Steam Turbine Prime Movers

chapter 1 1

Steam Turbine Prime Movers

1 1.1 Introduction We begin this chapter with some general considerations of prime movers and how they are

controlled. Following this general overview of prime movers, we concentrate on steam turbines and develop models that can be used to represent this type of machine in computer studies of the power system. Other types of prime movers are discussed in Chapters 12 and 13.

Figure 11.1 shows on overview of a large power system and the generation control struc- ture. The system control center measures the power produced by all generators and the inter- change power with neighboring systems. It compares the tie line flows with their scheduled values, and these flows are coordinated with neighboring utilities. The control center receives measurements of all generator outputs and compares these values with desired values, which are based on the economic dispatch of generation considering individual unit generation costs. Then, as the system load varies, the control center can change the generation dispatch to eco- nomically meet the demand in the most efficient manner, while still maintaining prudent re- serves to assure adequate generation if unforeseen unit outages should occur. Note that the control center does not measure the system loads. The measurement of system frequency is used to assure adequate total generation to meet load and maintain rated speed, thereby assuring constant long-term system frequency.

The system dispatch computer sets the governor input signal to control the mechanical torque of the prime mover, computing a unit dispatch signal (UDS), as shown in Figure 11.2. The governor compares the speed reference or load control signal against the actual speed and drives the governor servo amplifiers in proportion to this difference, which can be interpreted as a speed error. The servomotor output is a stroke or position YsM, which indicates the position of the turbine control or throttle valves. Note that this control is different on an isolated system, where the governor input is set to hold constant speed or frequency.

The fast dynamics of the generation of each unit is the solution of Newton’s law, which we write per unit as

(11.1)

where 7j = a time contant related to the unit moment of inertia in seconds w = shaft angular velocity in radians per second

T, = the mechanical torque output of the turbine in per unit Te = the electromagnetic torque or load of the generator in per unit Ta = the accelerating torque in per unit

430

Steam Turbine Prime Movers

r-----l

I I Generation , I

1 1 Unit v ’ Generated Generator

43 1

\ # Tie Line Syste; Loads Power

System

SYSTEM

TRANSMISSION

NETWORK

Tie Line Frequency Reference

Fig. 1 I . 1 Power system generation control.

The excitation system is used primarily as a voltage controller and acts much as a single-input, single-output system with V, as the output. There exists a cross-coupling to the torque output T,, but this effect is secondary.

The system dispatch computer determines the desired generator output and sets the gover- nor input signal to control the mechanical torque of the prime mover. The governor compares the speed reference or governor speed changer (GSC) signal against the actual speed and drives the servomotor amplifiers in proportion to this difference, which can be interpreted as a speed error. The servo motor output is a stroke or position Y,,, which indicates the position of the turbine control or throttle valves.

Finally, the prime mover term in Figure 11.2 is a transfer function that relates the turbine control valve position to the mechanical (shafi) torque. In some cases, this block can be represented by a constant and in others it may be a simple first-order lag. In general, if the system is to be studied over a long time period, the turbine should be represented in greater detail as an energy source transfer function. In some modem thermal units, for example, the energy source controller receives feedback signals from several points, including the generated power (or load control signal) and the turbine throttle pressure, to control simultaneously the turbine valve position, the boiler firing rate, and the condensate pumping rates.

432 Chapter 1 1

Tie Line Flqws

VREF

PTs and

I + xcitation System

Fig. 1 1.2 Block diagram of a generating unit.

1 1.2 Power Plant Control Modes The controls of the steam generator and turbine in a power plant are nearly always consid-

ered to be a single control system. This is true because the two units, generator and turbine, operate together to provide a given power output and, since limited energy storage is possible in the boiler-turbine system, the two subsystems must operate in unison under both steady-state and transient conditions. In this section, the different control modes commonly used by the industry are presented and compared.

1 1.2.1 The turbine-following control mode

The control system shown in Figure 11.3 is usually called the “turbine-following” control, although it is sometimes referred to as “base boiler input” and “admission pressure control” systems (the latter mostly in Europe). In this control mode, a load demand signal is used to adjust the boiler* firing rate and the fluid pumping rate. As the boiler slowly changes its energy level to correspond to the demand signal, the pressure changes at the throttle (the turbine control valves). Then a back-pressure control on the turbine changes to hold the throttle pressure constant. This back-pressure control is very slow, even for a rapidly responding boiler. Thus the system response is very slow, monotonic, and very stable.

Turbine following may be used on a base-load unit, where the unit will respond only to changes in its own firing and pumping rates. It is often used in start-up or initial stages of unit operation. Turbine following is also used in some modem complex systems when the boiler capability is limited for some reason, such as a fan or pump outage. In general, turbine following is seldom used because of its slow response and its failure to use the heat storage capability of the boiler in an optimal manner to aid in the transition from one generator load level to another.

*The term “boiler” used here should be taken in a general way to indicate a steam generator and that receives its thermal energy from either a fossil fuel or nuclear energy source.

Steam Turbine Prime Movers 433

Fig. 11.3 The turbine-following unit control system [I].

1 1.2.2 The boiler-following control mode A more conventional mode of boiler control is called “boiler-following” mode. This con-

trol mode is shown in Figure 11.4. This control mode is sometimes called the “conventional mode” or (in Europe) the combustion control mode. This control scheme divides the control function such that the governor responds directly to changes in load demand. The response is an immediate change in generator load due to a change in turbine valve position and the resulting steam flow rate. The boiler “follows” this change and must not only “catch up” to the new load level, but also must account for the energy borrowed or stored in the boiler at the time the change was initiated. This type of control responds quickly, utilizes stored boiler energy effec- tively, and is generally stable under constant load [ 11. Boiler-following control has the disad- vantage that pressure restoration is slow and the control is nonlinear. There also may be trouble- some interactions between flow, pressure, and temperature variations. If a change in demand exceeds the boiler stored energy, the result may be an oscillation in steam flow and electric power output until the pressure reaches a final, stable value.

Boiler-following control is widely used as the normal control mode of many thermal generating units, particularly the older drum-type boiler units. Many newer units employ a more complex control system in which all control functions are integrated into one master control, but even in these more complex controllers, boiler following is offered as an optional control mode that may be required if there are limitations in turbine operation.

1 1.2.3 The coordinated control mode Most modern thermal generating units employ a control scheme that is usually called an in-

tegrated or coordinated control system. This type of system simultaneously adjusts firing rate,

Throttle Pressure

Fig. 11.4 The boiler-following unit control mode [I] .

434 Chapter 1 1

Loaa Load P,."h..-Sl rinng

IBoiler

Fig. 11.5 The coordinated control mode.

pumping rate, and turbine throttling in order to follow changes in load demand. Such a coordinated control mode is shown in Figure 1 1.5.

In this type of control, both pressure and generated output are fed back for the control of both boiler and turbine. In this manner, it is possible to achieve the stable and smooth load changes of the turbine-following mode and still enjoy the prompt response of the boiler-following mode. This is accomplished by making maximum use of the available thermal storage in the boiler. Both pumping and firing rates are made proportional to the generation error so that these efforts are stabilized as the load approaches the required value. Pressure deviation is controlled as a function of both the thermal storage and the generation error.

A comparison of the three control methods described above is shown in Figure 1 1.6

i

THROTTLE PRESSURE set - *.e* +--.____ Point -.. -e----

9. *-e----- I

.

COORDINATED CONTROL SYSTEM

. . I I I I 1

d 1 2 3 4 5 6 7 Time in minutes

Fig. 1 1.6 Comparison of the results of different control methods [2].


1 1.3 Thermal Generation The most universal method of electric power generation is accomplished using thermal

generation, and the most common machine for this production is the steam turbine. In the Unit- ed States over 85% of all generation is by powered by steam-turbine-driven generators [l]. The size of these generating units has increased over time, with the largest units now being over 1200 MW.

The prevalence of thermal energy production in the generation mix of the United States is shown in Table 1 1.1, which summarizes data compiled by the U.S. Department of Energy for the years 1997 and 1998.

A more descriptive way to compare these results is by plotting the numerical values, as shown in Figure 11.7. Here, it is clear that coal is by far the largest energy source used in the United States, at least for the time period represented. As coal becomes depleted or more costly to extract, this could change. The second largest in order of size is nuclear generation. The role of hydro generation is rather small taken on a national basis; however, hydro is very important in certain regions, such as the Pacific Northwest, which is more dependent on this energy source. This is true in many parts of the world, where the predominant energy generation depends on available local natural resources.

The steam used in electric production is produced in steam generators or boilers using either fossil or nuclear fuels as primary energy sources. Fossil generation uses primarily coal, natural gas, and oil as fuels. Nuclear generation uses fission reactors that operate by breakup of high-mass atoms to yield a high energy release that is much greater than that produced from chemical reactions such as burning. Fossil fueled plants generate the majority of the electrical energy, but this may gradually change as the sources of fossil fuels are depleted or become more expensive to recover and process than nuclear fuels.

By “thermal” generation we usually mean a system that operates on the physical principle of the vapor power cycle or Rankine cycle. Usually, variations of the straight Rankine cycle are used, with two important innovations being the reheat cycle and the regenerative cycle. We will not belabor these concepts here as our primary motive is to study the system operation and control, but a thorough understanding of this important subject is available through many fine refer-

Table 11.1 Net Generation, U.S. Electric Power Industty by Energy Source in GWh

1997, 1998, 1997, 1998, Energy Source GWh GWh Percent Percent

Coal (1) 1,843,831 1,872,186 53.76 51.72

Natural gas (3) 497,430 544,765 14.23 15.05 Nuclear 628,644 673,702 17.99 18.61 Hydro, conventional 358,949 328,581 10.27 9.08

Petroleum (2) 92,727 129,104 2.65 3.57

Other (4) 73,763 72,867 2.11 2.01 Pump storage (5) -4,040 -4,478 -0.12 -0.12 Other (6) 3,137 2,905 0.09 0.08 ( 1 ) Includes coal, anthracite, culm, coke breeze, fine coal, waste coal, bituminous gob, and lignite waste. (2) Includes petroleum, petroleum coke, diesel, kerosene, liquid butane, liquid propane, oil waste, and tar oil. (3) Includes natural gas, waste heat, waste gas, butane, methane, propane, and other gas. (4) Includes geothermal, biomass (wood, wood waste, peat, wood liquors, railroad ties, pitch wood sludge, municipal

(5) A more complete designation of this source is hydro pumped storage. (6) Includes hydrogen, sulfur, batteries, chemicals, and purchased steam.

solid waste, agricultural byproducts, straw, tires, landfill gases, and fish oils), wind, solar, and photo voltaic.

436 Chapter 11

15x10 ' E: ...1

3 1 .o

8 6

k 0.5 8

0.0

1 coal ................. ................. i ..................................... i ......... 2 Petroleum

i 3 NaturalGas i 4 Nuclear

5 Hydro 6 Geothermal, etc 7 Pumped Storage 8 Hydrogen, etc.

.'

............. .................................................................

I I I I

1 2 3 4 5 6 7 8

Fig. 11.7 Net generation by type of energy source, 1998 (top line) and 1997.

ences on the subject [2-51. Our objective here is to study the physical design of thermal power plants with the intention of understanding how these plants work and respond to controls.

1 1.4 A Steam Power Plant Model Steam power plants are of two general types: those fueled by fossil fuels such as natural gas

or coal, and those fueled by nuclear energy produced in a thermal reactor. The overall unit control is largely independent of the source of energy, as both types of plants must have a means of controlling the power output as well as the frequency. Figure 1 1.8 shows a block diagram of the controls for a thermal power plant, in which the source of thermal energy is a steam generator

Fig. 1 1.8 The control system for a thermal generating unit.


that could utilize either fossil or nuclear fuel. The term “boiler” is used here to designate any type of steam generator.

The boiler control inputs are the unit demand signal (UDS), the generated power (PGEN), and the speed or frequency (w). The unit demand signal is set by the system dispatch computer based on the method of dispatch and on the level of load to be served. The generated power of the unit is fed back to the control center so that any error in generated power can be corrected. The unit speed is used by the speed governor as a first-order control on this parameter. The speed governor acts as a continuous, proportional controller to make fast, automatic adjust- ments to unit speed in response to a speed error. This mechanism is much faster than the gover- nor speed changer (GSC) adjustment of the boiler controller. The input from the dispatch computer is optional and is not used when the unit is on local control. In that case, the U D S is hand set by the plant operator. Note also that the boiler controller can be turbine following (adjusting firing rate according to desired power), boiler following (adjusting firing rate to hold throttle pressure), or a completely integrated or coordinated control that does both simultaneously.

The degree of detail required for computer simulation of the power system depends on the length of time required in the simulation. Studies of system performance of a few seconds, for example, need consider only those system components with response times of a few seconds, such as the generator, exciter, and speed governor. Studies of several minutes would usually require some consideration of the steam generator and steam system controls, and may require some consideration of the dispatch system. Thus, it is seen that the longer the desired simulation, the more system components that might enter into consideration. For very long periods of interest, the fastest responding components might be represented in a very simple manner and may not be required at all.

In transient stability studies of 1-10 seconds duration, it is common to consider the generator, network, and the steam turbine and turbine controls. If there is interest in extending the studies to several minutes, then it is probably necessary to add at least a simple boiler model to the simulation, and it may be necessary to consider the dispatch computer as well. The general block diagram of Figure 1 1.8 would be applicable to these longer-duration studies.

1 1.5 Steam Turbines A large portion of the conversion of thermal to electrical energy occurs in steam turbines.

This is due to the many advantages of the steam turbine over reciprocating engines. Among these advantages are the balanced construction, relatively high efficiency, few moving parts, ease of maintenance, and availability in large sizes.

Internally, the steam turbine consists of rows of blades designed to extract the heat and pressure energy of the steam, which is usually superheated, and convert this energy into mechanical energy. To accomplish this goal, high-pressure steam is admitted through a set of control valves and allowed to expand as it passes through the turbine, to be exhausted, usually to a condenser, at relatively low pressure and temperature. Thus, the type and arrangement of turbine blading is important in extracting all possible energy from the steam and converting this energy into the mechanical work of spinning the turbine rotor and attached electric generator.

Two types of turbine blading are used; impulse and reaction blading. In impulse blading, the steam expands and its pressure drops as it passes through a nozzle, leaving the nozzle at high velocity as shown in Figure 1 1.9 (a). This kinetic energy is converted into mechanical energy as the steam strikes the moving turbine blades and pushes them forward. Reaction blading operates on a different principle, as illustrated in Figure 11.9 (b). Here the “nozzle” through which the steam expands is moving with the shaft, giving the shaft a torque due to the unbal- anced forces acting on the blade intake and exhaust surfaces. A somewhat more realistic picture of the combined impulse-reaction blading is shown in Figure 1 1.10. The two moving stages on

430 Chapter 11

Fig. 1 1.9 Two types of turbine blading.

the left of the figure are impulse stages, whereas those on the right are reaction stages. In many turbines, impulse stages are used at the high-pressure, high-temperature end of the turbine and reaction blading at lower pressures. This is because there is no pressure drop across impulse stages and hence there is little tendency for the high-pressure steam to leak past these stages without doing useful work.

As the steam expands in passing through the turbine, its volume increases by hundreds of times. At the lower pressures, reaction blading is used. Here, the steam expands as it passes through the blading and its pressure drops. The steam velocity increases as it passes through fixed blading as shown in Figure 1 1.10, but it leaves the moving blades at a speed about equal to the blade speed. The impulse stage nozzle directs the steam into buckets mounted on the rim of the rotating disk and the steam flow changes to the axial direction as it moves through the rotating disk. In reaction blading, the stationary blades direct the steam into passages between the moving blades and the pressure drops across both the fixed and moving blades. In impulse blading, pressure drops only across the nozzle. In the velocity compound stages, steam is discharged into two reaction stages. The velocity stage uses a large pressure drop to develop a high-speed steam jet. Fixed blades then turn the partially slowed steam before it enters the second row of moving blades, where most of the remaining energy is absorbed.

Because of the tremendous increase in the volume of steam as it passes through the turbine, the radius of the turbine is increased toward the low-pressure end. In many turbines, the steam flow is divided into two or more sets of low-pressure (reaction) turbines. Figure 10.1 1 shows several typical tandem compound configurations and Figure 1 1.12 shows several typical cross- compound designs. In some designs, the steam is reheated between stages to create a reheat cycle, as noted in the figures, which increases the overall efficiency. In other designs, a portion of the steam is exhausted from the various turbine pressure levels to preheat water that is entering the boiler, which is called a regenerative cycle system.

The various valves that control the turbine operation are shown in Figure 1 1.12 and will be discussed in the order encountered by the steam as it moves through the system.

Steam leaves the main steam reheater of the boiler at high pressure and is superheated, in most cases, to high superheat temperature. For example, a large fossil fuel unit uses superheated steam at 2400 psi and 1000°F for a 1.0 GW unit [15]. A modem 750 M W nuclear design uses 850 psi saturated (0.25 percent moisture) steam [16]. The steam heaters contain steam strainers


Fixed Fixed Steam Pressure Fixed t t t

Fig. 1 1.10 Combined impulse and reaction blading [6] .

to catch any boiler scale that could damage the turbine. A typical steam generator and turbine system is shown in Figure 11.13 [7].

The main stop valve or throttle valve (#2 in Figure 1 1.13) is one means of controlling the steam admitted to the turbine. It is often used as a start-up and shut-down controller. During startup, for example, other inlet valves may be opened and steam admitted gradually through the stop valve to slowly bring the turbine up to temperature and increase the turbine speed to nearly synchronous speed, at which point the governor can assume control of the unit. This mode of control is known as full-arc admission. The main stop valve is also used to shut off the steam supply if the unit overspeeds. The unit may be under automatic or manual control, but is usually controlled automatically through a hydraulic control system.

A typical example of the several valves controlling a large steam unit is presented in Figure 11.13 [7]. This system is typical of many large steam power plants, having both superheater and reheater boiler sections and three separate turbines, representing high pressure (HP), intermediate pressure (IP), and low pressure (LP) units.

The admission or governor valves, also known as control vaZves (#3 in the figure), are located in the turbine steam chest and these valves control the flow of steam to the high-pressure turbine. In large units there are several of these valves, and the required valve position is determined by the governor (D in the figure).

An overview of the turbine control for a typical steam power plant is shown in Figure 11.14. Steam is admitted through the main stop valves to a set of control valves and admission of steam into the high pressure turbine is regulated by a set of nozzles distributed around the periphery of the first stage of turbine blading. If only a few of the control valves are open, the

A40 Chapter 11

Single-Casing Single-Flow

t Single-Casing Opposed-Flow

t Two-Casing Reheater Two-Casing Double-Flow Double-Flow-Reheat

Reheater Three-Casing Tripple-Flow-Reheat

Reheater Four-Casing Quadruple-Flow-Reheat

Fig. 1 1 . 1 I Typical tandem compound steam turbine designs with single shaft [6] .

steam is said to be admitted under partial arc of the first stage rather than through all 360 de- grees of the circumference. This is called “partial arc admission.”

Two types of overspeed protection are provided on most units. The first is the normal speed control system, which includes the control valves and the intercept valves. The second type of overspeed control closes the main and reheat stop valves, and if these valves are closed, the unit is shut down.

Two types of control valve operation are used. In one type, the control valves are opened by a set of adjustable cum Zijlers, as shown in Figure 1 1.15. In this arrangement, the valves can be opened in a predetermined sequence as the cam shaft is rotated. In response to a load increase, the flow of steam to one input port may be increased and a closed port may simultaneously be cracked

Steam Turbine Prime Movers 44 1

Reheater Reheater

t 1 t 1

Two-Casing Two-Casing Four-Casing Double-Flow Double-Flow-Reheat Quadruple-Flow-Reheat

Four-Casing Quadruple-Flow-Reheat

Reheater

r""l I I

Five-Casing Sextuple-Flow-Reheat

Six-Casing Six-Casing Sextuple-Flow-Double-Reheat Octuple-Flow-Reheat

Fig. I 1.12 Typical cross-compound steam turbine designs with multiple shafts [6] .

442 Chapter 1 1

1 rlll

Fig. 1 1.13 Example of a large boiler configuration showing major system components and controls 171.

I I- - - - - - -

Steam Generator

I-,,,,-

Overspeed ' I High -b Pressur Trin

Main

Valve Crossover stop

F

Intermediate Low -. Pressure Pressure--

Turbines I - - _

I I ! Valves I -

L-----2&' Intercept ' Valve

Reheat

-- Condenser

-- Jr

Reheater

n Generator

J. Load

Fig. 1 1 . I4 A reheat turbine flow diagram.


Fig. 1 1.15 Cam lift steam turbine control valve mechanism.

open. This distributes the steam around the periphery of the first stage, assuring a uniform temperature distribution and controlling the power input. The cam shaft is controlled by the governor acting through a power servomotor, as shown in Figures 1 1.13 and 1 1.14.

The other type of steam admission control is called the “bar lift” mechanism. This type of valve control is shown in Figure 1 1.16; each valve in a line of valves is lifted using a bar, but each valve is a different length so that the valves open sequentially. As load is added to the turbine, the bar is raised and steam flow is not only increased to the first-opening valve, but additional valves are also opened. The separate valves feed steam to different input ports around the periphery of the first-stage blading and thus increase the power input to the turbine. The bar lift is actuated by the governor servomotor through a lever arrangement.

Fig. I 1 . I6 Bar lift steam turbine control valve mechanism [2].

444 Chapter 1 1

The high-pressure turbine receives steam at high pressure and high temperature, and con- verts a fractionfof the thermal energy into mechanical work. As the steam gives up its energy, it expands and is cooled. Steam is also bled from the turbine and piped tofeedwater heaters. This has proven economical in reducing the boiler size and also reducing the size required at the low-pressure end of the turbine. The turbine extraction points vary in number from one to about eight, the exact number being dictated by design and economy.

In the reheat turbines, shown in Figure 1 1.14, the steam exhausted from the HP (high-pressure) turbine is returned to the boiler in order to increase its thermal energy before it is introduced into the intermediate-pressure (IP) turbine. This reheat steam is usually heated to its initial temperature, but at a pressure that is somewhat reduced from the HP steam condition.

Following the reheater, the steam encounters two valves before it enters the IP turbine, as shown in Figures 1 1.13 and 1 1.14. One of these is the reheat stop valve and serves the function of shutting off the steam supply to the IP turbine in the event the unit experiences shut-down, such as in an overspeed trip operation. The second valve, the intercept valve, shuts off the steam to the IP turbine in case of loss of load, in order to prevent overspeeding. It is actuated by the governor, whereas the reheat stop valve is actuated by the overspeed trip mechanism.

The IP turbine in Figure 1 1.13 is similar to the HP turbine except that it has longer blades to permit passage of a greater volume of steam. Extraction points are again provided to bleed off spent steam to feedwater heaters.

The crossover, identified in Figure 1 1.14, is a large pipe into which the IP turbine exhausts its steam. It carries large volumes of low-pressure steam to the low-pressure (LP) turbine@). Usually, the LP turbine is double or triple flow as shown in Figures 1 1.1 1 and 1 1.12. Since a large volume of steam must be controlled at these low pressures, doubling or tripling the paths available reduces the necessary length of the turbine blades. The LP turbines extract the remaining heat from the steam before exhausting the spent steam to the vacuum of the condenser. It is desirable to limit condensation taking place within the turbine, as any water droplets that form there act like tiny steel balls when they collide with the turbine blades, which are traveling at nearly the speed of sound.

We previously specified that the HP turbine extracts a fractionfof the thermal power from the steam. Then the IP and LP turbines extract the remaining 1 - f of the available power to drive the shaft. Usually,fis on the order of 0.2 to 0.3. For example, in a certain modern 330 MW turbine,fis determined to be 0.24. This is a rather typical value.

1 1.6 Steam Turbine Control Operations The controls for a steam turbine can be divided into those used for control of the turbine

and those used for the protection of the turbine. It is difficult to sketch a “typical” control system for a steam turbine since these controls depend on the age of the unit and the type of controls available at the time of unit installation. Since power plants operate for many years, there are likely to be many different controls, using different technologies, on any given power system. However, we can summarize the most common controls as being either “traditional” or “modem,” with those terms also having a somewhat variable meaning due to the steady ad- vance in control technology.

The control operations that are usually considered to be “traditional” are listed in Table 1 1.2. These are controls that have been required for many years and that require only the very basic technologies for their operation. It is apparent that plant control systems become more complex due to the demands of interconnected operation and the availability of more modem methods of control. The newer controls provide many functions that were not considered necessary for older units, and some that were not available due to limitations of the available technology at the time of manufacture.


Table 11.2 Traditional and Modem Steam Turbine Generator Controls

Traditional Controls Modem Controls

Speed control, near rated speed Overspeed protection Load control-manual or remote Basic control and protection

Initial pressure Vacuum Vibration Others, as needed

All traditional controls and protections Long-range speed (zero to rated speed) Automatic line speed matching Load control; automatic load setback Admission mode selection Automatic safety and condition monitoring On-line testing of all safety systems Fast or early valve actuation Interface to the plant computer Interface to area generation control system

Many of the plant controls are hydraulic, using high-pressure oil supplied by a shaft- mounted main oil pump. These high pressures are practical for the operation of power servomo- tors for control purposes. For example, many control valves are actuated by hydraulic means. In modem plants, many systems also use electric controls as well.

The control functions for the turbine include the servomotor-driven control or governing valves and the intercept valves, which control the amount of steam admitted to the turbine. Po- sitioning intelligence for these valves comes primarily from the speed governor, the throttle pressure regulator, or from an auxiliary governor. There is also an interlocking protection between the control and intercept valves so that the control valves cannot be operated open when the intercept valves are closed.

The protective controls include the main stop valve (throttle valve) and the reheat stop valve. The reheat stop valve is always either fully open or fully closed, and is never operated partially open. The main stop valve may operate partially open when used as a startup control. Both valves are under control of a device that can rapidly close both valves, shutting down the turbine on the occurrence of emergency conditions such as overspeed trip, solenoid trip, low- vacuum trip, low bearing oil trip, thrust bearing trip, or manual trip. During normal operation, both of these stop valves are completely open.

A primary function of the main stop valve is to shut off the steam flow if the unit speed exceeds some predetermined ceiling value, such as 1 10% of the rated value. Steam turbine blading experiences mechanical vibration or oscillation at certain frequencies. The turbine designer as- sures that such oscillations occur above or below synchronous speed, with a generous margin of safety. Also, with the longer blades traveling at nearly the speed of sound, destructive vibration levels may be reached if the speed is permitted to increase substantially beyond rated speed. Thus, speed control on loss of load is very important and is a carefully designed control function. [9].

The operation of a steam turbine on loss of load is approximately as shown in Figure 1 1.17. It is assumed that the generator breaker opens at t = 0 when the unit is fully loaded. On loss of load, the turbine speed rises to about 109% in about one second. As the speed increases, the control valves and intercept valves are closing at the maximum rate and should be completely closed by the time the speed reaches 109% of the rated value, at which time the turbine speed begins to drop. At about 106%, the intercept valves begin to reopen so that a no-load speed of 105% might be achieved. If the speed changer is left at its previous setting, the unit will contin- ue to run at 105% speed on steam stored in the reheater. There is usually sufficient steam for one to three minutes of such operation. Once the reheater steam supply is exhausted, the speed will drop to near 100% and the governor will reopen the control valves.

The definition of what constitutes an emergency overspeed [IO] is a figure agreed upon by

446 Chapter 1 1

110-1 Intercept Valve starts lo! 101

101 l o 2 1

- . - on Generator \ iliary Load

Remaining on Generator \ I

0 1 Time in minutes

2

Fig. I I . 17 Estimated speed versus time following sudden reduction from a maximum load to the values noted.

turbine manufacturer and purchaser, but may be in the region of 1 10 to 120% of the rated value. If the speed reaches this range, an emergency overspeed trip device operates. Usually the overspeed trip mechanism depends on centrifugal force or other physical measurements that are not dependent on the retention of power supply. Some devices include an eccentric weight or bolt, mounted in the turbine shaft, with the weight being balanced by a spring. At a predetermined speed, such as 1 1 1%, the centrifugal force overcomes the spring force and the bolt moves out radially far enough to strike a tripper, which operates the overspeed trip valve.

1 1.7 Steam Turbine Control Functions We now investigate the transfer functions that describe the operation and control of a typi-

cal steam turbine.* The system under investigation is the reheat steam turbine of Figure 1 1.13, with controls as described in the preceding sections. The block diagram for this system is shown in Figure 11.18 [lo], with controls as described in the preceding paragraphs. Our immediate concern is with the thermal system between the control valves, with input q2 and turbine torque T. The symbols used in Figure 11.17 represent per-unit changes in the variables, as defined in Table 1 1.3.

For the present, we will accept the transfer functions of governor and servomotor and re- serve these for later investigation. Let us examine the functions between qz and T in Figure 1 1.18 more carefully. The control valve transfer function is nearly a constant and would be ex- actly 1 .O were it not for nonlinear variations introduced by control valve action. This is due to a combination of nonlinearities. First of all, the steam flow is not a linear function of valve lift, or displacement, as shown by the right-hand block of Figure 11.19. It is, in fact, quite nonlinear, exhibiting a definite saturation as the valve opening increases. One way to counteract this nonlinearity is to introduce a nonlinearity in the valve lifting mechanism, as shown in the left block of Figure 11.19. This is accomplished with a cam lift mechanism, as shown in Figure 11.20. Here, the cam acts as a function generator providing an output

*We follow closely here the excellent reference by the late M. A. Eggenberger [lo] who did significant work in this field. The authors are indebted to Mr. Eggneberger for having shared his work, some of which is unpublished.


. Fig. 1 1.18 Block diagram of mechanical reheat turbine speed control [lo].

L =f(v2, L) (1 1.2)

in which the output L is a function not only of q2 but also of L. In this way, the transfer function of the two blocks taken together are nearly linear for any given valve. Still, a small nonlinearity exists in the overall transfer function, as shown in Figure 11.18, due to “valve points,” as this phenomenon is known in the industry. This refers to the point at which one valve, or set of valves, approaches its rated flow and a new valve (or valves) begins to open.

Table 11.3 Definition of Per-Unit Change Variables

Per Unit Change Variable Defining Equation Remarks

N R = Rated speed

TmR = Rated full load torque

N A Speed of rotation (T= - N R

Developed torque q - = - TmA

TmR

Load torque

Steam flow

A = &

QA

QR

TeR = Rated electrical torque

Q R = Rated steam flow in Ib/sec

TeR

P = -

YzR = Servomotor position for steady rated load Y2A

Y2R Servomotor stroke 172 = -

Y I R = Speed relay stroke for full load

RR = Reference position at rated load and rated speed

YIA Speed relay stroke Y , R

R A Speedlload reference P = -

R R

711 = -

XR = Speed governor stroke for 5% speed change l= - X A Speed governor stroke

Speed error signal E Speed relay input X R

Valve steam flow HP turbine torque Reheat pressure IP + LP torque

EL” Control valve output 7HP HP turbine output variable +R Reheater output variable

q-IP&LP IP + LP turbine torque Accelerating torque 7,

Chapter 1 1

,&{ lift k Fig. 1 1.19 Block diagram for camshaft and valve function generators [IO].

This causes the transfer function to consist of a series of small curved arcs, as shown in Figure 11.18.

To compute the transfer knction of steam flow versus servomotor stroke, we write

Pv K3= (11.3)

If it were not for valve points, the curve expressing the function K3 would be a constant with value of unity, with the incremental regulation at the operating point the same as that of the governor (usually 5%). If we define incremental regulation Ri as [ 101

du ' dP

R.= - (11.4)

where u is the per-unit speed, P is the per-unit power, and Ri is evaluated at the operating point. If we let Rs be the steady-state regulation or droop

L Valve Lift

(11.5)

Fig. 1 I .20 Mechanical function generator (cam-operated control valve).


then we have

RS K3= (11.6)

Eggenberger [lo] points out that Ri is often between 0.02 and 0.12 over the range of valve strokes and may be taken as 0.08 as a good approximate value. Using this value, we would compute for a typical case

0.05 0.08

K3 = - = 0.625 (11.7)

From Figure 1 1.8, we see that the steam is delayed in reaching the turbines by a bowl delay T3, expressed in terms of servo stroke and turbine flow parameters as

(11.8)

where T3 is the time it takes to fill the bowl volume VB (ft3) with steam at rated initial conditions, with specific volume initially of v (lbdsec), or [ 101

V B

VQY T3 = - seconds (11.9)

Typical values of T3 are given as 0.05 to 0.4 seconds. For a straight condensing turbine with no reheat, the torque versus servomotor stroke is

given by (1 1.8). This situation is illustrated in Figure 1 1.21 and is accomplished mathematical- ly by replacing pT in (1 1.8) by 7. This is equivalent to setting the fractionfof torque provided by the HP turbine to unity.

For a reheat turbine, there is a large volume of steam between the HP exhaust and the IP inlet. This introduces an additional delay in the thermal system. From Figure 1 1.18 with elemen- tary reduction, we have [ 101

( 1 1.10)

Fig. 1 1.21 Torque production as controlled by servomechanism stroke.

450 Chapter 11

where f is the fraction of the total power that is developed in the high-pressure unit and is usually between 0.2 and 0.3. The parameter TR is the time constant of the reheater and is defined in a manner similar to (1 1.9) or

(11.11)

where

QR,. = full load reheater steam flow, lbdsec VR = volume of reheater and piping, ft3

v, = average specific volume of steam in the reheater, Et3/lbm

Since the reheat temperature is not constant, computation of TR involves taking averages, but it is usually in the neighborhood of 3 to 11 seconds. This long time constant in the reheater causes a considerable lag in output power change following a change in valve setting. In HP turbines, there may be a delay of up to 0.5 seconds, depending upon control valve location. A much larger delay occurs in the IP and LP sections, however. This is due to the large amount of steam downstream of the control valves, and this steam must be moved through the turbines and reheater before the new condition can be established. These delays are both shown in Figure 1 1.22, where the control valve is given a hypothetical step change and the power output change is plotted [lo]. A five second value for TR is assumed.

The speed-torque transfer function is given in Figure 1 1.18 as [ 101

0 1 r T4s -=-. (11.12)

The time constant T4 is the total time it would take to accelerate the rotor from standstill to rated speed if rated torque, T,, is applied as a step function at t = 0. At rated speed, the kinetic energy in the rotating mass is

1 2

Wk = - J w ~ (11.13)

70%

60%

Control Valve Position

0 1 2 3 4 5 6 7 8 9 Time, seconds

Fig. 1 1.22 Reheat turbine response to a control valve change.

Steam Turbine Prime Movers 45 1

and the differential equation of motion is

Jh = Ta = a constant

where we take

Ta = TmR

the rated value of torque. Solving (1 1.14) for constant torque gives

since TmR = Pr/wR. From ( 1 1.16) and (1 1.13) we can compute

wk T4 = - seconds Pr

where the units must be consistent. We usually compute

0.83( WR2)N,2 3600 x lo6

MWs - -

so that

seconds (WR2)N? T4 = (2.165 x 109)Pr

(11.14)

(11.15)

(11.16)

(11.17)

(11.18)

where P,. = rated power in MW

WR2 = rotor inertia in lbm-fi2 NR = rated speed in rpm

Another useful constant is the so-called specific inertia of the turbine-generator [lo]:

WR2 N 2

JSP= ( F)( &) x lbm-ft/MW (11.19)

and this is convenient since it usually turns out to be nearly unity. In terms of this constant,

T4 = 5.98 Jsp seconds (1 1.20)

Actually, as the turbine speed increases, the load torque increases and the loss torque varies as some power of the speed. Eggenberger [ 101 shows that this can be accounted for by replacing the single block in Figure 1 1.18 that relates (T to T by a feedback system wherein a portion of the speed increase is fed back as a negative torque [ 101. However, as the losses are very small, this is usually neglected.

A set of typical constants for all values shown in Figure 1 1.18 is given in [ 101 and is valu- able for making comparisons of the various system lags under consideration. These constants are shown in Table 1 1.4.

Additional insight into the control of the steam turbine system is gained through an evalua- tion of system performance by the root locus method [12]. Referring to Figure 11.14 and equations (1 l .3) through (1 l . 12), we may write the open-loop transfer function as

K(s + llfT,) S(S + ~/T,)(s + 1/T2)(~ + ~/T,)(s + l/TR)

KG(s) = (11.21)

452 Chapter 11

Table 11.4 Typical Values of Constants Used in Steam Turbine Analysis

Parameter Non-reheat Reheat

Turbine Turbine

C, Normalized speed governor constant (5% regulation) 20 20 TI Speed relay time constant 0.08 to 0.14 s 0.08 to 0.18 s T2 Servomotor time constant 0.15 to 0.25 s 0.15 to 0.30 s K3 Valve gain at no-load point 0.625 0.6 to 0.8 T3 Valve bowl time constant 0.05 to 0.3 s 0.05 to 0.4 s

3 t o l l s f Load on HP turbine per unit - 0.2 to 0.3 T4 Turbine characteristic time 6t012s 5to12s

TR Reheater time constant -

where

Considering the range possible for each variable as shown in Table 11.4, we have a range of pole-zero locations and gains as shown in Table 11.5.

The range of values shown in Table 1 1.5 has some influence on system behavior, as shown in Figure 1 1.23, where poles of a nonreheat turbine are plotted as a band of values rather than as a point in the s plane. It is obvious that, since the system response depends on these pole locations, this system may be designed with a wide range of response characteristics. This is especially true for the valve bowl delay, which may vary from 0.05 to 0.3 seconds [IO]. Other com- ponent values affect the response as well, especially the servomotor pole, which may be quite close to the origin.

A similar plot for the reheat turbine is shown in Figure 11.24. Here, the four poles due to the inertia, servomotor, speed relay, and valve bowl are far enough from the origin to be off- scale for the scale chosen for this figure. This means that the reheater pole and zero will always be relatively close to the origin and will, therefore, have a great influence on the system dynam- ic response, even for small disturbances. For large disturbances, the problem is greatly compli- cated because the reheater should then be treated as a nonlinear model to account for the spatial distribution of flow and pressure in both reheater and piping.

A convenient method of analyzing steam turbine systems is to use the root locus technique [12]. Two examples, one for the straight condensing (nonreheat) turbine and one for the reheat turbine will illustrate the method.

Table 11.5 Range of Values for Poles, Zeros, and Gains

Item Nonreheat Reheat

PoleIZero Symbol Minimum MaximUln Minimum Maximum

Pole 1/T, 7.15 12.50 5.55 12.50 11T2 4.00 6.67 3.33 6.67 l/T3 3.33 20.00 2.50 20.00 1/TR - - 0.091 0.333

Zero 1 JJTR - - 0.303 1.667 Gain K 46.3 5340 9.27 1600


-- (.I s

z 0

8 fi .- IP mzAw

w I U I \)U \u \I Ilr I n I AA M

-20 -15 -10 -5

valve bowl delay

+5

0 \

“0 -

---5

Fig. 11.23 s Plane plot of poles for the nonreheat turbine.

< Zero Range F

I 1 I 1 * * U I V I I l l R

-2 -1.5 -1 -0.5

Range M

Example 11.1 Prepare a root-locus plot for a nonreheat turbine with the following constants:

TI = 0.1s T2 = 0.2 s T3 = 0.0667 s T4 = 10.0 s

Determine the damping ratio and undamped natural frequency for the two least damped roots if K3 = 0.625 and C, = 20.

Solution The block diagram for this system is that shown in Figure 11.25. The open-loop transfer

function is

K s4 + 30s3 + 225s2 + 750s

- - (1 1.22) K

s(s + 5)(s + lO)(s + 15) KG(s) =

For the constants given in this example, we can compute the gain K as

0 -

-- -0.5

K = KG = 937.5 T,T2T3T4

(1 1.23)

Fig. 1 1.24 Pole and zero for the reheater.

454 Chapter 11

Fig. 1 1.25 Block diagram for the nonreheat turbine

We also compute the following constants, which are required in order to construct the root locus plot:

1. The excess of poles over zeros = P - Z = 4 - 0 = 4 2. The asymptotes lie at angles of

(2’+ 1)”O0 = *450, *I350 e, = P - z

3. The center of gravity is located at XP - XZ -30

= - =-7.5 4

C.G. = P-z 4. Write the polynomial

D(s) + KN(s) = 0

(1 1.24)

(1 1.25)

(1 1.26)

In our case, we have

s(s + 5)(s + lO)(s + 15) + K = s4 + 30s3 + 275s2 + K (1 1.27)

From (1 1.27), we construct the Routh’s table [ 131 to find the critical value of gain and the point of the w-axis crossing:

s4 1 275 K s3 30 750 0 S2 740 3K S‘ 55500 - 9K 0 SO K

For the first column in this array to be positive, we require that

K 5 6167

The auxiliary polynomial [ 131 is

740s2 + 3(6167) = 0

or

s = *j5 (11.28)

5. The locus “breaks away” from the negative real axis at points kl and k2 defined by the equations


\ / \ /

1 1 +-+- 1 kl 5-kl 10-kl 15-kl

1 1 5 - k ~ kz-10 k2-5 k2

1 -- _ -

+ - +- 1 1 1 -=-

We solve (1 1.29) by trial and error to find

k, E 1.91 (actually -1.91)

and, by symmetry,

k2 = 15 - 1.91 = 13.09

/

(1 1.29)

(11.30)

(11.31)

6. Incorporating information accumulated in equations (1 1.24) to (1 1.3 l), we construct the root locus diagram shown in Figure 11.26. We can also locate the point corresponding to the assumed gain of 937. With this value of gain, the damping ratio is

s = 0.7 (1 1.32)

Fig. 1 I .26 Root locus for a nonreheat turbine system.

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