-
An Adaptive Load Shedding Technique for Controlled
IslandingMaria Vrakopoulou Goran Andersson
ETH Zurich, Switzerland ETH Zurich,
[email protected] [email protected]
Abstract - The main contribution of this paper is the
de-velopment of a novel load shedding methodology so as to
reg-ulate unacceptable frequency deviations, with least disrup-tion
of service, in the case of controlled islanding. To achievethis, an
abstracted model of each islanded area, consistingof one lumped
generator and turbine model, is used. Sincein the controlled
islanding the bounds of the areas are deter-mined, a good
estimation of the generation-load mismatchcan be obtained. Taking
advantage of the latter an amountof load to be shed in the
load-rich areas, at the moment ofthe area separation is proposed.
This amount is optimallyselected so as to minimize the total load
shed, taking into ac-count the primary frequency control dynamics
and the con-ventional Underfrequency Load Shedding schemes
(UFLS).Markov Chain Monte Carlo (MCMC) methods and ModelPredictive
Control (MPC) are the two optimization tools thatare used to solve
the resulting optimization problem. Theeffectiveness of the
proposed technique is evaluated via sim-ulation on the IEEE 118 bus
network.Keywords - Load shedding, controlled islanding, model
pre-
dictive control, randomized optimization methods.
1 Introduction
As the operation of power systems is getting closer toits
stability margins it is more likely for large disturbancesto drive
the system into a wide-area blackout through cas-cading events.
Controlled islanding is a promising schemethat prevents the failure
spreading in the rest of the system.The system is intentionally
split into islands and conse-quently the generation-load balance is
lost. If the magni-tude of the imbalance is such that the primary
frequencycontrol is either slow or the reserves are not enough
tomaintain the frequency in the desired range, emergencycontrol
actions take place.
In the generation-rich island, generators may gettripped by the
operator or in the end by protection devicesrendering though the
system closer to its nominal equilib-rium point. The load-rich
island is more crucial since afrequency drop of around 2.5-3 Hz can
trigger the under-frequency generator protection and thus trip the
generator.This leads to a larger generation-load mismatch and in
theworse case, after a sequence of outages, to a total
blackout.Hence appropriate load shedding schemes are essential
forthe load-rich areas.
Conventional UFLS methods are based on the fre-quency drop or
also, in some cases, on the rate of the fre-quency deviation. The
under-frequency relay settings arepredefined according to the
desired performance of the en-tire system and thus cannot assure
the optimal amount ofload shed in the case of islanding. Another
issue is that
modern power systems are rich in distributed generation,which
may lead to inefficient load shedding, since the loadshedding
action will also eliminate distributed sources ofgeneration
[1].
Main contribution of this paper is that it provides anadaptive
load shedding technique for regulating unaccept-able frequency
fluctuations in the load-rich controlled is-landed areas. This
method utilizes the knowledge of thegenerator and load
characteristics of the formed islandin order to estimate the
magnitude of the generation-loadmismatch. That way, the average
rate of change of thegenerators frequency can be more accurately
determined.Adaptive load shedding schemes based on the rate of
fre-quency decline have been also used in [18], [19].
The proposed scheme is built under the assumptionthat loss of
synchronism can be quickly detected and thecontrol islanding is a
centralized action that includes thefast detection of the coherent
generators and determinationof the borders of the islands. In [20]
and [2] controlledislanding is set using coherency algorithms
presented in[21] and determining also the boundaries via
optimizationalgorithms for minimizing the resulting
generation-loadmismatch. However, the detection of loss of
synchronismis obtained in a decentralized way. The increasing,
though,development in Phasor Measurement Unit (PMU) tech-nology and
the communication infrastructure is promisingthat in the near
future angular instability could be detectedrapidly enough so as
the information to be processed cen-trally.
For the design of an optimal load shedding policy anaggregated
model of each island is used [15]. Low orderfrequency response
model, so as to estimate the frequencybehavior of a large power
system, have been earlier pre-sented by [17]. This consists of one
generator, determinedby the classical model, its turbine and
governor dynam-ics. UFLS is also taken into account, since the
describedmethod does not cancel its scope but takes action
centrallyfrom a higher layer of the hierarchical monitoring and
con-trol structure.
The main idea of the proposed method is that at thetime the
borders of the islands are decided, instead of wait-ing for the
UFLS to act, an initial amount of load shed-ding is applied. The
risk of negative dynamic effects isalso minimized by unloading the
system immediately inthe load shedding schemes focused in voltage
stability,presented in [5]. In our method, the value is chosen soas
to minimize the total amount of load shed, which isdefined as the
sum of the initial and any additional loadthat may be shed by the
conventional UFLS action, over
Maria Vrakopoulou and Goran Andersson are with the Power Systems
Laboratory, ETH Zurich, Switzerland, Physikstrasse 3, CH-8092,
Phone:+41446323252, Fax: +41446321252.
-
the dynamic response of the frequency. This is a typi-cal
optimization problem with linear but hybrid dynam-ics, and
constraints imposed by physical limitations. Thehybrid nature
arises due to the conventional load shed-ding scheme and the
saturation of the primary control. Tosolve this problem, two
different methods are employed.The former is a randomized
optimization technique, whichis based on Markov Chain Monte Carlo
methods [4],whereas the second is based on Model Predictive
Control(MPC) [3]. The latter provides efficient theoretical
andcomputational tools to solve optimization problems evenonline,
by shifting the computational burden offline. Moredetails regarding
these optimization methods will be givenin Section 3. The
effectiveness of the proposed scheme isverified via simulations on
the IEEE 118-bus network.
The remainder of the paper is organized as follows.In Section 2
a description of the models used is provided,whereas in Section 3
information regarding the adoptedoptimization techniques is given.
Section 4 provides thesimulation results obtained from the
application of thesemethods on the IEEE 118-bus network. Finally,
Section 5provides some concluding remarks and directions for
fu-ture work.2 Physical description and mathematical modeling
As stated in the introduction, objective of this paper isto
quantify the potential improvement, if an initial amountof load is
shed, in the load-rich island, prior to the actionof conventional
UFLS, in the case where the network isdivided into islands as an
effect of a disturbance. To de-termine this amount of load, each
island is represented byan aggregated model, consisting of the
dynamics of a sin-gle generator with turbine and governor dynamics.
Thelatter is reasonable, since the strong coupling of the co-herent
generators allows us to represent each area with asingle unit, so
as to estimate the frequency response ofthe system. Moreover, the
discrete events, due to the con-ventional UFLS actions and the
governor saturation, arealso modeled, resulting in the hybrid
system used in theoptimization process. Figure 1 provides a block
diagram,which illustrates the described technique.
Steam turbine dynamics
1-
-1S 1+ sTCH
11+ sTRH
1
+
+
+
- f(2HSB)sfo
governor
Pe
Pload
Pm
++
1Dl
SB =5300 MVAH = 3 sTCH=0.4 sTRH=7 s =0.2S=0.05 p.u.P_sat= +/-
400MW
system inertia
+
+u (t =0)
UFLS
UFLS (conventional) Stage1 Stage 2 Stage 3 Stage 4 Stage 5
f threshold (Hz) 0.7 1 1.3 1.6 1.9
Load shedding (pu) 5% 5% 5% 10% 10%
May 29, 2011 1PSL annual meeting
Pch
+
Pmismatch
i
Figure 1: Block diagram of the aggregate model.To derive such a
model, we define the lumped areas
swing equation as in [15]
f =f0
2HS B(Pm Pe), (1)
where f denotes the deviation of the frequency from itsnominal
value f0, and Pm, Pe represent the deviationof the total mechanical
and electrical power from their setpoints respectively. The
parameters H and S B are the so
called total inertia time constant and the total rating
power,and are defined by
S B =j
S B j ,
H =
j H jS B jj S B j
,
where j denotes the number of generating units inside
thearea.
By including also the turbine (a steam turbine with areheating
unit was used) and governor dynamics as shownin Figure 1, the
overall system can be represented by fPmPch
=
f02HS B
(Pm Piload 1Dl f Pmismatch u) 1TRH Pm + ( 1TRH aTCH )Pch + aTch
Pp1
TCH(Pch + Pp)
,(2)
where Pm and Pch are denoted in Figure 1, TCH , TRHare the
turbine time constants, S is the speed droop of theprimary
controller, and Dl represents the frequency depen-dency of the
load. Pmismatch denotes the initial mismatchbetween the generation
and load in a controlled islandingarea, whereas Piload denotes the
amount of load shed upto stage i of the conventional UFLS, and will
be describedin the sequel. Pp captures the saturation of the
primarycontroller, as shown in the block diagram. Specifically,
Pp =
Pminp if 1S f Pminp 1S f if Pminp < 1S f < PmaxpPmaxp if
1S f Pmaxp
The block UFLS in Figure 1, stands for
conventionalUnderfrequency Load Shedding, and could be thought ofas
a sequence of predetermined actions. More specifically,when the
frequency drops below some thresholds, a cer-tain value of load is
shed. The values for the differentstages of the conventional UFLS,
that were used in thesimulations are depicted in Table 1. Normally,
there isalso a delay in these switching actions, which for
simplic-ity is not taken into account in this abstracted version
ofthe network, but is modeled in the IEEE 118-bus system.
UFLS(conventional) Stage 1 Stage 2 Stage 3 Stage 4
fthreshold(Hz) -0.7 -1 -1.3 -1.6
Loadshedding(pu) 10% 10% 10% 15%
Table 1: Stages of the conventional load shedding scheme.
The saturation of the primary controller and the vari-ous stages
the conventional UFLS contributes to the hy-brid nature of the
system dynamics. More details aboutthe different modes of operation
are given in Section 3.2.
Variable u denotes the initial value of load shedding,that based
on the description so far, will be determined viaan optimization
method. For illustrative purposes, Figure2 depicts the frequency
response of an example systemand the corresponding load shedding
behavior for the case
-
where u = 0MW (blue) and u = 100MW (green).These results were
obtained based on MCMC optimiza-tion that will be described in the
next section, but havebeen included here so as to get a qualitative
idea of thebehavior of the system (2), and the potential
improvementafforded by performing an initial load
shedding.Example
Generation loss of 1000 MW
just conventional load shedding
800 MW
conventional load shedding + 95MW initial load shedding
630 MW
- - - UFLS stages
December 5, 2010 2PSL annual meetingFigure 2: Frequency and
total load shedding response based on the ab-stracted model.
3 Optimization techniques3.1 Randomized methods
Markov Chain Monte Carlo (MCMC) method is arandomized
optimization technique, which explores thesearch space via a Markov
chain. In this setting, theproblem of optimizing a certain
criterion J(u) is trans-formed to the problem of approximating its
optimizerby extracting candidate solutions u from a proposal
dis-tribution of our choice. Variable u R denotes thedecision
variable, which for the purpose of this pa-per represents the
initial value of load that should beshed so as to minimize the
total amount of load shed-ding. The algorithm involves then a
sophisticated accept-reject mechanism, and hence the optimal u can
be iden-tified. The following algorithm summarizes the basicsteps
of the so called Metropolis-Hastings algorithm.
Metropolis-Hastings algorithm1: Let u0 denote an initial choice
for u.2: Define as N the total number of iterations.3: For i = 0 :
N
Extract ui+1 pu(|ui)
= min{1,
pu(ui|ui+1)pu(ui+1|ui)
J(ui+1)
J(u)},
ui+1 ={
ui+1 with probability ,ui with probability 1 ,
end
At each step i of the algorithm, the extracted variableui is
accepted with a probability , as this is defined in thealgorithm
above. Otherwise, it is rejected and the previousstate of the chain
is replicated. At the end of the algorithm,the extracted points are
concentrated at different regions,
and based on the peakedness, the optimal value for u
isdetermined.
For this example the objective function was chosen tobe
J(u) = e(Total load shed), (3)
where the total load shed is defined as the sum of u andthe
action taken by conventional load shedding techniques(UFLS).
Variable is a tuning parameter, and in a simu-lated annealing
setting [6], as increases the peakednessof J(u) is also increasing.
The probability density pu(|ui)denotes the proposal distribution,
which at the first stepwas chosen to be a uniform distribution, so
as to searchaccurately the decision space. At a next step the
entireprocess was repeated , this time by sampling from gaus-sian
distributions centered at the accepted samples of thefirst run.
That way, a local search was performed, and amore accurate
optimizer was identified.
The main limitation of this method is that since itis a
simulation-based process, and relies on sampling, itcan not be
applied for online optimization problems, andhence is limited to
offline applications. Nevertheless, itwas employed in the specific
application due to the guar-antees that it provides to converge to
the optimum in lowdimensional problems (only one decision variable
in ourcase). Hence it serves as a benchmark, that allows usto
compare the solution obtained by the following MPCscheme, which
makes use of a linearized version of themodel. Alternatively, in
the absence though of theoreti-cal guarantees, any other efficient
heuristic (i.e. GeneticAlgorithms) could be employed.
3.2 Model Predictive Control
Model Predictive Control (MPC) provides an efficientway of
solving optimal control problems [7]. In the casewhere both the
model dynamics and the constraints arelinear, and the cost is
either linear or quadratic, the result-ing optimization problem is
a linear or quadratic program,and can be efficiently solved
online.
Systems like the one described in Section 1, are gov-erned by
linear dynamics and include polyhedral con-straints, but exhibit a
hybrid behavior. For the load shed-ding case, this is due to the
discrete modes introduced bythe action of the conventional load
shedding scheme, andthe saturation of the primary frequency
control. These sys-tems are hence described by Piecewise-Affine
dynamics,which are active over different partitions of the state
space.Since MPC is formulated in discrete time [3], let
x(k + 1) = Aix(k) + Biu(k) + i,y(k) = Cix(k) + Diu(k) + Gi,
(4)
denote the discretized version of (2), where [x(k) u(k)]T Pi,
and Pi denotes the partition i. Following the detaileddescription
of [8], [9], the partitions Pi are characterizedby the so called
guard lines of the form
Gi,xx(k) +Gi,uu(k) Gi,c. (5)
-
Figure 3: Mode illustration of the piecewise-affine system.For
simplicity of notation, let mi = Piload denote the
amount of underfrequency load shedding up to stage i ofUFLS. To
formulate the system described in Section 1 inthis framework, we
augment the state space with an artifi-cial state s(k + 1) = mi,
where mi corresponds to the totalamount shed at each mode due to
conventional UFLS. Fig-ure 3 illustrates the proposed partition.
The horizontal axisis the artificial state s, whereas the vertical
axis denotesthe frequency. At the modes M1, M2, M3, where no
loadshedding action is taken, we have that s(k + 1) = m0 = 0.From
these modes, M2 corresponds to the case where thesaturations of the
primary controller are not active, andM1,M3 represent the case
where the controllers output issaturated to the lower and upper
limit respectively. Whenthe frequency drops below 0.7Hz (M4), the
first amountof load is shed, and hence s(k + 1) = m1. Then a
dis-crete jump will be triggered instantaneously, and the sys-tem
will operate at M5, unless the frequency drops below1Hz, where the
system will operate at M6 (s(k+1) = m2).Similar reasoning can be
used for the case of more loadshedding stages.
Given this representation, let N denote the MPC pre-diction
horizon. The only free control input is u(0), as{u(k)}N1 are
restricted to be equal to u(0), since u(0) repre-sents the initial
load shedding amount, which is then keptconstant. The optimization
problem can be then definedas
minu(0)
J(N) = minu(0)|(s(N) + u(0))|, (6)
subject to umin u(0) umax and the dynamics (4). uminand umax are
selected over a reasonable region towards thegoal of minimum load
shedding. By s(N) we denote theamount of load shed at the end of
the horizon N.
Non-standard cost functions, like (6), can be easily en-coded in
the MPT toolbox [8], which was used in this pa-per. The latter is
due to the Yalmip interface, developedby [10], which allows to add
arbitrary constraints and ob-jective functions to an MPC setup.
4 Computational analysis4.1 Test system
The proposed technique is applied to the IEEE 118-busnetwork and
time domain simulations are carried out so as
to demonstrate its effectiveness. This model is
consideredcomplex enough to capture the difficulties that may
arisein a realistic scenario. The data of the model are
retrievedfrom a snapshot available at [11]. Since there were
nodynamic data available, typical values provided by [12]were used
for the simulations. All generators are repre-sented by the
classical model and are also equipped withprimary frequency
control, Automatic Voltage Regulator(AVR) and Power System
Stabilizer (PSS). The model ofthe IEEE 118-bus network is
implemented in MATLABby [14]. For more details on the generation
data used,the reader is referred to [2]. The stages of the
conven-tional UFLS that the entire network is equipped with,
aredescribed in Table 1. Two kind of delays are taken into ac-count
for these switching actions. Specifically, load shed-ding is
triggered with 10 msec relay delay, given that thefrequency has
been already maintained below the specificthreshold for at least
100 msec.
For the demonstration needs of the paper, we consid-ered the
IEEE 118-bus network to be divided in two areasaccording to the
controlled islanding decision after a dis-turbance that leads to
loss of synchronism. These two ar-eas are illustrated in Figure 4
in Neplan environment [13]for better visualization.
1December 5, 2010 PSL annual meeting
Area 1
Area 2
Figure 4: IEEE 118-bus network.
From these two areas, Area1 is characterized by a gen-eration
deficit of 539.6 MW and hence Area 2 is a gener-ation rich island
with 539.6 MW generation excess. Sincethis paper is devoted in a
under frequency load sheddingstudy, Area 1 is represented by the
abstracted model de-scribed in Section 2.1. Area 1 consists of the
generatorsG10, G12, G25, G26, G46, G49, G54, G59, G61 and G66.The
parameters of this abstracted model are summarizedin the following
table.
S B (MVA) H (s) Pgen (MW) Pload (MW) f0 (Hz)2457.8 3.4509 2054
2593.6 50Dl ( HzMW ) S (
HzMW ) TCH(s) TRH(s) a
0.0129 0.001 0.4 4 0.2Table 2: Parameter values for the
abstracted model of Section 2.
4.2 Optimization results
To determine the optimal value of u, the optimizationmethods
described in Section 3, have been employed. Forthe MCMC algorithm,
two stages were performed. Thefirst comprises of 10000 random
samples (chain of the dis-tribution) extracted from a uniform
distribution and 6354
-
states of this chain were accepted. At the next stage, an-other
10000 candidate solutions were extracted, this timefrom a gaussian
distribution around the accepted states ofthe previous run, and
3562 states were accepted. The valueof u that gave the higher
performance was found to beu = 126MW.
For the MPC implementation, an explicit controllerwas calculated
using the Multi-Parametric Toolbox (MPT)[8]. For the
implementation, a time horizon of N =10 steps was used, the
discretization step was fixed atTs = 0.2 sec, and u was considered
to be constrained in1138MW u 0MW. This minimum value corre-sponds
to the total possible conventional load shedding ac-tion (for this
case 45% of the load). The optimal choice ofthe values N and Ts is
always a trade-off, but for this caseno parametric study was
conducted. The optimal valuewas found to be u ' 150MW. Although MPC
has theadvantage that could be applied online, it may lead to
asuboptimal solution due to the discretization error. Sim-ilarly,
MCMC can determine only an approximate opti-mizer of the
corresponding cost function since it is basedon sampling.
Nevertheless, for the specific case, wherethe decision space is one
dimensional, MCMC may leadto high accurate solutions. In general,
when applied to therealistic network, the value of u will only be
suboptimal.
0 1 2 3 4 5 6 7 8 9 1048.5
49
49.5
50
50.5
t(sec)
f(Hz)
0 1 2 3 4 5 6 7 8 9 100
200
400
600
800
1000
t(sec)
load
she
d (M
W)
u = 0 MWu= 50 MWu= 200 MWu= 150 MW
u = 0 MWu= 50 MWu= 200 MWu= 150 MW
Figure 5: Area1 aggregate system frequency and load shedding
response
4.3 Simulation results
Both the MCMC and MPC solutions were tested. Forthe simulations
though shown in this subsection only thevalue generated from MPC
was considered, even thoughMCMC led to better results. This was
decided due to thefact that MPC has the potential to be applied
online.
For illustrative purposes, Figure 5 shows the frequencyand load
shedding response of the abstracted system forthe case where the
optimal u = 150MW is applied. Inthe same figure, the outcome of the
simulation results foru = 200MW, u = 50MW and u = 0MW are
alsodepicted, and as expected the optimal value for u leadsto the
minimum total load shedding value. Note that
u = 50MW leads to a higher total amount of load shedcompared to
u = 0MW. This is due to the fact that in bothcase the same number
of stages of UFLS are activated.
0 1 2 3 4 5 6 7 8 9 1047.5
48
48.5
49
49.5
50
50.5
51
51.5
52
t(sec)
f(Hz)
0 1 2 3 4 5 6 7 8 9 100
100
200
300
400
500
600
t(sec)
load
she
d (M
W)
Figure 6: Area1 aggregate system frequency and load shedding
response
0 1 2 3 4 5 6 7 8 9 1047.5
48
48.5
49
49.5
50
50.5
51
51.5
52
t(sec)
f(Hz)
0 1 2 3 4 5 6 7 8 9 100
100
200
300
400
500
600
t(sec)
Load
she
d (M
W)
Figure 7: Area1 frequency dynamics and load shedding of the
118-bussystem
For comparison purposes, the IEEE 118-bus network(splitted in
two areas at 0.27sec) was simulated for thecase of conventional
load shedding (u = 0). The resultsare depicted in Figure 7, where
the upper plot shows theresponse of the frequencies of Area 1, and
the lower figureillustrates the load shedding action. The response
of thisdetailed system is compared with that of Figure 6,
whichcorresponds to the same scenario for the abstracted versionof
the system though. The frequency trajectories of Fig-ures 7, 9
represent the frequencies of the buses in Area 1,and those that
exhibit high transient behavior at the split-ting instance
correspond mainly to the buses at the endof the tripped lines. The
duration that the frequencies areinitially below the UFLS frequency
thresholds is less than100 msec and for that reason conventional
load sheddingstages are not activated. It should be also noted,
that Fig-ures 7, 9 are slightly shifted to the right compared to
those
-
of Figures 6, 8, since the IEEE 118 network was splittedin two
areas at 0.27 sec. It is clear that the aggregate sys-tem captures
quite accurately the behavior of a complexnetwork, and apart from
some oscillations, their averageresponses are almost identical.
0 1 2 3 4 5 6 7 8 947.5
48
48.5
49
49.5
50
50.5
51
51.5
52
t(sec)
f(Hz)
0 1 2 3 4 5 6 7 8 9 100
100
200
300
400
500
600
t(sec)
load
she
d (M
W)
Figure 8: Area1 aggregate system frequency and load shedding
responsewith 150MW initial load shedding
The same study was repeated, this time by applying aninitial
amount u = 150MW of load shedding, which wasfound to be optimal by
the MPC algorithm. Note that thisis applied at 0.27sec, when the
system is divided in two ar-eas. The results of the detailed and
the lumped system arereported in Figures 9 and 8 respectively. Once
again, theabstracted system and the IEEE 118-bus network exhibita
very similar behavior. Moreover, this simulation servesas a proof
of concept of this paper, since application of theoptimal u
designed based on a simplified model, managedto reduce the total
amount of load shed to 20.3%, in a real-istic simulation
environment. It should be also remarked,that the total amount of
load shedding for the two cases isalmost identical.
5 ConclusionIn this paper a novel load shedding methodology
is
presented. The problem of identifying an initial amountof load,
which will be shed immediately after the decom-position of the
network into islands, was investigated. Todetermine the optimal
load shedding value, optimizationtechniques based on MPC and Monte
Carlo methods foran abstracted model equipped with a conventional
loadshedding mechanism, were employed. The outcome ofthis method
was applied to the IEEE 118-bus network, andtime-domain simulations
were carried out. The results in-dicate a potential improvement
compared to conventionalapproaches.
Similar arguments hold also for the over-frequencycase. It is
then proposed that the generation to be shed willpreferably belong
to distributed units so as to reduce therestoration time compared
to big power plants. As statedalso in [16], this is feasible under
the assumption of fu-ture networking in the distribution level
which allows in-
dependent manipulation of the distributed generation andthe
actual loads.
0 1 2 3 4 5 6 7 8 947.5
48
48.5
49
49.5
50
50.5
51
51.5
52
t(sec)
f(Hz)
0 1 2 3 4 5 6 7 8 90
100
200
300
400
500
600
t(sec)
Load
she
d (M
W)
Figure 9: Area1 frequency and load shedding response with
150MWinitial load shedding
In future work, we plan to extend the aggregate modelso as to
capture more accurately the response of the realsystem. On the one
hand a more detailed model for the tur-bine (i.e considering also
valve speed saturation) could beemployed in the one mass system
representation. On theother hand, one could also consider the fact
that in a real-istic case the islanded area may consist of
generators withdifferent control systems and/or turbine dynamics.
Thesimilar ones could be then lumped into one aggregatemodel. The
latter will lead to an abstraction with morethan one generators
connected with each other accordingto the reduced admittance matrix
of the islanded network.
Moreover, this approach will be tested exhaustivelyvia
simulations for both load-rich and generation-rich is-lands for
various disturbances that lead to the need of con-trolled
islanding, in order to collect statistics regarding itsperformance.
Another issue is to adopt a receding horizonimplementation in the
MPC setting, instead of optimizingonly over the initial load
shedding value. The latter willprovide feedback in the design
process and hence it willaccount for model mismatch and parameters
uncertainties.
AcknowledgmentResearch was supported by the European
Commission
under the project VIKING, FP7-ICT-SEC-2007-1. Theauthors would
also like to thank Dr. Turhan Demirayfor providing the power system
simulation environmentin MATLAB and for his valuable support during
the mod-eling phase.
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