.

Fig. 5. Block diagram of the governor with speed drop

Figure 6 shows the time response of the valves controlled by the speed governor to a step change in the frequency deviation. TG is known as a time constant of speed governor, usually the order of a fraction of a second (0.5 s).

From the transfer function in figure 6, a function given by equation (4), one can notice that the value of the steady-state frequency shift f required to produce a variation of 1 p.u. at the valve of the turbine V is R. This parameter is known as "speed control".

$$\frac{\text{\AA}\,\text{valve}\,\left(\text{p.u.}\right)}{\text{\AA}\,\text{frequency}\,\left(\text{p.u.}\right)} = \frac{1}{\text{R}\,\left(\text{l} + \text{s}\,\text{T}\,\text{G}\right)}\tag{4}$$

The parameter R can also be expressed in percentage as

$$\mathbf{R\%} = \frac{\left| \mathbf{N}\_0 - \mathbf{N} \right|}{\mathbf{N}\_{\mathbb{R}}} \times 100\%$$

where:

384 Mechanical Engineering

Due to the integrative action of the main servo motor, it is evident that y reach a new

The governor with the configuration of figure 2 will therefore reduce the frequency error to zero in steady state and move the valve position, within physical limits, to any position that

Note that a frequency shift may occur either by variation of the actual frequency, or change in the reference value f0, which is accomplished through a change in the pivot point, usually via a screw mechanism, triggered by a "synchronization engine", or change of speed level

Isochronous governors are not used in multiple machines systems, because of the need for appropriate division of load between the machines. The division itself is ensured by providing a regulation and speed decrease in the governor action or speed control (Kundur,

Figure 4 shows the schematic of a governor with speed drop or adjustment of equilibrium. The characteristic drop is due to the connection between the pilot valve and the main servo

is necessary to make such reduction. It is known as an isochronous governor.

1 2 <sup>d</sup> ( y) kk f dt 

<sup>y</sup> k k f dt 1 2 (3)

where:

or

motor.

1994).

motor

**2.2 Governor with speed drop** 

k2 = proportionality constant.

These equations are described in the block diagram in figure 3.

Fig. 3. Block diagram of the isochronous type speed governor

equilibrium state only when f reaches zero.

N0 = speed in steady-state at no load (valves closed);

Steam Turbines Under Abnormal Frequency Conditions in Distributed Generation Systems 387

However, figure 8 presents the block diagram of a steam turbine in a simplified form. It is one of the models adopted by the IEEE – Institute of Electrical and Electronic Engineers

(Anderson & Fouad, 2003). It is noteworthy that for a steam unit T4 = 0s.

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

a severe overload imposed on the system with the occurrence of a generation deficit.

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

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

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 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

the following discussion is related to the steam turbines (Anderson & Fouad, 2003).

In figure 7 was used the following notation:

TS = Charging time of the steam turbine; TG = Time constant of the governor.

TR = Reheater time constant;

M = (MS + MR + MH) = combined inertia moment; D = PL / = damping characteristics of the load; Rs = Regulation of steam without reheating; Rr = Regulation of steam with reheating;

Fig. 8. Model for a thermal turbine speed governor

as soon as possible the system frequency close to nominal.

**3.1 Turbine limits** 

"stress" or fatigue.

N = steady-state speed at full load (valves completely opened); NR = rated speed.

Fig. 6. Throttle response controlled by the speed governor in figure 4 to a step change in the frequency deviation.

Thus, a regulation of 5% means that a frequency deviation of 5% causes a 100% change in power or at the valve outlet. In the terminology of process control, the governor would be characterized as a proportional control of a proportional gain of 1/R, or a proportional band of R×100%.

In order to familiarize the reader with the methodology used to perform computer simulations of dynamic software analysis, it is presented through figure 7 the block diagram of a steam turbine with reheat, figure 7(a) and without reheating, figure 7(b). However, they are representations for a system that is being represented by a single equivalent electric machine.

Fig. 7. Block diagrams for isolated systems represented by a single equivalent machine: (a) steam without reheat, (b) steam with reheat

In figure 7 was used the following notation:

386 Mechanical Engineering

Fig. 6. Throttle response controlled by the speed governor in figure 4 to a step change in the

Thus, a regulation of 5% means that a frequency deviation of 5% causes a 100% change in power or at the valve outlet. In the terminology of process control, the governor would be characterized as a proportional control of a proportional gain of 1/R, or a proportional band

In order to familiarize the reader with the methodology used to perform computer simulations of dynamic software analysis, it is presented through figure 7 the block diagram of a steam turbine with reheat, figure 7(a) and without reheating, figure 7(b). However, they are representations for a system that is being represented by a single equivalent electric machine.

Fig. 7. Block diagrams for isolated systems represented by a single equivalent machine: (a)

steam without reheat, (b) steam with reheat

N = steady-state speed at full load (valves completely opened);

NR = rated speed.

frequency deviation.

of R×100%.

M = (MS + MR + MH) = combined inertia moment; D = PL / = damping characteristics of the load; Rs = Regulation of steam without reheating; Rr = Regulation of steam with reheating; TR = Reheater time constant; TS = Charging time of the steam turbine;

TG = Time constant of the governor.

However, figure 8 presents the block diagram of a steam turbine in a simplified form. It is one of the models adopted by the IEEE – Institute of Electrical and Electronic Engineers (Anderson & Fouad, 2003). It is noteworthy that for a steam unit T4 = 0s.

Fig. 8. Model for a thermal turbine speed governor
