Resilience of High Voltage Transmission System

doi:10.4236/epe.2011.35075

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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

E-mail: [email protected]

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



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)



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



jii i

Rwqt w













(2)

where

Δqi—indicator change;

Δti—time change.

100%

Sustainability Index Q(t) [-]

Time t [hh:ss]

100%

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

esilience engineering is applied in a number of systems

N. H. AFGAN ET AL.

603

Electricity cost

Investment cost

Ice Layer

Power Consumption

Human Behaviours

normalization of sampled values – q

-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

 

Qtq t







11 1

Rw qt









22 2

Rw qt













333

Rw qt













jii

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.

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