Download Control of Electric Power Systems

Control of Electric Power Systems*
9-
Olle 1. Elgerd
Generator
Department of Electrical Engineering
University of Florida
Gainesville, Florida
Transformer
Bus
Coding
1
1
2
Introduction
A powersystemmust be abletomeetreasonablepower
demands by large
and
small
customers
of domestic.
commercialand industrial type. It mustwithstand with
reasonable security the capricious forces
of nature. In an
age of high energy costs it is called upon to transform the
prime energy resources into electric form with an optimum
overallefficiency.Thecontrolfunctions
areobviously
many and varied.
Some control and decision processes, exemplified by the
optimal utilization of the controlled flow of river systems
involvedynamicswithmonth-longtimeconstants.Other
phenomena,like thetransientsonthetransmissionlines
followinglightningstrikes,
run theircourse
in afew
milliseconds.
Theslowercontrolprocesses
arenormallyhandled
by
computer-assistedhumanoperators.The
faster
control
functions are trusted to fully automatic control systems of
either open or closed-loop nature.
The objective of this article is first to outline briefly the
basic functional features of a power system and, secondly,
describe some of the more important controls required for
its satisfactory operation. Finally some of the more relevant
research and development areas are identifiedand discussed.
Bus
[I-
Circuit breaker
///
Tobus*12
4
neighboringsfstem
/
f
To bus*
7
Fig. 1.
Power system
symbols.
2. Load Characteristics and Generator Mix
The loads vary widely over daily, weekly and seasonal
cycles.Fig. 2 showsa typicaldaily fluctuation. Electric
power travels onthe lines at a speed closeto that of light. In
addition,the
linesthemselves(unlikegastransmission
lines)havenoenergystoragecapacity,andasaconsequence the electric power mustbe generated at the instant it
is being demanded by the loads. The installed generating
capacity of the system must thus equal
the peak demand plus
a spinning reserve of 10-20 percent, the latter consisting of
partially loaded generators.
1. The Power Grid
Fig. 1 shows a one-fine diagram of a section of a larger
system. The electric power is produced in the generators.
transformedto an appropriatevoltage level in the transformers and then via the buses sent out on the transmission
fines forfinal distribution to the loads. Via tie-lines the
system is connected to neighboring systems belonging
to the
same pool.
Fig. 1 does not show the low-voltage distribution portion
of thesystem,whichcontains
themajority of the load
objects. For most important system studies it is sufficient to
use lumped or composite representations of the loads. The
load symbols in Fig. 1 are of the latter type.
The circuir
breakers
permit
the
tripping
of
faulty
componentsandalsosectionalizing
of thesystem. High
voltage dc (HVDC) is being used in special cases. However,
thevastmajority
of theworld’selectricpower
is being
generated, transformed, transmitted and distributed as high
voltage ac (HVAC) of the threephase variety. Collectively
thegenerators,transformers,buses,
lines and loadsconstitute the power network or grid.
A
Spinning R e s e w
I
6
12
18
24
Noon
Midnight
Fig. 2.
*Received January 8, 1981; in final form March 12. 1981. Accepted in
final form by Associate Editor L. H. Fink.
6
12
Noon
18
-t
Hours
Daily load fluctuation.
0 2 7 2 - 1 7 0 8 / 8 1 / ~ $ W . 7 . 5 @ 1 9 8 1 IEEE
4
The power demand in Fig. 2 is met by a generator mix
All othervoltageandcurrent
phasors are measured
consisting of
relative to V I .
1. Baseloaded units, running fulloaded on a 24 hour basis.
The bus current. I ; , is defined as the difference between
Nuclear and large fossilfired units fall in this category.
the generator current IGland the load current I L i , i.e.
Reactor cores and huge boilers do
not tolerate fast power
changes once thermal balance has been reached.
2 . Controllable units,consisting of hydrogenerators and
smaller fossil units. All such units have rate limits giving
The bus potver consists of two components, the real and
the fastest rates (MW/sec) with which their loads can be reactive powers, P iand Q, respectively, defined as follows:
changed.
3 Peakloaders, whichcan pick up load relativelyfast.
Gasturbine-driven
generators
are
common,
but also
generators
driven
from
short-time
energy storage
facilities like pumped hydro, compressed gas or thermal
storage (ref's. 1 and 2 ) .
where Q i is the relative phase between V , and I ; , i.e.,
3. The Power Flow Equations (PFE)
Central to all analysis of power systems are the physical
laws
that
determine
the
flow
of the electric
power
throughout the system. We give a brief-presentation of this
important topic. (For more details see ref. 3.)
p i and Q , represent the generated minus the load power at
bus i, measured in MW and Mvar par phase resp.
It can be readily shown that P I and Q, satisfy the complex
equation
0
where
( )*
denotes "conjugate."
As the network is linear, electric circuit theory tells us
that the followinglinear relationship exists between theV i ' s
and l i ' s :
(9)
' b u s = 'busVbus
The N-dimensional vectors
\ I
I
'bus
and VbUSare defined by
\
\
v
ni outgoing lines
Fig. 3.
Bus voltage and current symbols.
The N
X
N busadmittance matrix
Consider an N-bus system. For a typical
US power system
N > 100. For very large systems N > 1000. Fig. 3 details
bus # i of such a system, containing generation, load and tzr
outgoing lines. For typical systems
is symmetric and contains the elements yG which are complex of
the form
The bus is characterized by the bus voltage phasor V ,
measured between the reference phase and ground. V I has
magnitude and phase defined by
As a result of the nonequality ( l ) , Ybusis a sparse matrix,
i.e., most of itsoff-diagonalelementsarezero.
(A nonexisting line between buses i and j means that yi, is zero.)
Upon substitution of the ith of equations (9) into eq. (8)
we obtain
We choose bus # 1 as reference bus and assign to it the
voltage
5
Separation of thereal and imaginaryparts of eq. (13)
yields the 2N real equations:
where Xkl is the line reactance. As this power increases, the
line power angle, 6 k - Si, may reach 90” in which case we
have reached the static power limit
Any attempt to further increase the power would result in
theloss of synchronismandtransmissioncollapse.
For
relatively short lines (less than 200 miles) the thermal limit
For long linesthe
typicallydeterminesthelineloading.
situation is reversed and the static power limitnow becomes
the critical concern.
These arethe famous power flow equations (PFE). In
contrast to eq’s (9) they are highly nonlinear. Physically
they expressreal and reactivepower balance at the N buses.
We can view the bus powers P i and Q i as control inputs.
By their manipulation we can affect or control the voltage
sfafe variablesI V i [and hi. In accepted control lingowe thus
have the state and control vectors
5. The State Transition Diagram
Dy Liacco (ref. 4) defined the various “states” in which a
power system may be found. Fink and Carlsen (ref. 5) went
further and suggested the state transition diagram shown in
Fig. 4. This diagram provides a good conceptual picture of
the overall control requirements of a power system.
E,I
NORMAL
and
I
Restarts
“Load pickup
11
Preventive
I
‘.‘M.....”i
Thevectors x and u eachare of dimension 2N. The
subvectors 6 , lVl,P and Q each are of dimension N.
“Control
RESTORATIVE
4. NormalOperating State
I
A power system operates in a normal state if the following
conditions are met:
(1) All the load demands are met andthe
k oPFE’s
n t r oare
l satisfied.
( 2 ) The frequency, f, is constant (60 Hz in USA)
(3) The bus voltage magnitudes IVi I are within prescribed
limits.
(4) No components are overloaded.
According to Fig. 2 the demands vary slowly with time.
Thus, in order to track the loads to meet requirement# 1 the
normal state is “drifting” as the hours wear on.
Frequency constancy is required for a number of reasons;
electric clocks must be accurate, steamturbines mustnot be
subject to blade resonance,
motor speeds must be kept constant.
However, the most important reason for keeping f constant is
that its constancy indicates that total system powerbalance is
maintained (Sect.9).
Voltage constancy isrequiredbecause
all loadobjects
from lightbulbs to giant motors are voltage rated.
Component overload must be avoided as it results in elevated
temperatures andrisk for damage. For a transmission line
thermal damage isonly half the problem. It can be shown (ref.
3) that the real power, P,,,transmitted on the line connecting
buses k and 1 follows the formula
I
1
Resynchron bation
Emergency
--
E,I -
E,!
EXTREMIS
A
’
EMERGENCY
I
’E’ = Equality Constraint
’I‘ = Inequality Constraint
’-‘ = Negation
Fig. 4. Statetransitiondiagram.
For more than 99 percent of the time we find the system in
its normal state as defined in the previous section. In sect. 7
we shall discuss thenormal state controls required to keep the
system in this state. The symbol “E” refers to “equality”
and means that the PFE‘s are satisfied and frequency and
voltageconstancyobserved.Thesymbol
“1” refersto
“inequality” and means that we are operating within rated
component limits.
Assume now that the system would suffer the sudden loss
of a generator or experience some other event that would
reduce the security level. The system would
now enter the
alert state. The “E” and “I” would still be satisfied and,
6
withluck,
we couldoperate
in this state indefinitely.
The four Jacobian submatrices J , ... J4 have as elements
However, by preventive controls (for example start-up of
thepartialderivativescomputed
in thenormalstate.The
reserve generators) we would seek to return the systemto its matrices are sparse.
normal state.
We can write eq (20) in “component” fornx
Withthesystemstill
in thealertstatesomeadditional
disturbance may occur, for example the tripping of a tie-line A P z J l A 6 + J , A I VI
or the loss of an additional generator. The resulting power
+ J , A l VAl Q z J 3 A 6
(2 1)
shift may then overload a line. The system remains intact,
i.e., “E” is still satisfied but “ I ” is negated. The system
In a typical power networkthe impedance elements are
now enters the emergency state. By means of emergency
almost
purely reactive which means that the angles yij of the
try
to relieve the overload
controls, we would now
Ybus
elements
are close tof90”.In addition we seldom operate
situation. For example, by lowering the bus voltages, one
with
line
power
angles,
6 j - t i i , above 30”. Underthese
would force a reduction in the loads (“brownouts”).
circumstances
it
is
easy
to
show that the submatrices J , and J4
Should the emergency controlsfail then the overloaded line
dominate
over
52
and
J3 and in a first approximation eq’s (21)
must be tripped. We may then see a series of cascading events
which may lead to the extremis state. Typically, the system thus canbe written in simpler form:
be
would nowbreakup
into islands, each ofwhichwould
operating attheir own frequencies. Both “E” and “I” are now
APzJlA6
negated. Eachisland would typically be characterized by severe
AQ z J 4 A l V I
(22)
power imbalance and“heroic” control measures like load
shedding or generator tripping would be tried to saveas much as
In words: A change in the reactive bus power components
possible of the system. On rare occasions, however, the efforts
will result in changes in the bus voltage magnitudes with
might fail and the system would end up in a total “blackout.”
only
minor
effects
on
the
bus
voltage
phase
angles.
involvesgeneratorrestarts,reThe restorativestate
Similarly, changes in the real bus power components bring
synchronizationandgradualloadpickup.Thisisaslow
about changes in bus voltage phase angles with very minor
process and can in severe cases last for hours and days.
effects on the voltage magnitudes.
6. Normal State Control-A
Property
Noninteraction
We make these additional important observations:
1 . Assumethat we manipulatethebuspower at one bus,
Maintaining a power system in its normal state is a high
#k,only. As a resultthevoltages
of all buses will
priority control function. The job is made relatively simple
change.Thechanges
will be largestatbus
k and
by noninteraction
a
property
characterizing
all
power
diminish with the distance from this bus. However, all
systems. We presently discuss this property.
changes AIVi( and a S i will be of the same polarity as
Considerasystem operating
initsnormal
state. Small
AQk and A P k respectively. For example, if we increase
changes AP and AQ are now made in the control vectors p
AQk thenthevoltagemagnitudes
of a f f buses will
and Q. As a result the state vectors 6 and IVl will undergo
increase with the largest increase measured at bus k .
small changes A6 and AlVl respectively. Eq’s(14) yield the 2 . The increments APk and AQk added at bus k will divide
following
relationships
between
the
control
and
state
and flow out on the nk lines terminating in bus k . At the
changes:
ends of these lines there will
be a further subdivision,
dissipates as it flows
etc. Powerinjection at a bus thus
out in the network. This “dissipation effect” makes
it
possible toanalyzephenomena
in powersystems by
modelingonlythelocalportion
of thenetwork.For
example, the Florida and California grids are electrically
interconnected, but anetworkdisturbance
in Florida,
will have no measurableeffects in
even amajorone,
California.
7. The Normal State Controllers
for i = 1 .-, N
Wecanwritetheselinearrelationships
vector-matrix form
In sect. 4 we stated the four conditions that must be met
for the system to remain in its normal state. The obvious
way to maintain a perfect power balance at each bus would
be to continuously keep the generated powers, PGi and QGi
in balance with the changing load powers PLiand QLi.This
then would maintain allAPi and AQi at zero levels and thus
all busvoltages and line powers at constant values.
This, of course,isneitherdesirable
nor possible. It is
undesirable because constant line powers would defeat the
real purpose of transmission lines which is to make possible
~
in thecompact
7
at each moment themosteconomicaltransfer
of power.
Neither would it be possible since most buseslack both real
and reactive power sources.
The most important power sources are the synchronous
generators. Typically, generators are available only at less
than five percent of the network buses. At these “generator
buses” both P , and Q, can be controlled. The real power is
controlled via the turbine torque, the reactive power via the
“exciter” and field winding.
Generators obviously represent themost important means
forsystemcontrol.
Eachgeneratorisequipped
with two
separate automatic feedback control loops both depicted in
Fig. 5. TheAutomaticVoltageRegulator(AVR)loop
maintains
control
of the bus
voltage
by means of
manipulation of the reactive power output. The Automatic
Load-Frequency Control (ALFC) loop maintains a constant
frequency by manipulation of the real power output. Both
these loops are designed to operate around the normal state
withsmallvariableexcursions.Thus
the loops maybe
modeled
with
linear,
constant
coefficient
differential
equations and representedwith linear transfer functions. We
look separately at the two loops.
8. The Automatic Voltage Regulator Loop
Depending upon size and typeof the generator, excitation
systems come in several different models. Ref. 6 gives a
detailed classification. Here we briefly point outsome
of
the more important features, that are typical of most AVR
loops.
AS shown in Fig. 5 the busvoltage is measured via a
potential transformer (PT). After rectification and filtering
the output is compared with a reference. The resulting error
voltage,afteramplificationserves
as inputto an exciter
which feeds directly into the generator field. A drop in the
terminal voltage causes a boost
inthefield current. This
increasesthereactivepoweroutput
of themachinethus
tending to offset the initiating voltage drop.
Theanalysisoftheloopis
not difficult(ref. 3 ) . The
amplifier, exciter and field circuit each represent separate
timeconstantsthelatterreaching valuesashigh
as 5-10
sec’s.Thethreetimeconstantsadd
thethreerealand
negative open-loop poles markeda, b and c in Fig. 6. There
will be threeclosed-looproot lociandthreeclosed-loop
poles the latter marked A, B and C in the same figure.
-
ALFC LOODS
A
/
Secondary ALFC Loop
r
Tietine powers
A
AVR Loop
\,
\ -
..
voltage error
\
Primary ALFC Loop
IviI
\L
Signal
mixer
\;F&$$,;
Rectifier
& Filter
Frequency
-
Sensor
f
Trans
Former
-
Burr’ i
*PL
Local
Load
\
To
Network
AP
I
Fig. 5 . Basic generatorcontrol loops.
fix points” in the network. One normally needs additional
such fix points to assure an overall good voltage profile.
This can be achieved by installing banks of shunt capacitors
at certain key buses. A capacitor delivers reactive power
and constitutes thus a “Q-source.”
If negative bus power
generation also is required banksof shunt reactors must also
be installed. By controlling these capacitor and/or reactor
banks from an error voltage similarto that of the AVR loop,
automatic closed-loop voltage control canbe achieved. The
control itselfcan be done in on-off fashion by means of
circuit
breakers.
Modem
installations
utilize
thyristor
control which permits continuous variation of the reactive
power.
Normally, the closed loop should respond
in less than 0.1
seconds. To overcome the slow field circuit and also for
sufficient
static
accuracy
we
purposes of achieving
obviously require very high loop gain. But this gain would
pushtheconjugatecomplexpolepair
(A, B) into the
unstables-plane.The
AVR loop is clearly in need of
effective stabilization if speed and accuracy requirements
bothhave to be met.Ref. 6 describesvariouspractical
means for achieving stability compensation.
TheAVRloopmaintainsreactivepowerbalance
at a
generator bus by indirectly maintaining a constant voltage
level. The generator buses thus can be considered “voltage
8
decrease will accelerate the
unit.
In either
case
the
generator frequency will undergo a change, Af, which thus
Actually there is not one ALFC loop but two, designated becomes an indicator of the existing power unbalance.
“primary“ and “secondary“ in fig. 5. The purpose of both
The ALFC loops are designed to maintain power balance
theseloopsis
to achieverealpowerbalance,
or “load by an appropriateadjustment of theturbinetorque.
By
tracking,” in the system. Just asthe AVR loopachieves
means of the “primary” loop a
relatively fast but coarse
Q-balance by maintainingaconstantvoltage,the
ALFC frequency control is achieved. Theresponsetime
of this
loopsachieveP-balance
by maintainingaconstantfreloop is limited by the inherent speed of the turbine and is
quency.
typically measured in seconds.
Thereisanimportantdifference,however.The
AVR
The “secondary” ALFC loop works in a slow reset mode
loopisable tomaintainperfectQ-balanceonly
at those to eliminate the small frequency errors which still remain
buses that are voltage controlled. The ALFC loops maintain after the actionsof the primary loop. This loop also controls
primarily P-balance at the generator buses but because rhe the power interchange between poolmembers.We now look
frequencyis the samethroughout the systemthey
thus at these two loops in more detail.
collectively, achieve P-balance on a system wide-basis.
To understand the functioningof the ALFC loopswe need 10. The Primary ALFC LoopMathematical Modeling
to brieflyreviewthemechanismwherebythegenerator
supplies power to the network. Consider thus the generator
The purpose of this loop is to achieve the fastest possible
in Fig. 5 to operate initsnormalstate.Itdeliversthe
adjustment of the turbine power in response to a change in
constant electrical power, PC’ megawatts, to the network.
frequency. To this
end
the
speed
governor
measures
Through a rather intricate mechanism (ref. 3, chap. 4) the
continuously the frequency(or speed) and produces a power
generatorcurrentsand
therotormagneticfieldcreatea
command, P C ,of the linear form
constant electro-mechanical decelerating torque TG’ which
is related to the generator power through the equation
9. The Automatic Load-Frequency Control
PG O
TGO=
7
wrn
(Ref. 3 gives hardware details)
Pre. is areferencepowersetting.Theconstant
Kg has
dimension MW/Hz. Its inverse value (Hz/MW) is referred
in
to as“regulation”
andinforms
of the staticdrop
generator expressed in radtsec.
The turbine delivers a constant accelerating torque, TTo frequency as caused by increased power output. In USA the
which if expressed in turbine power, amounts to
regulation is typically set at 5% meaning that the frequency
would drop 5% ( = 3 Hz) for a change in power between zero
PT’ = w, TTo
and full load.
Thecommand, AP,., is fed into a hydraulicamplifier
The torques T G o and TTo(and the powers P G o and P r o ) which causes a position change, A P v , of the steam control
are in complete balance and the speed andfrequency,P, are valve (or control gate in the case of a hydrogenerator).
The hydraulic amplifier typically has a transfer function
thus constant.
This equilibrium is suddenly upset by an electrical load
to achange,
AP,,
change, A P G , (Fig. 5 ) dueeither
in the local load or a change, AP , , in the line* power or
both. The load incrementAPL due, for example,to an added
motor will be referred to as “new” load, in contrast
to where the time constant TH lies in the range 0.1-0.2 sec’s.
changes in already connectedor “old” loads (see also Sect.
The change in valve (or gate) opening translates in the
11C). As a result of these load changes the generator power
turbine into a power increment, A P T .
changes instantaneously with the amount of AP,. Electrical
We can now readily assemble the block diagram shown in
power balance requires that
Fig. 7. (Disregard for the time being the dotted portion.) The
portions labeled “network” and “turbine“ require further
elaboration.
amo
isthemechanicalrotationalspeed
of theturbine-
’
In the moments following this electrical loadchange no
change takes place in the turbine torque, and the turbinegenerator thus experiences a slight torque
or power imbalance.
If the electrical load change is positive signifying a load
increase the
turbine-generator
will
decelerate.
A
load
11. Network Dynamic Representation
The turbine power, A P T , will be used for four different
purposes:
1 . To supply the demanded “new” load APL.
2. To accelerate the turbine-generator, thus increasing the
kinetic energy, Wkin, of the unit.
3. To increase the powers in outgoing lines, i.e., A P , .
*For simplicity we assume only one outgoing line in Fig. 5 .
9
Fig. 6. Root-loci for uncompensated AVR loop.
Semndary ALF C loop
A
1
\
Primary ALFC loop
A
/
\
Network
A
Speed
governor
II
-
* PC1
-
A
ApL
KN
1~
l+rTH
Hydradim
Af
pv
T N
Turbine
1
I;
2XT.'I
A f - Afj
t_
l2-J
Line
Af
7-1
A fi
Fig. 7.
4. increase
Tothe
meet
We
discuss
briefly
in the "old" load.
the three last power
components.
Modeling of ALFC loops.
(from bus j)
d
dt
@kin
=- (Wkin)
dt
L
A . Kinetic Power Increment, AP,,,
Thekineticenergyserves
as a buffer storage. For
example when
a
customer suddenly
connects
a
100 kW
motortothesystem
it obviouslycannot
be met by a
corresponding increase in the slowchanging turbine power.
Instead, the generator will supply it by "borrowing" from
the kineticenergy.Since
the latter varies as the square of
the speed this power component can be expressed as follows
10
dt
2Wkin0
%-
fo
d
-
dt
(An
where Wkino representsthekineticenergy as
normal speed.
(28)
measured at
B . Line Power Increment, A P ,
12. Turbine Representation
For simplicity we assume there is only one outgoing line
connecting our generator bus, # i , with an other generator
bus, # j .
From
eq
(17)obtain
we
turbine
types.
(More
details
Theturbinedynamicsis
of centralimportance. It will
vary widely &pending upon type of turbine used. We give
thetransferfunctionrepresentationforthreedifferent
can
obtained
be
from ref. 7.)
A5
A6
=
2.rrSAfdt we can write
Reheater
where the parameter, T u , the synchronizing coefficient of
the line, is defined by
Valve
Steam
-
chest
turbine
APT
turbine
C . Frequency Dependency of ‘‘Old” Load
I
As the frequency increasesso will the speed of all motors
fedfromthebus.Addedspeed
meansaddedtorque
and
power.One may expressthis frequencydependency
of
existing load by an empiric parameter, D, having the unit
MW/Hz. Thus the increase in the ”old” load equals DAf.
By Laplace transforming all the above power components
andadding themthe dynamic powerbalance at the bus
reads:
\\
‘Head’
Fig. 8 . Turbine types:(a)
To Condenser
’
Non-reheat steam,(b)
( c ) Hydro.
Reheat steam, and
A . Non-Reheat Steam Turbine
We can rearrange this equation as follows:
Thisturbinetype(Fig.8a)has
a simpledesign. After
passing the control valve the high pressure steam enters the
turbine via the steamchest. The chest introduces a delay,
TcH, in the steamflow resulting in the transfer function
where
KNo
1
Typical values for TCHlie in the range 0.2-0.5 sec‘s.
-
D
(34)
B . Re-heat Steam Turbine
This type of turbine has several turbine stages, between
which the steam is led via reheaters. The design increases
efficiency and is always used for large units.
Assume that the two stagesin Fig. 8b are rated at half total
powereach. If we alsoassume that thereheatercan
be
Putting eq (33) in blockdiagramformyieldsthepart
labelled “network” in Fig. 7.
11
represented by a timeconstant, T R H ,then the total turbine
power equals (neglecting the delay in the chest):
The overall transfer function would be
(37)
TRH hastypicalvalues
in therange 4-10
resulting in slow overall response times.
sec’sthus
whole“area”which
in practicetypicallycanembracea
whole power system.
If this “area” via tie-lines is connected to neighboring
“areas” then we talk about multi-area dynamics.
In such
situations all the power commands are executed in unison
amongallgenerators
that areundercontrol.
If each
generator in the area has the samepercentage“regulation’ ’ then each generator will participate in proportion to
its rating.
The secondary ALFC loops in multi-area systems contain
controlsignals, now referred to as “areacontrolerrors”
Af, also
(ACE), which in additiontofrequencyerror,
in thecontractedtie-linepowers.A
containtheerrors
typical such ACE would be of the form
ACE =
C . Hydro Turbine
Depending upon the magnitude of water “head” (fig. 8c)
this type of turbine is of varying design. Without proof (see
ref. 7) we give the following transfer function
+ SAf
(39)
15. Optimal LQR Design
The AVR andALFCloopswerederived
on the assumption of total noninteraction.
There
is,
however,
1 - ST,
crosscouplingbetween the channels,whichunder certain
GT=1 + sTp
circumstances willhavenoticeable
effects,sometimes of
verydeleteriousnature(ref.
3, chap. 9). Forexample,
T p isthetime it takesforthewaterto
pass through the sometimes whole areas will start to oscillate at frequencies
around 1 Hz. Theoscillationsshow up in frequencyand
penstock.
tie-linepowersandcangrow
tolevelswhendesynchroFig. 9 showsacomparisonbetweenthethreeturbine
types in regards to the time response to a stepchange in the nization occurs.
In principle it is not difficult to expand the mathematical
valve position. It is interesting to note the momentary power
decrease for a hydroturbine. (Electrical engineers refer to models toaccountforthesephenomena.However,the
models become of high dimensionality and classic control
this type of behavior as “non-minimum-phase.”)
design becomes difficult.
13. The Secondary ALFC Loop
Insituations likethisoptimum
LQR designbecomes
attractive.
Following
initial
attempts
by Yu, Elgerdand
The primary ALFC loop would yield a frequency drop of
8,
9)
many
additional
contributions
have been
Fosha
(ref.
about 3 Hz between zero and full-loadof the generator. This
is where the reported (ref. 10). Space does not permit a discussion here,
poor accuracy is entirely unsatisfactory. This
3 formoredetailed
“secondary“loopenters
the picture. It performs slow butthereaderisreferredtoref.
“reset”adjustments
of thefrequency
by changing the coverage.
reference power command Pref.
16. Emergency Controls
The dotted portion of Fig. 7 shows how this can be best
Allpreviousdiscussionshaveconcernedcontrol
loops
accomplished by a low-gain integrator loop.
in its
whichareintended
tomaintainthepowersystem
Followingasudden
load increase, AP,, theturbine
output, APT, is increased to a new value as rapidly as the normal state. In sect. 5 we indicated how cascading events,
primary ALFC loop will permit.
Aswe noted, the turbine or multicontingencies, can bring the power system into an
if not properlycontrolled
can
response sets
the
pace.However,
we are
left
with a emergency state,which
considerable negative frequency error, which now causes a deteriorate into an extremis state. Due to the slow turbine
slowly
growing
positive integrator
output
and
a cor- responsethe ALFCloopsareineffective
in emergencies.
responding increase in power reference setting. Whereasthe The AVR loopsarefasterbut
the limitedexciterpower
primary loop responseis over in seconds. the secondary fine renders even these loops essentially useless.
adjustment may take of the order of one minute andwill not
Powersystemcomponents,especiallygenerators.are
stop until the frequency error is zero.
veryexpensiveand
theprimaryobjective
of emergency
controls is topreventdamage totheequipment.Forthis
14. Extension to “Multi-Area’’ Systems
reason one always finds a first line of defence consisting of
The loop model in Fig. 7 is in strictest sense valid for a protective devices organizedinto unitprotectilme svstenzs.
singlegeneratoronly. We havenoted. that the frequency For example, generators, transformers.lines and buses have
which
dynamics is relatively slow.Thistends tomake a whole their own specialized fastacting protective devices.
mostly
are
set
to
operate
i
n
preset
or
openloop
mode.
group of generatorsmove in unison.or coherently. thus
a circuit
permitting us to represent them all with the same Af. For Typicallya r e l q detects thefaultandinitiates
this reason it is common to let the model
in Fig. 7 represent a breaker trip. It is important that tripping involves onlythose
12
components that are subject to damage and the relays must
thushave
high selectivitx. Microprocessorsarefinding
increased use in modern relay design.
Thesecondobjective
oftheemergencycontrols
is to
perform
automatic
re-energizing
of components. For
example, following the tripping of a line in most instances
the shortcircuit will “heal” in a fraction of a second and the
lineafter reclosure canfunctionnormally.The
reclosing
must take place fast and automatically to be successful.
The third objective of emergency control is to prevent the
system from desynchronization. i.e.. breaking up into parts.
A system is said to be rrunsientstable foraparticular
disturbance if thegeneratorrotors,
following the initial
transient angular swings, tend to stick together. The system
may not in itself haveasufficientlystrongsynchronizing
“glue“ and it will then be necessary to insert on
a
temporary
basis
components
designed to enhance the
stability.
The fourth and final objective of emergency controls is to
save a deteriorating frequency.
17. Transient Stability ControlClassical Approach
Under normal conditions the turbinepower. P,. and
generatorpower,
P , . are in balance
and
the turbinegenerator unit is running at constant speed. During major
fault
disturbances
P , remains
approximately
constant
whereas P , undergoessudden
and large changes.The
postfault difference power P , - P G . depending upon sign.
will
either
accelerate
or
decelerate
the unit.
The
accelerations of thegenerator units follow from the sMsitzg
equariorzs
and 4 to open. At that instant the generator powers P C , and
PG2 change to match the local loads which will remain at
their prefault values*.Unit # 1 thus findsitself with a power
surplus of 300 MW causing an acceleration. Unit #2 will
haveapowerdeficiency
of 300 MWand will thusdecelerate. The angles 6 , and 6 2 will thus move apart at an
accelerating rate. If line reclosure can be accomplished fast
enough the two machines will regain synchronization.
t!
i
Non-reheat
\
4;
t, sec‘s
Fig. 9.
1
A comparison of turbine responses.
-
300 MW
2
500 MV!
Fig. 10. A two-busexamplesystem
where S is the angular rotor coordinate andM = Wki,o/lrfo
is the rotor inertia constant.
The name “swing equation” implies that power systems
are oscillatory in nature. When brought out of balance the
machine rotors tend to perform torsional oscillations which
are
quite
undamped.
As
the electrical
restoring,
or
synchronizing,powers
of thelines(eq’s
17, 29) are
nonlinearfunctions of theangularcoordinatesthe
oscillations become nonlinear of the limit-cycle Qpe.
A transient stability study involves the integration of the
coupled swing equations(40). The coupling takes place via
thenetwork. In sucha simulated study it is, of course,
necessary to make contingency assumputions.
Classically, transient stability controlhas centered on use
of fast:acting circuit breakers. For example, consider
the
two-machine system in Fig. 10. Initially the system is in its
normal
state
characterized
by the powerflows
shown
(disregard the dotted portion).
A sudden short on the line causes the circuit breakers
1
*The bus voltages will change (in spite of the best efforts by the AVR
loops) and as the voltages change so will the loads. We neglect this in our
discussion.
18. Transient Stability Control-New
Approaches
Consider now the following alternative chain of events.
of linetrippingthecircuitbreaker
#2
Atthemoment
inserts a 300 MW “brake” resistor R. At the same instant
300 MW of the load at bus # 2 is disconnected in a “fast
load-shed.” These breaker operations will in effect restore
power balance at each rotating unit, thus
avoidingsevere
angularaccelerations.
At the later moment when line
reclosure takes place the brake resistor is disconnected and
the load is restored at bus 2.
The combined use of brakeresistor and “loadskipping”
obviously is a more active approach to preserving transient
stability. It has lately received considerable attention (refs
1 1 , 12). For this type of control to be effective the control
decisions must be arrived at fast. The controllers must also
be robust as they must function under vastly different fault
conditions.
19. Frequency Control and Longterm Dynamics
Following a major fault the transient stabilityis typically
determined within oneorseveralseconds.
Even if the
system remains
initially
synchronized,
faultinduced
problems often occurwhich make themselves known within
several seconds or possibily
minutesandwhich will give
rise to longterm frequency dynamics.
Forexample,thelinetrip
in theaboveexample
may
cause voltage swings so severe that a feedwaterpumpmotor
will trip making it necessary to take G 2 out of service, thus
creating a systemwide generation shortage of 200 MW. If
the system were partof a power pool, support power would
immediately flow in overthetie-lines.
If thesystem is
operating alone the 200 megawatts will be taken from the
kinetic storage resulting in a rapid frequency deterioration.
Power balance must be rapidlyrestoredand
permanent
loadshedding will often be the last resort. It can be done
manually by the operator or automatically upon command
from underfrequency relays.
Simulation of the
frequency
dynamics
could,
theoretically, be performed by extending the integration of the
swing equations (40). now rewritten in the frequency form
As some of the generators are performing relatively fast
intermachineswingsthisintegration
procedurerequires
smallintegrationsteps
(zO.01 s). Aconsiderably more
practical approachis to turn theattention to the average
frequency of all the area generators.
We thus define a lumped area
generator having lhe inertia
and its rotor position ("center of inertia") defined by
The frequency of this imaginary machine then equals
and can be integrated from a "lumped" swing equation
As the frequency, f,,.is a fairly slowly changing variable
the integration steps can now be chosen fairly large ( 2 I 5 ) .
20. Future Trends
In this brief exposition of power system control we have
focused on the normal
and
emergency
state
control
problems
as
being
the
most relevant ones from the
operator's point of view. Other important control problems
related to resource optimization. security enhancement and
environmental protection have been excluded due to space
limitation. Due to the
enormous
capital
investments,
changes in power
systems
technology tend to
be
of
evolutionary rather than revolutionary nature. We presently
identify some of the areas that probably will be subject to
increased
future
attention
by control
and
systems
researchers.
The graph in Fig. 2 depictsone of the basic problems
facing
the
power systems planner-disparity
between
maximumand minimum loading-which
results.on the
average, in poor utilization of generating equipment. In an
earlierand moreplentiful
energy era the electricutilities
never attempted to interfere with the customer's power use
habits.However.adding
new generatingcapacity is exceedinglyexpensive in bothmonetaryandenvironmental
terms. By shaving the demand peaks it is possible to either
cancel or at least postpone for several yearsthe construction
of new plants and/or the installation of expensive peaking
units. Controlling the power demand. or load management,
hasthus today becomea very high priority item on the
engineering agenda of most utility industries.
Load control can in principle be achieved in a number of
ways ranging from the totally
voluntary
approach
to
compulsory shutoff (ref's. 13, 13). Using microprocessors
in combination withnovelrate
schedules(ref. 15) offers
new possibilities. The industry is looking urgently for new
and imaginative ideas in this field.
Areawide
blackouts
although
rare
have
dramatic
impacts
and
often
serious
consequences.
Increased
operating security thus is high on the industry priority list.
Finding improved methodsforpredictingtransient
and
frequency stability- and developing new emergency control
methods are tasks singularly suited
to the control specialist.
Determination of transient stability has classically
been
performed indirectl! by integration of the swing equations.
Time-domain simulation
is
computationally
costly
and
of contingensies that
places a constraint upon the number
can bestudied. Direct stabilityanalysismethodsseem
to
offerbetter
promise in thisregard.These
methodsare
known
under
the
acronym
TESA
(Transient
Energy
StabilityAnalysis).Directstability
assessmentmethods
exemplified by the famous "equal area criterion" (ref. 3)
have been used by powerengineersfor many years.The
TESA methods based as they all are upon Lyapunov theory
are not new either. However, recentcontributors(ref.
16)
claim a "breakthrough" in the use of these methods as a
resultofphysicallybasedenergyfunctionsandamore
intuitiveinterpretation
of computerresults.
An ultimate
goal in TESA researchwould
be to developamethod
whereby the system operator could assess in real time the
degree of stabilitycharacterizingthe system at acertain
operating time and in a certain operating configuration.
In sect. 18 we brieflymentioned the new emergency
controlschemes the theory of which has been recently
studied by ZaborszkyandMeisel
(ref's. 1 1 . 12). Those
methods
represent
distinct
a
departure
from existing
14
“Aggregation” is theonelarge-scalesystemtechnique
practice of emergencycontrolsince
they would require
extensiveaddition of controlhardwareto
the system at that maypossibly offer the best payoffs in futurepower
every generating bus. The proposed control schemes would systemscontrol. It is awell-knownfact
that all power
systemdynamics, both of thesmalland
large magnitude
function as follows:
A few critical state variables would be locally monitored varieties, is characterized by “coherency,” i.e., groups of
at each control point. When the variables would indicate a generators tending to swing in unison. For example, it is
new emergencycontrolmethods
major disturbance a local microprocessor would determine intuitivelyfeltthatthe
be greatlysimplified
by taking
the best control strategy for applying
the locally available discussedabovecould
controlforces
advantage of this feature. Rather than installing the control
in an attemptto
achieveoptimalpower
balance in the overall system.
devicesateachgeneratorbus
they may proveequally
into a few “switching
together
Theauthorsdemonstrate
impressivesuccess with their effective if lumped
respective control strategies during fault situations in large centers.”
scale systems. Of course, at this early stage O E ~ Ysimulated
data is available.Extensive follow-up work is needed before
the utility industry will gain confidence in these methods.
Theauthors
limit theirstudies to symmetrical network
faults.Extensive simulation seems required to check the
robustness for allthe various types of unbalanced faults that
canbefallpowersystems.Mostimportantly,hardware
studies-performed
first at reducedpower
levels-must
confirm beyond any doubts that the added equipment does
not in factintroducemoresecurity
problems than it is
intendedtocure.At
this stagethe workrepresents an References
exciting new development in power systems control which I . Brown Boveri Review, Aug. 1980, vol. 67, Baden/Switzerland.
2. Olle I . Elgerd, Basic Electric Power Engineering, Addison-Wesley
deserves the attention by more investigators.
USA. 1977.
Publ. Co., Reading. Mass.,
Inrecentyearscontrol
of “large-scale” systemshas
3. Olle I. Elgerd. Electric Energy Systems T h e o y , McGraw-Hill Book
C o . , New York, N.Y. 1971. (A second edition due in Jan. 82).
become a popularresearch area of control theoreticians. It is
E. Dy Liacco, “The Adaptive Reliability Control System,” IEEE
not surprising that power systemsin particular have become 4. T.
Trans., Vol. PAS-86, May 1967.
the focus of much attention, since typical largescalesystem 5. L. Fink and K . Carlsen, “Operating under Stress and Strain,“ IEEE
Specrrum, March 1978.
topics like aggregation and decentralized control long have
“ComputerRepresentationofExcitationSystems.”IEEECombeenofgreatconcern(underdifferent
names) by power 6. mittee
Report, IEEE Trans.. Vol. PAS-87. No. 6. June 1968.
systems
engineers.
The
“dissipation
effect”
(sect.
6) 7. IEEE Committee Report, “Dynamic Models for Steam and Hydro
Turbines in Power System Studies.” IEEE Transactions on Power
manifesting itself in localization of even major disturbances
6 , pp.1904-1915,
Apparatus and Systems, Vol.PAS-92,No.
haslong beenknown and been the basic reason why soNovember/December,1973.
called
“area
control”
has
historically
emerged
as an 8 . Y. Yu and H.A.M.Moussa.“OptimalStabilizationofMultimachine Systems,” IEEE Trans.Power Apparatusand Systems,
unquestioned natural feature of power systems control. The
Vol. PAS-91, No. 3, May/June 1972.
division into“areas”
wasoftenperformed on apolitical
9. 0. I. Elgerd and C. E. Fosha, “The Megawatt-Frequency Control
basis.
IEEE
Problem:A New ApproachViaOptimalControlTheory.’‘
Trans. Power Apparatus and Systems. Vol. PAS-89. No. 4, April
The intuitive use of decentralized control did not always
1970.
turn successful. The classical example was the
emergence
IO. T. W . Reddoch,“Load-FrequencyControlPerformanceCriteria
of the “tie-line frequency-bias“ control
law described by
with Reference to the Use of Advanced Control Theory,” Systems
Engineering For Power:StatusandProspects,Henniker.
New
equation (39). Originally the attempt was made to delegate
Hampshire.Aug. 17-22. 1975.
regulation of thetie-linepowers
to the individualpower
1 1 . J. Zaborszky, etal.. “Monitoring, Evaluation and Control of Power
companies but let the frequency control be handled by one
SystemEmergencies,”DOEConferenceonSystemsEngineering
(usually the largest) company. It turned out that this pool
for Power, Davos. S e p t . 4 c t . 1979, Proceedings #CONF-790904PI.
memberexperienced
unacceptablylargepower
swings.
12. J. Meisel,etal..“EmergencyOperatingStateControlon
Bulk
Sharing the controlof both the frequency and tie-line power
Interconnected Power Systems,” Ibid.
as implied by eq. (39) was suggested by Cohn (ref. 17) and 13. “Load Management,” EPRI Journal, pp. 6-1 I . May 1977.
14. G. Kaplan.“Two-WayCommunicationforLoadManagement,”
proved a radical improvement.
IEEE Spectrum, pp. 47-50, August 1977.
The powerful analysis toolsof modern linear control have 15. J.C. Mears.“Consumer-InteractiveReal-timePriceSignalling
laterconfirmedthesoundness
of theempirically found
Load Management Scheme,’’ Masters Thesis. Dept.
of El.Eng.,
Univ. of Florida, 1978.
formula (39). For example, it was pointed out in ref. 9 how
16. R. Athay et al., “A Practical Method for the Direct Analysis of
use of only local state variables in the optimal control of a
Transient Stability,’. IEEE Transactions, Vol. PAS-98, No. 2, pp.
two-area system added only insignificantly to the optimum
573-584. March/April.1979.
integral index. This has been confirmed by later researchers 17. N. Cohn, Control of Generation and Power Flow on Interconnected‘
Sysrems, Wiley, New York, 1971.
working with much larger systems andusing more extensive
18. M. Jamshidi, Large-Scale Systems-Modeling, Controland Applicamodels. A good discussion is given in ref. 18 which also
lions, Elsevier North-Holland Book Co., New York, N.Y.,(Chapt.
contains a substantial bibliography on related topics.
9) to appear.
15
IEEE Professional Activities and the
Control Systems Society*
Tim JohnsonfProfessional Activities Coordinator
This is the first in aseries of short
articles about IEEE professional activities as they relate to the Control System
Societ?, member. In this article, we look
at IEEEprofessionalactivitiesandexamine their relationship to the primarily
technical activities of theControlSysterns Society. Future
installments
will
deal with organization and financing
of
professionalactivities.programplans
and
performance
assessment,
specijic
programareasrelevantto
thecontrol
engineer, and future activitieswhich can
be pursued through the Control Systems
Society.
SignificantgrowthinIEEEprofessional activities has occurred mostly over
thelastdecadeandhasinvolvedprimarily U.S. MembersoftheInstitute.
Some of thefactors whichled to the
institutionalization of IEEE professional
activities-representedbytheestablishment of the
United
States
Activities
Board (USAB)-arose
fromthesocial
activismofthe 1960’s. Withthespace
program and the rapid evolution of computer technology. many members recog+ReceivedJan. 8. 1981. recommended by
D. H . Elliott, AssociateEditor-Features.
?Bolt Beranek and Newton Inc.. Cambridge, MA
nized that engineering developments unavoidably have a profound effect on the
sociopoliticalsystemandonindividual
lifestylesandemployment.Fortheengineer tomaintainhistraditionaldeon such
tachedandobjectiveviewpoint
matters would be irresponsible to society
and moreover suicidal to the profession.
A large number of laws, including social
legislationand R&D funding,appeared
to be
“dealing-out”
engineering
and
science. Not enough attention was being
paid to engineeringandscienceenrollmentsandmuchlessattentionandsupport was being voiced for education. In
some instances,engineerswerevictimized by wage-squeezes,flawedpension
programs, or managementpressuresto
overlook public safety. Under these circumstances, theconsequences of inactivitywereclear:government,society,
big business
and
even
big
education
would be free to push engineers around at
will. Without any form of organization,
theefforts ofindividualstocounteract
such influences would be largely in vain.
In spite of theengineer‘straditionally
conservativeandindividualisticimage,
the cost of doing nothing had become so
highthatorganization,planning,anda
financial commitment had become inescapable.
Suffice ittosaythatthesehaveall
16
come about within the decade, and some
of the details will be described in future
articles inthisseries.Ourpresentpurpose is to develop a framework in which
to view IEEE professional activities and
by which the relationship ofour technical
and professional activities as control and
systemsengineers can beunderstood.
These considerations apply more or less
equally
to
U.S. and to international
members of the Control System Society.
The fact that IEEE professional activities
arecurrentlyfinancedby,andforthe
benefit of, the U.S. membershipshould
be regardedaslargelyapragmatic
del
is no
velopment;ithappensthatthere
other significantly
large
professional
organizationtorepresentelectricalengineers intheUnitedStates,andatthe
sametimethere
are probably too few
IEEE members in most other countries to
warrant such a substantial investment in
professional activities through the IEEE.
Such developmentsareoccurringindependently, insomeinstances,through
other appropriatenationalengineering
organizations abroad.
Fitting enough, feedback is a concept
central to theunderstanding
of IEEE
professional activities. Societymaybe
viewed as a complex interconnection of
socioeconomicgroups,someofwhich
are institutionalized. Anystudentofin-