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D 2.3 DELIVERABLE

PROJECT INFORMATION

Project Title: Systemic Seismic Vulnerability and Risk Analysis for Buildings, Lifeline Networks and Infrastructures Safety Gain

Acronym: SYNER-G

Project N°: 244061

Call N°: FP7-ENV-2009-1

Project start: 01 November 2009

Duration: 36 months

DELIVERABLE INFORMATION

Deliverable Title: D2.3 – Definition of system components and the formulation of system functions to evaluate the performance of electric power systems

Date of issue: June 2011

Work Package: WP2 – Development of a methodology to evaluate systemic vulnerability

Deliverable/Task Leader: University of Rome La Sapienza

REVISION: Final

Project Coordinator:Institution:

e-mail:fax:

telephone:

Prof. Kyriazis Pitilakis Aristotle University of Thessaloniki [email protected] + 30 2310 995619 + 30 2310 995693

i

Abstract

The first target of this report, that is the definition of the taxonomy for the components of an Electric Power Network (EPN), has been achieved through a survey of the technical literature on fragility models for such components. Details on this survey are included in deliverable report D3.3. This work has been also carried out with the purpose of producing a state-of-the-art of available performance indicators, useful to assess the performance of the whole system and its components when subjected to a seismic hazard. The reported performance indicators are consistent with the systemic approach to the simulation of an EPN within the SYNER-G general methodology for infrastructural systems vulnerability assessment. The latter adopts a capacitive, detailed flow-based modelling with propagation of short-circuits over the network and requires internal modelling of the substation logic.

Keywords: component-level, system-level, connectivity, mechanical damage, power-flow analysis.

ii

Acknowledgments

The research leading to these results has received funding from the European Community's Seventh Framework Programme [FP7/2007-2013] under grant agreement n° 244061.

iii

Deliverable Contributors

UROMA Paolo Emilio Pinto

Francesco Cavalieri

Paolo Franchin

Ivo Vanzi

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Table of Contents

Abstract ........................................................................................................................................ i

Acknowledgments ...................................................................................................................... ii

Deliverable Contributors ........................................................................................................... iii

Table of Contents ....................................................................................................................... iv

List of Figures ............................................................................................................................. v

List of Tables .............................................................................................................................. vi

1 Taxonomy of electric power networks ............................................................................. 1

1.1 DESCRIPTION AND ANALYSIS OF AN ELECTRIC POWER NETWORK ................. 1

1.2 IDENTIFICATION OF THE MAIN TYPOLOGIES FOR ELECTRIC POWER NETWORK COMPONENTS IN EUROPE ................................................................... 8

2 Performance Indicators .................................................................................................... 10

2.1 EXISTING PERFORMANCE INDICATORS .............................................................. 11

2.1.1 System-level PI’s ........................................................................................... 11

2.2 PROPOSED PERFORMANCE INDICATORS ........................................................... 12

2.2.1 Component-level PI’s ..................................................................................... 12

2.2.2 System-level PI’s ........................................................................................... 12

2.3 DISCUSSION ............................................................................................................. 13

References ................................................................................................................................. 15

v

List of Figures

Fig. 1.1 Power plant ................................................................................................................ 1

Fig. 1.2 High voltage transformer ............................................................................................ 2

Fig. 1.3 Sketch of a T&D system for an EPN (TL = Transmission Lines, D = Distribution lines, TD [HV→MV] = Transformation (from high to medium voltage) and Distribution station, TD [MV→LV] = Transformation (from medium to low voltage) and Distribution station, L = Load) ......................................................... 3

Fig. 1.4 Typical topological structures, grid-like (on the left) and tree-like (on the right), respectively for transmission and distribution systems ........................................ 4

Fig. 1.5 European high voltage transmission grid (V ≥ 220 kV). Higher voltage lines in blue, lower voltage lines in red. Line thickness is proportional to voltage. ................... 4

Fig. 1.6 Substation .................................................................................................................. 5

Fig. 2.1 Evolution of the expected value of SSI (left) and MAF of SSI (right) ....................... 11

vi

List of Tables

Table 1.1 Main typologies of EPN components in Europe ...................................................... 8

Taxonomy of electric power nerworks

1

1 Taxonomy of electric power networks

1.1 DESCRIPTION AND ANALYSIS OF AN ELECTRIC POWER NETWORK

A modern Electric Power Network (EPN) is a complex interconnected system that can be subdivided into four major parts:

o Generation

o Transformation

o Transmission and Distribution

o Loads

These are briefly described in the following sections. A more detailed treatment can be found in deliverable D5.2 “Systemic vulnerability and loss for electric power systems”. The interested reader can also see Saadi (2002).

Generation of electric power is carried out in power plants. A power plant (Fig. 1.1) is composed of several three-phase AC (Alternate Current) generators known as synchronous generators or alternators. Synchronous generators have two synchronously rotating fields, one of which is produced by the rotor driven at synchronous speed and excited by DC (Direct Current), while the second one is produced in the stator windings by the three-phase armature currents. The DC current for the rotor windings is provided by the excitation systems, which maintain generator voltage and control the reactive power flow. Because of the absence of the commutator, AC generators can generate high power at high voltage, typically 30 kV. In a power plant, the size of generators can vary from 50 MW to 1500 MW.

Fig. 1.1 Power plant

At the time when the first EPNs were established in the world, individual electric companies were operating at different frequencies anywhere, in US ranging from 25 Hz to 133 Hz. As the need for interconnection and parallel operation became evident, a standard frequency of 60 Hz


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was adopted throughout the US and Canada, while most European countries selected the 50 Hz system. These two AC frequencies are still in use at the present time.

The source of the mechanical power, commonly named “prime mover”, may be hydraulic turbines at waterfalls, steam turbines whose energy comes from the burning of coal, gas and nuclear fuel, gas turbines or occasionally internal combustion engines burning oil. Many alternative energy sources, like solar power, geothermal power, wind power, tidal power and biomass, are also employed.

One of the major components of a power network is the transformer (Fig. 1.2), which transfers power with very high efficiency from one level of voltage to another level. The power transferred to the secondary winding is almost the same as the primary, except for losses in the transformer. Therefore, using a step-up transformer of voltage ratio a will reduce the secondary current of a ratio 1/a, reducing losses in the line, which are inversely proportional to voltage and directly proportional to distance. This makes the transmission of power over long distances possible. At the receiving end of the transmission lines step-down transformers are used to reduce the voltage to suitable values for distribution or utilization.

Fig. 1.2 High voltage transformer

The purpose of a power delivery system (simple sketch in Fig. 1.3), also known as transmission and distribution (T&D) system, is to transfer electric energy from generating units at various locations to the customers demanding the loads.


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TL

D

TD [HV→MV]

TD [MV→LV]

L

L

L

L

L

TL

D

TD [HV→MV]

TD [MV→LV]

L

L

L

L

L

Fig. 1.3 Sketch of a T&D system for an EPN (TL = Transmission Lines, D = Distribution lines, TD [HV→MV] = Transformation (from high to medium voltage) and Distribution station, TD [MV→LV] = Transformation (from medium to low voltage) and Distribution

station, L = Load)

A T&D system is divided into two general tiers: a transmission system that spans long distances at high voltages on the order of hundred of kilovolts (kV), usually between 60 and 750 kV, and a more local distribution system at intermediate voltages. The latter is further divided into a medium voltage distribution system, at voltages in the low tens of kV, and a low voltage distribution system, which consists of the wires that directly connect most domestic and small commercial customers, at voltages in the 220-240 V range for Europe. The distribution system can be both overhead and underground.

The transmission and distribution systems are generally characterised by two different topological structures: the transmission system is an interconnected redundant grid, composed of stations as nodes and transmission lines as edges, while the distribution system is a tree-like network, following the main streets in a city and reaching the end users. Fig. 1.4 shows the two topological structures.


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Fig. 1.4 Typical topological structures, grid-like (on the left) and tree-like (on the right),

respectively for transmission and distribution systems

The European high voltage transmission grid, composed of lines with a voltage greater or equal to 220 kV, is displayed in Fig. 1.5. The image has been taken from Poljanšek et al (2010).

Fig. 1.5 European high voltage transmission grid (V ≥ 220 kV). Higher voltage lines in

blue, lower voltage lines in red. Line thickness is proportional to voltage.


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The lines at different voltages are terminated in substations. In general, an electric substation (Fig. 1.6) is a facility that serves as a source of energy supply for the local distribution area in which it is located, and has the following main functions:

o Changing or switching voltage from one level to another, by means of transformers.

o Delivering power.

o Providing points where safety devices such as disconnect switches, circuit breakers, and other equipment can be installed.

o Regulating voltage to compensate for system voltage changes.

o Eliminating lightning and switching surges from the system.

o Converting AC to DC and DC to AC, as needed.

o Changing frequency, as needed.

Depending on their functions, substations can be grouped into three typologies, in particular:

1. Transformation substations.

2. Distribution substations.

3. Transformation/distribution substations.

An important component inside a substation is the bus, a redundant system of bars transferring energy between lines entering or exiting from the station. When the transformation function is required (type 1 and 3 above), two buses at two different voltages are present. For type 3 only, where also power delivery is required, one or both buses are load buses. For distribution substations, only one bus is present, that is a load bus.

Fig. 1.6 Substation

Substations can be entirely enclosed in buildings where all the equipment is assembled into one metal clad unit. Other substations have step-down transformers, high voltage switches, oil circuit breakers, and lightning arresters located outside the substation building.

The electric power is delivered to the single customers through distribution circuits, that include poles, wires, in-line equipment, utility-owned equipment at customer sites, above ground and


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underground conductors. Distribution circuits either consist of anchored or unanchored components.

Finally, loads of power systems are divided into industrial, commercial and residential.

Industrial loads are served directly from the high voltage transmission system or medium voltage distribution system. Commercial and residential loads consist largely of lighting, heating and cooling.

Loads are independent of frequency and consume negligibly small reactive power. The real power of loads is expressed in terms of kilowatts (kW) or megawatts (MW).

The magnitude of load varies throughout the day and power must be available to consumers on demand. The greatest value of load during a 24-hr period is called peak demand. Smaller peaking generators may be commissioned to meet the peak load that occurs for only a few hours. In order to assess the usefulness of the generating plant the load factor is defined, which is the ratio of average load over a designated period of time to the peak load occurring in that period. Load factors may be given for a day, a month or a year.

The analysis of an EPN in a seismically active environment can be carried out, as for other lifeline systems, at two different levels. The first basic one focuses on connectivity only and can only lead to a binary statement on whether any given node is connected with another node and, specifically, whether it is connected to a generation node through the network. This level of analysis is particularly inadequate for a system such as the EPN since the tolerance on the amount and quality, in terms of voltage and frequency, of the power fed to any demand node for maintaining serviceability is very low. The actual power flow in the node must be determined to make any meaningful statement on the satisfaction of the power demand at the node, not just its state of continued connectivity. The latter is an intrinsically systemic problem since it depends on the determination of the flows on the entire (damaged) network. Further, before being able to evaluate flows it is necessary to determine what is the EPN portion still up and running after an event. This does not simply mean what components are damaged since damage to components has non-local consequences. Indeed, damage to the components of a substation can lead to a short-circuit that may or may not propagate further away from that substation to adjacent others, generating in extreme cases very large black-outs. Hence power-flow analysis follows the analysis of short-circuit propagation. This is the modelling approach adopted within the SYNER-G general methodology.

Within a power-flow analysis the target is to determine the voltage and power in all stations, as well as the current, power and power loss in all transmission lines. Voltage, power and current are phasorial quantities, thus they are complex numbers. The first step is to retrieve the two voltage parts (magnitude and phase) in all stations where they are unknown. To this aim, a set of algebraic non-linear equations are available, representing the active (or real) and reactive power balance in the nodes. The system is written as

( )

( )

1

1

0 cos sin

0 sin cos

θ θ

θ θ

=

=

= − + +

= − + −

∑

∑

N

i i k ik ik ik ikk

N

i i k ik ik ik ikk

P V V G B

Q V V G B (1.1)

where iP and iQ are the real and reactive power at node i, kV and iV are the voltage magnitude at nodes k and i, ikG and ikB are the real and imaginary parts of the ik term in the


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bus admittance matrix Y, θik is the difference of voltage phases between nodes i and k. The solution is found by using one the classical derivative algorithms, for instance Newton-Raphson. Once known the stations voltages, it is straightforward the computation of the lines currents and powers in both directions, the lines power loss and the powers (real and reactive) in all generation stations. These issues are further explained and dealt with in deliverable report D5.2.


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1.2 IDENTIFICATION OF THE MAIN TYPOLOGIES FOR ELECTRIC POWER NETWORK COMPONENTS IN EUROPE

The electric power networks components (that can considered vulnerable or not) can be grouped on the base of five different vulnerability analysis scales of the network. The main typologies, with particular reference to the European context, are listed in Table 1.1.

Table 1.1 Main typologies of EPN components in Europe

Typology Vuln. analysis scale Element code Electric power grid Network EPN01 Generation plant Station EPN02 Substation Station EPN03 Distribution circuits Distribution-system EPN04 Macro-components Substation’s component Autotransformer line Substation’s component EPN05 Line without transformer Substation’s component EPN06 Bars-connecting line Substation’s component EPN07 Bars Substation’s component EPN08 Cluster Substation’s component EPN09 Micro-components Substation’s component Circuit breaker Substation’s component EPN10 Lightning arrester or Discharger Substation’s component EPN11

Horizontal disconnect switch or Horizontal sectionalizing switch Substation’s component EPN12

Vertical disconnect switch or Vertical sectionalizing switch

Substation’s component EPN13

Transformer or Autotransformer Substation’s component EPN14 Current transformer Substation’s component EPN15 Voltage transformer Substation’s component EPN16 Box or Control house Substation’s component EPN17 Power supply to protection system Substation’s component EPN18 Coil support Substation’s component EPN19 Bar support or Pothead Substation’s component EPN20 Regulator Substation’s component EPN21 Bus Substation’s component EPN22 Capacitor bank Substation’s component EPN23 Transmission or distribution line Line EPN24


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Overhead lines are generally not considered as vulnerable elements. On the contrary, underground lines, which are scarcely diffused in Europe, can be vulnerable, depending on some technological features of their laying.

It has been noted from the literature review that authors often assign different names to the same micro-component.

It has to be remarked that most authors do not explicitly distinguish between micro- and macro-components. This distinction is useful in terms of reliability analysis when the approach to network modelling is capacitive (i.e. power flows are computed) and the internal logic of substations is modelled, i.e., partial functioning (continued service with reduced power flow) is accounted for. In this latter case the modelling effort, which is much higher than when a substation is considered as a single component with a binary state (fail/safe), can be reduced by assembling sub-sets of micro-components that are serially arranged within the substation in order to reduce them to a single element: the macro-component. The substation layout is then composed of general (non-serial) arrangement of macro-components which can lead to partial functioning states, depending on the distribution of damage.

Looking again at Table 1.1, it should be now clear how components EPN01 and EPN03 are not of interest within the SYNER-G analysis framework where the level of detail / resolution in the description of the EPN, and in general of lifelines, is higher.

Performance Indicators

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2 Performance Indicators

Within the seismic reliability analysis of an EPN it is needed to assess the performance of the whole system and its components when subjected to a seismic hazard. The quantitative measure of this performance is given by Performance Indicators (PI’s), that express numerically either the comparison of a demand with a capacity quantity, or the consequence of a mitigation action, or the assembled consequences of all damages (the “impact”).

In general, for an Infrastructure (system of systems) performance indicators can be categorized according to the level in the hierarchy of the Infrastructure to which they refer. Thus one has:

o Component level PI’s

o System level PI’s

o Infrastructure level PI’s

With reference to the system EPN, the following two sub-sections present some performance indicators, existing in the literature or proposed by the authors, and belonging to the first two categories above. For all indicators, two properties are indicated, each of them with two possible values:

o Connectivity / Capacitive modelling

o Deterministic / Probabilistic

The first property tells if the indicator is able to capture the system performance focusing on connectivity only or accounting for the actual power flows in the network.

If the indicator is deterministic, its value can be computed within a single run of a simulation (performed according to the Monte Carlo method, for instance). A probabilistic indicator, on the other hand, can be computed only when the results of two or more runs of a simulation are available, thus accounting for the uncertainty modelling, as explained in deliverable report D2.1. This latter indicator most commonly consists of a moment (e.g. expected value) or distribution of a deterministic indicator, or a function of the above. As an example, Fig. 2.1, left, shows the evolution, with the number of runs, of the expected value of a common PI, the System Serviceability Index (SSI), while in Fig. 2.1, right, is displayed the Mean Annual Frequency of exceedance of SSI, computed at the end of the simulation.

A probabilistic indicator can also be defined as probability of events (e.g.

( )( )

1

00 =

>> ≅

∑N

i

I PIP PI

N, where N is the total number of runs and I is the indicator function).


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0 20 40 60 80 100 120 140 160 180 200

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1.00E[

SSI]

sample #

Evolution of E[SSI] with simulation runs

μμ+σμ-σ

0.7 0.8 0.9 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

SSIλ

SSI

MAF of exceedance of SSI

Fig. 2.1 Evolution of the expected value of SSI (left) and MAF of SSI (right)

2.1 EXISTING PERFORMANCE INDICATORS

2.1.1 System-level PI’s

o Connectivity Loss, or CL [deterministic, connectivity modelling] (Poljanšek et al, 2011). This index, whose definition is based on the concept of connectivity, for a generic system measures the average reduction in the ability of sinks to receive flow from sources: 01= − i i

s iCL N N

where denotes averaging over all sink vertices, while isN and 0

iN are the number of sources connected to the i-th sink in the seismically damaged network and in non-seismic conditions, respectively. With reference to an EPN, sinks are load buses and sources are power plants.

o Power Loss, or PL [deterministic, connectivity modelling] (Poljanšek et al, 2011). This index upgrades the connectivity loss with the size of the power plants (in MW) to which sink vertices are still connected to:

01= − i is i

PL P P

where isP and 0

iP are the sum of the real power of all the power plants connected to the i-th load bus in the seismically damaged network and in non-seismic conditions, respectively.

o Impact factor on the population, or IP [deterministic, connectivity modelling] (Poljanšek et al, 2011). Considering the population POPi assigned to the i-th load bus, it is possible to assess the portion of the population affected by the power loss. Assuming that the fraction of the population receiving power from the i-th load bus equals its normalized power supply in the damaged network, 0

i isP P , the IP index is defined as:


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( )01,...,1 == −∑

D

i is ii N

all

P P POPIP

POP

where DN is the number of load buses in the EPN and allPOP is the total population of the area fed by the EPN.

o System Serviceability Index, or SSI [deterministic, capacitive modelling] (Vanzi, 1995). This index is defined as the ratio of the sum of the real power delivered from load buses after an earthquake, to that before the earthquake:

( ),01,...,

,01,...,

1100=

=

⋅ − ⋅= ⋅∑

∑D

D

i i ii N

ii N

P R wSSI

P

where ,0iP is the real power delivered from the i-th load bus in non-seismic conditions, i.e. the demand. In order to compute the eventually reduced power delivered in seismic

conditions, two factors are considered. The first one, , ,0

,0

−= i s i

ii

V VR

V, with ,i sV and ,0iV the

voltage magnitudes in seismic and non-seismic conditions, is the percent reduction of voltage in the i-th load bus and if , ,0<i s iV V one has 1− =i iR VR ( iVR is introduced in the

next section). The second factor, iw , is a weight function accounting for the small tolerance on voltage reduction: in particular, its value is 1 for 10%≤iR and 0 otherwise. The SSI index varies between 0 and 100, assuming the value 0 when there is no solution for the power-flow analysis and 1 when the EPN remains undamaged after the earthquake. The above definition assumes that the demand remains fixed before and after the earthquake, since the index looks only at a single system, without considering the interactions of the EPN with the other infrastructure systems.

2.2 PROPOSED PERFORMANCE INDICATORS

2.2.1 Component-level PI’s

o Voltage Ratio, or VR [deterministic, capacitive modelling]. For each bus inside the substations, this index is defined as the ratio of the voltage magnitude in the seismically damaged network to the reference value for non-seismic, normal conditions:

, ,0=i i s iVR V V The voltage computation requires a power-flow analysis on the network. Hence this index expresses a functional consequence in the i-th component of the physical damage to all system components. When interactions with other systems are modeled, VRi expresses the functional consequence in the i-th component of the physical damage to components of all the interacting systems, i.e. it is the value of the index that changes due to the inter- and intra-dependencies, not its definition.

2.2.2 System-level PI’s

o Enhanced System Serviceability Index, or ESSI [deterministic, capacitive modelling]. This index is an enhancement of the SSI, being able to capture the interaction of the


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EPN with the built area of the study region, consistently with the approach adopted within the SYNER-G general methodology for infrastructural systems vulnerability assessment (see deliverable report D2.1). In order to model this interaction, the power demand is eventually reduced after the earthquake by considering the collapsed buildings and thus the fraction of population not requiring power anymore. The indicator is defined as follows:

( ) ,,01,...,

,,01,...,

1

100

∈

=∈

∈

=∈

⋅ − ⋅ ⋅

= ⋅

⋅

∑∑ ∑

∑∑ ∑

i

D

i

i

D

i

j COj Ii i ii N

jj I

j COj Iii N

jj I

NP R w

NESSI

NP

N

where iI is the set of tributary cells for the i-th load bus, jN is the total number of

buildings inside the j-th tributary cell and ,j CON is the number of not collapsed buildings

inside the j-th tributary cell. As the SSI, also the ESSI index varies between 0 and 100, assuming the value 0 when there is no solution for the power-flow analysis or all buildings in the study region are collapsed and 1 when the EPN remains undamaged after the earthquake.

o Moving average µ and moving standard deviation σ of deterministic indicators. [probabilistic, connectivity/capacitive modelling]. These parameters represent the evolution of the expected value and the standard deviation of the PI’s during the simulation, until the current run.

o Mean Annual Frequency (MAF) of exceedance of deterministic indicators. [probabilistic, connectivity/capacitive modelling]. The MAF of the generic performance measure Y exceeding threshold value y is computed as:

( ) ( ) ( ) ( )λ λ λ λ= = =∑ ∑0, | 0 | 0| |Y i Y i i Y i Yi iy G y i p G y i G y

by post-processing of the vector of sampled values of Y to first obtain the complementary (experimental) distribution function ( )YG y . Then this distribution is multiplied by the MAF

of all earthquakes in the region, λ λ= ∑0 0,ii. The probability

λλ

= 0,

0

iip that, given an

earthquake, it occurs on source i is respected in the complementary distribution ( )YG y where results come from events sampled in the correct proportion among the different sources.

2.3 DISCUSSION

As stated above, the analysis of an EPN in a seismically active environment can be carried out at two different levels, the first one focusing on connectivity only, whereas the second one considers the power-flow solution. Correspondingly, the appropriate PI’s will be limited to CL, PL and IP if the analysis is of the former type, while will include the remaining indicators for a capacitive analysis.

The only component-level PI, VR, as well as two of the system-level PI’s, SSI and ESSI, are meaningful since they require the computation of voltage in all load buses, thus allowing to measure the actual serviceability of the EPN under seismic action. If a repair time is set for


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components and hence for the whole network, multiplying such repair time by the power not delivered yields the energy not delivered.

The remaining system-level PI’s, although are based just on connectivity, can nonetheless give some useful indications about the state of the damaged network. They can be considered as indices of mechanical damage, that is a damage due to both seismic action and short-circuits spread. Similar indices to be considered could also be the number of buses isolated from the rest of the network and the number of components failures grouped by component.

Further, it is possible to define a system-level PI accounting for both mechanical damage and reduced energy delivery. Since the two types of damage are non homogeneous, both of them are assigned a cost, so to make it possible to sum such costs and retrieve the PI.


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