Figure 19 shows the structure of circulation of information in the application of cascade effects to this scenario. Besides the probability function regarding to the fragility curve of the electric system and to the probability of having ignition after the electric cable failure, three categories of inputs must be previously available on the world state, namely: the location of the electricity network, the intensity distribution of the earthquake and the fuel cover in the area of interest.
Figure 19: Flow of information during the running of cascade effects for the selected scenario. “Application 1” is referred to the transition EQ-DEN and “Application 2” is referred to the transition
DEN-FF.
The probability of having a cable failure in the electric system (Application 1 in Figure 19) and the consequent formation of an electric arc results from the intensity distribution of the earthquake and the fragility curve of the electric devices. The intensity of the earthquake along the electric network is a part of the world state and information is available on the shake map. The fragility curve relates the intensity of the earthquake to the potential damage caused in the electric network along the line.
The probability of having an ignition started by an electric discharge (Application 2 in Figure 19) results from the fuel classification of the area where the electricity cable failure is located and the probability model of ignition by electric discharge. The fuel classification is a part of the world state and is provided by the fuel map of the area. If the electric discharge occurs in a non-fuel area, as for example a road, the probability of ignition is null. However, if the electric discharge occurs in a fuel area, as for example a grass land, the probability of ignition shall be determined by the use of the probability ignition model that will be detailed later.
If we attend to the whole event chain EQ-DEN-FF, the probability of having a fire ignition due to an earthquake is given by the product of the probability of having an electric cable failure and the probability of having a fire ignition triggered by an electric cable failure. 3.2.2.2. Input data from the wold state
Since the cascade effect model is appealed and the user selects the event chain linking the earthquake to damage to electricity network (cable failure) and to forest fire, some information regarding to the world state is required. That information is following detailed.
Location of the electric network
The location of the electric network used for this example is not real since it was defined in the most opportune locations. For convenience of Pilot D, the electric line was designed to pass close to the Village of Castel del Monte in order to have a forest fire threating this community. On the other hand, this line was designed to cross the area of interest to have
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as many probabilities calculations as possible. Apart those two assumptions, the poles are randomly located only taking precautions to do not put a pole in an unlikely place such as in the middle of a river. The separation between two successive poles is around 300m.
Figure 20: Geographic distribution of the electric poles.
Map of EQ intensity distribution
The occurrence of a Mw5.6 earthquake in the NE part of the domain has been simulated as the triggering event for this scenario. The shake map of this event, represented by the intensity of the ground motion in the area of interest, is shown in Figure 21. Using the shake map of this event, the peak ground acceleration (PGA, in %g) of the ground motion is calculated at the base of each of the poles of the electric network considered for this example.
Figure 21: Map of the triggering earthquake intensity distribution with location of the electric power network (distribution lines – smaller poles).
Fuel map
The fuel map is important to evaluate the probability of ignition as it has the information of the class of fuel where each electricity pole is located.
To be harmonized with the fire behaviour prediction model FireStation, the classes used in the fuel map are consistent with those used in FireStation. As can be seen in Figure 22, in the area of interest there are seven different fuel classes. Grassland is that one with higher representativeness.
Figure 22: Fuel map for the region of L’Aquila.
The fuel map showed in Figure 22 was developed, in April 2014, by the ArcFUEL Project Consortium from a cooperation protocol established between CRISMA Project and the European LIFE+ Project ArcFUEL.
3.2.2.3. Transition probability data for the cable failure triggered by an earthquake
The cables connected to low voltage distribution lines (evidenced in red in Figure 23) are those considered as the most vulnerable ones to external shocks (e.g. seismic excitation). Small poles have a high probability to fall down during or after an earthquake than larger poles. However, during a seismic event, all the poles (low, medium and high voltage) shake and the stress induced in the electric cables may cause its breakage.
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Figure 23: 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) (adapted from D5.2
Deliverable of the EU project SYNER-G).
In particular, the electricity poles used in electricity distribution lines may be subdivided based on the material (wood, reinforced concrete or tubular steel), diameter and height. The tubular steel electric poles are very common and for this reason we concentrated on this typology. In Figure 24 there is an example table classifying the electricity poles of this category according to the diameter and height.
Figure 24: An example of tubular steel poles classification (from a commercial producer). In order to assess the probability of the cable failure, a number of pole classes are studied. In particular, referring to a generic class, the fragility curve represents the probability of attaining a limit value of displacement at the pole top varying the intensity of the seismic input. Such limit value is represented as a fraction of a displacement XMAX (three
hypotheses are considered: 0.5 XMAX, XMAX and 1.25 XMAX, where XMAX is defined as the
displacement corresponding to the static application of the design force T1 (see Figure 25)
Figure 25: Definition of top displacement XMAX.
The intensity input may be expressed with various measures. Here we adopt the peak ground acceleration.
In order to determine the probability of attaining xlim, an Incremental Dynamic Analysis
(IDA) is performed (Vamvatsikos and Cornell, 2002). Figure 26 shows the normalized pseudo-acceleration spectra of the selected records, together with the mean spectrum and comparison with EC8 based representation.
Figure 26 – Normalized pseudo-acceleration spectra.
In order to perform the IDA, the pole is schematized as a Single Degree Of Freedom System (SDOF) with a concentrated mass on top (see Figure 27), suitably characterized by stiffness k and elastic period T; 5% critical damping is assumed.
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Figure 27: Representation of the electric poles and the mass on the top. Figure 28 shows an example IDA obtained for the pole type 12B14.
Figure 28: IDA for the pole type 12B14.
Elaborating IDA results with the approach proposed in (Porter et al., 2007) the fragility curves can be obtained. Figure 29 show the fragility curves derived for pole type 12B14.
Figure 29: Fragility curves of electric poles to a transversal force T1.
In order to simplify the use case, all the electricity poles of the area of interest will follow the fragility curve XMAX.
Transition probability data for fire ignition triggered by cable failure
The transition from the electric cable failure to a fire ignition has two evolutionary steps: 1) the production of the electric arc from the electricity cable to the fuel bed, and 2) the ignition of the fuel bed by the electric arc.
It is assumed that the failure of an electric cable imperatively causes an electric arc. Due to the existing protection systems the electric charge is normally interrupted in case of failure and after that, for brief instants, the residual electric charge continues flowing. After the cable breakage, the cable takes some time to land or to reach a sufficient distance to establish the electric arc. The time to ignition by electric arc with high voltage is very short (tenths of seconds) and therefore in this sense it is reasonable to consider the production of an electric arc for a short period as inevitable. On the other hand, the time to ionize the air path from the cable failure to the fuel bed and the consequent production of the electric arc is strongly dependent on the distance and on the resistance of this path. This dependency is a function of many additional factors such as topography, cable height, air humidity, and pressure. For simplification reasons we will not take those aspects into consideration in this document, but rather assume that the cable failure will always drive to an electric arc that reaches the fuel bed.
In a laboratory environment, several tests were carried out in order
to determine the total amount of energy required to ignite a certain
amount of fuel. These tests were performed for straw and pine
needles (Pinus pinaster) for a range of fuel moisture content (FMC)
between 9.2% and 12.2% (APPENDIX (2) Main parameters of the
laboratorial tests for the determination of ignition by industrial
electric discharge.
0 5 10 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Fragility 12B14
PGA(g) P [X > X L 3 ] 0.5 X MAX X MAX 1.25 X MAX31.08.2014 | 30
). A bouquet of the fuel material was exposed to an industrial electrical arc of certain power (P [kVA]) as can be seen in Figure 30. The time (t [s]) elapsed from the beginning of discharge until the evidence of combustion was measured. The energy (E[kJ]) required for ignition was determined using Equation 4.
a) b) c) d)
Figure 30: Sequence of images of a laboratorial test to determine the energy required for ignition by industrial electric discharge.
t P
E [4]
It was found that the probability of ignition was not significantly different for the several tests at different conditions of FMC or different types of fuel (straw or pine needles) and also the fuel load does not seem really relevant for the probability of ignition. This statement should be considered preliminary since not many tests with fuels other than straw and pine needles were carried out and the range of fuel moisture content was not very extensive.
Using the data collected in the laboratory experiments, we estimated the parameter of different competing probabilistic models in order to find the distribution providing the best description of the laboratory observations. As possible competing models we used the Log-normal, Gamma, Normal, Weibull and Exponential distributions. We estimate the model parameters for each candidate model using a Maximum Likelihood Estimate (MLE) approach, and use the Akaike Information criteria (AIC, Akaike 1974) for the model selection. The AIC is a tool based on the concept of entropy, and offers a relative measure of the information lost when a given model is used to describe some data (a tradeoff between accuracy and complexity of the model).
Table 3 summarizes the functional form of the PDF, estimated (MLE) parameters (and uncertainties), and the AIC for all the probabilistic models considered. Using a Kolmogorov–Smirnov test, we cannot reject the Log-normal, Gamma, and Normal hypotheses (at significance level of 0.05), which means that, from a statistical point of view, all these probability models successfully explain the observed data. However, according with the AIC values, the preferred model (i.e. that with the lowest AIC value) is the Log-normal.
Table 3: Candidate distributions, PDF, estimated (MLE) model parameters and uncertainties, and Akaike Information Criteria (AIC). According to the AIC information, the model that best describes
the data is the Lognormal.
Model Probability density Parameters
(MLE) AIC Log-normal ( , ) = ( | , ) = ( ) =6.334 [6.329,6.339] =0.246 [0.243,0.250] – 62803 Gamma (a,b) = ( | , ) = ( ) a=16.68 [16.22,17.14] b=34.84 [33.87,35.83] – 62845 Normal ( , ) = ( | , ) = ( ) =581.0 [578.1,583.8] =146.3 [144.2,148.3] – 63319 Weibull (a,b) = ( | , ) = a=637.1 [633.7,640.6] b=3.87 [3.81,3.92] – 63832 Exponential ( ) = ( | ) = =581.0 [569.7,592.6] – 72815
Figure 31a shows the cumulative probability (CDF) of the candidate distributions and the empirical CDF of the observed data, while the Figure 31b shows the CDF and related uncertainties of the Log-normal model.
a) b)
Figure 31: a) Plot of the Cumulative Distribution Function (CDF) of Log-normal, Gamma, Normal, Weibull, and Exponential competing models, and the empirical CDF of the observed data; b) CDF of
the Log-normal (with parameters as those presented in Table 3), selected as the best model describing the observations.
Therefore, the model selected to describe the energy required to start an ignition is a Log- normal with parameters =6.334 [6.329,6.339] and =0.246 [0.243,0.250], where the values in parenthesis represent uncertainty bounds. The Log-normal model is therefore used for the determination of the probability of fire ignition given the occurrence of an electric discharge. As for simplicity we consider that an electric cable failure will always generate an electric discharge, this model consequently also represents the probability of a fire ignition given a cable failure.
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As previously mentioned, there was no significant difference in the results achieved for pine needles as compared to straw. Therefore, for simplification, we assume that the model can provide the probability of ignition for all fuel classes other than urban areas, where the probability of ignition by electric discharge is assumed to be zero. This assumption seems reasonable as commonly, for prevention reasons, the area below electric cables is cleaned of heavy fuels.
3.2.2.4.
3.2.2.5. Output results
With all the required inputs available, the cascade effect model is prepared to show the most interesting outputs to the end user. In this application there are two different use cases: (1) earthquake – cable failure, and (2) earthquake – cable failure – fire ignition.
Earthquake – Cable failure
Figure 32 shows the distribution of probabilities to have a cable failure in the electric network after a seismic event with a Mw 5.6. Probability distribution results from the earthquake intensity distribution (Figure 21) and the fragility curve of the poles (Figure 29).
Figure 32: Map for probability of cable failure.
Obviously, only in the electric network is possible to have cable failure. As it was previously explained the cable failures which we are dealing with occur close to the electric poles. Therefore, the information on the cable failure probability is presented around the poles. In this case, a unique electric poles fragility curve was used (XMAX=1) and therefore
the probability of cable failure depends exclusively on the distance between each pole and the seismic epicentre.
Earthquake – Cable failure – Fire ignition
Besides the visualization of the map for probability cable failure due to the earthquake, the user may want to access the probabilities of fire ignition due to cable failure. This information is provided in the form of a distribution map as showed in Figure 33. The map for distribution of fire ignition by electric cable failure is obtained from the fuel map (Figure
22), the geographic location of the electric network (Figure 20) and the probability function of fire ignition (Equation 5).
As previously explained, the probability of fire ignition is very dependent on the energy released by the electric discharge. The value of energy released during the discharge was determined assuming a trigger time (electric interruption) of 0.1s, a power of 8000kVA (current of 53A and voltage value of 150kV) and consequently 800kJ of energy for the first 20km of electric line (first 67 poles on the right side of Figure 33). It was also assumed a withdrawal of 100kJ of energy due to energy consumption and losses for every 20km of electric line having as consequence a decrease of fire ignition probability along the electric network.
Figure 33: Map for probability of fire ignition due to an electric cable failure.
If the user intends directly evaluate the fire ignition probability triggered by electric cable failure due to a seismic event, it is necessary to apply a combined probability. In this use case, the probability of fire ignition is the product of the probability of cable failure due an earthquake of a certain seismic intensity distribution and the probability of having a fire ignition due to a cable failure (Equation 6). Figure 34 shows the probability map of fire ignition triggered by electric cable failure due to a seismic event.
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Figure 34: Map for probability of fire ignition by electric cable failure due to earthquake. Supported by the information on the probability to have a fire ignition around each pole, the user may simulate an ignition in a certain location according to the most likely spot to have an ignition, the proximity of an important infrastructure or any other convenience. The simulation may be performed accessing FireStation fire behaviour simulation tool in order to simulate the spread of the fire and other important parameters (Figure 35). The comparison of impacts caused by both earthquake and forest fire in a cascade effect event may be an important information to support the decision making. The cascade effect tool is used only to assess the probability of occurrence of a predefined event chain, in the present case Earthquake damage to electricity network (cable failure) fire ignition. The use of FireStation and the analysis of impacts are out of the use of cascade effect tool but it is integrated in the general CRISMA tool where the user must return to perform this last simulation.
(a) (b) (c)
Figure 35 – Map of the evolution of the forest fire (a) after the ignition by the electric discharge from a probable ignition point and other possible outputs from the FireStation software: b) rate of spread, c)