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Prime Movers and Governing SystemsPrime 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 GoverningHydraulic Turbines and Governing
SystemsSystems
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
1. Hydraulic Turbine Transfer Function1. 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 ∆ρ−=
∆
ρ
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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
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Governors for Hydraulic TurbinesGovernors 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 GovernorMechanical 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 GovernorElectro-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 SystemsTuning 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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2. Steam Turbines and Governing2. Steam Turbines and Governing
SystemsSystems
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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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 ModelSteam 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 SteamSimplified Transfer Function of a Steam
TurbineTurbine
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 ResponseTurbine 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 ControlsSteam 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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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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3. Gas Turbines3. 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
CIGRE TF: 38.02.25 report published in April 2003
addresses modeling issues
