Electric Power Systems Research 79 (2009) 837–845
Contents lists available at ScienceDirect
Electric Power Systems Research
journal homepage: www.elsevier.com/locate/epsr
Regional frequency response analysis under normal and emergency conditions
Hassan Bevrani a,∗ , Gerard Ledwich b , Zhao Yang Dong c , Jason J. Ford b
a
Department of Electrical and Computer Engineering, University of Kurdistan, Sanandaj, PO Box 416, Iran
School of Engineering Systems, Queensland University of Technology, Brisbane, Qld 4001, Australia
c
Department of Electrical Engineering, The Hong Kong Polytechnic University, Hong Kong
i n f o
a b s t r a c t
Article history:
Received 24 December 2007
Received in revised form 4 August 2008
Accepted 10 November 2008
Available online 24 December 2008
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Keywords:
Frequency regulation
Frequency response model
Load disturbance
Primary control
Supplementary control
Emergency control
This paper presents a frequency response analysis approach suitable for a power system control area
in a wide range of operating conditions. The analytic approach uses the well-known system frequency
response model for the turbine–governor and load units to obtain the mathematical representation of the
basic concepts. Primary and supplementary frequency controls are properly considered and the effect of
emergency control/protection schemes is included. Therefore, the proposed analysis/modeling approach
could be gainfully used for the power system operation during the contingency and normal conditions.
Time-domain nonlinear simulations with a power system example showed that the results agree with
those predicted analytically.
© 2008 Elsevier B.V. All rights reserved.
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a r t i c l e
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1. Introduction
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The recent power system events and blackouts show that
improvement of overall power system emergency response
requires better detection mechanisms, more effective analysis and
modelling, and control strategies in order to obtain a new tradeoff between system security, efficiency and dynamic robustness.
Following a large disturbance, the power system frequency may
drop quickly if the remaining generation no longer matches the
load demand. System frequency changes of a large scale power
system are a direct result of the imbalance between the electrical
load and the power supplied by system connected generators [1].
Any short-term energy imbalance will result in an instantaneous
change in system frequency as the disturbance is initially offset
by the kinetic energy of rotating plant. Significant loss of generating plant, without adequate system response, can produce extreme
frequency excursions outside the working range of plant.
Off-normal frequency can directly impact on power system
operation and system reliability. A large frequency deviation can
damage equipment, degrade load performance, cause the transmission lines to be overloaded and can interfere with system protection
schemes, and ultimately lead to system collapse [2]. Fig. 1 shows
that depending on the deviation range, supplementary control such
as load-frequency control (LFC) and emergency control may be
required in addition to the natural governor response.
∗ Corresponding author. Tel.: +98 871 6624774; fax: +98 871 6660073.
E-mail address: bevrani@uok.ac.ir (H. Bevrani).
0378-7796/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsr.2008.11.002
The f0 is nominal frequency, and f1 , f2 and f3 show frequency variation ranges corresponding to the different operating
condition based on the accepted standards. Under normal operation, frequency is maintained near to nominal frequency by
balancing generation and load. Small frequency deviation (f1 ) can
be attenuated by the governor natural autonomous response (primary control). To ensure that the control area is able to restore
area frequency if it deviates more than f1 Hz, LFC systems are
deployed. LFC is required to maintain the system frequency and
time deviation within the limits specified in the frequency operating standards. The frequency deviation f2 is mainly determined
by the available amount of operating reserved power [3]. For
a larger frequency deviation and in a more complex condition,
emergency control schemes are used to restore the system frequency.
Most published works on the power system frequency regulation have considered separate modeling and even analysis
spaces for the normal, LFC and emergency conditions [4–9].
This paper presents an analytic approach to examine the frequency regulation and evaluate the frequency response under
normal, LFC and emergency operating conditions. This work
attempts to adapt the well-known conventional LFC model for
use in contingency and emergency circumstances by including
the effects of emergency protection and control dynamics. The
paper first presents the mathematical representation of the frequency response and important related concepts for a control
area using a low-order dynamic model. Following that, the presented analytical results are examined on a two control area power
system.
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H. Bevrani et al. / Electric Power Systems Research 79 (2009) 837–845
sharing rate of each participant generator unit in the LFC task. For
a control area we can write
n
˛i = 1;
0 ≤ ˛i ≤ 1
(2)
i=1
The balance between connected control areas is achieved by
detecting the frequency and tie line power deviations to generate the ACE signal which is then utilized in the control strategy as
shown in Fig. 2. The ACE for each control area can be expressed
as a linear combination of tie-line power change and frequency
deviation.
ACE = Bf + Ptie
w=
N
op
y
In typical LFC implementations, the system frequency gradient
and ACE signal must be filtered to remove noise effects before use.
The ACE signal then is often applied to a proportional integral (PI)
control block [11,19]. Control dead band and ramping rate are different for various systems [18]. The control can send higher/lower
pulses to generating plants if its ACE signal exceeds a standard
limits.
The signal w in Fig. 2 can be defined as follows:
Tij fj
j=1
j=
/ i
(4)
According to Fig. 2, the output signal of the mentioned system
has the following form:
PSi (s) = ˛i KP +
so
Usually, a simple low-order linear system is used for estimating the frequency behavior of a real power system. A large scale
power system typically consists of a number of interconnected
control areas. Consistent with standard practice, we use low-order
transfer functions to model generator, turbine and power system
(rotating mass and load) units. The mentioned low-order structure is well discussed in Refs. [7,8]. It was shown that the aggregate
load-frequency dynamic response of a control area power system
following a disturbance can be represented by a reduced model
including an equivalent system inertia H, system load damping D,
system regulation R and turbine–governor model M(s).
Here, to cover the variety of generation types in the control area,
different values for turbine–governor parameters and the generator regulation parameters are considered. Fig. 2 shows the block
diagram of typical control area with n generator units. The shown
blocks and parameters are defined as follows:
(3)
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2. Control area dynamic model
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Fig. 1. Frequency range and different control actions.
KI
s
ACE(s)
(5)
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3. Frequency response analysis
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Frequency deviation,
Governor valve position,
Supplementary control action,
Primary control action,
Net tie-line power flow,
Load deviation,
Equivalent inertia constant,
Equivalent damping coefficient,
Tie-line synchronizing coefficient between areas i and j,
Frequency bias,
Drooping characteristic,
Area control error,
Participation factors,
Low-order governor–turbine model,
Proportional Integral controller.
Au
f
Pm
PS
PP
Ptie
PL
H
D
Tij
B
Ri
ACE
˛i
Mi (s)
PI
As shown in Fig. 2, the frequency performance of a control area
is represented approximately by a lumped load generation model
using equivalent frequency, inertia and damping factors [10].
H = Hsys =
N
i=1
Hi ,
D = Dsys =
N
Considering the effect of primary and supplementary controls,
the system frequency can be obtained as follows:
1
f (s) =
2Hs + D
n
Pmi (s) − Ptie (s) − PL (s)
where
Pmi (s) = Mi (s)[−PPi (s) + PSi (s)]
(1)
i=1
Following a load disturbance within the control area, the frequency of the area experiences a transient change and the feedback
mechanism generates appropriate rise or lower signal to the participating generator units according to their participation factors ˛i to
make generation follow the load. In the steady state, the generation
is matched with the load, driving the tie-line power and frequency
deviations to zero. As there are many generators in each area, the
control signal has to be distributed among them in proportion to
their participation. Hence, the ACE participation factor shows the
(7)
and
PPi (s) =
f (s)
Ri
(8)
PSi (s) = ˛i KP +
KI
s
(Ptie (s) + ˇf (s)]
(9)
Practically, the integral coefficient KI is enough small and can be
ignored in the computation. The expressions (7)–(9) can be substituted into (6) with the result
Di
(6)
i=1
1
f (s) =
2Hs + D
−
n
i=1
KP
Mi (s)
n
˛i Mi (s) − 1 Ptie (s)
i=1
1
Ri
− ˛i ˇKP
f (s) − PL (s)
(10)
For the sake of load disturbances analysis we are usually interested in PL (s) in the form of a step function, i.e.,
PL (s) =
Pd
s
(11)
H. Bevrani et al. / Electric Power Systems Research 79 (2009) 837–845
839
1
g2 (s)
Ptie (s) −
Pd
g1 (s)
sg1 (s)
(12)
where
g1 (s) = 2Hs + D +
n
Mi (s)
i=1
1
Ri
− ˛i ˇKP
(13)
and
n
˛i Mi (s) − 1
(14)
i=1
s.f (s) = 0 −
n
1
Au
s→0
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Several low-order models for representing turbine–governor
dynamics Mi (s) to use in power system frequency analysis and control design have been proposed. In these models, the slow system
dynamics of the boiler and the too fast generator dynamics are
ignored. A second-order model was first introduced in Ref. [7]. Also,
a simplified first order turbine–governor model was proposed in
Ref. [3].
Substituting Mi (s) from [7] or [5] in (13) and (14), and using the
final value theorem, the frequency deviation in steady state (fss )
can be obtained from (12).
fss = Lim
D+
(1/Ri ) − ˇKP
i=1
n
˛
i=1 i
Pd (15)
By definition [11], system’s frequency response characteristic (ˇ)
is equivalent to
1
ˇ =D+
Rsys
1
i=1
Ri
=
4. Estimation of steady state frequency and disturbance
magnitude
For the sake of dynamic frequency analysis in the presence
of sudden load changes, it is usual to model the multi machine
dynamic behavior by an equivalent single machine [5]. Using the
concept of an equivalent single machine, we can simplify the control area block diagram (Fig. 2) as shown in Fig. 3. Here, Pd covers
local load disturbance and the effects of electrical and tie-line power
changes.
From (20), the magnitude of the disturbance Pd can be estimated as follows:
1
Rsys
Pd = −
(16)
1 − KP
fss
Rsys
PS = −Pd =
1 − KP
fss
Rsys
Pd
(D + (1/Rsys ))(1 − KP )
−1
Pd (s)
2Hs + D
Pd (t) = −2H
df (t)
− Df (t)
dt
(17)
(18)
(19)
(23)
or,
Since the value of droop characteristic Ri is bounded between
about 0.05 and 0.1 for most generator units (0.05 ≤ Ri ≤ 0.1) [5], for
a given control system according to (17) we can write
Rsys ≤ Rmin
(22)
As previously mentioned, for a large disturbance we can summarize the all probable load power changes through a single power
imbalance parameter Pd . Therefore, according to Fig. 3, we can
write
Eq. (15) can be rewritten into the following form
fss = −
(21)
To compensate the power imbalance Pd , the total necessary
secondary regulation should be
f (s) =
and assuming
n
(20)
so
g2 (s) = KP
Rsys Pd
Rsys Pd
∼
=−
1 − KP
(DRsys + 1)(1 − KP )
fss = −
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f (s) =
and for a small enough DRsys (18) can be reduced to
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Substituting PL (s) in (10) and summarizing the result yields
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Fig. 2. Frequency regulation loops for a general control area.
Fig. 3. Simplified control area model.
(24)
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H. Bevrani et al. / Electric Power Systems Research 79 (2009) 837–845
2HRsys
DRsys
f (t1 )
[f (t1 ) − f (t0 )] +
1 + KP
TS (1 + KP )
(25)
where the t0 and t1 are boundary samples within the assumed
interval. The result can be used in (21) to calculate the size of Pd .
2H
[f (t1 ) − f (t0 )] − Df (t1 )
TS
(26)
so
Pd = −
er
For a control area with a small enough damping factor (26) can
be approximated as follows:
2H
[f (t1 ) − f (t0 )]
TS
(27)
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Pd ≈ −
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f (TS ) =
the frequency response model. Since they influence the power generation/load balance, the mentioned emergency control dynamics
can be directly included to the system frequency response model.
This is made by adding an emergency control/protection block to
the block diagram of Fig. 3, as shown in Fig. 4. The PUFLS (S),
PUFGT (S), and POFGT (S) represent the dynamics effects of the
UFLS, UFGT, and OFGT actions, respectively. In order to cover
the variety of generation unit types in a power system, different
governor–turbine models Mi (s) are considered.
The emergency control schemes and protection devices
dynamics for sever conditions are usually represented using incremented/decremented step behavior. Thus, in Fig. 4, the related
blocks can be represented as a sum of incremental (decremental)
step functions. For instance, as shown in Fig. 5, for a fixed UFLS
scheme [4], the function of PUFLS in the time domain could be considered as a sum of the incremental step functions of Pj u(t − tj ).
Therefore, for L load shedding steps:
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Comparing the magnitude of total load change in (21) and (24),
the area average frequency during a sampling period TS , can be
estimated as following difference equation:
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Fig. 4. The frequency response model considering the emergency control/protection dynamics.
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Thus, the frequency gradient in a control area is proportional to
the magnitude of overall disturbance in that area. This result agrees
with the obtained results in other published works [12–15]. The factor of proportionality is the system inertia H. Actually, the inertia
constant is loosely defined by the mass of all the synchronous rotating generators and motors connected to the system. For a specific
load decrease, if H is high, then the frequency will fall slowly and if
H is low, then the frequency will fall faster.
5. Considering of emergency control/protection dynamics
As mentioned, in the case of a large generation loss disturbance, the scheduled power reserve may not be enough to
restore the system frequency and the power system operators may
follow an emergency control plan such as under-frequency load
shedding (UFLS). The UFLS strategy is designed so as to rapidly
balance the demand of electricity with the supply and to avoid a
rapidly cascading power system failure. Allowing normal frequency
variations within expanded limits will require the coordination
of primary control and scheduled reserves with generator load
set points; for example under-frequency generation trip (UFGT),
over-frequency generation trips (OFGT), or over-frequency generator shedding (OFGS), and other frequency controlled protection
devices.
The conventional frequency response model shown in Fig. 3
gives the free response of the primary control system following
a contingency. In the case of contingency analysis, the emergency
protection and control dynamics must be adequately modelled in
PUFLS (t) =
L
Pj u(t − tj )
(28)
j=0
where Pj and tj denote the incremental amount of load shed
and time instant of the jth load shedding step, respectively. Similarly, to formulate the POFGT , PUFGT , and other emergency control
schemes, appropriate step functions can be used. Therefore, using
the Laplace transformation, it is possible to represent PEC (s) in the
Fig. 5. L-step UFLS scheme.
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H. Bevrani et al. / Electric Power Systems Research 79 (2009) 837–845
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Fig. 6. Two-control area power system.
following summarized form:
N
P
s
l
e−tl s
th
o
PEC (s) =
l=0
(29)
Au
where Pl is the size of equivalent step load/power changes due to
a generation/load event or a load shedding scheme at tl .
Generally, frequency stability problems are associated with
inadequacies in equipment responses, poor coordination of control and protection equipment, or insufficient generation reserve.
The frequency stability may be a short-term phenomenon or a longterm phenomenon. During frequency excursions, the characteristic
times of the processes and devices that are activated will range
from fraction of seconds, corresponding to the response of devices
such as UFLS and generator controls and protections, to several
minutes, corresponding to the response of devices such as prime
mover energy supply systems and load voltage regulators [20]. The
supplementary control response is usually slower than primary
response and much slower than emergency dynamic response (e.g.,
load shedding). Thus, the supplementary loop response is not usu-
ally taken into account in emergency frequency control studies and
analysis. This is similar to what is done in Section 3 by ignoring KI .
Now, consider a step decrease in the regional frequency, following a generation tip. It can be assessed whether the frequency passes
the frequency threshold (to execute an emergency control action)
or not. According to (21), the maximum amount of available area
power reserve PRmax can compensate the following steady state
frequency deviation.
Rsys
fmax = 1 − KP
PRmax (30)
Therefore, the load shedding frequency threshold, which can be
determined as follows:
Rsys
ft = f0 − fmax = f0 − 1 − KP
PRmax (31)
if the frequency passes the load shedding frequency threshold ft ,
the UFLS as an emergency control plan is needed to recover the
system frequency [9,21].
Table 1
LFC participation factors.
Sub-area
A
Generation unit
Participation factor
Gen 1
0.4257
B
Gen 2
0.0676
Gen 3
0.1689
Gen 4
0.1689
Gen 5
0.1689
Gen 9
0.0998
Gen 10
0.6603
Gen 11
0.2399
H. Bevrani et al. / Electric Power Systems Research 79 (2009) 837–845
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6. Study system
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An actual power system with two interconnected control areas
is considered as study system to support the addressed analytic
approach in the previous sections. The study system simulates the
LFC scheme of the Kyushu island of Japan [16,17]. The configuration
of the study system is shown in Fig. 6. Areas I and II are interconnected through a 500 kV tie-line. Area I consists of four sub-areas
A–D. The sub-areas A–D have eight, five, seven, and three thermal
units, respectively. Sub-areas A and B are responsible to main-
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It is notable that the frequency (and even its rate of decline)
is difficult to determine from individual measurements locations
during a transient condition, because of the inter-area oscillations. For example, the local and inter-modal oscillations following
large disturbances can cause f and df/dt at different relays to measure quantities different from the actual underlying system f and
df/dt. Using f and f/t settings, which are averaged over an
appropriate time interval, gave values closer to the real system frequency and its rate change, and less influenced by other oscillations
[22].
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Fig. 7. Turbine–governor models for nonlinear simulation: (a) non-reheat steam unit; (b) reheat steam unit.
Fig. 8. Tie line power fluctuation and supplementary control actions following a ramp and a random load changes in sub-areas A and B.
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H. Bevrani et al. / Electric Power Systems Research 79 (2009) 837–845
nonlinear simulations, a random load change in the sub-area A and a
ramp load change of 200 MW for 100 s in sub-area B are considered.
The frequency response and the LFC system performance are shown
in Figs. 8 and 9. Fig. 8 shows the applied load change patterns in
sub-areas A and B, tie line power change between Area I and Area
II, and LFC control signals in sub-areas A and B. The relatively large
fluctuation of the tie line power (nearly 200 MW) is mainly caused
by the random load change in the sub-area A.
Frequency deviations in different locations of system are shown
in Fig. 9. To clarify the impact of the LFC control action, the system response with and without supplementary control is shown.
The dotted line in Fig. 9 shows the pure governors response following the applied disturbances. In steady state, the frequency
deviation (fss ) reaches the value given by (18) if KP is fixed at
zero. Using the supplementary control loop, since the frequency
deviation remained within f2 and the available LFC power reserve
could match the power demand, the system recovered within tens
of seconds to few minutes.
As second test scenario, the system frequency response is examined following a step loss of generation 500 MW in sub-area D
(Fig. 10a). The frequency deviation and the corresponding frequency gradient for all sub-areas (in Area I) and the external area are
shown in Fig. 10b and c. The highest frequency rate change occurs
in sub-area D. Recalling (27), this behavior is easily understandable.
The rate of frequency change is proportional to the power imbalance, and it also depends on the area system inertia. From Fig. 10,
it can be concluded that the disturbance location affects the frequency behavior of power systems and consequently the design
and selection of a suitable emergency control plan.
As mentioned, the supplementary (LFC) control is responsible
for maintaining system frequency by using the available instantaneous reserve to raise the frequency back to the nominal level. In
the event of a large disturbance, or an insufficient reserved power,
the frequency (in steady state) may stay in an off-normal condition.
As an extreme test scenario, consider the system frequency
response following a large load disturbance of 3000 MW in subarea A (Area I). Here, the total area load demand is much higher
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tain the frequency close to specified value among the Area I. Here,
we have mainly focused on dynamic characteristics and frequency
response of Area I.
Five and three LFC units are there in the sub-areas A and B,
respectively. The participation factors for the participated LFC units
in these sub-areas are given in Table 1. As can be seen, the participation factors in sub-areas A and B satisfy (2). The power system
parameters are considered similar to the practical system, which is
described in Ref. [16,17].
The power generation from the nuclear units (in the sub-areas
D and C), from the hydro units (in the sub-area D) and also from
the other utility units in the Kyushu Electric Power System are not
included in the simulation model because they are not in use for
the frequency regulation purpose. In this nonlinear simulation, the
generation rate constraints, dead bonds and time delays are all considered. Both reheat and non-reheat steam type units are used in
the LFC units.
In a real frequency control system, rapidly varying components of system signals are almost unobservable due to various
filters involved in the process. Thus, the speed governor dead band
and generation rate constraint (GRC) must be properly taken into
account. Over the years, several methods have been developed to
consider the GRC and speed governor dead band for the analysis/synthesis of frequency control systems.
Here, for the frequency response analysis and simulations, these
nonlinear dynamics are considered by adding a limiter and a hysteresis pattern to the governor–turbine system models, as shown
for reheat and non-reheat steam turbine in Fig. 7. The VU and VL are
the maximum and minimum limits that restrict the rate of valve
(gate) closing (opening) speeds.
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Fig. 9. Frequency deviations following a ramp and a random load changes in sub-areas A and B; with supplementary control (solid), and only primary control (dotted).
7. Simulation results
It is assumed that the maximum LFC reserved power PRmax in
Area I to track the area power imbalance is fixed at 1000 MW. For the
first scenario, to evaluate the efficiency of the LFC system during the
H. Bevrani et al. / Electric Power Systems Research 79 (2009) 837–845
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are disconnected at 70, 80 and 85 s, respectively (here, the MW base
is 1000 MW).
so
than the PRmax in (30). The normal and LFC controls are not able
to maintain the frequency at the nominal value and the steady state
frequency may pass the threshold frequency ft (31). Fig. 11 shows
the simulation results for this case.
In this case, the system is in an emergency condition and a
suitable load disconnection (load shedding) procedure is needed
to recover the system frequency. Considering the applied disturbance (Fig. 11a) and the overall area load disturbance magnitude
(21), assume that a three staged load shedding plan is investigated
and started at 70 s, as shown in Fig. 12. The loads 0.15, 0.1 and 0.05 pu
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Fig. 10. System response following a step load change in sub-area D at 50 s; sub-area A (dotted), sub-area B (line-dotted), sub-area C (dashed), sub-area D (bold solid), Area
II (solid).
(32)
Design of an appropriate load shedding scheme is out of the
scope of the present paper. Interested readers can find a suitable
adaptive load shedding methodology in the authors’ previous work
[21].
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PUFLS (t) = 0.15u(t − 70) + 0.1u(t − 80) + 0.05u(t − 85)
Fig. 11. System response for insufficient frequency regulation following a large load disturbance: (a) load disturbance; (b) frequency deviation in all sub-areas of Area I; (c)
rate of frequency deviation in all sub-areas of Area I; and (d) tie line power change.
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8. Conclusion
[7] O.I. Elgerd, C. Fosha, Optimum megawatt-frequency control of multiarea electric energy systems, IEEE Transactions on Power Apparatus and Systems PAS-89
(4) (1970) 556–563.
[8] C. Fosha, O.I. Elgerd, The megawatt-frequency control problem: a new approach
via optimal control, IEEE Transactions on Power Apparatus and Systems PAS-89
(4) (1970) 563–577.
[9] Q. Zhao, C. Chen, Study on a system frequency response model for a large
industrial area load shedding, Electrical Power and Energy Systems 27 (2005)
233–237.
[10] P.M. Anderson, A.A. Fouad, Power System Control and Stability, IEEE Press, Piscataway, NJ, 1994.
[11] H. Bevrani, Y. Mitani, K. Tsuji, Robust decentralized load-frequency control using
an iterative linear matrix inequalities algorithm, IEE Proceedings-Generation
Transmission and Distribution 150 (3) (2004) 347–354.
[12] V.V. Terzija, Adaptive under-frequency load shedding based on the magnitude of the disturbance estimation, IEEE Transactions on Power Systems 21
(3) (2006) 1260–1266.
[13] J.G. Thompson, B. Fox, Adaptive load shedding for isolated power systems,
IEE Proceedings-Generation Transmission and Distribution 141 (5) (1994)
492–496.
[14] J.S. Thorp, X. Wang, K.M. Hopkinson, D. Coury, R. Giovanini, Agent technology applied to the protection of power systems, in: C. Rehtanz (Ed.),
Autonomous Systems and Intelligent Agents in Power System Control and Operation, Springer, Berlin/Heidelberg, 2003, pp. 113–154.
[15] H. You, V. Vittal, Z. Yang, Self-healing in power systems: an approach using
islanding and rate of frequency decline-based load shedding, IEEE Transactions
on Power Systems 18 (1) (2003) 174–181.
[16] T. Hiyama, S. Koga, Y. Yoshimuta, Fuzzy logic based multi-functional load frequency control, in: Proceedings of the IEEE PES Winter Meeting, vol. 2, 2000,
pp. 921–926.
[17] T. Hiyama, G. Okabe, Coordinated load frequency control between LFC unit
and small sized high power energy capacitor system, in: Proceedings of the
International Conference on Power System Technology, 2004, pp. 1229–1233.
[18] H. Bevrani, Decentralized Robust Load-Frequency Control Synthesis in Restructured Power Systems, PhD dissertation, Osaka University, 2004.
[19] H. Bevrani, T. Hiyama, Robust load-frequency regulation: a real-time laboratory experiment, Optimal Control Applications and Methods 28 (6) (2007) 419–
433.
[20] P. Kundur, J. Paserba, V. Ajjarapu, et al., Definition and classification of power
system stability, IEEE Transactions on Power Systems 19 (2) (2004) 1387–1401.
[21] H. Bevrani, G. Ledwich and J. J. Ford, On the use of df/dt in power system emergency control, Proceedings of IEEE Power Systems Conferences and Exposition
(CD Record), Seattle, Washington, USA, 2009, in press.
[22] D.E. Clarke, Tasmanian experience with the use of df/dt triggering of UFLSS,
Final Report, Transend Networks Pty Ltd., No. D08/22185, 2008.
Acknowledgements
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This paper presents an analytic power system frequency
response modeling approach suitable for a wide range of operation,
from normal to emergency operating condition. The area frequency
response and related characteristics such as steady state frequency,
disturbance magnitude and load shedding frequency threshold are
determined. The conventional low-order frequency response model
is updated by adding the effects of emergency control/protection
dynamics. Finally, nonlinear simulation results for an actual two
control area power system showed that the results agree with those
estimated analytically.
na
Fig. 12. (a) Load shedding plan; (b) frequency deviation in all sub-areas of Area I; (c) rate of frequency deviation in all sub-areas of Area I; and (d) tie line power change.
References
Au
This work is supported by Australian Research Council (ARC)
under grant DP0559461. The authors would like to thank Prof.
Takashi Hiyama from Kumamoto University for his kind assistance
to provide the power system example and suitable simulation data.
[1] P. Kundur, Power System Stability and Control, McGraw-Hill, Englewood Cliffs,
NJ, 1994.
[2] B.J. Kirby, J. Dyer, C. Martinez, R.A. Shoureshi, R. Guttromson, J. Dagle, Frequency
control concerns in the North American Electric Power System, Technical report, 2002, available online: www.ornl.gov/sci/btc/apps/Restructuring/
ORNLTM200341.pdf.
[3] L.-R. Chang-Chien, Y.-J. Lin, C.-C. Wu, An online approach to allocate operating
reserve for an isolated power system, IEEE Transactions on Power Systems 22
(3) (2007) 1314–1321.
[4] D.L.H. Aik, A general-order system frequency response model incorporating
load shedding: analytic modeling and applications, IEEE Transactions on Power
Systems 21 (2) (2006) 709–717.
[5] P.M. Anderson, M. Mirheydar, A Low-Order System Frequency Response Model,
IEEE Transactions on Power Systems 5 (3) (1990) 720–729.
[6] M.B. Djukanovic, D.P. Popovic, D.J. Sobajic, Y.H. Pao, Prediction of power system
frequency response after generator outages using neural nets, IEE ProceedingsC 140 (5) (1993) 389–398.