43
Power System Controls
Power System Controls
Outline
•Overview of Power System Controls
–Voltage Control
–Frequency Control
•A closer look at Frequency Control –
–Steady State analysis of Governor control and LFC in
single and interconnected areas.
–Transient analysis of Frequency Control Schemes
•Laboratory: Load Frequency Control Simulation.
References
•Glover, Sarmaand Overbye
Pow
er S
yste
ms
Analy
sis
Chapter 11 Power System Controls. This is a good
overview of voltage and frequency control but it doesn’t
really cover small signal analysis. Also it should be noted
that to the best of my knowledge the accompanying Power
World simulator does not m
odel frequency variations and
is not suitable for Load Frequency modelling.
•Conlon, Michael P
ow
er F
requen
cy C
ontr
olclass notes.
We will be using this as the main text for small signal
analysis. Simulinkis used to model the Laplace tranforms
involved in small signal analysis.
Power System Controls -Overview
•The tw
o important variables that must be kept within designated lim
its
are Voltageand Frequency.
•Load Flow
Analysis taught us that
Reactive Power Q controls Voltage
Real Power P Controls Frequency
•Voltageis a local variable and is largely subject to local control but we
still need to ensure system wide Q balance.
•Frequency (and therefore P) is a system wide variable subject to
tight
centralised control but in order to provide rapid local responseto
disturbances generators also have their ow
n local frequency controls
operating under the centralised scheme.
A Hierarchy of Controls
Local controls provide the fastest response to local disturbances but these must be
subordinated to slower system wide control schemes that ensurespower generation
matches demand in an econom
ically optimal fashion.
Voltage Control
Voltage Control
•Voltage is a local parameter and substantial
variations (+/-10% or so) may occur across
the transmission network but since the
operation of everything connected to the
network depends on voltage so local voltage
controls are still required.
•The primary mechanism for voltage control is
reactive power (Q) injection. Generators are a
controllable source of Q. Static Var
compensators and capacitor banks can be
used at other points in the network.
•Tap changing transformers are then used to
fine tune the voltage at any point in the
network but this does not remove the need to
ensure that there is a balance between vars
consum
ed by the network and varsgenerated.
EirgridGrid Code 3.1 April 2008
Generator Voltage Control
•Every generator monitors its terminal voltage and
controls it via a process of Automatic Voltage
Regulation
•The voltage regulator adjusts the excitation of the
generator to raise or lower the terminal voltage as
required.
•Analysis of a synchronous generator operating on
an infinite bus shows that increasing the excitation
voltage increases Q injection helping to raise the
terminal voltage while reducing excitation reduces
Q injection and therefore lowers terminal voltage.
Autom
atic Voltage Regulation
Frequency Control
Network Power Balance
•An imbalance between the power from turbines and the power being
fed to the network will cause the stored kinetic energy of the system to rise. Kinetic energy for an
individual generator W = 0.5 J ω
2so a power im
balance will cause the generators to speed up or slow down.
•The speed of traditional alternators is locked in sychronismwith the frequency so any frequency variation is indicative of a change in system kinetic energy which in
turn im
plies an im
balance between total Turbine Power and Systemdemand. Therefore by tightly controlling frequency we can ensure that stored kinetic energy is not
changing and that we are supplying exactly the correct amount ofpower from the turbines to meet the system demand.
•Frequency is a global parameter so any generator can measure theglobal system frequency and control its own contribution to meeting the power demand.
•System
frequency is more tightly regulated than voltage: The normal frequency range for the Irish transmission system is 49.8H
z–50.2Hz. Further more any
temporary frequency error is integrated and com
pensated out so the long run average frequency is spot on 50Hz. Prior to the introduction of quartz clocks the electric
supply frequency was often used as an accurate time reference.
∫dt
Power from
Turbines
P g (Note this is
mechanical
but w
e assume
100%
generation
efficiency)
Power to
network P d
P accel
Stored Kinetic
Energy W
kin
Power
Balance
A Layered Hierarchy of Frequency
Controls
•Turbine Governor Control (also known as Droop) Refers to the local speed
regulation of each turbine.
•Load Frequency Control is the centralised direction of system power to
ensure that total generation matches demand and in the case of interconnected
systems to ensure that power im
port / export equals its scheduled value.
•Economic Dispatch aims to ensure that the most cost effective mix of
generation is used to meet demand. Cost versus power curves for each
generating unit are used to determine the best mix at any given level of
demand.
•Optimal Power Flowfurther constrains economic dispatch to ensure that all
transmission system com
ponents (transformers and lines) are operated within
safe limits. Traditionally transmission system com
ponents were overdesigned
to accom
modate the worst case power flow they were likely to encounter but
the de-regulation of power systems has made optim
al power flow
consideration much more signifcantfor control of network congestion and
pricing.
Turbine Governor Control
Taken from Michael Conlon’s Notes on Load Frequency Control
Modelling Frequency Control
(Steady State)
Some Definitions and Principles
•Small Signal Analysis:Our models are valid for small
variations of parameters about their current operating
point: ∆p, ∆f and so on. For these small variations we can
assume that the system responds linearly.
•For Major excursions (such as occuerduring fault
conditions) the large signal analysiswhich takes non
linearity (such as power and speed limits) into account.
•Often it is convenient to use the per unit system
. By
convention we convert powers to per unit by dividing by a
common Sbasebut w
e leave frequency in Hz.
•Be careful w
hen problems have generators of different
rating. You will need to convert their output to a common
per unit S
basebefore com
bining.
Turbine Governor Control 1
•Steady State Control Relationship
∆p g=generated power (small signal deviation ) controlled by the turbine
∆p c=power reference from central dispatch (small signal deviation)
∆f=frequency (small signal deviation from
nom
inal)
R = droop measured in Hz/MW or Hz/puMWor just in %
Warningpercentage droop is calculated as percentage power / percentage frequency based on nominal pow
er and
frequency. You will generally need to multiply it by the nominalsystem frequency to convert to Hz/PuMW. For
example a 5%
droop means that the power will change by 1PU
for a5%
of nominal frequency change.
fR
pp
cg
∆−
∆=
∆1
Turbine Governor Control 2
fR
pp
cg
∆−
∆=
∆1
•This equation is applied locally at every generator.
•It allows each generator to instantly respond to any frequency
variation by ram
ping up its generation if frequency falls and vice
versa.
•In this way power balance is quickly restored after any change in
demand even before central dispatch has tim
e to respond.
•Turbine governor control w
ill cause a shift of frequency away
from
nom
inal. In the medium term central dispatch must readjust
power references ∆p cto accom
modate the changed system
demand thereby restoring nominal frequency.
•In the language of control theory Turbine Governor control is a
form of proportional control and therefore gives rise to a steady
state error. We need integral action in order to rem
ove steady
state error. This is provided by adjusting ∆p c
Multi Generator System
•Each generator will have its individual droop characteristic and
they
will share any resulting power variation due to frequency changein
proportion to their respective droops.
•The system droop characteristic can be found from
•The above calculation can be done in per unit If you convert to a
common system S
base
•It may be noted that if all generators have the same pu
droop (or %
droop) in terms of their own rated power then they will share any
power variation in proportion to their nominal ratings.
...1
11
1
32
1
++
+=
RR
RR
sys
Example
•A 50H
z system has three generating units:
a. 500MVA
R=5%
b. 400MVA
R=2.5%
c. 1000 MVA
R=5%
Q1. What w
ill the respective changes in generation from
each unit be in response to a 0.01 Hz reduction in
frequency?
Q2. What is the system droop characteristic expressed as a
percentage (using total system power as a base)?
Answer: Q
1: a: 2MVA, b: 3.2MVA, c: 4MVa Q2: 0.0011 Hz/MVA = 4.1%
Area Frequency Response
Characteristic AFRC
•AFR
C tells us how the system frequency will
respond to a change in demand.
•AFR
C depends on system droop but it also
depends on the load characteristic. If the system
has a lot of motor loads for example then an
increase in demand will cause a reduction in
frequency which will reduce the speed and load of
the motors compensating somewhat for the
original demand increase.
AFR
C cont.
...1
11
1
(1
32
1
++
+=
=∂∂
==
+=−
=
RR
R
R
posi
tive
)
(ass
um
edfr
equen
cy
to
resp
ect
w
ith
dem
and
of
ch
ange
of
ra
te
the
fP
D
vari
ati
on.
freq
uen
cy
of
ef
fect
ng
com
pen
sati
bef
ore
dem
and
under
lyin
g
in ch
ange
M
puM
W/H
z)
or
MW
/Hz
RD
is
AF
RC
th
ew
her
e
βM
∆f
:va
riati
on
freq
uen
cy
a
cause
w
ill
Mof
dem
and
in
change
st
ep
A
sys
d
sys
β
Note: Glover and Sarmause a simplified definition of AFRC which does not take load
variation with frequency into account.
AFR
C derivation
sys
sys
dg
g
sys
g
c
sys
cgd
RD
Mf
MR
Df
f
for
so
lvin
g
fD
Mf
R∆
P∆
P
poin
t
whic
hat
re
store
d
is bala
nce
pow
er
unti
l
fall
ing
or
ri
sing
ke
ep
wil
lfr
equen
cy
th
e
but
sys
tem
)th
e
on
gen
erato
rs
the
all
fr
om
ch
ange
pow
er
tota
l
the
is
case
th
is
in P
(n
ote
fR
P
so
P
yet
re
sponded
thasn
'
contr
ol
ce
ntr
al
ass
um
ing
fR
PP
resp
ond
w
ill
contr
ol
G
ove
rnor
T
urb
ine
fD
MP
dem
and
s
yste
mact
ual
in
change
T
he
1)
1(
1
1
0
1
+−
=∆
⇒−
=+
∆
∆
∆+
=∆
−⇒
=
∆∆
−=
∆
=∆
∆−
∆=
∆
∆+
=∆
Responses to a change in demand
1.Frequency dependent loads (such as motors) will tend to
reduce the actual change in demand.
2.The Kinetic energy stored in the system inertia will be
released as the frequency drops (our steady state
modelling hasn’t shown this transient effect).
3.The Turbine governor controls will rapidly change
power generation in order to restore power balance at the
cost of a frequency error.
4.Eventually after som
e seconds central control will issue
updated power references to rebalance power and restore
frequency to its nominal value.
A block Diagram of Turbine
Governor Control
We will analyse this more closely when we look at
transient m
odelling later.
Taken from Michael Conlon’s Notes on Load Frequency Control
Load Frequency Control
•In order to restore frequency to its nominal
value central control needs to update the
generator power references ∆p cto
accommodate the change in demand.
•This process is also known as “Reset”
Reset using an integrator
•If you have studied control theory you may realise that Turbine Governor
control is a proportional control scheme. The change in power isproportional
to the frequency error. This is the reason why a steady state frequency error
exists.
•To eliminate the steady state error we need to introduce an integratorinto
our control scheme. Integrators have a memory. The output of theintegrator
depends not just on the error at this mom
ent –
it depends on the historical
error. An integrator can sustain a change in power even after the frequency
error has returned to zero.
puMW
or
MW
in
gain
integrator
the
is K
.
i
∫∆−
=∆
dt
fK
pi
c
Block Diagram of Single Area
control scheme with Reset
Taken from Michael Conlon’s Notes on Load Frequency Control
Response to a Step change in
demand of magnitude M
curv
e.
excu
rsio
nfr
equen
cy
th
e
under
are
a
the
us
te
ll
does
It
dyn
am
ics.
s
yste
mth
e
on
dep
ends
th
at
- ta
ke
wil
lex
curs
ion
freq
uen
cy
th
e
path
ex
act
th
e
us
te
ll t
does
n'
eq
uati
on
T
his
rest
ore
d.
be
to
freq
uen
cy
nom
inal
fo
r
sec
onds
in ti
me
th
e
is T
wher
eKM
dt
for
Mdt
fK
Mp
fach
ieve
d.
is
ate
ste
ady
stnew
a
and
va
lue
it
s
hold
s
inte
gra
tor
T
he
ze
ro.
to
retu
rned
has
f
and
M
p
as
ti
me
s
uch
unti
l
f)
neg
ati
ve
a fo
r
risi
ng
(o
r
fall
ing
ke
ep
wil
lin
tegra
tor
th
ep
ze
ro
non
is
f
as
lo
ng
A
s
∆f.
dt
Kp
re
mem
ber
and
RD
Mp
f
fR
DM
∆p
sof
DM
∆f
R∆
p
∆p
∆p
bala
nce
pow
er
ate
ste
ady
stF
or
∆f.
dt
K∆
p :
Res
et
act
ion
In
tegra
l
fD
M∆
p
:dem
and
act
ual
in
Change
∆f
R∆
p∆
p:
Gove
rnors
T
urb
ine
T
i
T
ic
c c
ic
c
cc
dg
ic
d
cg
∫
∫
∫
∫
−=
∆
=∆
−⇒
=∆
⇒=
∆
∆=
∆∆
∆∆
−=
∆+−
∆=
∆⇒
∆+
+=
∆+
=−
=
−=
∆+
=
−=
0
0
.
.0
1
)1
(1
1
Frequency Excursions in response to
a demand change
i
T
KMdt
f−
=∆ ∫ 0
.
Taken from Michael Conlon’s Notes on Load Frequency Control
Time Error
•You can actually run a clock by counting cycles of the
electrical supply frequency but any frequency deviation will
cause tim
ing errors
•In practise such accum
ulated time errors are com
pensated
out at least daily by adjustments to the nominal frequency so
the utility frequency can be used for accurate tim
ekeeping
an accurate clock. Until the advent of quartz clocks this was
the basis of many electrical clocks.
i
erro
r
T
o
erro
r
Kf
Mt
dt
ff
t
0
0
0
change
load
step
aAfter
frequency
system
nominal
the
is f
where
.1 −
=
∆=
∫
Load Frequency Control of
Interconnected Systems
Area 1
Area 2
Tie Lines
(Assum
e an AC link
so area 1 and area 2
must be
synchronised)
p 21
p 12
Interconnected Systems
•Each Area has its own centralised control but
power may be transferred between them according
to an agreed schedule.
•The ability to share pow
er between interconnected
grids (egEuropean Synchronous grid) helps with
normal operation, can reduce the individual
networks requirements for reserve and can also be
used to deal w
ith emergency situations.
Interconnected Systems
Taken from Michael Conlon’s Notes on Load Frequency Control
Definitions
•∆p 1
2is the deviation in pow
er flowing into area 1
from
Area 2 in the PU
base of area 1 (S
base1).
•∆p 2
1is the deviation in pow
er flowing into Area 2
from
Area 1 in the PU
base of area 2 (S
base2).
•Assum
ing no losses ∆p 2
1=a 12.∆p 1
2where a12is
minus Sbase1/S b
ase2
•T12is the synchronising coefficient in puMW/Hz
which measures the impact of a phase difference
between Area 1 and Area 2 on the power flowing
in the link.
Interconnected Systems without LFC
•Turbine governor control w
ill still re-establish
power balance but the change in demand will be
shared between regions and the link power may
change from its scheduled value.
•The link will force the frequencies in each region
to equalise so in the steady state ∆F 1= ∆F2
•You can work out the steady state frequency
variation by considering the combined areas as
one system with D
total=D1+D2 and Rtotal
=1/(1/R
1+1/R2).
•The com
bined AFR
C is βtotal=D
1+D2+(1/R
1+1/R2)
LFC
with interconnected Areas
1.As with an isolated grid each area should
assist in returning the steady state
frequency error to zero.
2.Each area should also try to maintain the
tie line pow
er flow at its scheduled value.
Effectively this means that each area must
absorb its own load changes.
Taken from Michael Conlon’s Notes on Load Frequency Control
Modifying LFC to accom
modate
multiple Areas
•Single Area LFC uses an integrator on ∆f to drive ∆p cand force ∆f to zero.
•One method proposed by N. Cohn for interconnected regions is to use a new control
objective called the area control error
• •B1and B2 are the frequency bias constants, not to be confused with the AFRC, β.
However Cohn has shown that choosing B = βgives satisfactory performance.
area
each
in
errors
frequency
the
are
,
end
either
from
seen
as
power
tie
in the
error
the
are
,
11
2112
22
212
11
121 f
f
pp
fB
pA
CE
fB
pA
CE ∆
∆
∆∆
∆+
∆=
∆+
∆=
LCF in interconnected Regions
•Each area now
uses integral control to reduce its
own ACE to zero
00
0)
)(
0)
:
00
,,
122
21
21
22
11
21
22
211
1
22
11
=∆
=∆
⇒=
∆+
∆=
∆=
∆∆−
=∆
=∆
+∆
+∆
+∆
=∆
+∆
=∆
+∆
−=
∆−
=∆
∫∫
pa
nd
ff
B(B
so
ff
f
ate
ste
ad
y st
the
in
an
dS
com
mo
np
pb
ut
fB
fB
pp
( :A
dd
ing
thes
ea
dd
can
we
then
Sco
mm
on
au
sew
eIf
fB
pa
nd
fB
p
so
reg
ion
ea
ch
in ze
ro
to A
CE
th
e
forc
e
even
tua
lly
w
ill
sco
ntr
oll
er
inte
gra
l
Th
ese
dt
AC
EK
pd
tA
CE
Kp
1
base
12
12
base
12
ic
ic
A brief look at System Demand
The Daily Load Cycle
Eirgrid: System Demand 10 March 2010
Base Load
Controlled Units
Peaking Units
Spinning Reserve
•Base Load–Units with the smallest variable cost (Nuclear
and Large Fossil Fuel Plants) are run continuously to
supply base load.
•Controlled Units –Medium sized fossil fuel and Hydro
are controlled to supply the variable part of the load and
implement frequency control.
•Peaking –Sm
aller less efficient units with rapid response
times (open cycle gas or oil fired, pum
ped storage ) are
used to meet peak demand
•Spinning Reserve –These units are paid to remain on
active standby to cover any unexpected peaks.
Economic Dispatch
•LFC
allows centralised control to maintain power balance and constant frequency but there
can be significant cost variations between controlled units. LFC
tells us how much extra
power needs to be dispatched. It does not tell us which units itshould be dispatched to.
•Economic Dispatch provides the econom
ic optimum
allocation of pow
er between
generating units.
•The mechanism for im
plem
enting economic dispatch is to balance the increm
ental
operating cost of all controlled units:
•This topic is covered more completely in Gas and Electricity Markets
...33
22
11=
==
dp
dC
dp
dC
dp
dC
