The Online Journal on Electronics and Electrical Engineering (OJEEE)
Vol. (2) – No. (3)
Estimation of the Lifetime of Electrical
Components in Distribution Networks
M. Mamdouh Abd El Aziz, Senior Member, IEEE, Doaa Khalil Ibrahim, Member, IEEE and Hany Araby Kamel
Electrical Power and Machines Department, Faculty of Engineering, Cairo University
Abstract- The aim of this paper is to establish a
reference system of the reliability models which may also
be applied for different utilities. Due to the large amount
of electrical equipments and the costs of an individual
diagnosis in distribution networks, a life assessment of the
representative electrical components is necessary. Several
models are used to estimate the life time of each
component but introduced model can estimate the life
time for every component in general. The data of
historical failure events from distribution networks is
collected and evaluated in a special failure statistic and
ageing phenomenology is taken into account. For such a
purpose, the relationship between lifetime, electrical
stress, mechanical stress and temperature as well as their
effects on ageing processes and on reliabilities of electrical
components are studied. A review of models of
transformer and cables will be introduced for
comparison.
Keywords- ageing, failure statistic, lifetime, transformer,
cable.
I. INTRODUCTION
In the liberalized market, an optimized asset management
should consider the reliability of supply and other power
quality aspects as well as the reduction of maintenance and
capital costs, the key question is to find an acceptable balance
between cost effectiveness and supply quality. Power system
is composed of a number of components, such as lines,
cables, transformers, circuit breakers, disconnectors etc.
Every component in a power system has an inherent risk of
failure. In addition, outside factors influence the possibility of
component failure; e.g. the current loading of the component,
damage by third parties (human or animal), trees and
atmospheric conditions–temperature, humidity, pollution,
wind, rain, snow, ice, lightning and solar effect [1].
It is often taken for granted that the lifetime of installed
electrical equipment is less than 40 years [2]. The statistical
failure rates rise over the years according to the increasing
right wing of the well-known bathtub curve [3]. Models used
for estimation life time are based on stress tests (electrical,
mechanical, thermal) such as Arrhenius, Inverse Power
models, loading cycle, analysis of furfurals, degree of
polarization (DP) and the others are based on historical
outage data and Markove model of mean time to first fail [410]. Proposed model is electro-thermo-mechanical life model
Reference Number: W10-0002
derived from a suitable combination of single-stress models,
e.g. the Inverse-Power- model and the Arrhenius model [11].
On the basis of the probabilistic approach, the application
of special analysis is carried out; the fitted curves are only a
mathematical simulation that is not concerned with any
information about the technical parameters of electrical
equipment and the operating conditions of networks, thus
they can not give a complete understanding of the physical
implications of failures. Extensive basic research work has
detected the ageing phenomena and ageing processes of
typical insulating materials under test or working conditions
[12]. However, the experimental data can only describe sparse
and incomplete ageing behaviors of electrical components in
distribution networks. Therefore, a new approach should not
only reflect and respond to the way electrical equipment fail
but also deduce the failure consequences by connecting
statistical data to durable evaluation models.
II. PHENOMENOLOGICAL AGEING THEORY
According to IEC, ageing can be defined as "irreversible
deleterious change to the serviceability of insulation systems.
Four types of parameters have been defined as ageing factors
by IEC; temperature, electrical stress, mechanical stress, and
environmental factors. When an insulation system is
subjected to one or several of these ageing factors, deleterious
changes will take place at certain rates characteristics for the
particular combination of ageing factors. Models for thermal,
electrical and mechanical stresses, singly applied, have been
available as Arrhenius model for thermal stress:
LT  L0 exp(BT ) , T=1/ θ0-1/ θ
(1)
where LT is life time, B = AE /k, AE is the activation energy of
the degradation process, k is the Boltzmann constant, θ , θ0
are the absolute and reference temperature and L0 is the life
time at temperature θ0. The Inverse Power model for
electrical stress is:
LE=L0 (E/E0)-n
(2)
where E0 is the value of electrical stress below which
electrical ageing can be neglected and failure under
multistress conditions is the consequence of ageing produced
by the other stresses, Lo is life for E = Eo and n is the voltage
endurance coefficient for the inverse-power models.In the
next sections, life models for two main electrical component:
transformers and cables are introduced in details.
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The Online Journal on Electronics and Electrical Engineering (OJEEE)
Transformer fails due to insulation failures caused by
pyrolosis (heat), oxidation, acidity, moisture, design and
manufacturing errors caused by loose or unsupported leads,
loose blocking, poor brazing, inadequate core insulation,
inferior short circuit strength, foreign objects left in the tank,
oil contamination, corrosive sulfur, carbon tracking,
overloading, fire or explosion, line surge, maintenance
/operation, flood, and loose connections [19-21]. Some
models used for estimation of transformer life are [4-20, 21]:
1-Transformer insulation life according to IEEE standard:
Beginning with the most recent IEEE Standard C57.911995
Per unit life  9.8  10 –18 e (15,000/(T
_ hs  273))
(3)
where 110 °C is the reference temperature (T_hs is the hotspot temperature) so for a reference temperature of 120 °C,
15,000/ T
Per unit life  2.65  10 –17 e 
_ hs  273 
(4)
For older transformers with 55 °C average winding rise
insulation systems with a rated hottest-spot rise over ambient
of 65 °C and a 30 °C ambient, the reference temperature is 95
°C. The equations for per unit life are:
Per unit life  2.00  108 e 15,000/(T
_ hs  273)
For IEEE C67115-1991 that assumes 110
reference:
Log . life  hours of life    13.391 
6972.15
T _ hs
(5)
o
C as
instant t1 to time instant t2, in integral form or according to the
expression (7) in a discrete form, depending on the featured
measurement data are:
L
1t 2
 V .dt
t t1
T
3- There is other models which simulate the ambient
temperature as long-term temperature drift neglected method,
long term temperature drift included and alternate approach
for life estimation; that are used in the previous models of
IEEE and IEC to estimate the elapsed life [8].
4- Elapsed Life of Oil-Immersed Power Transformers (OIP)
based on the DP (Degree of Polarization):
6 3 2 8 .8
_ hs  273
The more important byproducts of the processes leading to
thermal degradation of OIP are carbon oxides (COx) and a
class of hydrocarbons including what are called furans. The
life model is [9]:
In transformers constructed according to IEC 60076, the
hot spot temperature, at which there is normal ageing rate
equals 98 0C at nominal load and ambient temperature of 20
0
C. The relative ageing rate can be expressed in the following
manner:
 HS 98
6
(7)
where θHS is the hot spot temperature and V is the relative loss
of life. The relative ageing, over a time period from time
Reference Number: W10-0002
Hot spot 0C
Figure 1: Ageing rate (pu.) depending on the hot spot
temperature according to IEEE and IEC
2- Loss of Life with 55°C or 65°C winding rise according to
IEC Standards [7, 9]:
V 2
(8)
6 3 2 8 .8
_ hs  273
For the 55 C insulation systems
T
1 N
Vn
N n 1
(6)
0
Log. life =  1 1 . 9 6 8 
L
where n is the number of each time interval, N is the total
number of equal time intervals, Vn is relative ageing rate and t
is time. The loss of life according to IEEE equals 180000
hours, and in the IEC standards the total loss of life is not
defined, but it is usually mentioned that the transformer loss
of life is 30 years. The difference existing in the dependence
of the ageing rate on the hot spot temperature as shown in
Figure 1.
For ANSI/IEEE C57.91-1981, at 65 0C insulation systems:
Log. life =  1 1 . 2 6 9 
and
Ageing rate (pu)
III. LIFE MODELS FOR TRANSFORMERS
Vol. (2) – No. (3)
 1100 
Elapsed life  20.5  ln 

 DP 
year
(9)
The empirical formula given is based on an initial value of
mean DP of about 1100, for a fresh transformer paper.
5- Emsley Method:
This method concluded that a so-called ‘thermally
activated’ kinetic process that can describe paper ageing as:


1
1
E

 A  exp 
 t
DPold DPnew
 R (T  273) 
(10)
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The Online Journal on Electronics and Electrical Engineering (OJEEE)
where T is the temperature, E is the activation energy, A is a
parameter depending upon the chemical environment, R' is
the molar gas constant, and t is the elapsed ageing time. Here
DPold and DPnew are, respectively, the DP-values after and
before ageing period where the new paper will have a DP of
about 1200. Ageing experiments approved that model is:
1
1

DPend DPstart
 13350 
Expected Life 
 exp 

A  8760
 T  273 
(11)
IV. LIFE MODELS FOR CABLES
The majority of cable failures are mainly due to natural
ageing of insulation, cable imperfections or water treeing.
Other failure modes involve corrosion or damage to the
concentric neutral and metallic ground shields, and the loss of
good contact between metallic shield and the semiconducting
shield. Some models used for estimation of life are:
1- Physical models:
The search for physical models are based on the description
of specific degradation mechanisms assumed as predominant
within proper ranges of applied stresses. Such models are
characterized by “physical” parameters that can, at least in
principle, be determined by measuring directly physical
quantities. Some examples of physical models are following
[10, 14-18]:
a. Field emission model.
b. Treeing growth models which describe the treeing growth
period and, thus, hold only during that period. Some
examples are the models proposed by Bahder, Dissado
and by Montanari.
c. Thermodynamic models which are based on the concept
of thermally-activated degradation reactions that are
responsible for material ageing. They are Crine’s model,
Electrokinetic Endurance (EKE) Model and Space-charge
model.
2- Models with Full Size Cables as Zhurkov model and
Arrhenius-IPM model.
3- VLF (voltage low frequency) Method: this model is used
to estimate the remaining life of XLPE cable by VLF test
[18].
V- LIFE ESTIMATION BASED ON FAILURE
STATISTICS
The introduced method is suitable for all electrical
components but it requires practical information about the
available failure statistic from distribution networks, and by
using the electro-thermo-mechanical life model as following:
Reference Number: W10-0002
Vol. (2) – No. (3)
 E 
L  L0 

 E0 
( n bT )
 M 
.

M0 
m
.exp( BT )
(12)
where E, M, T and L are electrical, mechanical, thermal
stresses, and lifetime respectively. E0 and M0 are the scale
parameters for the lower limit of electrical and mechanical
stresses respectively (below which the ageing can be
neglected) and L0 is the corresponding lifetime. n, m and B
are the voltage-endurance coefficient, the mechanical stress
endurance coefficient and the activation energy of thermal
degradation reaction, respectively, b is the correct coefficient
which takes into account the reaction of materials due to
combined stress application. T=1/θ -1/ θ0. Where: θ and θ0 are
the absolute and reference temperatures. The failure
probability of an electrical component is expressed under the
influences of ageing, electrical, and mechanical stresses as
[11]:
  E  ( n bT )  M m 
P (L )  1  exp   



  E0 
M0 



 L   BT
  e
 L0 




(13)
where α is the shape parameter; the probabilistic failure
density f(t), the failure rate h(t) and the expected lifetime μ(L)
can be determined by the failure probability P(L):
 (t )  d P (t  L ) / dt
(14)
h (t )  d P (t  L ) / [1  P (t  L ).dt
(15)

 (L )   Lf (L ) dL
(16)
0
Table 1: Parameters of equation (13)
B (K)
17000
M0(N/mm2)
10-4×2.4
b (K)
6000
E0 (kV/mm)
5.0
m
2.3
θ0(K)
298
n
7.0
L0(year)
4.5×104
In this case, the parameters of equation (13) are optimized
at α = 1, θ = 25°C, E = E0 and shown in Table 2.
Table 2: Parameters of equation (13) for random failure
interrupter
joint
D-transformer VPE- cable
39 M0
39 M0
35 M0
31 M0
T-transformer
housing
paper-cable
conductor
29 M0
29 M0
25 M0
23 M0
About 120.000 failure data of historical events in the
special failure statistic from the year 1920 to 2005 is collected
as shown in Table 3 [21].
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The Online Journal on Electronics and Electrical Engineering (OJEEE)
Table 3: Failure statistics
Table 5: Calculated results for each component
Electrical Mech. random
failure failure failure
Component
Failure location
Overhead
line
Conductor
3%
64%
33%
Paper-cable
VPE-cable
Joint
Termination
Housing
D-transformer
Interrupter
CB
T-transformer
Disconnector
60%
35%
93%
96%
1%
32%
48%
9%
20%
4%
1%
1%
2%
1%
86%
48%
41%
85%
67%
94%
39%
64%
5%
3%
13%
20%
11%
6%
13%
2%
Cable
system
Secondary
substation
Switchgear
station
Vol. (2) – No. (3)
Component
Conductor
Paper-cable
VPE-cable
Joint
Termination
D-transformer
Housing
Interrupter
CB
T-transformer
Disconnector
Failure
probability
for 15 years
0.3
0.16
0.57
0.07
0.002
0.14
0.07
0.09
0.004
0.007
0.016
Failure
probability
for 30 years
0.54
0.57
0.88
0.58
0.49
0.53
0.24
0.31
0.44
0.39
0.64
Lifetime
(year)
31
27.3
16
27.6
28.6
29.5
31
30
29.4
30
26.6
Component
Conductor
Paper-cable
VPE-cable
Joint
Termination
D-transformer
Housing
Interrupter
CB
T-transformer
Disconnector
α
E
M
θ
8.1
8.2
6.6
4.5
9.2
9.9
9.3
13.3
8.3
11.6
7.1
2.6
1.3
1.5
1.3
1.3
2
1
2.1
2
2.2
1
22.5
1
1
1
1
7.4
22.5
7
7.2
6.8
24.2
25
60
60
60
60
40
25
40
40
40
25
The calculated failure probability for the above components
for 15 and 30 years are introduced in Table 5 in addition to
the estimated life time.
The failure rate and failure probability of some components
are shown in figures 2, 3.
Time
(year)
Figure (2) The failure probability of D-Transformer, housing
and interrupter
D-transformer
Failure rate = 1/ year
Table 4: Parameters of equation (13) of different components
Failure Probability
Using tabulated parameters shown in Table 4 for E, M, α
and θ of different components: conductor, paper-cable, VPEcable, joint, Termination, D-transformer, housing, interrupter,
CB, T-transformer, and disconnector to calculate failure
probability and estimated life time.
Time
(year)
Figure (3) The failure rate of D-Transformer
VI. THE EFFECT OF COOLING AND RELATIVE COST
The thermal effect is the most ageing factor affects on the
life of insulation material; IEC recommends absolute hot spot
temperature not more than 98°C. 6°C deviations on the hot
Reference Number: W10-0002
272
The Online Journal on Electronics and Electrical Engineering (OJEEE)
spot will double the aging rate. In our electro-thermalmechanical model the temperature taken from statistical
history for distribution transformers is 40oC which gives 29.5
years as an expected life time. If this temperature is reduced
by 2oC will increase the life to 39 years by good cooling for
transformer; also the well ventilation will lead to this result
taking into account the cost of the cooling. The cost of 1000
KVA self cooled transformer is 23,640.00 $, the hot spot
temperature 55oC, the average losses 9.1 kW. The ventilation
required to conserve the temperature at 38oC is 2000 m3/hr
from the cook book for indoor transformer ventilation. The
fan used is SODECA HCD-40-4M, the cost of fan is 500.0 $
including the running and maintenance cost. Then:
[4]
The cost without cooling = 23,640.00/29.5 = 801.4 $/year
[9]
[5]
[6]
[7]
[8]
The cost with cooling = (23,640.00 +500)/39= 619 $/year
The saving cost / year = 801.4-619= 182.4
$/ year.
[10]
[11]
VII. CONCLUSION
On the basis of the ageing mechanisms occurring in
different materials, simple phenomenological and statistical
reliability models are proposed in this work. The models
provide a means of connecting physical and statistical
processes of component failures. This approach appears to be
a useful tool to assess the component reliability, as it can
clarify how those consequences of failure result from
different kinds of failure causes. The typical ageing of
insulating materials in electrical components often contributes
to the failure due to the presence of degradation stresses such
as electrical, thermal, mechanical and environmental stresses.
Therefore the ageing processes are transferred into a life
model, which is represented by several models. In reliability
calculations, the multi-model from the life model and the
probabilistic model is applied to provide effective predictions
for the lifetime. These results provide the validity of both the
proposed models and the method for calculation. The
assessment of the calculated results for electrical components
can be viewed as objective evidence that the reliability
requirements of electrical components will be satisfied by the
proposed technical parameters and the appropriate
maintenance activities. It is not practical to specify all the
parameters for every example. If experiences are obtained
from other power systems, it may prove desirable to
supplement or modify the model parameters needed in a
particular application.
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