anisii razvan eng.pdf

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Electric Power Systems Research 80 (2010) 287295

Contents lists available at ScienceDirect

Electric Power Systems Research

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e p s r

Generic reconfiguration for restoration

David Kleppinger a,, Robert Broadwater a, Charlie Scirbona b

a Department of Electrical and Computer Engineering, Virginia Tech, 1214 Univ. City Blvd, H-95 Blacksburg, VA 24060, USAb Distribution Engineering, Orange and Rockland Utilities, One Blue Hill Plaza, Pearl River, NY 10965, USA

a r t i c l e i n f o

Article history:

Received 1 July 2009

Received in revised form

10 September 2009Accepted 14 September 2009

Available online 27 October 2009

Keywords:

Reconfiguration

Dependencies

Graph Trace Analysis

Priority

a b s t r a c t

This paper introduces and compares four algorithms by which reconfiguration for restoration of an arbi-

trary number of interdependent critical infrastructure systems can be achieved. A method of modeling

systems called Graph Trace Analysis is used to enable generic operation on various system types. The

algorithms described are compared with each other and with prior work when run on a model of an

actual electrical distribution system. The described algorithms are also run on an example model to

demonstrate the ability to reconfigure interdependent infrastructure systems.

2009 Elsevier B.V. All rights reserved.

1. Introduction

Modern society depends on a set of critical infrastructure sys-

tems. These systems include electrical distribution, potable water,

sewage, gas, and others. When a problem occurs in one of these

systems, it can cause disruption of services not only in its system

but also in other systems.

In this paper loads are considered to be any device which

requires service from a system. Based upon the mission of the sys-

tem, some loads aremoreimportant than others, andthe mission of

thesystem may change. Thus, theimportanceof a load maychange.

Reconfiguration for restoration is the process whereby disruption

in services to loads is responded to and the system or systems in

question are altered to restore service to the loads.

In all of these systems there are devices which can be operated

to alter the system topology or even cut off entire sections of the

system in order to isolate faults. These sectionalizing devices are

the core of reconfiguration. In this paper all sectionalizing devicesthat are available for use, whether they be valves in fluid systems

or breakers in electrical systems, will be referred to as switches.

The goal of reconfiguration is to operate switches in order to

arrive at a system state where service disruptions are minimized

while adhering tosystem constraints.Also, basedupon thedesire to

keep service flowing to certain loads, system operating constraints

may change.

Corresponding author.

E-mail address: [email protected] (D. Kleppinger).

Loads on a system are not of equal importance. Often there is a

hierarchy of importance among system loads, and thus reconfigu-

ration must take this prioritization into account when determining

where to restore service. Priorities cancome from multiple sources.

Utilities frequently maintain lists of critical customers which can

be used to derive discrete priority assignments forindividual loads.

In addition, some loads may have their priorities implied by the

goals of the system, or its mission. For example, a warship not

engaged in battle would consider its propulsion systems more

important than its weapons systems, and load priorities would

flow from that [1]. Furthermore the importance of a load may

change based upon what the system is being asked to do, or its

mission.

Critical infrastructure systems are not independent of each

other. Each has elements which depend on elements in another

system. For example, water systems employ pumps. These pumps

are often driven by electrical motors, which are loads on the elec-

trical system. These intersystem dependencies must be consideredby reconfiguration.

The work here considers a system of systems model. A disrup-

tion in one system often results in a disruption in another system.

For valid solutions these interdependencies must be considered.

An electrical outage can result in an outage in the potable water

system, and depending upon the length of the outage, the potable

water system may need to be flushed for some period of time prior

to using the water. In some systems electrical power equipment

depends upon cooling water. If the cooling water suffers a disrup-

tion, after some period of time the electrical equipment needs to

be turned off or suffer failure due to overheating.

0378-7796/$ see front matter 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.epsr.2009.09.011
http://www.sciencedirect.com/science/journal/03787796http://www.elsevier.com/locate/epsrmailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.epsr.2009.09.011http://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.epsr.2009.09.011mailto:[email protected]://www.elsevier.com/locate/epsrhttp://www.sciencedirect.com/science/journal/03787796


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288 D. Kleppinger et al. / Electric Power Systems Research 80 (2010) 287295

1.1. Past work

Previous reconfiguration solutions that address priority gener-

ally restrict loads to vital and non-vital classes, with perhaps a

third semi-vital class [24]. Such priority modeling, particularly

in more complex systems, may not provide enough granular-

ity in priority levels. For such systems a method that allows

for an arbitrary number of priority levels is desirable. Further-

more, the load priorities should be a function of the system

mission(s). If the mission is to fight fire, one set of loads is

needed, whereas if the mission is to fight flooding another set of

loads is needed. The work here considers an arbitrary number of

priority levels, where a loads priority level is a function of mis-

sion.

Previous reconfiguration solutions frequently rely on matrix-

basedtechniquesfor modeling systems and checking for constraint

violations [2,4,5]. This results in topology management with sparse

matrices. Such solutions are difficult to distribute over multiple

processors. Making changes to the model also proves problem-

atic for such methods, as adding or deleting a component can

force a substantial reformulation of the problem. The Cotree

Switch method, one of four methods presented here is similar to

the method described by Shirmohammadi and Hong, except the

method consideredhere is notrestricted to weakly meshed systems[2,3,5,6].

Other solutions attempt to solve the reconfiguration prob-

lem with agent-based methods or evolutionary algorithms [811],

which face significant problems of their own. Evolutionary algo-

rithms sufferfrom longer solution times thanmore straightforward

heuristic methods, and agent-based methods require the instal-

lation of agents with equipment in the monitored systems,

creating another infrastructure system on top of what already

exists.

Previous solutionsalso rely on simplifying thesystem, using lin-

earized, aggregate models to estimate flows rather thanperforming

full, non-linear flowcalculations on thesystem model or restricting

themselves to radial systems [5,7,8]. Such simplifications limit the

ability of the solution to accurately determine the state of a sys-tem following a disruption. The fact that infrastructure systems do

not operate in a vacuum is also rarely taken into consideration, and

very few solutions recognize or attempt to address the problem of

system interdependencies.

1.2. New algorithms

This paper proposes and compares several reconfiguration

algorithms. Thealgorithms proposed arebasedon a methodof ana-

lyzing systems referred to as Graph Trace Analysis. Each algorithm

allows for full load prioritization and handles system interdepen-

dencies. Furthermore, the proposed algorithms are independent

of the system type(s) such as electrical, gas, or fluid being ana-

lyzed.

2. Graph Trace Analysis

Graph Trace Analysis (GTA) is a method of analyzing systems

predicated on graphs [12]. GTA uses the concepts of graphs, sets

generated by tracing through the graph, where traces are imple-

mented with iterators, and set operators. The set operators used in

GTA are for the most part the same as those used in the Object Con-

straint Language (OCL) [12,13]. In a GTA model, each component

in the system corresponds to an edge of a graph. Furthermore, the

graph is thought of just in terms of edges. That is, it is an edge-edge

graph, and nodes are not treated as separate entities, but become

part of the edge itself.

2.1. GTA notation

The primary focus of GTA is on sets and sequences, which are

collections of objects which are either unordered (sets) or ordered

(sequences). For this reason, GTA notation is based on the Object

Constraint Language; a language devised for the purpose of work-

ing with sets and sequences [13]. Since OCL is non-destructive and

not designed for writing algorithms, modifications were required

in order to allow such actions as looping and assignment. While

algorithms written with GTA notation do feature single-item vari-

ables, the operators provided by GTA are primarily intended to

make working with collections of items easy. Operators specific

to sets and sequences and members of GTA sets, sequences, and

complex data structures are accessed using the symbol. Sets are

denoted by{ }andsequences by[ ].Partsof anexpression contained

within parenthesis are executed before the rest of the expression.

The most important operator in GTA is the collect() operator.

collect() operates on a set or a sequence, and takes as an argument

an expression that evaluates to true or false for each element of

the set or sequence in question. collect( ) then returns a collection

consisting of all elements of the collection on which collect( ) was

called for which the given expression is true. If the collection on

which collect( ) is called is a set, so is the output collection. If the

collection on which collect( ) is calledis a sequence,then theoutputcollection is a sequence where each element is in the same order

as in the input collection. For example, if sequence A = [1,2,3,4,5],

then A collect(p|p% 2 == 1) would return [1,3,5], where % is the

modulus operator. The collect( ) operator is a powerful tool in GTA

for creating new sets and subsets of related objects, and is used

extensively in the reconfiguration algorithms described in this dis-

sertation.

The subset of GTA operators used in this paper is described in

Table 1. Columns a and b are the arguments used in the operation,

the Operation column shows the name and syntax of the operation,

the Resultcolumnshowsthe data type of theresult of theoperation,

and the Effectcolumn describes what the operation does.

2.2. GTA models and traces

In a GTAmodel, each componenthas oneand only onereference

source, which is the source in the system which defines the com-

ponents trace relationships. A source is a component which can

provide service (electricity, water, gas, etc.) to a system. Though

multiple sources can feed any given component, only one of those

sources can be its reference source. The combination of the refer-

ence sourceandthe graphtopologydefines a setof iteratorsforeach

component:forward, backward, feeder path,brother, and adjacent.

The forward and backward traces are used to trace through

every component with the same reference source once and only

once. The component in the forward trace from the current com-

ponent will receive flow from the current component, originating

with its reference source, if that component is not the brother ofthe current component. The brother represents the first compo-

nent in the forward trace of the current component not fed by the

current component. Thus, once all components fed by the current

component are included in the forward trace, the next component

in theforward trace is thecurrent components brother. In this way,

all components fed by the current component will be found in the

forward trace before any components not fed by it. The backward

trace is simply the reverse of the forward trace.

The feeder path trace for a given component gives the compo-

nent which immediately feeds the given component. The feeder

path trace is functionally complete, in that all other traces can be

derived from it [12].

The adjacent trace gives a component physically connected to

the current component but which may not have the same refer-


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D. Kleppinger et al. / Electric Power Systems Research 80 (2010) 287295 289

Table 1

GTA operators.

a b Operation Result Effect

set or seq a size int The number of elements in a

set or seq expr a collect(p|b) set or seq Returns all elements p in a for which b is true

set or seq expr a order(b) seq Orders a such that its elements are in increasing order

according to b. If a is a set, order makes it a seq

set or seq any a includes(b) bool Returns whether b is an element of a

set or seq expr a exists(b) bool Returns whether there is an element of a for which b is true

set or seq expr a forall(b) bool Returns whether b is true for all elements of aset or seq expr a sum(b) any Returns the sum of the expression b as applied to each

element of a. Requires that + be defined for the elements of

a.

any any a b set Returns a set that is the union of a and b

any any a = b Assigns b to a

any any a == b bool Returns whether a and b are equivalent

any any a < b bool Returns whether a is less than b. Works for any pair of data

types for which < is defined

any any a > b bool Returns whether a is greater than b. Works for any pair of

data types for which > is defined

any any a b, a b bool As > and


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Fig. 3. AND and OR dependencies.

Fig. 4. Component status definitions.

c = capacity, or rating of a component,

f = flow, where f c,

freq = required flow if type == LOAD,

ft, fpt, bt, brt, adjt = components related to C via forward, feeder

path, backward, brother, and adjacent trace, respectively, where a

value of 0 implies the component does not exist,

AD = set of AND dependency components,

OD = set of OR dependency components,

pri = component priority,

status = status of component-ON, OFF, FAILED,

statusdep = status of components dependencies,

operable = whether the component can be turned on or off YES,

NO.

Fig. 3 shows two situations with AND and OR dependencies.

In Fig. 3.1, component a has AND dependencies on components b

and c. If either component b or component c is unrestored, then

component asdependencies are unsatisfied. By contrast, in Fig. 3.2

component d has OR dependencies on components e and f. In Fig.

3.2, component ds dependencies are satisfied as long as either or

both of components e and f are restored.

A component is considered restored (status is ON) if its depen-dencies are satisfied and all components in its feeder path are

restored. A components dependencies are satisfied if all AND

dependencies are restored and at least one OR dependency is

restored. Fig. 4 illustrates GTA notation for a component with a

status of ON where dependencies are satisfied.

Finally, a switch component can be marked as operable or non-

operable. For non-switch components, C operable is set to NO.

Using this component structure in conjunction with GTA traces

and GTA notation, it becomes easy to work with the system model.

For example, if one wanted to find the set of operable switches in a

component ps feeder path, that could be done using the statement

FPTp collect(c|c type ==SWITCH AND c operable == YES).A

system S is a collection of components such that for each compo-

nent C S, Cs forward, backward,feeder path, brother, and adjacent

trace are also contained in S.

CjSj,Sj includes(Cj

ft,Cj bt,Cj fpt,

Cj brt,Cj adjt) (1)

Two more subsets of components, the sources R and loads L are

defined.

R= UjSj collect(p|p type == SOURCE) (2)

L= UjSj collect(p|p type == LOAD) (3)

Reconfiguration is then performed on a set of systems W. The

objective of reconfiguration is to maximize the amount of load

restored, weighted by the priority of the loads as follows:

g = max{L sum((p pri) (1/(1 + |p freq p f|)

(p statusdep) (p status))} (4)

In (4), a higherpriorityresults in a higher value fora loadsterm.

The flow on the load being closer to its required flow also results

in a higher value for that term. Finally, if the loads dependencies

are not satisfied or if it is not restored, the term drops out of the

function completely.

The reconfiguration solution is subject to the constraint that nocomponent in any system has a flow greater than its capacity:

SW,S collect(p|p f p c) size == 0 (5)

3. GTA-based reconfiguration algorithms

In this section, four algorithms to reconfigure a set of priori-

tized interdependent systems are presented. The first three start

with a model of the system(s) that has no switches turned on,

while the latter starts with a model of the system(s) that has all

switches turned on. Each algorithm is capable of responding dif-

ferently to a system than the others. The From Load and Hybrid

algorithms are well-suited for highly prioritized systems due to

the way they apply greater importance to load priorities when

determining which switches to operate. From Sources and Hybrid

balance load among the system sources better than the other

algorithms because of the incremental way in which they restore

service tothe system. TheCotree Switchalgorithmtendsto befaster

on larger systems where most switches are normally on, due to

the fact that it starts by turning on all switches rather than turn-

ing them off. Note that in an electrical system a switch is on

when it is closed and in a fluid system a switch is on when it

is open.

3.1. From Loads algorithm

The From Loads Algorithm seeks to restore service by starting

at the loads and closing switches back towards the sources in an

attempt to find a valid restoration path for each load.From Loads initiallyturns offall switches,the loadsare sortedby

priority and such that all loads not in another components depen-

dency list occur before any loads that are in another components

dependency list. This prevents the algorithm from restoring a sup-

porting load which received a high priority from a critical load

before a lower priority critical load if that high priority critical load

is unrestorable. A components dependency list is the list of com-

ponents in C AD and C OD. Restoration of each load is then

attempted in this order.


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For each load, the algorithm collects a set of components via

which the load could be connected to a source. That is, the feeder

path traces from these components will lead to sources that could

potentially supply service to the load. These components include

the feeder path trace of the load, as well as any components with

the same reference source as the load that have an adjacent trace.

Let these components be placed in the set RestorePathsl, where l is

the load of interest.

For each component in RestorePathsl, starting with the loads

feeder path trace, the algorithm creates a set Path l. If the compo-

nent c of RestorePathsl being examined is the loads feeder path

trace, then Pathl consists of the load l followed by ls feeder path.

Otherwise, Pathl consists of the load l, followed by the components

connecting l and c, then c adjt, and finally c adjts feeder path.

Once Pathl is created, the algorithmchecksif there areany com-

ponents with status== FAILED on that path. If so, the path is not

valid. Otherwise, the algorithm collects a set of decision points

along the path. Decision points are components which must have

some processing performed on them during restoration. They are

switches and components which have dependencies (AD or OD is

not empty).

(7)

The decision points are ordered by increasing distance from the

load being restored, and the algorithm addresses each one in turn,

by operating switches or by recursively restoring components to

satisfy dependencies.

If a load is restored, system constraints are checked for the

components that have been affected by the restoration. If any con-

straints are violated, the algorithm backs up the decision points list

and selects the next p from Pathl to try. If all paths are exhausted,

the load is deemed unrestorable and the algorithm moves on to

the next load until all loads have either been restored or deemed

unrestorable.

3.2. From Sources algorithm

The From Sources algorithm approaches restoration from the

opposite end of the system than the From Loads method. Rather

thanoperatingswitchesand satisfyingdependencies whiletravers-

ing from the load towards a source, this algorithm starts at the

sources andworkstowards theloads. This algorithmhas thepoten-

tial for resulting in a more even distribution of loading among the

sources.

From Sources utilizes a working priority. The working priority

is initially set to the highest priority present in the model, and the

algorithm focuses on restoring Loads with a priority at least equal

to the working priority. As Loads are restored, the working priorityis gradually reduced.

The first step of From Sources is to turn off all switches. Next

priorities are propagated from the loads back to the sources. For

each component in a loads feeder path, that components prior-

ity is set to the maximum of its own priority and that of the load.

In addition, if that component has any dependencies, the compo-

nents priority is recursively propagated down that dependencys

feeder path. The algorithm then iteratively turns on switches for

each source to expand the system area receiving service from that

source. To decide which device to turn on, the algorithm first col-

lects allof each sources bounding switches.The bounding switches

of a source are those switches that have a status of OFF such that

if they were turned ON, service would be provided to a segment of

the system which is currently unserviced. The bounding switch set

for a source is given by

(8)

The algorithm then turns on one of these bounding switches

with the highest priority. A number of checks are then performed

on thesystem segment with restored service. These checks prevent

the algorithm from violating system constraints and also help to

minimize the number of low-priority loadsrestored. Violations that

could occur include:

Flow constraint violations. New segment contains a failed component.

If anycheck fails,the switchis turnedback offand thealgorithm

continues through the bounding switch list until it is exhausted or

a valid switch is found.A load is considered resolved once the algorithm has attempted

to restore service to its segment by turning on a switch, whether

or not it was successfully restored. Later operations may restore a

load that is initially not restorable.

Once a switch has been turned on or the algorithm determines

there areno possible onswitchoperations, anaccounting is made of

the resolved loads. If all loads with priority greater than or equal to

the working priority have been resolved, the working priority is set

to the next lowest priority and the algorithm repeats the described

steps (exceptfor theprioritypropagation step) until either allloads

are restored or no switches can be successfully turned on.

3.3. Hybrid algorithm

The Hybrid algorithm combines aspects of the From Sources

and From Loads algorithms. Like the From Sources algorithm, it

approaches the problem from the sources, turning on switches as

it spreads towards the loads. Unlike the From Sources method, the

operable devices are limited accordingto thosewhich couldbe used

to restore the unresolved loads of the current highest priority.

After all switches are turned off and priorities have been propa-

gated(as in From Sources),the algorithmcreatesthe setof potential

feeder paths for each load of the current highest priority as in the

From Loads method. Each switch along those paths is marked as

operable. The algorithm then proceeds as it does in From Sources,

exceptthatit does notattemptto turn on anydevices notmarked as

operable. When all of the loads have been evaluated for the current

priority level, the algorithm marks the devices on potential feederpaths to loads of the next highest priority as operable.

In this way, by restoring service to the system starting from the

sources butonlyallowingoperation of devices that could feed loads

of highest priority at a given time, the Hybrid method keeps the

forced balance of the From Sources method while further minimiz-

ingthe numberof low-priorityloads restoredat theexpense of high

priority loads.

3.4. Cotree Switch algorithm

The Cotree Switch method attempts to minimize the number

of operations which must be performed in order to successfully

reconfigure the system(s). Unlike the other algorithms, it starts by

turning on all switches. Priorities are propagated from the loads as


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Fig. 5. First test system electrical only.

Table 2

Algorithm performance comparison in time.

Time Fro m Lo ads Fr om So urces Hybr id Co tr ee S witch DAOP

1 Stage 7.3s 12.7s 20.4s 8.4s 335s

2 Stages 14.2s 14.4s 44.2s 16.6s

Table 3

Algorithm performance comparison in loads serviced.

Amount serviced FromLoads

FromSources

Hybrid CotreeSwitch

DAOP

1 Stage 98.7% 98.5% 98.7% 98.7% 86.1%

2 Stages 98.7% 98.7% 98.7% 98.6%

in From Sources, and then any failed components in the system are

isolated by turning off switches.

A flow constraint check is then performed. If there are flow con-

straint violations, they are sorted by increasing priority. For each

violation, the algorithm collects all components feeding and fed by

the violation into a set FullPathviol. FullPathviol is then searched for

theturned-on switchwith thelowest priority.Thatswitch is turned

off, priorities are repropagated, and the flow constraint check is

performed again. Because turning switches off drops loads, this

graduallyreduces theflow on thesystem andthus eliminates viola-

tions. This is repeated until there are no flow constraint violations.

(9)

Table 4

Algorithm performance comparison in mean phase imbalance across sources.

Mean phase imbalance From Loads From Sources Hybrid Cotree Switch DAOP

1 Stage 21.57% 18.29% 16.57% 13.86% 17.29%

2 Stages 19% 18.86% 16.86% 11.42%

Fig. 6. Second test system electrical and fluid, with dependencies and missions.


7/9


Once all violations have been eliminated, the algorithm collects

all of the Cotrees in the system(s). Cotrees are switches which are

turned on and create independent loops in the system.

CotreesS = S collect(p type == SWITCH AND p

status == ON AND p adjt status == ON) (10)

Foreach Cotree, thealgorithm creates a setof theswitchesalongthe feeder path of the Cotree device and its adjacent trace. These

devices are then sorted by flow, and the one with the least flow is

turned off. A flow constraint check is performed, and if there is a

violation, the switch is turned back on. The algorithm terminates

once each Cotree has been addressed in this manner.

4. Performance examples

4.1. Example 1: Real-world electrical model

To examine the performance of these algorithms, an implemen-

tation of each was run on a model of a real distribution system and

compared to an implementation of the Discrete Ascent Optimal

Programming (DAOP) algorithm described by McDermott et al. [6].

Tests were performed using a 2.00GHz Intel Pentium M processor.

The model used in testing is shown in Fig. 5. It contained 1835

load points and seven sources. Parameters such as equipment

impedances,admittances, seasonal ratings, and customer priorities

were provided by the utility in a relational database. Constraints

considered by reconfiguration were seasonal overload ratings and

Fig. 7. (a) From Loads result, (b) From Sources and Hybrid result, and (c) Cotree Switch result.


8/9


Fig. 7. (Continued)

customer voltage levels. Constraint checks were performed using a

full non-linear power flow algorithm. The radial power flow algo-

rithm used relies on forward and backward sweeps (the forward

andbackwardtraces describedin this paper)thatare repeated until

a convergence criterion is met [14,15].

The yellow components in Fig. 5 indicate components which

have failed, dropping 234 loads. Switching operations were

restricted to three-phase devices, of which there were 171. Each

algorithm (except for DAOP, which did not provide this capability)

was run in both one and two stages. In the two-stage runs, the first

stage only allowed operation of major, automatic 3-phase devices,while the second stage allowed operation of all 3-phase devices.

In the runs with the DAOP algorithm all 3-phase switches were

operable.

Tables 24 show the results of the runs. All of the algorithms

proposed in this paper were able to run in under 21s in the single-

stage runs and under 45 s in the two-stage runs, configuring the

systemto provide service to no less than 98.5%of the load points. In

comparison, the DAOP algorithm took over five and a half minutes

to run, and was only able to provide service to 86.1% of load points.

Finally, Table 4 shows mean phase imbalance across the loads

in the system. By this measurement, DAOP falls in the middle of

the field, with the Hybrid and Cotree Switch algorithms producing

smaller phase imbalances and the From Loads and From Sources

methods providing larger ones.

4.2. Example 2: Sample integrated model

The proposed methods were also run in one stage on the system

shown in Fig. 6. This system contains both electrical and fluid cir-

cuits,as well as a number of logical loads defining systemmissions.

Missions are represented by the red squares and are dependent on

loads in the electrical and fluid systems. The fluid system is repre-

sented bythe green lines and the electrical system bythe black and

brown ones. The yellow line represents a component which has

failed. The missions AAW (Anti-Air Weapon, priority 5) and ASW

(Anti-Surface Weapon, priority 3) have OR dependencies on Radar

2, Gun, and Radar 1, each of which have at least one AND depen-

dency on one or more of the physical circuits. The three propulsion

missions (from left to right, priorities 9, 2, and 6) have AND depen-

dencies on electrical loads, and the two pumps in the fluid circuits

each have an AND dependency on an electrical load. There are five

independent electrical loads (those on which no mission is depen-

dent) with priorities of 9, 0, 0, 0, and 0. A number of the loads are

grouped into 2 panels fed by automatic transfer switches.

Fig. 7ad shows the results of running the proposed methods

on the system in Fig. 6 if the line feeding the right panel is failed.

Components which have become pink have lost service. Notable

differences between the solutions are circled in bright green. The

From Sources and Hybrid methods yielded the same result. Bothof them restore all loads except for the large priority 0 load on the

lower right of the left panel. The From Loads algorithm does not

restore Radar 2, because doing so was unnecessary to restore AAW.

The result of ignoring the loads supporting Radar 2 is that the large

load on the left panel was restorable. Finally, the Cotree Switch

method manages to restore all loads, but only does so by creating a

loop in the electrical system. The Cotree Switch method is the only

method which can create loops in this way.

5. Conclusions

This paper has proposed four algorithms for the reconfiguration

of interdependent critical infrastructure systems based on Graph

Trace Analysis. Allowances are made for arbitrary levels of priorityon system loads. The generic nature of Graph Trace Analysis allows

for the simultaneous analysis of multiple system types and their

interdependencies.

Testing shows that these algorithms are capable of reconfig-

uring systems with multiple interdependent infrastructure types.

Also demonstrated is that the proposed algorithms can find solu-

tions with balanced loading in short periods of time on real-world

systems.

Acknowledgements

The authors gratefully acknowledge support provided by the

US Army, the Office of Naval Research, and Orange and Rockland

electric utility.


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References

[1] D.L. Kleppinger, K.J. Russell, R.P. Broadwater, Graph Trace Analysis based ship-board HM&E system priority management and recovery analysis, in: IEEEElectric Ship Technologies Symposium, May, 2007, pp. 109114.

[2] K.L. Butler-Purry, N.D.R. Sarma, I.V. Hicks, Service restoration in naval ship-board power systems, IEEE Transactions on Power Systems 16 (November (4))(2001).

[3] Z. Ding, S.K. Srivastava, D.A. Cartes, S. Suryanarayanan, Dynamic simulationbased analysis of a new load shedding scheme for a notional destroyer classshipboard power system, in: IEEEElectricShip TechnologiesSymposium 2007,

Arlington, Virginia, May 2123, 2007.[4] S. Khushalani, J. Solanki, N. Shulz, Optimized restoration of combined AC/DC

shipboard power systems includingdistributed generation and islandingtech-niques, Electric Power Systems Research 78 (2008) 15281536.

[5] E.E.Lee II, J.E.Mitchell, W.A.Wallace,Restorationof servicesin interdependentinfrastructure systems: a network flows approach systems, IEEE Transactionson Man, and Cybernetics, Part C: Applications and Reviews 37 (November (6))(2007).

[6] T.E. McDermott, I. Drezga, R.P. Broadwater, A heuristic nonlinear constructivemethod for distribution system reconfiguration, IEEE Transactions on PowerSystems 14 (May (2)) (1999).

[7] D. Shirmohammadi, H.W. Hong, Reconfiguration of electric distribution forresistive line loss reduction, IEEE Transactions on Power Delivery 4 (April (2))(1989).

[8] W.M.Lin, H.C.Chin, A new approach for distribution feeder reconfigurationforloss reductionand service restoration, IEEETransactions on Power Delivery 13(July (3)) (1998) 870875;A.Augugliaro,L. Dusonchet, E.Riva Sanseverino, Servicerestorationin compen-sated distribution networks using a hybrid genetic algorithm, Electric PowerSystems Research 46 (1998) 5966.

[9] D. Zhang, Z. Fu, L. Zhang, An improved TS algorithm for loss-minimizationreconfiguration in large-scale distribution systems, Electric Power SystemsResearch 77 (2007) 685694.

[10] C.T. Su, C.F. Chang, J.P. Chiou, Distribution network reconfiguration for lossreduction by ant colony search algorithm, Electric Power Systems Research

75 (2005) 190199.[11] K. Huang, S.K. Srivastava, D.A. Cartes, L.H. Sun, Market-based multiagent sys-

tem for reconfiguration of shipboard power systems, Electric Power SystemsResearch 79 (2009) 550556.

[12] L.R. Feinauer, K.J. Russell, R. Broadwater, Graph Trace Analysis and GenericAlgorithmsfor interdependent reconfigurable systemdesign and control,NavalEngineers Journal 120 (March (1)) (2008).

[13] J.B. Warmer, A.G. Kleppe, The Object Constraint Language: Precise ModelingWith UML, Addison-Wesley, Reading, MA, 1999.

[14] W.H. Kersting, D.L. Mendive, An application of ladder network theory to thesolution of three-phaseradial load-flowproblems, in: Proc. IEEEWinter PowerMeeting, New York, NY, January, 1976.

[15] F. Li, R. Broadwater, Software framework concepts for power distribution sys-tem analysis, IEEE Transactions on Power System 19 (May) (2004) 948956.

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