Energy and Power En gi neering, 2011, 3, 600-606
doi:10.4236/epe.2011.35075 Published Online November 2011 (http://www.SciRP.org/journal/epe)
Resilience of High Voltage Transmission System
Naim H. Afgan1, Dejan B. Cvetinovic2
1Instituto Superior Tecnico, Lisbon, Portugal
2Laboratory for Thermal Engineering and Energy, Institute of Nuclear Science “Vinca”,
University of Belgrade, Belgrade, Serbia
Recieved March 2, 2011; revised April 20, 2011; accepted April 28, 2011
Abstract
The resilience of a system can be achieved by reducing its probability of failure as well as reducing the con-
sequences from such failures and the time to recovery. Quantification of resilience is first approached from
the broader societal context, from which the engineering sub-problem is formulated as an important building
block of the integrated tool ultimately needed. Nonlinear structural responses are considered, as well as the
impact of retrofit or repair. Impact on time to recovery is considered in all cases. The proposed framework
makes it possible to relate probability functions, fragilities, and resilience in a single integrated approach,
and to further develop general tools to quantify resilience. The high voltage transmission system is typical
engineering system which requires the assessment of the resilience as the measure for evaluation of the po-
tential hazard event development. In this respect the resilience of the high voltage transport system is highly
vulnerable: central generation creates high value targets, long vulnerable transmission lines, unique high
voltage transformers, vulnerable substations. The assessment of the resilience of the high voltage transmis-
sion system is based on the evaluation of the resilience index as the result of the sudden changes of the char-
acteristic indicators.
Keywords: Sustainability, Resilience, High Voltage System, Resilience Indicators, Catastrophic Events
1. Introduction
Energy losses represents nowadays between 2% and 4%
(depending of local climatic conditions) of total energy
electric power transmission. In Europe, this figure is ex-
pected to grow as a result of the expected economic de-
velopment of Southern and new EU states). For the case
of the high voltage transmission sector, the energy losses
depend on the temperature of the environment range. The
high voltage system is highly vulnerable: central genera-
tion creates high value targets, long vulnerable transmis-
sion lines, unique high voltage transformers, vulnerable
substations [1].
The electricity system currently experiences many dis-
ruptions due to natural hazards and human error. Large,
costly blackouts occur frequently. It is evident that:
 It is highly vulnerable to human attack. A worst case
scenario would be highly destructive.
 Many investments would simultaneously improve re-
liability & reduce vulnerability or the amount of da-
mage from terrorist attack.
 Evaluating the reliability and security benefits to-
gether would justify many new investments.
In this analysis of energy grid system (Figure 1) the
existing electricity distribution networks regulatory frame-
work will be taken also into account. A Smart Grids
Factor will be based on indicators such as grid volume
and distributed generation rate. This factor is introducing
the effect of regulation on the system, which is further to
the performance-based ratemaking (guaranteed or overall
standards). Using also the quality and efficiency factors
implemented, a “third pillar” (besides economy and
quality) for the regulation will be developed according to
the countries existing incentive and quality based regula-
tion [2].
This factor should reveal the current state of play, the
changes compared to previous years and should allow a
future outlook of the trends in network development. As
an incentive it should have positive effects directly on
the network operators’ revenues in case of an improve-
ment of the situation (less grid losses, more distributed
generation compared to previous year). In order to mea-
sure the performance of each individual network operator
nd to make results comparable, each regulator should a

N. H. AFGAN ET AL. 601
Figure 1. High voltage transmission system.
define reference values in advance. Different reference
values for the individual operators are foreseen to in-
clude structural varieties. If the operator didn’t reach the
expected level it should consequently reduce its revenues.
This would be an efficient method, which gives to net-
work operators a financial incentive to foster network
development in line with the approach of a Smart Grids
[3,4].
An electricity blackout causes us to freeze (sweat) in
the dark. We find it difficult to: commute (no traffic sig-
nals, no trains); get up and down in buildings (no eleva-
tor); work (no light, computers, copiers, faxes); cook (no
microwave, refrigerators, appliances, solid state ignition);
get entertainment (no TV, radio, VCR). Almost all mod-
ern activities depend on electricity.
The high voltage system is highly vulnerable: central
generation creates high value targets, long vulnerable trans-
mission lines, unique high voltage transformers, vulner-
able substations
System is disrupted frequently by natural hazards,
human error, and human attack. Worst Cases Scenarios:
Ice Storm: Quebec and NY in 1998, Hurricanes: Florida
in 2004, Earthquake: Bay area, California in 1989. Hur-
ricane Ivan: Almost occurred in 2004. Since these hap-
pened recently, a 500 year worst case would be much
worse [5].
2. Sustainability of High Voltage
Transmission System
Sustainability is the word which is used to create the
special meaning for the interaction of the different enti-
ties in our world. In its definition sustainability was at-
tributed to the interaction of system with its surrounding,
including, social, cultural, environmental, economic and
other aspects.
More than that, the sustainability has become a quality
measure of the system in the assessment and evaluation
of the respective system. It has been noticed that the sus-
tainability comprise complexity definition for the com-
plex system. In its definition the complex system is in-
troduced as the nonlinear interaction of large number of
elements functionally defined. Since, we can imagine a
number of examples of complex systems in our life, it is
of interest to verify some of them which are typical for
the energy system. Complexity of the strategy of energy
system is expressed through the multiple elements and
their interaction [6].
The high voltage transmission system comprise a num-
ber of elements which functionality is defined in accor-
dance with is role in the system. The complex system of
high voltage transmission system is characterized with
the specific number of the indicators reflecting individual
properties of the system, as shown on Figure 2.
3. Resilience Index for High V oltage
Transmission System
The sudden change of the indicator and its return to the
primary state is the measurement of the capacity of the
respective system to withstand the changes of the system.
There are several potential changes of every system
which may result in the eventual catastrophic event. It is
of interest to visualize characteristic behavior following
Figure 2. Sustainability high voltage transmission index.

N. H. AFGAN ET AL. 602

n
the sudden change of the indicator. Integral value of the
indicator in the time scale until it reaches the steady state
is the measuring parameter of the resiliency index [7-11].
Since the every sudden change of indicators may con-
tribute to the resilience index, the sum of individual in-
dicators of the sudden change as the resilience index is
the value representing the capacity of the system under
consideration. For the high voltage transmission system
the Resilience Index is the agglomeration of capacity of
the system reflecting the total change of the resilience
capacity of the system [12,13].
Figure 3 presents the sudden change of indicator value
and its return to the steady state.
The agglomeration of the changes of all indicator rep-
resent the integral value of the Resilience Index expres-
sed by Equation (1)

0
0
1
t
n
n
t
Rw q
 (1)
where
wn—weighting coefficient;
qn—indicator value in time scale;
n—number of indicators.
Figure 4 shows the Resilience Index monitoring
scheme with procedure for the indicator agglomeration
and presentation.
Definition of the Resilience Index can be simplified
with the assumption that the integral format can be de-
termined as the surface of the triangle formed by the am-
plitude of sudden change of indicator Δqi and time period
Δti, Equation (2), so that

1
0
00
12
tt
nn
i
jii i
i
tt
qt
Rwqt w








(2)
where
Δqi—indicator change;
Δti—time change.
t1
100%
Sustainability Index Q(t) [-]
Time t [hh:ss]
100%
t0
Rj
Figure 3. Resiliency index.
4. Resilience Indicators
In this analysis of the Resilience Index of High Voltage
Transmission System a following indicators are take into
a consideration, as shown on Figure 5.
4.1. Economic Indicator
The economic indicator are including: Electricity Cost
indicator and Investment Cost. Electricity Cost indicator
is representing financial loss due to electricity cut by the
sudden change of the electricity cost indicator measured
in the Euro/kWh. The maximum change of this indicator
is estimated to 1.2 cEuro/kWh.
4.2. Environment Indicator
It is very common that the change of environment in the
vicinity of High Voltage Transmission System is affect-
ing the power system wiring and producing the change of
the ice coating affecting the wire temperature. Due to the
sudden change in the wire temperature its recovery will
require the time period to reach recovered state. The
maximum sudden change the ice break will be δ/voltage
line diameter = 0.5.
4.3. Social Indicators
4.3.1. Blackout
Any disruption of the electric power system leads to the
change of power consumption. Its effect on the power
transmission to the human dwelling will affect the hu-
man life. The substitution to the power consumption de-
ficiency is a blackout and will lead to the change of re-
silience index of the high voltage transmission system. It
is anticipated that the maximum disruption of the elec-
tricity power system Δv/standard voltage = 20.
4.3.2. Human Behaviors
It is of interest to verify human behavior related to the
sudden electricity disruption. It is commonly accepted
that the human reaction is measured by number of people
being actively involved in the specific event. Particular
attention is devoted to the effect of human behaviors
during the accident if there is any. In definition human
behavior it is assumed that the human effect maximum is
Δnumber/total number of people = 10 being supplied by
the power transmission system.
5. Resilience Index of High Voltage
Transmission Options
R
esilience engineering is applied in a number of systems

N. H. AFGAN ET AL. 603
Electricity cost
x
1
Investment cost
x
2
Ice Layer
x
3
Power Consumption
x
4
Human Behaviours
x
5
normalization of sampled values – q
i
-collecting data in various forms
- all criterions are getting
Values between 0 and 1
- applying weighting
factors to criterions
- database building
- Sustainability index
monitoring
- Resilience index calculation
Trigger
Analysis
w
1
q
1
w
2
q
2
w
3
q
3
w
i
q
i
w
n
q
n
 
nn
n
Qtq t  

1
0
11 1
1
t
t
Rw qt 



1
0
22 2
1
t
t
Rw qt






1
0
333
1
t
t
Rw qt






1
0
0
1
t
n
jii
t
Rwqt





Figure 4. Resilience monitoring scheme.
Figure 5. Agglomeration scheme of the resilience index.
5.1. Options under Consideration
in order to justify potential stability limits which may
lead to the catastrophic events [14]. The resilience of the
high voltage transmission system is the capacity of the
system to withstand the sudden change of the internal or
external parameters of the system. It reflects the quality
of the system measured by the appropriate changes of the
indicators. The potential possibility of the high voltage
transmission system is to reach limits leading to the
catastrophic events require the investigation of the cases
which might be the qualitative measure of the stability of
the system. As regards the high voltage transmission
system a number of parameters are taken as the potential
changes to be used for the verification of the individual
cases.
In the definition of objects to be taken into a considera-
tion it is anticipated that the high-voltage system is de-
fined with the following parameters: Electricity Cost, In-
vestment, Ice Layer, Change in Power Consumption, and
Human Behaviour. Each of the object under considera-
tion is defined with the set quality indicators comprising
a specific value for every quality indicator. At this point
it is of interest to reveal that the meanings of specific val-
ues of the quality indicators are reflecting the object de-
scription as the complex system.
As it is known the sustainability index is an appropri-
ate parameter for the verification of the complex system.

N. H. AFGAN ET AL. 604
So, by the measurement of sustainability index under
consideration the quality of the objects are verified.
Since every object is defined as the specific option, we
will use the change of the sustainability index due to the
change of the specific indicator as the initial definition
for the system definition.
In this analysis a four options are taken into a consid-
eration with sudden change of indicators as shown in
Table 1.
In this analysis a following options are taken into a
consideration:
5.1.1. Option 1— C hange of El ec tr i city Cost
The electricity cost sub-indicator is one of the economic
indicators which is subject to sudden changes due to
market fluctuation. It is usually expressed in cEuro/kWh
reflecting the market change of the economic environ-
ment. It is anticipated to design the potential electricity
cost to be expressed as 5 cEuro/kWh. In this analysis the
maximum the sudden change electricity cost sub-indi-
cator is 20% of the standard electricity cost. In the design
of this option we will anticipate that the changes of other
indicators are participating in the definition of the object
as presented in Table 1.
5.1.2. Option 2—Change of Ic e Layer
Due to the adverse climate in the vicinity of the high
voltage transmission line there is potential possibility for
the formation of the ice layer on the power line wires.
This ice formation will have adverse effect on the power
transmission. There is potential development of the ice
layer. The change of the ice layer thickness leads to the
increase the weight of the ice which may cause fracture
of the power line. In the design of the power transmis-
sion line special precautions is made to preserve safety of
the power lines. In this respect the design of power line
include the maximum thickness as of the ice layer as the
limit to prevent eventual catastrophic events. In the de-
sign of this option it is anticipated that the maximum of
ice thickness is δ/d = 0.5 and other indicators will have
values as presented in Table 1.
Table 1. Resilience indicators.
Electricity
Cost Ice Thickness Public Consumption Human Behavior
ΔcEURO/kWh Δδ/d ΔkWh/cap ΔN/Total
Option 1 1 0 50 5
Option 2 0.5 0.5 0 2.5
Option 3 0.25 0.25 200 0
Option 4 0 0.125 100 10
5.1.3. Option 3— C hange of Pow er Consumptio n
The change of power consumption is an immanent prob-
lem for any high voltage transmission line. There is a
possibility to have sudden increase of the power demand
in some urban regions leading to the potential critical
state of the power transmission. It is of interest to notify
that the change in power consumption and its maximum
value may result in the catastrophic event. The sudden
maximum change of power consumption may lead to the
catastrophic event. In the design of this option the
maximum sudden change of the power consumption is
200 kWh/cap. All other indicators value are given in
Table 1.
5.1.4. Option 4— Change in Hum a n Be haviors
The social aspect of the potential sudden change of the
electric power consumption may lead to the diverse reac-
tion of the human behavior. In particular, the prediction
of the human behaviors is important issue which may
lead to the catastrophic events. The human dwellings are
designed with the respective communication space in
order to make possible human movement within the
dwelling under a severe power shortage. In the situation
when it happens there is a need for mass communication.
The maximum value of this indicator ΔN/Total = 10
persons/total number. For other options the values of the
sudden change human behavior is given in Table 1.
6. Case Demonstration
In this exercise a following cases are taken into a con-
sideration:
CASE 1—EC > IL = PC = HB
Case 1 represent situation when the priority is given to
the Change of Energy Cost indicator with other indica-
tors having the same value, as shown on Figure 6. It is
of interest to notice that if the priority given to the
Change of Electricity Cost Indicator the result prove that
the relation among options under consideration is having
the highest value of Resilience Index with Option 1.
CASE 2—IL > EC = PC = HB
The case 2 is designed with priority given to Change
of Ice Layer Indicator, as shown on Figure 7. The rela-
tion among options under consideration shows a mar-
ginal difference of the resilience index among options.
Priority rating in this case is: Option 2, Option 4, Option
3 and Option 1.
CASE 3—PC > EC = IL = HB
It is of interest to notice that case 3 presents the resil-
ience index relation for the priority given to Change of
Power Consumption, as shown on Figure 8. The contri-
bution of the other changes to the mutual relation is very
similar to the other cases under consideration.

N. H. AFGAN ET AL.605
Figure 6. Resilience index—c ase 1.
Figure 7. Resilience index—c ase 2.
Figure 8. Resilience index—c ase 3.
CASE 4—HB > EC = IL = PC
The change in Human Behavior effect on the rating
list among the options is very limited as regard resilience
index for the other option, as shown on Figure 9. In this
respect it is of interest to verify that the difference of the
resilience index value for of options are in following
rating: Option 4, Option 1, Option 2 and Option 3 as
shown on Figure 9.
7. Conclusions
The resilience index of high voltage transmission system
is the capacity to measure the stability of the system. The
potential occurrence of the adverse affect is an immanent
catastrophic event leading to the disruption of the high
voltage structure. There are a number of the indicators
which can be used for the assessment of the stability of
the system. The selection of appropriate indicators is a
primary goal in the design of the stability of the system.
It reflects the quality of the system measured by the ap-
propriate changes of the indicators. The potential possi-
bility of the high voltage transmission system is to reach
limits leading to the catastrophic events require the in-
vestigation of the cases which might be the qualitative
measure of the stability of the system. As regards the
high voltage transmission system a number of parameters
is taken as the specific indicators for the definition of the
potential changes to be used for the verification of the
individual cases [15,16].
In this analysis of the Resilience Index of High Volt-
age Transmission System a following indicators are take
into a consideration:
7.1. Economic Indicator
Electricity Cost indicators is representing financial losses
Figure 9. Resilience index—c ase 4.

N. H. AFGAN ET AL. 606
due to electricity cut by the sudden change of the re-
spect- tive indicator measured in the cEuro/kWh.
7.2. Environment Indicator
Ice Agglomeration on the High Voltage Wiring
It is very common that the change of the environment in
the vicinity of High Voltage Transmission System is
affecting the power system wiring and producing the
change of the ice coating affecting the wire temperature.
Due to the sudden change in the wire temperature its
recovery will require the time period to reach recovered
state.
7.3. Social Indicator
7.3.1. Blackout
Any sudden disruption of the electricity transmission to
the human dwelling will affect human life. In this respect
there will be need to ensure the capacity recovery of the
system if there will be any sudden change in the electric-
ity supply
7.3.2. Human Behaviors
It is of interest to verify human behavior related to the
sudden electricity disruption. It is commonly accepted
that the human reaction is measured by number of people
being actively involved in the specific event. Particular
attention is devoted to the effect of human behaviors
during the accident.
In general, any sudden change of the selected indica-
tors may lead to the change of the resiliency of the sys-
tem. For this reason the development of appropriate pro-
cedure for the resiliency index evaluation is a tool for the
assessment of the safety of high voltage system and pre-
vention of the catastrophic events leading to the structure
destruction.
Demonstration exercise of the high voltage transmis-
sion system has been introduced as the method of verify-
cation of the potential limits for the catastrophic events.
8. References
[1] H. De Kautender and A. Boggini, “Resilience Power Sup-
ply in Modern Office Building,” European Copper Insti-
tute, Washington DC, June 2005.
[2] A. Chalmers and F. A. Voorvaat, “High Voltage Trans-
mission System Lines: Proximity, Visibility, and Encum-
brabce Effects,” The Appraisal Journal, 2009, pp. 227-
245.
[3] European Smart Grid, “Directorate-General for Research
Energy System,” EUR 22040, 2006.
[4] The Smart Grid, “DOE Smart Grid Pdf,” USA Depart-
ment of Energy, Litos Strategic Communication, Wash-
ington DC, 2008.
[5] L. Lav and J. A. G. Blagin, “Waste Case Electricity Scena-
rio,” CREATE Symposium, University of South California,
Los Angeles, August 1995.
[6] W. N. Adger, “Vulnerability,” Global Environment Chan-
ge, Vol. 16, No. 3, 2006, pp. 268-281.
doi:10.1016/j.gloenvcha.2006.02.006
[7] H. Kainan, “Concept and Practices of ‘Resilience’,” US
Agency for International Development, Bangkok, 2006.
[8] E. Hollnagel, D. Woods and N. Levesen, “Residence En-
gineering: Concepts and Percepts,” Ashgate Publishing
Limi- ted, London, 2005.
[9] S. Atonsen, “Safety, Culture and Failure Foresight,” Pro-
ceeding of the Third Resilience Engineering Symposium,
Antibes, 28-30 October 2008, p. 1.
[10] C. S. Holling, “Resilience and Stability of Ecological Sys-
tem,” Annual Review of Ecology and Systematic, Vol. 4,
1973, pp. 1-23. doi:10.1146/annurev.es.04.110173.000245
[11] E. Hollnagel, P. Nemet and S. Dokker, “Resilience Engi-
neering Perspective,” Ashgate Publishing Limited, Lon-
don, June 2008.
[12] Th. Priestlaym and P. C. Ignelzi, “Transmission Line Im-
pact on Residents Communities,” Elisen Electric Institute,
Washington DC, June 1989.
[13] C. Folke, “Resilience: The Emergence of a Perspective
for Social-Ecological System,” Global Environmental
Change, Vol. 16, No. 3, 2006, pp. 253-267.
doi:10.1016/j.gloenvcha.2006.04.002
[14] N. Afgan and D. Cvetinovic, “Wind Power Plant Resil-
ience,” Thermal Science, Vol. 14, No. 2, 2010, pp. 533-
540. doi:10.2298/TSCI1002533A
[15] N. Afgan and M. G. Carvalho, “Energy System Assess-
ment with Sustainable Indicators,” Kluwer Academic Pub-
lisher, New, York, 2004.
[16] N. Afgan and M. G. Carvalho, “Quality, Sustainability and
Indicators for Energy Systems,” Begell House Publisher,
New York, 2009.