Transcript No Slide Title

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
Outline
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
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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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1. Hydraulic Turbine Transfer Function

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
Figure 9.2: Schematic of a hydroelectric plant

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
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The velocity of the water in the penstock is given
by
U  KuG H
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,
Pm  KpHU
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
LA dU   A ag H
dt
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
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
For small displacements (prefix ) about an initial
operating point (subscript "0") we can shows that
 Pm
1  Tw S

G 1 1 T S
w
2
where
Tw 
(9.11)
LU0
a gH0

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.
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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:
t 
 2


T
 Pm t   1  3e  w    G



Figure 9.3 shows a plot of the response of an ideal
turbine model with Tw = 4.0 s
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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 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
Tp =
Ks
TG
Rp
RT
TR
=
=
=
=
=
Sample data
Pilot valve and servomotor time
constant
Servo gain
Main servo time
Permanent droop
Temporary droop
Reset time
0.05 s
5.0
0.2 s
0.04
0.4
5.0 s
Constraints
Maximum gate position limit = 1.0
Minimum gate position limit = 0
Rmax open = Maximum gate opening rate
Rmax
= Maximum gate closing rate
0.16 p.u./s
0.16 p.u./s
close
Rmax buff
gbuff
= Maximum gate closing rate in
buffered region
= Buffered region in p.u. of
servomotor stroke
0.04 p.u./s
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 mechanicalhydraulic 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:
R T  2.3  Tw  1.0 0.15
Tw
TM
TR  5.0  Tw  1.0 0.5 Tw

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
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2. Steam Turbines 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
Figure 9.18: An example of nuclear unit turbine configuration
 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.
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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
TRH
TCO
Pm
Pmc
PMAX
FHP,FIP,FLP
MVAbase
= time constant of main inlet volumes and steam chest
= time constant of reheater
= time constant of crossover piping and LP inlet
volumes
= total turbine power in per unit of maximum turbine
power
= total turbine mechanical power in per unit of common
MVA base
= maximum turbine power in MW
= fraction of total turbine power generated by HP, IP, LP
sections, respectively
= 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:
ΔPm
FHP
1  FHP


ΔVCV 1  sTCH 1  sTCH 1  sTRH 

1  sFHPTRH
1  sTCH 1  sTRH 
It is assumed that TCO is negligible in comparison
with TRH, and that the CV characteristic is linear
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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 mechanicalhydraulic 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 9.25: Functional block diagram of MHC turbine
governing system

Figure 9.31 shows the block diagram of an MHC
speed governing system, including the overspeed
control (auxiliary governor) applicable to a specific
make
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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 lowpower 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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3. 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
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