The performance of a hydraulic turbine is influenced by the characteristics of the water column feeding the turbine: water inertia water compressibility pipe wall elasticity in the penstock The effect of water inertia is to cause changes in turbine flow to lag behind changes in turbine gate opening The effect of elasticity is to cause traveling waves of pressure and flow in the pipe - a phenomenon referred to as water hammer typically, the speed of propagation of such waves is about 1200 meters/sec traveling wave model required only if penstock is very long

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PRIME MOVERS AND GOVERNING
SYSTEMS
Copyright © P. Kundur
This material should not be used without the author's consent

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Prime Movers and Governing Systems
1. Hydraulic Turbines and Governing Systems
 Hydraulic turbine transfer function
 special characteristics of hydraulic turbines
 nonlinear hydraulic turbine model
 governors for hydraulic turbines
 tuning of speed governors
2. Steam Turbines and Governing Systems
 steam turbine configurations
 steam turbine models
 steam turbine controls
3. Gas Turbines and Governing Systems
 simple-cycle configuration
 combined-cycle configuration
Outline

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Hydraulic Turbines and Governing
Systems
 The performance of a hydraulic turbine is
influenced by the characteristics of the water
column feeding the turbine:
 water inertia
 water compressibility
 pipe wall elasticity in the penstock
 The effect of water inertia is to cause changes in
turbine flow to lag behind changes in turbine
gate opening
 The effect of elasticity is to cause traveling
waves of pressure and flow in the pipe - a
phenomenon referred to as water hammer
 typically, the speed of propagation of such waves
is about 1200 meters/sec
 traveling wave model required only if penstock is
very long

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 The representation of the hydraulic turbine and
water column in stability studies usually
assumes that (a) the penstock is inelastic, (b) the
water is incompressible, and (c) hydraulic
resistance is negligible
 The turbine and penstock characteristics are
determined by three basic equations relating to:
 velocity of water in the penstock
 turbine mechanical power
 acceleration of water column
Hydraulic Turbine Transfer Function
Figure 9.2: Schematic of a hydroelectric plant

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The velocity of the water in the penstock is given
by
where
U = water velocity
G = gate position
H = hydraulic head at gate
Ku = a constant of proportionality
The turbine mechanical power is proportional to
the product of pressure and flow; hence,
The acceleration of water column due to a change
in head at the turbine, characterized by Newton's
second law of motion, may be expressed as
where
L = length of conduit
A = pipe area
ρ = mass density
ag = acceleration due to gravity
ρLA = mass of water in the conduit
ρagH = incremental change in pressure at
turbine gate
HGKU u
HUKP pm 
    HaA
dt
Ud
LA g 



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 For small displacements (prefix ) about an initial
operating point (subscript "0") we can shows that
where
 Tw is referred to as the water starting time. It
represents the time required for a head H0 to
accelerate the water in the penstock from standstill to
the velocity U0. It should be noted that Tw varies with
load. Typically, Tw at full load lies between 0.5 s and
4.0 s.
 Equation 9.11 represents the "classical" transfer
function of the turbine-penstock system. It shows
how the turbine power output changes in response to
a change in gate opening for an ideal lossless turbine.
ST
2
1
1
ST1
G
P
w
wm





0g
0
w
Ha
LU
T 
(9.11)

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Special Characteristics of Hydraulic Turbines
 The transfer function given by Equation 9.11
represents a "non-minimum phase" system
Systems with poles or zeros in the right half of
s-plane are referred to as non-minimum phase
systems; they do not have the minimum amount of
phase shift for a given magnitude plot. Such
systems cannot be uniquely identified by a
knowledge of magnitude versus frequency plot
alone.
 The special characteristic of the transfer function
may be illustrated by considering the response to a
step change in gate position. The time response is
given by:
 Figure 9.3 shows a plot of the response of an ideal
turbine model with Tw = 4.0 s
  Ge31tP
t
T
2
m
w

















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Figure 9.3: Change in turbine mechanical power
following a unit step increase in gate position

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 Immediately following a unit increase in gate position,
the mechanical power actually decreases by 2.0 per
unit. It then increases exponentially with a time
constant of Tw/2 to a steady state value of 1.0 per unit
above the initial steady state value
 The initial power surge is opposite to that of the
direction of change in gate position. This is because,
when the gate is suddenly opened, the flow does not
change immediately due to water inertia; however, the
pressure across the turbine is reduced causing the
power to reduce.
 With a response determined by Tw, the water
accelerates until the flow reaches the new steady value
which establishes the new steady power output
 Figure 9.4 shows the responses of power, head, and
water velocity of a turbine-penstock system with Tw =
1.0 s for a reduction in gate opening by 0.1 pu by
(i) a step change, and
(ii) a 1-second ramp
 The linear model given by Equation 9.11 represents
the small-signal performance
 useful for control system tuning
 because of its simplicity, provides insight into the basic
characteristics

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Figure 9.4: Hydraulic turbine-penstock response to a step
change and a ramp change in gate position

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Governors for Hydraulic Turbines
 The speed/load control function involves feeding back
speed error to control the gate position. In order to
ensure satisfactory and stable parallel operation of
multiple units, the speed governor is provided with a
droop characteristic.
 Typically, the steady state droop is set at about 5%,
such that a speed deviation of 5% causes 100% change
in gate position or power output; this corresponds to a
gain of 20.
 For a hydro turbine, however, such a governor with a
simple steady state droop characteristic would be
unsatisfactory
Requirement for a Transient Droop
 Hydro turbines have a peculiar response due to water
inertia: a change in gate position produces an initial
turbine power change which is opposite to that
sought.
 For stable control performance, a large transient
(temporary) droop with a long resetting time is
therefore required. This is accomplished by the
provision of a rate feedback or transient gain
reduction compensation as shown in Figure 9.8

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 The rate feedback retards or limits the gate
movement until the water flow and power output
have time to catch up
 The result is a governor which exhibits a high droop
(low gain) for fast speed deviations, and the normal
low droop (high gain) in the steady state
Figure 9.8: Governor with transient droop compensation

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Mechanical Hydraulic Governor
 On older units, the governing function is realized
using mechanical and hydraulic components
 Speed sensing, permanent droop feedback, and
computing functions are achieved through mechanical
components; functions involving higher power are
achieved through hydraulic components
 A dashpot is used to provide transient droop
compensation. A bypass arrangement is usually
provided to disable the dashpot if so desired.
 Water is not a very compressible fluid; if the gate is
closed too rapidly the resulting pressure could burst
the penstock
 Consequently, the gate movement is rate limited
 Often, the rate of gate movement is limited even
further in the buffer region near full closure to provide
cushioning

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Figure 9.9: Schematic of a mechanical-hydraulic governor
for a hydro turbine

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Parameters Sample data
Tp = Pilot valve and servomotor time
constant
0.05 s
Ks = Servo gain 5.0
TG = Main servo time 0.2 s
Rp = Permanent droop 0.04
RT = Temporary droop 0.4
TR = Reset time 5.0 s
Constraints
Maximum gate position limit = 1.0
Minimum gate position limit = 0
Rmax open = Maximum gate opening rate 0.16 p.u./s
Rmax
close
= Maximum gate closing rate 0.16 p.u./s
Rmax buff = Maximum gate closing rate in
buffered region
0.04 p.u./s
gbuff = Buffered region in p.u. of
servomotor stroke
0.08 p.u.
Figure 9.10: Model of governors for hydraulic turbines

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Electro-Hydraulic Governor
 Modern speed governors for hydraulic turbines use
electric-hydraulic systems. Functionally, their
operation is very similar to those of mechanical-
hydraulic governors
 Speed sensing, permanent droop, temporary droop,
and other measuring and computing functions are
performed electrically
 Electric components provide greater flexibility and
improved performance with regard to dead-bands and
time lags
 Dynamic characteristics of electric governors are
usually adjusted to be essentially similar to those of
mechanical-hydraulic governors

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Tuning of Speed Governing Systems
 There are two important considerations in the
selection of governor settings:
 Stable operation during system islanding conditions or
isolated operation; and
 Acceptable speed of response for loading and
unloading under normal synchronous operation
 For stable operation under islanding conditions, the
optimum choice of the temporary droop RT and reset
time TR are as follows:
 For loading and unloading during normal
interconnected system operation, the above settings
result in too slow a response. For satisfactory
loading rates, the reset time TR should be less than
1.0 s, preferably close to 0.5 s.
 The dashpot bypass arrangement can be used to
meet the above conflicting requirements
  
M
w
wT
T
T
15.00.1T3.2R 
   wwR T5.00.1T0.5T 

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Steam Turbine and Governing Systems
 A steam turbine converts stored energy of high
pressure and high temperature steam into rotating
energy
 the heat source may be a nuclear reactor or a fossil
fired boiler
 Steam turbines with a variety of configurations have
been built depending on unit size and steam
conditions
 normally consist of two or more turbine sections or
cylinders coupled in series
 A turbine with multiple sections may be
 tandem-compound: sections are all on one shaft with a
single generator, or
 cross-compound: sections are on two shafts, each with
a generator; operated as a single unit
 Fossil-fuelled units can be of tandem-compound or
cross-compound design
 may be of reheat or non-reheat type

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Figure 9.16: Common configurations of tandem-compound
steam turbine of fossil-fueled units

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Figure 9.17: Examples of cross-compound steam turbine
configurations

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 Nuclear units usually have tandem-compound
turbines
 moisture separator reheater (MSR) reduces moisture
content, thereby reducing moisture losses and erosion
rates
 Large steam turbines for fossil-fuelled or nuclear
units are equipped with four sets of valves
 main inlet stop valves (MSV)
 main inlet control (governor) valves (CV)
 reheater stop valves (RSV)
 reheater intercept valves (IV)
 The stop valves (MSV and RSV) are primarily
emergency trip valves.
 The CVs modulate steam flow during normal
operation.
 The CVs as well as the IVs limit overspeed.
Figure 9.18: An example of nuclear unit turbine configuration

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Steam Turbine Model
 For illustration, let us consider a fossil-fuelled single
reheat tandem-compound turbine, a type in common
use
 Figure 9.21(a) identifies the turbine elements that need
to be considered
 Figure 9.21(b) shows the block diagram representation
 The CVs modulate the steam flow for load/frequency
control
 the response of steam flow to CV opening exhibits a
time constant TCH due to charging time of the steam
chest and inlet piping
 TCH is of the order of 0.2 to 0.3 s
 The IVs are used only for rapid control of turbine
power in the event of an overspeed
 control about 70% of total power
 the steam flow in the IP and LP sections can change
only with the build-up of pressure in the reheater volume
 the reheater time constant TRH is in the range 5 to 10 s
 the steam flow in LP sections experiences a time
constant TCO associated with the crossover piping; this is
of the order of 0.5 s

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Parameters
TCH = time constant of main inlet volumes and steam chest
TRH = time constant of reheater
TCO = time constant of crossover piping and LP inlet
volumes
Pm = total turbine power in per unit of maximum turbine
power
Pmc = total turbine mechanical power in per unit of common
MVA base
PMAX = maximum turbine power in MW
FHP,FIP,FLP = fraction of total turbine power generated by HP, IP, LP
sections, respectively
MVAbase = common MVA base
Figure 9.21: Single reheat tandem-compound steam turbine
model

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Simplified Transfer Function of a Steam
Turbine
A simplified transfer function of the turbine
relating perturbed values of the turbine power
and CV position may be written as follows:
It is assumed that TCO is negligible in comparison
with TRH, and that the CV characteristic is linear
  
  RHCH
RHHP
RHCH
HP
CH
HP
CV
m
sT1sT1
TsF1
sT1sT1
F1
sT1
F
ΔV
ΔP









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Turbine Response
The response of a tandem-compound turbine to a
ramp down of the CV opening is shown in Figure
9.22.
 has no peculiarity such as that exhibited by a
hydraulic turbine due to water inertia
 governing requirements more straightforward
Figure 9.22: Steam turbine response to a 1-second ramp
change in CV opening
TRH=7.0 s, FHP=0.3; TCH and TCO negligible

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Steam Turbine Controls
Functions:
 The governing systems have three basic functions:
 normal speed/load control
 overspeed control
 overspeed trip
In addition, the turbine controls include a number of
other functions such as start-up/shut-down controls
and auxiliary pressure control
 The speed/load control is a fundamental requirement
 achieved through control of CVs
 the speed control function provides the governor with a
4 to 5% speed drop
 the load control function achieved by adjusting
speed/load reference
 The overspeed control and protection is peculiar to
steam turbines
 of critical importance for safe operation
 speed should be limited to well below the design
maximum speed of 120%

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 The overspeed control is the first line of defense
 involves fast control of CVs and IVs
 limits overspeed following load rejection to 0.5 to 1.0%
below overspeed trip level
 returns the turbine to a steady-state condition with
turbine ready for reloading
 The overspeed or emergency trip is a backup
protection
 designed to be independent of the overspeed control
 fast closes the main and reheat stop valves, and trips
the boiler
 The characteristics of steam valves are highly
nonlinear
 compensation is often used to linearize steam flow
response to the control signal
 compensation may be achieved by a forward loop
series compensation, a minor loop feedback, or a
major loop feedback.

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Governing Systems
 Systems used for the above control functions have
evolved over the years:
 older units used mechanical-hydraulic control
 electro-hydraulic control was introduced in the 1960s
 most governors supplied today are electro-hydraulic
or digital electro-hydraulic

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 The functional block diagram of a mechanical-
hydraulic control (MHC) system is shown in Figure
9.25
 the speed governor is a mechanical transducer which
transformers speed into position output
 the speed relay is a spring loaded servomotor which
amplifies the speed governor signal
 the hydraulic servomotor provides additional
amplification to the energy level necessary to move
the steam valves
 Figure 9.31 shows the block diagram of an MHC
speed governing system, including the overspeed
control (auxiliary governor) applicable to a specific
make
Figure 9.25: Functional block diagram of MHC turbine
governing system

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Figure 9.31: MHC turbine governing system with auxiliary
governor

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 The electro-hydraulic control (EHC) systems use
electronic circuits in place of mechanical
components associated with the MHC in the low-
power portions
 offer more flexibility and adaptability
Fig. 9.33 shows an example of EHC governing
system. It has two special features for limiting
overspeed: IV trigger and power load unbalance
(PLU) relay.
 the IV trigger is armed when the load (measured
by reheat pressure) is greater than 0.1 p.u. It is
designed to fast close IVs when the speed
exceeds set value.
 the PLU relay is designed to fast close CVs and
IVs under load rejection conditions. It trips when
the difference between turbine power and
generator load exceeds a preset value (0.4 p.u.)
and the load decreases faster than a preset rate.

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Fig. 9.33 EHC governing system with PLU relay and IV
trigger

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Gas Turbines
 The heat source is a hydrocarbon-based fuel
 in either gaseous or liquid state
 fuel is burned directly in the working fluid
 like any internal combustion engine, requires external
source for startup
 The power produced by the gas turbine is used to
drive an alternator to produce electrical power at
frequencies compatible with local grids
 Exhaust heat is often used to generate steam, which
can be used for a process, as in the case of
cogeneration
 simple-cycle configuration
 Alternatively, steam produced using exhaust heat
can be used in a steam turbine to generate additional
electrical power
 combined-cycle configuration
 Many variations in configurations and controls
 no standard models; generic models have been
developed
 discussion here intended as an illustration of modeling
requirements
 CIGRE TF: 38.02.25 report, published in 2003,
addresses some of the modeling issues

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Gas Turbines: Principle of Operation
 Consists of three major components: compressor,
combustion chamber, and turbine
 Based on the principle of "Brayton Cycle"
Fig. 1 Schematic diagram of a gas turbine
Fig. 2a The Brayton Cycle

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 The compressor takes the input air and
compresses it; this increases the temperature and
pressure, and decreases the volume (A-B)
 Compressed air is fed into combustion chamber
where fuel is added and burned; this increases
temperature and volume with pressure constant (B-
C)
 temperature is raised to the permissible turbine inlet
temperature - determined by temperature
tolerance of turbine blades
 since the fuel-air ratio is very lean, chamber is
designed to burn the fuel with primary air, and then
mix the combustion products with the amount of
secondary air required to lower the temperature to
permissible limit
 This heated gas is then expanded in the turbine to
atmospheric pressure (C-D)
 power is extracted through decrease in
pressure/temperature and increase in volume
 energy of expanding air is converted to
mechanical energy

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Combined-Cycle Plants: Principle
 The gases exhausted from a gas turbine are hot and
contain substantial amounts of oxygen
 The use of exhaust heat in a heat recovery steam
generator (HRSG) is the basis for the combined
cycle gas turbine (CCGT) plants
 steam from HRSG is fed to a steam turbine based
on “Rankine cycle”
 The whole plant becomes a binary unit employing
both the Brayton cycle and the Rankine cycle
A
D
B
C
Volume
Pressure
Fig. 2b Rankine Cycle

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Simple-Cycle Gas Turbines and
Governing Systems
 Block diagram representation of a single-shaft, simple-
cycle gas turbine shown in Fig. 3
 based on 1983 ASME paper by W.I. Rowen [1]
 applies to full range of turbines 18 MW to 106 MW
 The control system includes speed control,
temperature control, acceleration control, and fuel
limits
 Speed governor can be set for either droop or
isochronous control
 The digital setpoint is the normal means of controlling
turbine output for interconnected operation using
droop governor
 loading limits and ramp rates can be set by operator
 in the event generator breaker is opened, setpoint is
reset to 100.3%; this limits overspeed on load rejection
 Temperature control:
 primary purpose is to limit both turbine firing
temperature and exhaust temperature to acceptable
levels - determined by temperature tolerance of
turbine blades
 normal means of limiting turbine output at a
predetermined firing temperature, independent of
variation in ambient temperature or fuel characteristics

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Fig. 3 Simple-Cycle Gas Turbine Dynamic Model with
Sample Data

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 Exhaust temperature measured using a series of
thermocouples with radiation shields
 output of thermocouples compared with a reference
value
 normally, the reference is higher and temperature
control output is at maximum limit
 when thermocouple output exceeds reference,
temperature control "output" decreases; if it becomes
lower than governor output, the unit operates on
temperature control
 Acceleration control:
 used primarily during startup to limit the rate of rotor
acceleration so as not to cause excessive thermal
stresses
 serves a secondary function of limiting overspeed by
reducing fuel flow in the event the generating unit
separates form the power system by a breaker other
than generator breaker
 The Low Value Selector lets through the lowest of
the three control output signals - speed governing,
temperature control, and acceleration control
 control function requiring least fuel is effective

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PM - 39
 The fuel demand signal is further limited
 maximum limit acts as back up to temperature control,
and is not encountered in normal operation
 minimum limit ensures adequate fuel flow to keep the
flame alive within the turbine combustion system
 typically set at a torque deficiency of 10%
 a hard limit representing maximum rate of
decceleration or torque absorption from the power
system
 The fuel systems are designed to provide energy input
to the turbine proportional to the product of the fuel
command signal (VCEl) and the unit speed
 speed of fuel pumps linked to rotor speed
 taken into account in model of Fig. 3
 Gas turbine requires a significant fraction of rated fuel
to support self-sustaining conditions under no load
 amounts to about 23%
 need to minimize operation at no-load conditions for
economy
 The capability of transiently absorbing power from the
power system is unique to gas turbines
 can be taken advantage of in special circumstances
 active control range of governor set to 16% to 100%
allowing a negative torque of about 10%

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Combined-Cycle Power Plants
 Typical configuration consists of
 a gas turbine
 heat recovery steam generator (HRSG)
 a steam turbine
 Fig. 4 shows the chain of submodels
 Often the power output of steam turbine is not directly
controlled by the governor
 simply follows the changes in gas turbine output as
the exhaust heat changes
 Gas turbine controls include
 speed governor, temperature control and acceleration
control which together determine fuel request signal
 inlet guide vane (IGV) modulations
 IGV modulated to vary air flow over a limited range
 maintains high turbine exhaust temperature levels to
maintain the desired level of heat transfer to HRSG
and achieve high steam cycle efficiency at reduced
loading
 As an example, Fig. 5 shows model developed for a
combined cycle plant in reference 3

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PM - 41
Fig. 4 Combined-Cycle Plant Chain of Submodels
Fig. 5 Combined-Cycle Plant Dynamics Model

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PM - 42
 The gas turbine proper is essentially a linear,
non-dynamic device, with the exception of rotor
time constant (inertia). Significant parameters:
 a small transport delay (ECR) associated with
combustion reaction time
 a time lag (TCD) associated with compressor
discharge volume
 a transport delay (ETD) to transport gas from
combustion system through the turbine
 Both the exhaust temperature (TX) and torque
characteristics are linear functions of fuel flow
(WF) and rotor speed (N)
 given by functions f1 and f2
 applicable over the speed range of 95% to 107%

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Simplified Gas Turbine, Governing
System Model
 Simplifications applicable for interconnected system
operation in a relatively "stiff" system
 small speed variations as in most system stability studies,
particularly rotor angle stability and voltage stability
 Referring to model of Fig. 3:
1. Speed governors can be changed to droop-only
configuration
2. Acceleration control can be neglected
 will not be active except under load-loss situations
3. Temperature control can be neglected
 temperature remains within interactive limit imposed by
the control
4. Turbine output predominantly controlled by the digital
setpoint
 eliminate the low value selector
5. Minor dynamics associated with gas turbine may be
neglected
 eliminate blocks involving time lag TCD, and transport
delays ECR and ETD

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Combined Cycle Unit Configurations
and Control Features
 Single-shaft units: gas turbine, steam turbine and
the electrical generator are all tandem compound on
a single shaft
 Multi-shaft units: one or more gas turbine each
typically with its own HRSG, feeding steam to a
single steam turbine, all on separate shafts with
separate generators
 In a combined-cycle power plant, steam turbine can
be operated in two different modes: (a) sliding
pressure control or (b) fixed inlet pressure. In
practice a combination of these two modes are used
depending on the level of power output
 The electrical power output of a combined-cycle
plant, without supplementary firing, is controlled by
the gas turbine only. The steam turbine will follow
the gas turbine by generating power with the steam
available from HRSG
 In order to sustain stable operation and extend the
life of the gas turbines, a frequency dead-band may
be introduced in the control system: typically,
0.025%
 Combined-cycle power plants can be operated to
provide frequency support (spinning reserve).
For frequency support, the gas turbine is operated
between 40% and 95% load, resulting in partial
loading of the steam turbine

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References on
Gas Turbines and Combined Cycle Power Plants
[1] W. I. Rowen, "Simplified Mathematical
Representations of Heavy-Duty Gas Turbines",
Transactions of ASME, paper No. 83-GT-63, Journal
of Engineering for Power, Vol. 105, October 1983,
pp. 865-869.
[2] IEEE Working Group on Prime Mover and Energy
Supply Models, "Dynamic Models for Combined
Cycle Plants in Power System Studies", IEEE Trans.
on Power Systems, Vol. 9, No. 3, August 1994, pp.
1698-1708.
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For a more recent comprehensive reference see: