System Power
Resume:
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. *, NO. *, NOVEMBER 2006 1
Implementing Fuzzy Reasoning Petri-nets for Fault
Section Estimation
Xu Luo, Member, IEEE, and Mladen Kezunovic, Fellow, IEEE
of knowledge acquisition and knowledge base maintenance,
Abstract Fuzzy Reasoning Petri-nets is a promising technique
to tackle the complexities of power system fault section estima- and slow response time due to conventional knowledge repre-
tion. This paper addresses several key issues in implementing sentation and inference mechanism.
Fuzzy Reasoning Petri-nets for fault section estimation, which
In recent years, Petri-nets (PN) technique, which possesses
include optimal design of structure of diagnosis models to
the characteristics of graphic discrete event representation
avoid large matrix size, utilization of fuzzy logic parameters to
and parallel information processing, has gained researchers
effectively handle uncertainties, realization of matrix execution
algorithm to achieve parallel reasoning and adaptability, and strong interests [7] [10]. References [7], [8] model fault
integration of more reliable input data to enhance estimation ac- clearance process as discrete events using Petri-nets and utilize
curacy. Case studies are presented to demonstrate the estimation
the reversed Petri-nets models for fault section estimation.
capability under complex scenarios. An implementation solution
Such models take circuit breaker statuses as inputs. Similarly,
residing in a control center is proposed.
reference [9] proposes Petri-nets models to estimate fault
Index Terms Fault section estimation, Fuzzy reasoning, Petri-
sections based on protective relay trip operations. Reference
nets, Power systems, Relays, SCADA systems.
[10] augments Petri-nets with additional places to introduce
net redundancy. Coding theory is applied to detect place faults
I. I NTRODUCTION which represent all kinds of errors during fault clearance
A process. These solutions, which are based on discrete event
POWER system is composed of lots of sections such
view of Petri-nets, have several limitations. The number of
as generators, transformers, bus bars and transmission
initial inputs are limited and it is dif cult to model inexactness
lines. These sections are protected by protection systems com-
and uncertainties. Consequently, to accurately identify fault
prising protective relays, circuit breakers and communication
sections under complex circumstances, substantial heuristic
equipments. When a fault occurs on a certain section of the
rules and information are additionally required.
power system, the protection devices will reach certain statuses
It has been proven that fuzzy rule-based reasoning can
accordingly. To identify the faulted section of a power system
be realized through Petri-nets formalism [11] [13]. Fuzzy
based on a set of observed statuses of protection devices
Reasoning Petri-nets (FRPN) gains the advantages of Expert
is called fault section estimation. This is a vital task for
System and Fuzzy Logic, as well as parallel information
system operators because it provides the most fundamental
processing. Reference [14] applies the formalism established
information for restorative actions. The task is stressful, time
in [11] to solve the problem of fault section estimation.
consuming, and the accuracy is restricted when multiple faults,
It builds graphical Petri-nets models which represent fuzzy
failures of protection devices, and false data are involved.
reasoning rules and validates the reasoning process. The paper
When all mix up, a large number of scenarios can be hy-
does not address the optimal design of the structure of FRPN
pothesized and the possibility of each scenario needs to be
diagnosis models and the matrix reasoning execution algo-
examined. Complexity of fault section estimation increases
rithm, which are two key factors for implementation of FRPN
signi cantly.
for fault section estimation. The structure of FRPN diagnosis
Since the late eighties, various fault section estimation
models affects diagnosis accuracy as well as implementation
applications based on Expert System (ES) technique have
performance. The matrix reasoning execution algorithm is the
been reported in literature [1] [4]. ES technique is suited for
core of parallel processing capability of FRPN.
a diagnosis problem like fault section estimation because it
Our paper presents a formal de nition of FRPN and dis-
mimics the behaviors of fault analysis experts to perform fact-
cusses several key issues in implementation of FRPN for
rule comparisons and consequent search steps. Coupled with
fault section estimation. First, the optimal design of structure
ES technique, Fuzzy Logic (FL) technique is also employed
of FRPN diagnosis models is detailed and the advantage
to solve the problem of fault section estimation, as reported
over the structure adopted in [14] is addressed. Then, the
in the literature [5], [6]. FL technique offers a convenient
graphical FRPN models built based on the optimal structure
means for modeling inexactness and uncertainties, hence a
are illustrated and the utilization of fuzzy logic parameters to
powerful solution to handle the uncertainties due to unexpected
effectively tackle uncertainties is discussed. Following that, a
operations of protective devices and false data. The major
matrix reasoning execution algorithm of FRPN is introduced.
drawbacks of ES based techniques are burdensome procedures
The algorithm is exempli ed by matrix rule representation
Manuscript received November 30, 2006; revised June 7, 2007. This work and reasoning execution for an FRPN diagnosis model which
was supported by Texas A&M University.
takes data from remote terminal units (RTU) of supervisory
X. Luo is with Areva T&D Inc.. M. Kezunovic is with Texas A&M
control and data acquisition systems (SCADA) as inputs.
University (emails: **.***@*****-**.***, *******@***.****.***).
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 1, NO. 1, NOVEMBER 2006 2
Integration of logic operand data of digital protective relays 1) : A B = D, where A, B, and D are all m n-
as additional inputs to enhance the estimation accuracy is dimensional matrices, such that dij = max{aij, bij }.
further discussed. That is followed by case studies on a 14- 2) : A B = D, where A, B, and D are (m p),
bus power system model which demonstrate the estimation (p n), (m n)-dimensional matrices respectively, such
capability under various scenarios. Finally our paper proposes that dij = max1 k p (aik bkj ).
a control center implementation solution which is adaptive to The execution rules include enabling and ring rules.
changes of input data, as well as power system and protection 1) A rule rj R is enabled if and only if pi is marked, or
system con guration. i = 1, pi {input propositions of rj }.
2) Enabled at marking, rj ring results in a new
II. F UZZY R EASONING P ETRI - NETS (p) = (p) O(p, rj ), p P .
The truth degree vector changes from to
A. De nition
(p) = (p) cj j O(p, rj ), pi P
A Fuzzy Reasoning Petri-net (FRPN) can be de ned as an
where
8-tuple [13]:
j = minpi r j {xi xi = i if I (pi, rj ) = 1;
(P, R, I, O, H,,, C )
xi = 1 i if H (pi, rj ) = 1}
where and
r j = {pi I (pi, rj ) = 1orH (pi, rj ) = 1, pi P }
1) P = {p1, p2, pn } is a nite set of places or called
3) All the enabled rules can re at the same time. A ring
propositions.
vector is introduced such that j = 1 if rj res. After
2) R = {r1, r2, rm } is a nite set of transitions or called
ring a set of rules, the marking and truth degree vectors
rules.
of the FRPN become
3) I : P R {0, 1} is an n m input matrix de ning
the directed arcs from propositions to rules. I (pi, rj ) =
= [O ] (1)
1, if there is a directed arc from pi to rj, and I (pi, rj ) =
0, if there is no directed arcs from pi to rj, for i = = [(O C ) ] (2)
1, 2, n, and j = 1, 2, m.
where
4) O : P R {0, 1} is an n m output matrix de ning
= [ 1, 2, m ]T, which is called control vector. :
the directed arcs from rules to propositions. O(pi, rj ) =
T {0, 1} is the ring vector. = ( 1, 2, m )T .
1, if there is a directed arc from rj to pi, and O(pi, rj ) =
0, if there is no directed arcs from rj to pi, for i =
III. I MPLEMENTATION OF FRPN FOR FAULT S ECTION
1, 2, n, and j = 1, 2, m.
E STIMATION
5) H : P R {0, 1} is an n m matrix de ning
A. Power System Under Study
the complementary arcs from propositions to rules.
H (pi, rj ) = 1, if there is a complementary arc from pi In this section, a 14-bus power system as shown in Fig. 1
to rj, and H (pi, rj ) = 0, if there is no complementary is used for the study of fault section estimation problem.
arcs from pi to rj, for i = 1, 2, n, and j = 1, 2, m. The system consists of 34 sections, including 14 buses and
6) is a truth degree vector. = ( 1, 2, n )T, where 20 transmission lines. The buses are denoted as Bnn. The
i [0, 1] means the truth degree of pi, i = 1, 2, n. transmission lines are denoted as Lnnmm. The protection
The initial truth degree vector is denoted by 0 . system of the 14-bus system consists of 174 protection devices,
7) : P {0, 1} is a marking vector. = including 40 circuit breakers, 40 main transmission line relays,
( 1, 2, n )T . i = 1, if there is a token in pi, and 40 primary backup transmission line relays and 40 secondary
i = 0, if pi is not marked. An initial marking is denoted backup transmission line relays and 14 bus relays.
by 0 . To explain the con guration and denotation of the protection
8) C = diag {c1, c2, cm }. cj is the con dence of rj, system, a portion of the 14-bus power system is taken as
j = 1, 2, m.
The 5-tuple (P, R, I, O, H ) is the basic FRPN structure that L1213 L1314
de nes a directed graph. The updates of the truth degree vector B12 B13 B14
CB1312 CB1413
CB1206 CB1213 CB1314 CB1409 L0914
CB1306
through execution of a set of rules describe the dynamic L0613
L0612
reasoning process of the modeled system. If the truth degree
CB0613 L0611 L1011 L0910
CB0612 CB0611 CB1106 CB1110 CB1011 CB1009 CB0910 CB0914
of a proposition is known at a certain reasoning step, a token is B06 B11 B10 B09
CB0605 CB0904 CB0907
L0409
assigned to the corresponding proposition, which is associated L0506 L0709
CB0409
with the value between 0 and 1. The token is represented by
L0405 L0407
CB0506 CB0504 CB0405 CB0407 CB0704 CB0709
a dot. When a proposition pi has no token, which means that B05 B04 B07
CB0501 CB0502 CB0402 CB0403 CB0708
L0304
L0205
the truth degree is unknown at that step, i = 0. L0204 L0708
L0105
CB0205 CB0204
L0102 L0203
CB0105 CB0102 CB0201 CB0203 CB0302 CB0304 CB0807
B01 B02 B03 B08
B. Execution Rules CB01G1 CB08G2
G2
G1
In order to describe the execution rules of a FRPN, the
Fig. 1. A 14-bus power system model
following operators are used:
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 1, NO. 1, NOVEMBER 2006 3
an example as shown in Fig. 2. The portion includes a to deal with failures of protective devices, backup protection
transmission line L1314, and its adjacent bus B13, B14 and operations need to be considered in the models. Third, to tackle
adjacent transmission lines L1213, L0613, L0914. The main false data problem introduced by defects of protection devices,
transmission line relay MLR1314 has forward protection zone measurement systems or communication systems, fuzzy logic
and protects the entire line L1314. It will operate to trip its concept needs to be effectively utilized.
We use backward reasoning concept to structure the FRPN
associated circuit breaker CB1314 to clear a fault on the line
diagnosis models and generalize the design for transmission
L1314. The bus relay BR13 protects the bus B13. It will oper-
lines and buses [15]. Fig. 3 and Fig. 4 illustrate back-
ate to trip the circuit breakers CB1312, CB1306, CB1314 if a
ward reasoning concept for structuring transmission line and
fault occurs on the bus B13. The primary backup transmission
bus diagnosis models respectively. The AND-OR structure
line relay BLR1314 is the local backup of the relay MLR1314
concisely represents all the possible combinations of main,
and has the same protection zone. If the fault clearance by
primary backup and secondary backup protection operations
the relay MLR1314 fails, the relay BLR1314 will operate to
for inferring a fault. Compared with the OR-AND enumera-
trip the circuit breaker CB1314 to clear the fault. Secondary
tion type of structure used in [14], our proposed structure ef-
backup transmission line relays SLR1213, SLR0613 are the
fectively covers more scenarios with smaller number of rules,
remote backup of the relays MLR1314, BLR1314. If the fault
which will eventually achieve higher diagnosis accuracy with
clearance by both the relays MLR1314, BLR1314 fails, they
smaller size of Petri-nets matrix. For example, for inferring a
will operate to trip their associated circuit breakers CB1213,
bus fault on a bus with 5 circuit breakers connected, Fig. 4
CB0613 respectively to clear the fault. The relays SLR1213,
represents all the 32 (25 ) different combinations of protection
SLR0613 are also the remote backup of the relay BR13. If the
operations (each circuit breaker is associated with main bus
fault clearance by the relay BR13 fails, they will operate to
protection operation or secondary backup protection opera-
trip circuit breakers CB1213, CB0613 respectively to clear the
tion). The model shown in Fig. 4(b) in [14] only enumerates a
fault. The relays MLR1413, BLR1413, SLR0914, BR14 and
small number of all the combinations of protection operations.
circuit breakers CB1413, CB1409, CB0914 have similar roles
In the scenarios of multiple failures of circuit breakers which
in protecting the line L1314 and bus B14. The con guration
the model does not represent, it is not able to identify the
and denotation of the protection system for other sections of
bus fault. If the model is expanded to enumerate all the
the 14-bus power system are similar.
combinations of protection operations, it will result in very
large petri-nets matrix size.
B. FRPN Diagnosis Model
Based on the proposed structure, all the FRPN diagnosis
When one or more faults occur on certain sections of the models are developed. As examples, Fig. 5 and Fig. 6 show
power system, protection devices will reach certain statuses the FRPN models for the transmission line L1314 and bus B13
accordingly. The observed relay trip signals and circuit breaker in Fig. 1 respectively.
status signals obtained from RTUs of SCADA systems are In Fig. 5, the places p1, p2, p12 represent the input
used as inputs for estimation of the faulted sections. The propositions, which are the operations of protection devices
strategy is to build one FRPN diagnosis model for each section associated with the transmission line L1314. Initially all of
of the power system. Each model establishes reasoning from a these places contain a token, which means that the truth de-
set of SCADA data to the conclusion of fault occurrence on its grees of these propositions are known. Each such proposition
associated section with certain truth degree value. In case of will be assigned a truth degree value describing the certainty
single fault, the conclusion with the highest truth degree value of observation of the operation of the protection device.
is the nal conclusion. In case of multiple faults, the several Under such an assumption, if the operation of a protection
conclusions with the highest truth degree values which are device is actually observed, the proposition will have a truth
greater than a threshold are regarded as the nal conclusions.
To build the FRPN diagnosis models, several issues should
be carefully considered. First, a sound methodology for struc- line fault Initial
Hypothesis
ture design needs be adopted to achieve good diagnosis
S End R End
performance while keeping the model size small. Second, protection protection
operation operation
secondary primary primary secondary
main main
backup backup backup backup
Intermediate
protection protection
SLR1213 protection protection protection protection
Hypothesis
operation operation
SLR1314 SLR1413 SLR0914 operation operation operation operation
BLR1213
BLR1314 BLR0914
BLR1413 secondary
secondary
MLR1213
backup
backup
MLR0914
MLR1314 MLR1413
... ... protection
protection
L1213
operation
operation
on Line Y
on Line X
CB1213 CB1312
L0914
L1314
CB1314 CB1413 CB1409 CB0914
L0613 B14 BLR B CB M MLR B
CB L MLR C CB N CB O SLR D
SLR A BLR C
Evidence
Open
Open Open Open Trip
Trip Trip Trip Trip
Trip
CB0613 CB1306
B13
- NOT - Hypothesis - Evidence
MLR0613 - OR - AND
BR14
MLR: Main Line Relay BLR: Primary Backup Line Relay SLR: Secondary Backup Line Relay
BLR0613
BR13
SLR0613
Fig. 3. Backward reasoning concept for structuring transmission line
Fig. 2. An example of protection system con guration diagnosis models
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 1, NO. 1, NOVEMBER 2006 4
degree value i which is bigger than 0. On the contrary, if
the operation of the protection device is not observed, the
Initial
bus fault
proposition will have a 0 truth degree value. i can be given by
Hypothesis
experience based on the reliability of the indication logic of the
protection device, measurement system and communication
CB X CB Y
protection protection
system. In this example, i will be given the same value of
operation operation
0.9.
Intermediate
secondary secondary Hypothesis
bus bus
The places p13, p14, p22 represent the propositions which
backup backup
protection protection
protection protection
operation operation
are intermediate reasoning results. The place p23 represents
operation operation
the output proposition a fault exists on the transmission line
CB Y
CB M
SLR B
SLR A CB X
CB L
L1314 .
Open
Open
Trip
Trip Open
Open
The transitions r1, r2, r15 represent rules in which an-
Evidence
tecedent propositions implicate consequent propositions. Each
BR A
rule rj is associated with a certainty factor cj, which describes
- NOT - Hypothesis - Evidence
- OR - AND
the con dence level of the rule. cj, j = 1, 2, 7 can be given
BR: Bus Relay SLR: Secondary Backup Line Relay
by experience based on the reliability of relays. Usually a main
relay has higher reliability than that of a primary backup relay.
Fig. 4. Backward reasoning concept for structuring bus diagnosis models
A primary backup relay has higher reliability than that of a
second backup relay. In this example, c1, c2, c3, c4, c5, c6,
c7 will be given the values 0.7, 0.7, 0.8, 0.9, 0.9, 0.8, 0.7
p1 (SLR0613 Trip)
respectively. cj, j = 8, 9, 15 will be given the same value
1.0.
p2 (CB0613 Open) r1 p13
It should be mentioned that from p6 to r1 and from p6 to
p3 (SLR1213 Trip) r8 p20 r14
r2, there are two complementary arcs, which means that if
p4 (CB1213 Open) r2 p14
the opening of the circuit breaker CB1314 is observed, the
operation of the corresponding secondary backup protection
p5 (BLR1314 Trip) p21
should be discredited. On the contrary, if the opening of the
p15
p6 (CB1314 Open) r3 r9
circuit breaker CB1314 is not observed, the operation of the
p7 (MLR1314 Trip) p16
r4 p23(L1314 Fault)
r10
corresponding secondary backup protection should be credited.
r15
The complementary arc from p9 to r7 have the same meaning.
p8 (MLR1413 Trip)
We use a weighted average operation to replace the min-
p17
p9 (CB1413 Open) r5 r11
imum operation de ned in [13] when calculating the truth
p10 (BLR1413 Trip) p18
r6 r12 p22
degree value of a consequent proposition from the truth degree
p11 (SLR0914 Trip)
values of its antecedent propositions. Fig. 7 illustrates the
operation for r1 in Fig. 5. The weighted average operation
p19
p12 (CB0914 Open) r7 r13
has two bene ts.
Fig. 5. A FRPN model for L1314 fault based on SCADA data First, the relative signi cance of antecedent propositions
in implicating the consequent proposition is recognized by
the weights of antecedent propositions. This is particularly
meaningful when the cause-effect relation among antecedent
p1 (BR13 Trip)
propositions is considered. In our assumption, circuit breaker
opening is the effect of relay trip. The circuit breaker opens
p2 (CB1306 Open)
proposition is generally given larger weight than that of the
r1 p11 r7
p3 (CB1312 Open)
relay trips proposition because circuit breaker opening indi-
p12 r8
r2
cates the completion of a protection operation more directly.
p4 (CB1314 Open)
p17
For example, regarding the rule r3 in Fig. 5, the proposition p5
p13
r3 r9
BLR1314 Trip will be given a weight 0.4; the proposition
p5 (BLR0613 Trip)
p6 CB1314 Open will be given a weight 0.6.
p20 (B13 Fault)
p6 (CB0613 Open) p14
r4 r10 p18 r13
p7 (BLR1213 Trip)
p1 (SLR0613 Trip)
1 11
p15
p8 (CB1213 Open) r5 r11
p19
p2 (CB0613 Open) p13
21
2 c1 13
p9 (BLR1413 Trip)
r1
61
p6 (CB1314 Open)
6
p16
p10 (CB1413 Open) r6 r12
13 =[ 1 11+ 2 21+(1 6) 61] c1
Fig. 6. A FRPN model for B13 fault based on SCADA data
Fig. 7. An example of weighted average operation
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 1, NO. 1, NOVEMBER 2006 5
Second, the false data problem is effectively handled by 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
averaging the truth degree values of antecedent propositions. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
For example, when the relay MLR1314 trips and the circuit 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
breaker CB1314 opens as a consequence of a fault on the 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
line L1314, and MLR1314 Trip is not observed, p15, which 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 0 0 0 0 0 0 0 0 0
stands for main protection operates, will still get a moderate 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
truth degree value instead of 0, hence a moderate truth degree I= O= 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
value for the nal conclusion. It is apparent that the larger 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
the number of input data, the impact of false data is more 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
effectively countered. 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
C. Matrix Execution Algorithm 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 1 1 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
The parallel reasoning process of FRPN is implemented by 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
matrix execution. Reference [13] presents an algorithm based
.4 0 0 0 0 0 0 0 0 0 0 0 0 00
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
on the execution rules discussed in Section II. We modi es the .3 0 0 0 0 0 0 0 0 0 0 0 0 00
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
algorithm to accommodate the weighted average operation.
Contact this candidate