A Graph Oriented Knowledge-Based System to Assist Restoration of Distribution Systems

Copyright © IFAC 12th Triennial World Congre ss. Sydney. Australia. 1993

A GRAPH ORIENTED KNOWLEDGE-BASED SYSTEM TO ASSIST RESTORATION OF DISTRIBUTION SYSTEMS C. Cavellucci* and C. Lyra** 'CPFL - CP . 1808. 1301i1i-900 Campina.l'. SP. Brazil **FEEIUNICAMP. CP . filOI. 13081-970 CampinaJ . SP. Brazil

AlJstrat."t.

Thb

cJistrihution links

de sc ribe s

PJPc r

sysll'm

symbo lic

opera{ors

<.Inll

system operators'

in

know/t:tlgc-t1<.l sctl

a

restoring compulalion

llulllerlcal

the

network

algorithms

system

cJcs ig ncti

arter a

faull.

is

to

A

assist

hybricJ

Fca tuf(:~

proposed .

e lectrica l

approach

(h4tl

that

depend

on

expe rience

ancJ norms of the utility arc inclucJecJ in a knowledge base. The reasonin g process is g Uitlcd hy an inference engine with a backward chaining strateg y. Electrical overl""cJ checks arc carriecJ out by a s imulator base d on th e method of momentums. The acJopUon or c on ce pt s and data struclure horrowed from network flow a lgorithms leacJs to the development of a very effic ient procedure . Keywords . DlstrifJ//(/(In s),stelll restoration. lirapir systems, network tJlw/yzl'rJ. litsJrlbutioll autumatio/l.

I. INTI{OJ)UCTION

tireory.

anu

service n: sl llral ion in a di strihut ion network aft e r a fault h large-scaiL: comhi natorial prohiL:m. Finding a fea si hle rl:~torati()1l s trategy for Jistribution network re quircs frolll L'xperil'nce d operators

All

the

s),st elll,

cunstraints.

knowlecJge

training,

detailed analysis or large numi>e r of p"ss ibilities. in order to de termine a swi lchi ng plan within acceptele c tric limit s that sa ti s fies res tri c tions, sm.:ial re quirelll e nts and luc al norm s.

o perating

represe ntecJ di s tin c tl y in sc he maticall y in Fi g. I .

The

ab I!.::

knowledg e- based

common

These

th e

acqUired sense

ex pert

hy

NA

reqUirem e nts

sys tem .

as

arc

s hown

previou s experience or

knowled ge,

anu

the

norms

adopted hy th e utility "re repre se nted in the knowledge b" se . The topology of th e ne twork is s t ored in ne twork data file acc esse d by the network

sL'c urily

m aniJgc r.

gathered

Inform at ion

hy

abou t

vo lt ages

the s imulator. Th e

and

currents

arc

inference engine draws

The necessity of clln~jdering cummon - s e nse knowkJgc, prior cxpcrknces acquired (In th e jnh, and evaluating non-quantitative tcchnic .,1 cOIl .... iderat!ons makes It

The main fe:.Jture s about lTIode ling iJnu implementing each

difficult

compo nent

to

use

a

pure

analytical

approach

s witching plan . So, huw can e mpirical t:..lkcn into acc o unt in a m alh e ma t il'al model '!

a

conclus ion s and contro ls th e whole rea soning process ,

to finding aspect s he

In

f'ir ~ t

th e

h L'. tlri ~ tic

UIlL',

procedures

arc

the model Ill o re "intl'i l igent" (Castrn cl ul" A more re ce nt approach relics on techniques f or representing and d e aling w ith kllllwiL:dge, the ohjcct of artineial intelli ge nce (AI) (Nilson . 1~ 1l2).

I I

wel l- cIdi ned

"",th e mal jcal

1980),

hase d

on

Ihis

lall e r

approach

are

arc

di sc ussed

in

the

DATA BASC

I

miJking

Syste ms

sys tem

I

I

to

NA

r-----------------

formulations.

added

the

I I

Two approaches n", y he used tD cJeal wil h the empirical aspects.

of

following sections,

I

I I I

, I

ca lled

I I

expl!rt Of knowledge - ha se d systellls.

~-----------

paper di sc l1 ~ses a kno w lcdgt.' -ha se d sys tem, namco NA (ne twork ~I s ... i ~ tant) , lksi~I1Cd to ass is t di stribution systcm operators in n.: s lllring the network. Th l! main mo tivation fur thh res~; 'rch was th e nee d to

-------------------------~

Thi s

supply

CPFL

(Pll\""r

and

Light

Fig . I . Ila s ic Architecture or th e NA System

('{lIl1 l);,n y or Sf", I'aulo)

with a tool ahle to 11l.: lp in manag illg the restoration the systcm, c oping with it s illl'feas in g compleXity and prcparing for distrihutioll . . automation. CPFL operates in an are a of ')O.(I!) I klll - ;lIul supplies ahout 2000 MW {o 1.7 mi I I ion cons umers .

of

The

paper

h yb rid

hrings

approach

J. TilE NETWOI{K MANA<;EI{ The

hy (;d di s cu ss ing a sy ml1ll1 ic and num e ri ca l

co ntrihut iun

thal

I inks

3. 1. The Network Th e

SYSTE~I

mana ge r

tak es

C:J fC

of

s torage

and

s tructure .

computation algorithm s :lIld (h) adapting con c epts and data struct un: horrowL'd fr om graph algurithms to achieve efficie ll cy in a s pL'l'i:d tailored simulator, based on the IlH.: thod of lllOlll l'n lulll S.

2. IIASIC

network

manipulation of the dat" structure that represents the di s trihuli on network . T hi s scctilln desc ribe s {he model ancl gives d~tall s on th e implem e ntation of the data

main

sess ing switc hes ,

AI{(,IIITECrUI{E

~Ifldc!

entili es

or

a

cJi s tribution s

fe s toration decisions f ee defs , s ubs tations,

ne twork

for

as-

loaJ blocks. a rc : the di s tribution and

ne twork itself . The lh.:cision ahout s witching plan (fur re s toration of a Ji s trihution sy ... tc m) re quires fro m the contro ller

complete

knowled ~e

ahout

the

ac tual

network

is convenient to represent thes e model A graph entities and their interrelationships. If G = (N,M) is

topology

795

a graph that represents the distribution network. N = (J.2 •...• n) is the set of nodes representing load blocks and M (1.2 ... .• k •...• m) Is the set of arcs (ordered pairs) k (i.j) representing switches or substation breakers (I.J E Nl.

as In optimal netwurk flow pmblems. This Insight was a key for achieving ci'ficiency in the algorithm .

Consider the primary feeder represented in Fig 3. The block loau PI' Plo Pj' Pi' arc considered constants.

If

k = (I.j). k

E

f

- - - op«Nd "'lkh

fk

is

the

puwer

flow

In

switch

M' (the set uf closed switches). then

:5 k

(0

k ::s m

---

- - cIoHd $rrlIch

fk

Fig. 2. Graph Model for a Distribution Network Fig. 3. A Primary Feeder

An example of a graph representation for a dlstrlbu tlon network Is shown in Fig. 2. The noues represent load blocks. with the exception of nodes S (n=I.2 •.. .> that represent substations and the root node R. an artificial noue included for mathematical reasons . Arcs that connect a load block to a substation represent substation breakers. and arcs that connect two load blocks represent switches. The arcs connecting nodes Sand R represent the

The methou of momentums computes voltag" drops block. f1V. by th e expre,,;on f1V = ALp. where A constant. L is the distance from the block to substation. and p is the block loau. The product Is the electrict! momentum exerteu by load p on feeder. The const ;mt >. is given by

at a Is a the L.p the

transmission network. r

The energized network Is represented by the trec T '" (N.M') (Jensen anu Barnes. 19S0) - say. a radial network - where M' is the set of closed switches. M' c M. In the tree T there Is a unique path linking any node j. j '" R. to root node R; the node j Is called successor of node i If I Is In the path from j to the root R. The set of successor nodes of I Is denoted by N . Thc set of nodes and arcs In the path Dj from I to the root Is denoted by NCI and M ' cl respectively.

where rand x are. respectively. the resistance and rea c tance per kilum eter uf the cabie. I{J is the angle of the power factur in the block and V Is the op

speCified operation vul ta ge. If a feeder uses only une type uf cable factor is the same for all loads . the voltage drops can he Simplified . Instance. the feeder repre se nt ed in Fig. 3.

A data structure calkd arc oriented (Jensen and Barnes. 1980). that has been extremely successful In optimal network flow problems (Bradley Cl al.. 1977; Lyra and Tavares. 1988). is adopted In system NA. The basic elements of this structure are a "from" node list elk} and a "to" node list .,,(k). If arc k Is directed away from node I. elk) I' If arc k Is directed toward node j • .,,(k) = j.

f1V

where I

J

I

is the distance from l1odt.: j to node i.

j

f1V

j

1,

(h e

ahove

computation

can

f1V + >'1 I'

be

(3)

j k

and

label. points to the first node in the path from I the root. Pr(l). named Ihread. points to an

f1V

Immediate successor or. if it doesn't exist. to an Immediate successor of a predecessor. A dlslance label P D(I) Indicates the number of arcs in the path from node I to the root. This label necessary. but its auoption enables gains In handling the network.

and the power computation of Consider. for Then.

>.1 (P . +

j

Using cqll~{joll simplifieu into

The tree representing the energized network Is stored with a data structure that employs three main labels: P • Pp and PI' The label PIl(i) points to the first arc n In the path from i to the root; PI' (j). named prcdcccsto

I V tip I

v'T"'

3.2. Dnt .. Structure

sor

+ xl a lllP

where

fk

I

lJ

the

h

puwer

connects bluck i to it '

fluw

:-' lI CCCS'Of

in

switch

k(i.j).

that

j.

Is not strictly some auultional Variatiun

Call

4. ELECTRIC CONSTRAINTS

p;

the

hluek

load

after

a

loau

variation

f1p

In

block I. p; = Pj + f1p. Thus. the new power flow f~ for This section describes a simulator that uses the method of momentums (Kasatkin and Pcrekalim. 1970) to evaluate power flows and voltage limits. In using this method the network Is manipulated In much the same way

all switches in the path frnm block I to the root Is f~ = fk + lip (k E M(). Note that the power flows for all switches outside thi s path remain unchanged .

796

The

voltage

drops,

IlV~,

for

from block I to the root (n IlV' = IlV n

where"

+ IIp''

E

all

blocks

In

the

closing switch k is nnt recommended. indicates that this SWitching is advisable.

path

=

A L \'

kEM

It

Nu) Is given by (4)

S. KNOWLEDGE FOR NETWORK OPERATION

n

The knowledge for network operation is represented by facts and production rules (Nilson, 1982; Sakaguchl and Matsumoto, l'i~3), stored in the knowledge base.

is the potential of block n, defined as

"

Otherwise

Facts

Ik

an,:

n:pn:scntcu

as

objcct-attribute-value

(O-A-V) triplets (Nilson, 1%2). Objects may be either physical entities such as a switch, or conceptual entities such as feeder. Attributes are general characteristics or propert ies a"oc iatcd wi th objects. Code and type arc attributes for the physical object switch. The final member of the triplet Is the value for an attribute. The value specifies the nature of an attribute in a particu",r situation or Instant. The value for the attribute code or the object switch may be 120, for instance, nr the switch type (another attribute) can he 1-0 (say, suitable for operation when loaded).

Cn

The voltage drops for all hlocks that arc successors of a block n In the path from block I to the root, IlV;, Is given by

4.4. The Simulation Algorithm The foregoing results arc Integrated In a simulator designed to foresee the consequences of switch operations. This simulator evaluates whether or not voltage drops and power flows arc within acceptable limits.

The rules (called production rules) arc another form of knowledge representation, used to describe relationships anlllng racts. They have the form of if-clause/then-clause. The if-clause is called premise and then-clause is called conclusion or action. Both premise and cOllclllsion can contain morc than one clause, cnnneeled by the logical operator alld.

6. TilE INFERENCE ENGINE

SI

•

k

The inference engine gUides the reasoning process in a knowlcdg~-hased systcm. Its main tasks arc: to evaluate existing racts and ru!cs, to add new facts to the knowledge base (say, to draw inferences) and to decide in what nrder rules arc evaluated (say, to control the reasnning process). Inference engines dirfer with respect to inference and control strategies. The approach that best suited the requirements of the NA system Is based on concepts used in the MYClN expert system (Buchanan and Shortlire, l'iXS) and on ideas proposed by Sakaguchl and Matsumoto (1')X1) that adopt a backward chaining strategy (Nilson, 1')~2). It might he recalled that backward chaining is very efficient when its possible outcomes an.: known and n.~a!')()nably few. This Is the Case for n:storatillll prohkms COl1silkrcu in the NA system.

i~i

L ___c ___ J

Fig. 4. Distribution Network After a Fault

The state of a distribution network after a fault Is illustrated in Fig. 4. The hachured hlocks arc in the energized network. The faulted block, represented In black, was previously Isolated, leaving the area shown within the rectangle unserved. Suppose that switch k Is a candidate to rc-energize the unserved area. Also, suppose that the total load In the unserved area Is IIp. The simulator must evaluate the state of the network after closing switch k. The evaluation Is carried out according to the follOWing sequence of steps:

The backward chaining strategy is implemented with two interrelated modules: MONITOR and FINDOUT. These moduies and other main modules or the inference engine arc shown schematically in Fig.S.

FACTS

SI. Initialization.

r.::::l

S2. Evaluates if the suhstation can support IIp; S3. Evaluates If power flow within acceptahle limits; S4. Evaluates voltage drop block", b ; r VOltilgC drop SS. Evaluates block", b·

in

switch

at

the

at

the

k

~

is

ATTRIBUTE

I

r::::l

VALUE

~~--...., VALUe

RULE L---.,r---'

"source

I

"load

c

RULE

GOAL RULE

"leaf voltage drops at the S6. Evaluates unserved blocks" (terminal hlocks) of the area; if the feeder of the source S7. Evaluates load block h can support the additional

Fig. S. Inference Engine of the NA System

The mndule MONITOR examines each clause In the premise of a rule. If all clauses arc trlle the action part is executed. If nlle of the premises is not true the rule is rejected. When examining rule, the MONITOR verifies if the values for all attributes In Its premise arc determined (le. arc already In the working memory). If not, the module FINDOUT is called.

f

IIp; S8. Evaluates if the voltage drops for the leaf blocks In the feeder of hluek b a r e r within acceptahle limits. If any voltage drop or power flow Is outside prescribed limits, the simulator Indicates that

The module FINDOUT looks for the missing values of the

797

talloreu to de.t! with r adial ne twork s , was develope d to evaJuJte operating constraints. This simulator uses th e melhou of momentum s enhanced by the adopllon of concepts an d uala st ruClure borroweu from optimal net work flow al gorithm s. Also, this data s tructure helped the uev e lopm en t of an usef ul gr"phlcal Int e rface .

attributes. In onkr tu uhe.t in th ese missing v;.tlues (or "to ins lan ce th e a[[ributes", as kn ow ledge engineers say) th e FINDOUT may either inquire of the use r, call thl.! module netwo rk l11 ;.t nage r, execute the si mulati on algorithm (to verify if vollage drops and power fl ows a rc w ithi n accepl ab le limit s), or draw inferences fr om rule s, ca llin g again the MONITOR . In oth e r words, MONITOR/FINDOUT is a re c urs iv<.: reasonin g process .

Prelimin ar y r es ults s howeu that comp ute r r eqUirements to carry ou t a consull ati on pn.ce dure are modes t. The main contrihulion ( 0 this effiC ien cy comes from the si mulati on a lgor ithm , w hi ch c nc Durag(;S to investigate the possihility of us ing it In d evis ing optimal feeder reconfiguration st ra(egks.

rule Whe n Ih e kn owledge-base d sys l em is called, name d "objec t rule" is eva lu ated to trigger th e reasoning proces s. Thi s rule con tains th e prob lems to b" so lv ed and actions to he t aken whe n a so lution Is f ound. The "object r ule" for the NA sys tem Is shown In Fig . 6.

Acknowkdglllent. Thi s re sea rc h was partially sponsored hy the Conselho Nacional d e Dese nvolvimento Cienllfico e Tec nolllgico (National Office for Scientific and Technologic.t! Dev e Inpm en l) nf [lr""i I.

Ih e fall/led block is i .w /olcd

If

and all stratcKY to re s tore lh e Il (, (work is kllow/1 th en

9 . R HER ENCES

di!J·pla y the swice/linK piu".

[lrauley, (;.W., (; . G. I3rown, " nd G . W. Graves (1977). Des ign and Implem e lll "tion of Large Scale Primal Transhi pm en t A 19ori (hms. MaJlagemellt Sclellce~ vol . 24, N. I , pp. 1- :14 . Buchanan, B.G., and E. 11 . Shortl ife (1985). Rule-based

Fig. 6 . NA ObjecI Rule Thi s rule specif ic s the goa ls to be achievt.:d, i. e., tu Iso late th e faulted block and look for switching pl an to energize unse rv ed ;.t reas ,

Experl StullJord

We s le y, Reading, Massachusells. Cas tr", C H ., J .B. Dunch, and T .M. Topka (I980) . (; e nel'a lil.ed Algllrilhms for Di s tribution Feeder Deployment and SecI illnali l. in g . IEEE TrallsacCion Oil Powt'r Apl'urlllll.\· and .)'y.,·t em, Vo!. PAS-99 , N. 2, pp. 54'1-557. J e nse n , P.A., and J . W. [larnes (19Mll). Nelwork Flow Pro/vaIJlIJliIlK. John Wi Icy & Sons , New York. Kasatkin, A., and N. Perekalln (1970). Basl e Eleclrical ElIl{llIarlll/i. MlR Publishers, Moscow. Lyra, c., 'II1U H. Ta va r es (191111). A Con tribution to the Midt~rm Sc hedu l ing or Large Scale Hydro thermal Powcr Sys te ms . 11:.: £ E TraJlsactlons OIJ Power .1'),.111' 111.\', Vol. 3, N. :1 , pp. M52-X57. Nilson, N.J. (l'IX2). Prlllclpl es uf ArCiflclal IlIl ellll{ellce. Tioga Publi sh ing Co. Palo Alto . Sakaguchi, T ., anu K. Mal , unlOto (I ')X3), Development of Kl10wlcu ge l3aseu System f or Power System Restoralion. I EEE TrulI.w(Ciolls UII Puwer ApparalUs alld SY.l'I ('fIl.l', VIII. PAS- I() 2, N. 2, pp. 320-329.

7. COMPUTER IMPLEMENTATION A fir s l version of s ys lem NA was deve loped for PC compatible microcompulers . The tra dili ona l modules of a knowledge-hased s yst e m ([he knowleuge base, infe ren ce cnginl.! and working l1ll.'ll111ry) we re coded In PROLOG. Th e network """,ager, anu Ihe simulator (numerical mou ules ) were codeu in C. A programm ing language, in s tcau of a commerCially available knowledge-e nginee ring tool, was used to d eve lop th e knowleuge nlOuule s since fleXibilit y was a req uirel1ll.'n t in th e dl.'~ign of ~Ul' h hybrid sys tem . PROLOG was l'lwsen for being readily available for microcomputers, and ha nu y for building ami upuating the knowledge ha se and inference eng ine. On the uther hand , C is th t.: natural l urrent choice tu code numerical algorithms whe n clTiciency ,md portabllity are import an t. computer requ i rements for th e numerical computalion are mod l.!st. For instanl'e, (h e whole s imuli.ttion to verify if s wikhing o pe ralion is feasihle at the network of Bauru, cily wi th 4 substations, IX feeders, 2 10 I""d bl"cb, 2K7 s w il ches, and % MVA of total load, takes les.s than 1J, 5 seconds in a PC XT compatible compu l er. This desi rahle featur e is a consequence of th e data s tructure anu s imul'-lti un algorithm hase d on gr:.Jph CllnL:l.'pts. Another desirabl e conseq uen ce of the data s tructure adopted is Ih at it a ll oweu a practical way t o u esign a graphical interfa ce that ui sp la ys the network topo logy during (he con s ultation process . This feature WaS recei ve d wit h enthusias m hy opcr~l ting c rews an d tra ining sta tT . The grap h ic~1 intcrfan.· a!:-.o di s plays rl.'vcrsion of power flows, s ig nali ng that th e protec(ion sche mc may no longe r be efl ect ive. If Ihal happens, the operator may d ec ide to accept a transitory ri sk or rejec t the sw it c hing plan (of cours c, the information Ca n also be used to r e prog ram microprnccssor-based relays).

H. CONCLUSIONS

Thi s paper d escrihed a hybrid knowleuge-based system dcsignl.: u to ass is t distrihution sys(c ms opc r;Jt ors during restorativl.! procedures. Thc system proposes swi tc hing plan s I""ed on e mpirical s l ore d knowledge and on eva lu atio n of electr ical clI ns trJ in[ s. A

very

eflicienl

~ i mlll:t (i lln

~dg() rithm ,

Sys l em. The Myclll Experlmellls o f lire Hellri s ti c ProJ;rummlllg Project. Addi son-

speCia ll y

798