Energy and Power Engineering, 2013, 5, 828-832
doi:10.4236/epe.2013.54B159 Published Online July 2013 (http://www.scirp.org/journal/epe)
High-speed Railway External Power Supply Reliability
Evalua t i o n o f B a y e s i an N e t w o r k
Zechuan Liang, Minwu Chen, Guoxu Shang, Baoyu Lv
School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China
Received April, 2013
ABSTRACT
Reliability evaluation is important in high speed railway external power supply design, based on probability reasoning
bayesian network applied in high-speed railway external power su pply reliability ev aluation, estab lish the minimum c ut
and the minimum path of bayesian network model, quantitative calculation external power supply system in each ele-
ment posterior probability, and the example analysis verified the feasibility and correctness of the above method. Using
bayesian network bidirection reasoning technology, quantitative calculation the posterior probability of each element in
external power supply system, realized the identification of weak link in external power supply. The research methods
and the results of the study can be used in the scheme optimization design of high speed railway external power supply.
Keywords: Bayesian Networks; The Minimal Path; The Minimal Cut; Extern al Power Source; Reliability Evaluation
1. Introduction
With the large-scale construction of electrified railway in
our country, especially, the high-speed railway opening,
reliability problem increasingly cause the attention of
people [1]. As the first level of power load, electrified
railway traction power supply system needs to provide
stable and reliable power system of the external power
supply. Due to the high speed rail (including passenger
dedicated line) operating speed is high, so the external
power supply in the event of failure, may result in trac-
tion power supply system of power supply interruption,
directly affect high-speed railway security, reliable and
efficient operation. So on the outside of the high speed
railway power supply scheme is essential in the design of
power supply reliability assessment, the quantitative cal-
culation of the external power supply reliability, accurate
identification of external power supp ly of the weak links,
optimizing the design of the external power supply
scheme, has important theoretical significance and ap-
plication va l ue.
Through based on probabilistic inference of bayesian
network used in high-speed railway external power sup-
ply reliability evaluation, aiming at traction substation
power supply without interruption, establishing bayesian
networks model, writing the reliability calculation pro-
gram, quantitative evaluation caused by external power
failure probability of traction power substation. Bidirec-
tional reasoning technology based on bayesian network,
identification the weak links of high speed railway ex-
ternal power supply to opti mize the design of high speed
railway external power supply scheme.
2. Summary of Bayesian Network
In recent years, the method of bayesian network has been
successful used in many fields. bayesian network in lit-
erature [2] is applied to fault diagnosis of power grid,
bayesian network in literature [3] is applied to reliability
evaluation of distribution network, bayesian network in
literature [4] is used in power system reliability assess-
ment. After years of development and perfection , bayes-
ian networks has become an effective evaluation of reli-
ability, general method.
Bayesian networks also called the reliability network
is a kind of probability netwo rk, it is based on probabilis-
tic graphical network [4]. A bayesian network is a di-
rected acyclic graph, it is represented by variables of
nodes and connecting the nodes of directed ar c s.
Bayesian use nodes to represent variables and directed
arcs between nodes represent the relationship between
variables, through the graphical expression of uncertain
knowledge, through annotations of the conditional prob-
ability distribution can be expressed local conditions de-
pendency in the model[5].
Because bayesian network has bidirectional reasoning
technology, so it can be calculated after the occurrence of
certain events T, X occurs the a posteriori probability of
the event, specially, 1 represents the event occurs, spe-
cific as follows:

Z. C. LIANG ET AL. 829
Posterior probability from the Angle of the fault diag-
nosis reflects the importance of the components in the
system size, especially suitable for weak links in recog-
nition system, fault diagnosis and inspection and repair
planning[6].
3. Bayesian Network Model and Algorithm
Based on the traditional shortest path set method or the
minimum cut set method when evaluating the reliability
of the system, finally will involve the minimization algo-
rithm of path sets and minimum cut sets processing, to-
quantitative calculation of system reliability finally. But
when the system is v ery complex, the element number is
larger, the minimization algorithm processing will be
complicated. Because bayesian network itself contains
the conditional independence between the node variable
precision, so based on shortest path set method or mini-
mum cut set method of bayesian networks need not
minimum cut set or sets the path minimization algorith m
processing[7].
Based on shortest path set method or minimum cut set
method of bayesian network model using the path set
method or minimum cut set method of bayesian networks
is established. Specific steps are as follows[8]:
1) Finding out the path sets and minimum cut sets of
the system;
2) Setting the components in the path set and mini-
mum cut as initial model element node;
3) Setting all the node path sets and minimum cut as
subsystem node;
4) Using conditional probability tables to describe the
relationship of the subsystem node and the initial element
nodes.
Logical relationship in here is mainly refers to “or”
and “and”, conversions with the bayesian network are
shown in Figure 1[9]:
(a) Or gate
(b) And gate
Figure 1. Logic relation and Bayesian network transforma-
tion.
After convert the path sets and minimum cut sets to
bayesian networks, reliability indices can be reasoning
calculationcan. The algorithm about precise reasoning of
bayesian networks is mainly based on Poly Tree Propa-
gation, Bucket-Elimination, Clique Tree Propagation.
Bayesian networks are precise reasoning algorithm is
mainly based on Poly real Tree Propagation method, the
method based on combinatorial optimization problems,
and based on Clique Tree Propagation method. The me-
thod of Poly Tree Propagation is only applicable to sim-
ply connected, Bucket - Elimination and Clique Tree
Propagation fit with both simply connected also with
multiply connected, but when there are multiple asked
node in the system, often using a Clique Tree Propaga-
tion method.
4. Example Analysis
4.1. High Speed Railway External Power Supply
Reliability Index
Using the reliability evaluation model of international
general IEEE RBTS - (6) system as an example, putting
forward high-speed railway external power supply
scheme which is based on shortest path set method of
bayesian network and bayesian network based on mini-
mal cut set method to quantitative ev aluation the scheme
of power supply reliability of the traction substation, re-
spectively.
RBTS (6 nodes) system are shown in Figure 2:
Figure 2: a power on bus 1, 2, one bus in the power
plant has fou r generatin g un i ts，they are G11、G12、G13、
G14, and its capacity are P11, P12, P13 and P14, P11 =
P12 = 40 MW, P13 = 20 MW, P14 = 10 MW; Bus 2
Figure 2. RBTS（6 node）syste m .

Z. C. LIANG ET AL.
830
there are 7 station in power plant, namely, G21, G22,
G23, G24, G25, G26 and G27, its capacity is P21 , P22,
P23, P24, P25, P26 and P27, the P21= 40 MW, P22 =
P23 = P24 = P25,= 20 MW 、P26 = P27 = 5 MW. The
reliability of components of the system parameters are
shown in Tables 1-2[10]. Assumes that the bus bars in
Figures 2-4 respectively with the traction substation
TPSS2 - TPSS6, these traction substation to supply one
high speed railway.
4.2. Bayesian Network Based on Shortest Path
Set Method
Based on high-speed rail as shown in Figure 2 external
power supply network, can respectively calculate the
traction substation power supply of the path set, here in
traction substation TPSS2 on bus 2 as an example, using
Boolean determinant method, can get the shortest path
sets of TPSS2: G1L3, G1L1L2L4 G1L1L4L7,
G1L2L4L6, G1L1L2L5L8 G1L1L5L7L8, G2,
G1L4L6L7, G1L2L5L6L8 G1L5L6L7L8. According
to the shortest path of TPSS2 set can make corresponding
bayesian networks, shown as in Figure 3.
Figure 3: L1, L2, L3,... , L9 respectively represent
L1 - L9 in the system of RBTS (6 nodes); A1, A1, A2,...
A5, representing the path G1L3, G1L1L2L4, G1L1L4L7,
G1L2L4L6 G1L4L6L7, G1L1L2L5L8; the relationship
A1, A2,... , A5 and T is “or”. In combination with the
conditional probability tables of A1, A2,... , A5, T and
the failure rate of components, and connecting with the
development of reliability assessment based on bayesian
networks we can calculate P(T)2:

6
PT2 6.634810


Among them, P (T) 2 is the outage probability of the
traction substation on bus 2. Similarly, we can calculate
the probability o f power traction substatio n outage on the
bus 3 to 6 bus on as follows:





6
3
6
4
6
5
4
6
P T=6.634810
P T=6.634810
PT=6.720610
P T=2.967110








which we can see, the probabilit y of power outag e on the
bus 6 (P (T)6) is greater than the rest of the few relatively
traction substation, because the bus 6 use single wire(L9)
accessing, so the failure rate is relatively large.
Table 1. IEEE-RBTS (6 node) system line data
Line Bus from to Permanent outage
rate (per year)
1 1 3 1.5
2 2 4 5.0
3 1 2 4.0
4 3 4 1.0
5 3 5 1.0
6 1 3 1.5
7 2 4 5.0
8 4 5 1.0
9 5 6 1.0
Table 2. IEEE-RBTS(6 node) system generating set data.
Unit
Size(MW) Type Fsilure Rate Per year
5 hydro 2.0
10 thermal 4.0
20 thermal 5.0
40 thermal 6.0
Figure 3. the minimal path of bayesian network(bus 2).

Z. C. LIANG ET AL. 831
4.3. Bayesian Network Based on Minimal Cut
Set Method
Based on high-speed rail as shown in Figure 2 external
power supply network, can respectively calculate the
traction substation power supply of the minimum cut set,
here in traction substation TPSS2 on bus 2 as an example,
using Boolean determinant method, can get the min imum
cut set of TPSS2: G1G2、L1L3L6G2、L3L4L8G2
L3L4L5G2、L2L3L7G2. Accord ing to the minimum cut
set of TPSS2 can make corresponding bayesian networks,
shown as in Figure 4.
Based on bayesian networks is shown in Figure 4,
combining with the development of the bayesian netwo rk
reliability evaluation calculation program we can calcu-
late P(T)2:

6
2
P T=6.634810 
Among them, P (T) 2 is the outage probability of the
traction substation on bus 2.Comparison shows that this
result with bayesian network based on shortest path set
method in the example calculation results P (T) 2 is the
same, in the same way,we can also verify TPSS3 -
TPSS6 power outage probability and minimum path set
method of the calculation results are the same, therefore,
by comparing the calculation results of the two methods,
verify the feasibility of high speed railway external pow-
er supply reliability assessment and accurate.
4.4. Bayesian network Identification System
Vulnerabilities
Because the bayesian network can bidirectional reason-
ing, so it can calculate when system failure, the po sterior
probability of each component, then through analysis the
posteriori probability of each element, you can easily
identify weak links of the system.
For high-speed rail external power supply system as
shown in Figure 2, the posteriori probability of various
components as shown in Table 3.
T
L1 L2 L3 L4 L5 L6 L7 L8 G1 G2
A1 A2 A3 A4 A5
Figure 4. The minimal cut of bayesian network(bus 2).
Table 3. Main parts of posterior probability.
Bus 2 Bus 3 Bus 4 Bus 5 Bus 6
L1 5.10×10-4 4.30×10-4 4.30×10-4 4.30×10-4 4.30×10-4
L2 1.43×10-3 1.43×10-3 1.43×10-3 1.52×10-3 1.43×10-3
L3 1.14×10-3 1.14×10-3 1.14×10-3 1.13×10-3 1.11×10-3
L4 2.90×10-4 2.90×10-4 2.90×10-4 5..46×10-4 2.96×10-4
L5 2.90×10-4 2.90×10-4 2.90×10-4 1.28×10-2 5.73×10-4
L6 4.3×10-4 4.30×10-4 4.30×10-4 4.30×10-4 4.30×10-4
L7 2.90×10-4 1.43×10-3 1.43×10-3 1.52×10-3 1.43×10-3
L8 2.90×10-4 2.90×10-4 2.90×10-4 1.28×10-2 5.73×10-4
G1 1 1 1 0.98725 0.97735
G2 1 1 1 0.98744 0.02425
L9 0 0 0 0 0.0257

Z. C. LIANG ET AL.
832
Through analysis posteriori probability of the various
components in Table 3, high-speed railway external
power of the weak link are L9 and G1, G2, so reduce the
failure rate and maintenance time of generator G1, G2,
and L9, will significantly improve the reliability of high
speed railway external power supply.
5. Conclusions
1) Based on probabilistic inference of bayesian net-
work used in high-speed railway external power supply
reliability evaluation, established the minimum cut set
and minimum path set method of bayesian network mod-
el, and develops the corresponding program for calculat-
ing the credible degree.
2) Using the IEEE RBTS system as an example to es-
timate the reliability of high speed railway external pow-
er supply scheme, and quantitative calculate the
high-speed railway traction power substation of probabil-
ity, proving the correctness and feasibility of the method
which can be applied to high speed railway external
power supply reliability evaluation.
3) Based on bidirectional reasoning technology of
bayesian network, we can quantitative calculation the
posterior probability of each elements in the external
power supply system, and realize the identification of
weakness about th e external power supply, providing the
basis for carrying out external power supply reliability
distribution in the further.
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doi:10.1109/59.32623