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Data‐driven spatio‐temporal analysis of wildfire risk to power systems operation

Data‐driven spatio‐temporal analysis of wildfire risk to power systems operation INTRODUCTIONThe increasing magnitude and frequency of power outages induced or motivated by wildfires affects the operation of critical services and leads to lost opportunity costs [1]. The California Department of Forestry and Fire Protection estimates damages from the 2018 Woolsey and Camp fires to be about $4 and $11 billion respectively [2], with Campfire responsible for about 84 deaths [3]. Additionally, wildfire threats in October 2018 and 2019 led Pacific Gas and Electric (PG&E) to shut off power to a sizeable number of customers in extreme risk areas of northern California leading to lost opportunity costs when no wildfires occurred [4]. Subsequently, the 2020 Zogg fire saw PG&E facing 31 criminal charges, including manslaughter, for the utility's role in the fire that claimed 4 lives and destroyed more than 200 building properties [5]. More recently, the 2021 Dixie fire was caused by the blowing of two fuses when a Douglas fir fell on a PG&E line [6]. The fire gulped more than $630 million in suppression efforts and led to tangible losses including damages to approximately 1500 residential and commercial property, injuries, and fatalities [7].Background and motivationIn response to wildfire threats, utilities have significantly invested on wildfire monitoring systems and analytical tools, which generally rely on observations from remote automated weather stations to evaluate current weather conditions [8] that are disseminated and retrieved [9] from many sources such as Synoptic's Mesonet API. These data are then used to estimate and strategise for optimal operation in the face of wildfire threats, but with room for improvements. In fact, the decisions of a utility to shut off power to more than sixty thousand northern California customers in 2018 and nearly a million in 2019, was controversial [10]. It may be, however, impossible to assess if this was an overestimation of impact and utility resources (“conservative”), but the passing of the California Senate Bill 901 required states investor‐owned utilities with the California Public Utilities Commission to file wildfire mitigation plans, increasing research on the topic [11].Conventionally, electric power utilities have often performed fundamental analysis to indicate wildfire threat alert on coarse resolutions of spatial areas while not utilising the richness of historical data, evident in indices such as the fire potential index (FPI) [12]. This index, for instance, utilises a linear summation of present weather variables and fuels to provide threat levels (extreme, elevated, normal) for predefined regional‐scale threat areas. This may arguably lead to over‐estimation of risk, over‐allocation of operational resources, and consequently “conservative” risk analysis for utilities.Literature reviewStudies on wildfire prediction and estimation [13–15] have mainly focused on numerical quantification [16] and fire scale [17], often using techniques such as regression [18], in an effort to aid mitigation. In ref. [19], wildfire variables are studied to predict spatial patterns of ignition producing national‐level ignition risk maps. To aid pre‐wildfire planning, ref. [20] implements fire danger mapping system based on numerical weather prediction and derived moisture content of live fuels. Historical data for vegetation, climate, and locational features have been utilised in ref. [21] to predict the risk of wildfire ignition. However, these region‐specific wildfire models are simply aggregated over space or time with approximated/linear and spatially constant effects [22]. Hence, their accuracy can be affected by the limited integration of the non‐linear influence of variables, and similarly, do not fully utilise recent wildfire monitoring investments of grid utilities. Wildfire risk prediction has also been done where model performance using machine learning approaches have been evaluated [23]. Artificial intelligence techniques have also been effective for wildfire analysis and outperform conventional statistical methods [24–26]. Additionally, interactive maps have been garnering literary and industry application to supply information on wildfires in real‐time. For instance, in ref. [27], a real‐time fire prediction system is developed for visualising wildfire risk at specific locations based on a machine learning model. Although these methods prove effective, they generally have not been designed to integrate with the power grid operations.The effect of this on the power system side is the assumption of already progressing wildfires, while geographical uncertainties of spatio‐temporal variables are often assumed [28] and not investigated. For instance in ref. [29], energy dispatch is optimised assuming an already progressing wildfire. The same progressing wildfire assumption is applied in ref. [30] to dynamically change thermal ratings of power lines and in ref. [15] to optimise resource preparation.Approaches, contributions, and paper structureThis paper develops a deep learning based framework for analysing the expected spatio‐temporal impacts of stochastic wildfire threat on the power grid. The proposed framework, as shown in Figure 1, integrates a detailed spatio‐temporal wildfire analysis model to evaluate system risk. The model incorporates information from real databases towards potential wildfire ignition maps, as the spatio‐temporal wildfire “readiness” of a location does not necessarily imply an ignition until a fire source is applied. Therefore, a model is proposed to estimate the spatio‐temporal probability of a potential wildfire ignition which can be applied to power transmission and distribution systems. The advantage in modelling potential ignitions pre‐wildfire is to prepare for critical scenarios and proceed with optimal strategies to better mitigate risks arising from extreme wildfire events, thereby reducing the propensity of outages and power shutoff to customers. As wildfires can be caused by power system failure or by exogenous causes (human, natural events), the applications of the estimation result are twofold. First, it provides spatio‐temporal risk for proactive de‐energisation against potential power system failure‐induced wildfire [28]. Second, it generates a spatio‐temporal spreading model for optimal grid operations against potential exogenous wildfires [15]. Depending on the application, risk metrics quantifying potential wildfire operational impact, power utility response time for mitigation, and strategy‐enabling metrics for mitigation vs. restoration, are developed in the second‐stage.1FIGUREStructure of spatio‐temporal wildfire risk assessment modelIn summary, the main paper contributions are as follows:We develop a comprehensive spatio‐temporal wildfire risk analysis framework using a data‐driven deep learning approach that efficiently incorporates publicly‐available historical wildfire and GIS data for estimating wildfire ignition risk and its impact on power grid.Novel quantitative risk metrics that capture potential effects of fuel, vegetation, and wind speed, on wildfire propagation are proposed, while the weighted impacts of wildfire predictive variables are furnished to serve utility operations and stakeholder strategies.The framework can provide information to power utilities towards optimising the grid operation, i.e. the proactive de‐energisation to prevent endogenous power system failure induced wildfire and the response strategy, e.g. “let‐burn”, against exogenous wildfire threats.The rest of the paper is organised as follows: overview of the proposed spatio‐temporal framework is outlined in Section 2 where the geographical formulation and data requirements are also discussed. In Section 3, the wildfire estimation model is discussed and the result utilised in the power grid risk assessment model as presented in Section 4, which also develops the quantitative power system risk metrics. Simulations are conducted and numerical results are illustrated on the IEEE 24‐bus test system as presented in Section 5, while the conclusions are drawn in Section 6.OVERVIEW OF THE PROPOSED MODELWildfires are influenced by a number spatial and temporal factors that can be unique in different geographical locations which can lead to inaccuracies in specified mathematical models. Hence, the objective of the proposed framework is to drive operational strategy with data‐driven situational awareness to wildfire. As in Figure 1, the framework consists of two sequential stages. First, the spatio‐temporal wildfire estimation model predicts the probability of potential wildfire ignition, utilising the spatio‐temporal wildfire ignition probability predictor model (STWIP), and estimates potential wildfire spread, producing important parameters such as ignition probability maps and the rate of spread of potential ignitions to critical power components. These parameters are then passed to the proposed power grid wildfire risk assessment model, which aims to optimise power system operations and risk assessment such that outage cost is minimised. The risk assessment model optimises power system operations by GIS‐enabled mapping of these parameters to the power network and generating wildfire threat scenarios. Part of the risk assessment model also includes proposed power system‐wildfire metrics that enable optimal operational strategies such as choosing mitigation vs. restoration (“let‐burn”). Both Stage 1 and 2 models incorporate effective wildfire analysis, enhancing power system resilience, reduction in customer outages, and hence, operational cost during wildfire threats.The rest of this section discusses the structure of the proposed model and data requirements, while the spatio‐temporal wildfire estimation and power grid wildfire risk assessment models are discussed in detail in the next two sections.Geographical structure of the modelA spatial location is a point i with geospatial coordinate i.loc$i.loc$ defined by a latitude and longitude (lat,lon) at any location in a grid cell. The grid cells here are 3 km × 3 km polygons which have uniform past spatio‐temporal wildfire characteristics and a centroid. Each grid centroid also has geospatial coordinates gc.loc$g_{c}.loc$. For instance, the past spatio‐temporal characteristics of a historical sample ignition occurred in i is obtained by its association with gc.loc$g_{c}.loc$ of the grid cell g∈G$g \in G$ in which it is situated, since the centroid is processed to bear the characteristics of g. Each grid has a set of historical wildfire ignition events with geospatial coordinates i.loc$i.loc$. These historical events, which form sample points in the training data, have a set of variables, x=[x1,x2,…,xD]${\bf x} = [x_{1}, x_{2}, \ldots, x_{D}]$, obtained for their unique i.loc$i.loc$ and dates of ignition. Here, D denotes the dimensionality. These wildfire‐informative variables are referred to as wildfire predictor variables (WPVs) and are usually sourced from weather stations geographically situated at locations of interest. Their interactions and correlation can be modelled towards wildfire prediction. They can vary spatially and/or temporally, are indicative of wildfire occurrence, and are often called explanatory variables [31].Data requirementsThe proposed framework proceeds with data pre‐processing and integration (solid green arrows), feature extraction and training the predictor (solid black arrows), these precursors are as illustrated in Figure 2 and discussed as follows.2FIGURESpatio‐temporal wildfire prediction modelData pre‐processingThis stage proceeds with obtaining the grid centroids together with spatial data, e.g. land‐use and terrain data, from databases such as the National Oceanic and Atmospheric Administration's High Resolution Rapid Refresh (HRRR) model [32].The temporal probabilities, πj$\pi _{j}$ of wildfire ignition, as shown in Appendix A.4, are also calculated in this stage from the US Geological Survey historical ignition data and can be used as a feature to improve estimation. This assumption of a same climate period is enabled by the similarity in the data distribution over the historical period of analysis as illustrated in Appendix A.2, Figure 14. Also in this phase, the python scrapper is coded to request and clean meteorological data for unique spatial locations on days of interest. These days of interest depend on user applications but for this work, meteorological variables on historical ignition and non‐ignition days are duely processed for training/validation of the predictor while forecasted meteorological variables are requested for days that wildfire potential is to be predicted.Data integrationThe next phase is data integration which proceeds in two levels. The first is the spatial integration, where i.loc$i.loc$ of historical ignitions are associated to gc.loc$g_{c}.loc$ to obtain the past ignition characteristics of g. The goal here is to enable spatial locations in the training data inherit wildfire attributes of the grid cell in which they are located. The second occurs after feature extraction during integration into python's pandas dataframes in preparation for training. This dataframe is a two dimensional data structure with columns of multivariate data. The month in which the training ignition sample occurred is incorporated as a feature to account for temporal relation of features, and is also critical to the utilisation of only one fundamental deep network.Feature extractionPast spatio‐temporal ignitionThis feature captures sequential changes in characteristics of spatial wildfire ignition over time and is crucial in the capability of the predictor to use one fundamental deep network. It is calculated from the historical wildfire database and is the initial (historical) ignition probability of a spatial location in the same climate period. To this end, we compute the past wildfire ignition probability mg,j$m_{g,j}$ of a grid cell g in period j of our comprehensive year. Since this attribute is inherited by all i in grid cell g, we refer to this attribute as mi,j$m_{i,j}$. Specifically, because the climate pattern of the multiple‐year‐dataset is assumed constant, the conditional probability of an ignition occurring in grid cell i given the study area, is used to calculate mi,j$m_{i,j}$ given that grid cells are a subset of the studied geographical area as in Equation (1).1mi,j≈ng,jN,\begin{eqnarray} m_{i,j} \approx \dfrac{n_{g,j}}{N}, \end{eqnarray}where ng,j$n_{g,j}$ is the total number of wildfires occurred in cell g in period j, and N is the total number of wildfires that occurred in the multiple year period. Assuming constant climate, the multi‐year period (e.g. 1996–2016) can be modelled as a comprehensive year. As mentioned earlier, in order to enhance the computation of mi,j$m_{i,j}$ considering the scarcity of historical ignitions in some grid cells, the Monte Carlo population technique is employed in pre‐processing the original dataset to further populate grid cells.Temporal (meteorological) featuresWildfire occurrence is influenced by non‐linear and complex meteorological features which are temporally related. Temporal meteorological input includes temperature, rain, humidity, sunshine hours. The choice of these features are informed by indices such as the Angstrom, Nesterov, and Canadian Forest Fire Weather Index as well as the US Fire Danger Rating System [33].Spatial (static) featuresThese features characterise spatial locations for same climate periods and are influential to wildfire occurrence [34]. Spatial data of land‐use and terrain can be obtained from sources such as the HRRR model which have standard grid points that can serve as grid centroids and enable division of the studied geographical area into grid cells with the same spatial and spatio‐temporal features. Historical ignition events that fall within a grid cell are used to obtain mi,j$m_{i,j}$ of the respective cells which are in turn inherited by the sample points i within g, during training.In addition, the past ignition probability and ignition month are also included as spatio‐temporal and temporal features respectively. Additional details can be found in Appendix A.1 and A.3.Data constructionHere, we discuss the logic behind constructing the training data as there is little to none pre‐existing for wildfire analysis. Since training samples are based on historical ignition/non‐ignition days, the dates (dd/mm/yy) and corresponding i.loc$i.loc$ are extracted from the historical ignition database and are utilised to automatically request training sample variables. Once the features are extracted from obtained variables, this training sample point is assigned with a classification label 1, meaning the historical status of ignition was active for the sample. Next, the feature data are requested for the same i.loc$i.loc$ and another (dd/mm/yy) prior to the active ignition date, when no wildfire ignitions were reported to have occurred and this is labelled a 0, meaning that the historical status of ignition was inactive for the sample. In particular, the ignition label for a training sample is defined as:2Ign=1,ifign(j)recorded0,ifign(j−n)¬recorded\begin{equation} Ign = {\begin{cases} 1, & \text{if}\nobreakspace \quad ign_{(j)}\nobreakspace \text{recorded} \\ 0, & \text{if}\nobreakspace \quad ign_{(j-n)} \nobreakspace \lnot \text{recorded} \end{cases}} \end{equation}where Ign$Ign$ is the historical wildfire ignition status in day j, and n={1,2,…,30}$n = \lbrace 1,2,\ldots,30\rbrace$ depending on any day in the given month and year where an ignition was not recorded. This process constitutes the dataframe for training the STWIP. For the 0‐labelled samples, dates prior to ignition (1‐labelled sample) of an i.loc$i.loc$, are chosen since historical ignition could have significantly tampered with temperature, fuel and vegetation, rendering later dates deceptive for use as 0‐labelled training samples. It is worth noting that although we assume true absence points, these 0‐labelled samples are pseudo‐absence points since it is unknown if ignition could not occur (there was no potential for ignition) or simply did not occur (there was no source of ignition) in that historical date and i.loc$i.loc$.SPATIO‐TEMPORAL WILDFIRE ESTIMATION MODELAfter data construction, the dataframe is fed into STWIP as input data following some transformations discussed herein. The input data is cleaned, missing values are filled with an average of their nearest neighbours. A major part of training data processing includes rescaling the features to have the properties of a standard normal distribution (μ=0,σ=1$\mu = 0, \sigma = 1$). The need for rescaling arises as features are multivariate with different units. Also, since feature magnitudes in instance xi${\bf x}_{i}$ play a role in the updates applied to the weights during gradient descent, rescaling becomes important. This standardisation is implemented using the Z‐score as follows:3z=x−μσ.\begin{eqnarray} z = \dfrac{x - \mu }{\sigma }. \end{eqnarray}Then STWIP predicts the expected ignition potential of a spatial location in period j as discussed further.Spatio‐temporal wildfire ignition probability predictorThe aim is to train a neural network with the problem objective formulated as follows. Given a collection of sample points i with geospatial coordinates i.loc$i.loc$ of (lat,lon) ∈ historical ignition data, where features of the sample point i are known, we aim to predict the potential of a wildfire ignition at periodic intervals. We propose a model based on supervised learning of spatial, spatio‐temporal and temporal features to capture complex and non‐linear interactions between WPVs using a deep neural network (DNN).The DNN is the prediction algorithm of the STWIP and unlike traditional methods of wildfire estimation with simple logistic regression [18, 35], the DNN is capable of modelling non‐linear correlations between the WPVs as illustrated in Equation (4), and can update the network's basis functions in specific input space directions.4ŷ=σ∑h=1HwohTh∑i=1DwhiT∗xi+wh0+wo0,\begin{eqnarray} \widehat{y} = \sigma {\left(\sum _{h=1}^{H} w_{oh}^{T} h{\left(\sum _{i=1}^{D} w_{hi}^{T} * x_{i} + w_{h0} \right)} + w_{o0} \right)}, \end{eqnarray}where w is the vector of adjustable weight parameters, with input variables xi$x_{i}$, σ is a threshold function, and {i,h,o}$\lbrace i, h, o \rbrace$ represent the input, hidden, and output layers. By adjusting the weight vector through different training epochs the predicted labels are mapped closer to the target labels, estimating the probability of potential wildfire ignition, πi,j$\pi _{i,j}$, as follows:5πi,j=f(x).\begin{eqnarray} \pi _{i,j} = f({\bf x}). \end{eqnarray}The STWIP architecture is a three layer fully connected network as shown in Figure 3, utilising the Adam optimiser, ReLU activation, and softmax activation at the output layer.3FIGUREInputs and predicted outputThe hidden layers' (12,3) neurons, respectively, are chosen to avoid over‐fitting and enhance prediction accuracy. The data input, x, is fed into the input layer. The output layer consists of two neurons that output probabilities of potential ignition/non‐ignition in one hot encoded format. The network is trained and minimised over the cross‐entropy loss. The trained STWIP is illustrated in Algorithm 1 in Appendix A.5.Wildfire spread estimationIn modelling wildfire behaviours including spread, software such as Prometheus and Burn‐P3 have been developed, but however, may require predefined inputs such as initial ignition grids from all historical fires, the different ecoregions, percentage of escaped fires and more, which may not be readily available to the user. In literature, models such as the FLAME [36] have been developed to rely on observable field assessments to consider areas of high fire spread rates. In refs. [37, 38], the developed model seeks to attain the fire front using a variation of the Thomas Equations shown in Equations (6) and (7).6Vf=k(1+Vw)ρb\begin{align} &V^{\rm f} = \frac{k(1+V_{\rm w})}{\rho _{\rm b}} \end{align}7ri,j,ω,tf=ri,j,ω,t−1f+Vω,tfΔtcos(ϕi,j,ω,tw)\begin{align} &r_{i,j,\omega ,t}^{\rm f} = r_{i,j,\omega ,t-1}^{\rm f} + V^{\rm f}_{\omega ,t} \nobreakspace \Delta t\nobreakspace \text{cos}(\phi ^{\text{w}}_{i,j,\omega ,t}) \end{align}where Vw is wind speed, k is fire‐type parameter, ρb is the bulk density, rf is the radius from the initial ignition point to the fire boundary, and ϕw is wind direction.However, if a wildfire ignites in a cell i in period j, its spread rate depends on surrounding fuel types and wind speed, which can be captured by the wildfire‐fuel spread characteristics. Hence, we adapt an approximate radial spread rate using the fireline assessment method [36], that can be determined by assessing the fuel type and wind speed at each HRRR grid point nearest to the potential wildfire ignition location. In this paper, instead of arbitrary values of spread rates, practical datasets that adapt the considered geographical area to different fuel types is utilised.The study area is mapped, by a consulted fire expert, Robert Ziel, to three common fuel types namely crown, litter, and grass as illustrated in Table 1 which also shows the coverage of each fuel type in our study area in northern California. Hence, this paper considers three common vegetation/fuel types (crown, litter, and grass) with spread rates modelled as a function of wind speed, W, as in Equation (8) and as shown in Figure 4. Note that in the case of multi‐fuel types such as litter and crown, the fuel type with higher spread rate was chosen. Constant but atypical wind speed directed towards the power system components is assumed, in order to account for the worst case scenarios of wildfire spread in the spatio‐temporal assessment.8ωgrass=14.4(W)1.232,ωcrown=4.87(W)1.146,ωlitter=1.03(W)1.213.\begin{eqnarray} \omega _{\sf grass} = 14.4(W)^{1.232},\nobreakspace \nonumber \\ \omega _{\sf crown} = 4.87(W)^{1.146},\nobreakspace \nonumber \\ \omega _{\sf litter} = 1.03(W)^{1.213}. \end{eqnarray}Armed with the potential rate of spread of the wildfire, utilities are able to optimise operations based on parameters such as expected distance and the time it takes a potential ignition to reach critical grid components.1TABLERelating the land‐use features to fuel typeValueLabelFuelStudy area coverage1Evergreen needleleaf forestLitter/crown46.139%2Evergreen broadleaf forestLitter/crown0.000%3Deciduous needleleaf forestLitter0.000%4Deciduous broadleaf forestLitter0.000%5Mixed forestLitter/crown0.000%6Closed shrublandsLitter/crown0.000%7Open shrublandsLitter/crown0.000%8Woody savannasGrass11.611%9SavannasGrass14.306%10GrasslandsGrass9.583%11Permanent wetlandsBarrier0.000%12CroplandsBarrier/grass17.028%13Urban and built‐upBarrier0.722%14Cropland/natural vegetation mosaicBarrier/grass0.000%15Snow and iceBarrier0.000%16Barren or sparsely vegetatedBarrier0.028%17WaterBarrier0.583%18Wooded tundraLitter/crown0.000%19Mixed tundraGrass0.000%20Barren tundraBarrier0.000%4FIGURERate of spread as a function of wind speed (1 ch/h = 0.005588 m/s)POWER GRID WILDFIRE RISK ASSESSMENT MODELThis section presents the proposed model for the power grid risk assessment, utilising the outputs of wildfire estimation model presented in Section 3. The wildfire potential ignition map (ignition probability map), produced by the STWIP, aids in proactive de‐energisation to prevent endogenous fires caused by power system failure [28] while the spread estimation aids improvement in adaptive operation of power grid against exogenous wildfires [15]. Specifically, a set of grid component outage scenarios are first generated by incorporating the output parameters of the first stage estimation model with GIS information of the power grid. In particular, given πi,j$\pi _{i,j}$, scenarios are sampled given the distribution of the wildfire potential ignition map and potential ignition locations, generating expected scenarios for the power system risk assessment model. Note that the granularity of πi,j$\pi _{i,j}$ can be improved to hourly depending on user application. In this paper, we estimate the hourly probabilities from πi,j$\pi _{i,j}$ as follows:9(1−pi,h)H=(1−πi,j)\begin{equation} (1-p_{i,h})^{H} = (1-\pi _{i,j}) \end{equation}where pi,h$p_{i,h}$ is the hourly probability of potential wildfire ignition in i, and H is the cardinality of hours in day j. Based on these scenarios, three risk metrics, namely, critical response time, scenario based damage cost, and the expected damage cost are calculated to assess risk.Power grid outage scenario generationWe aim to generate the outage scenario of grid component c at time t of operational day j of the year. Assume that the wildfire ignition happens at time t∗=0$t^*=0$, and we aim to assess the operation of power grid for the subsequent 24 h after the potential incident. In other words, the utility operator's thought process is: “if the potential wildfire occurs given scenario, s, and I have knowledge of the spread rates given s, I should estimate what component outages can be induced or motivated by this fire so I can be better prepared for such scenarios”.Let πs$\pi _{s}$ denote the probability of occurrence of scenario s corresponding to a set Ijs$\mathcal {I}^s_j$ of potential ignition locations of day j. The spreading rate ωis$\omega _i^s$ of the ignition in location i in scenario s is obtained by using the spread model presented in Section 3.2 with the corresponding values of forecast wind speed and fuel types around i. The GIS data of the power grid is mapped into the considered area. The characterisation of a wildfire induced (exogenous) grid outage scenario is illustrated in Figure 5. In particular, the component (e.g. transmission line) is assumed to be damaged if the potential fire crosses its safety zone defined by Δc$\Delta _c$ and the status of power grid component c is characterised by a scenario dependent parameter δc,ts$\delta ^s_{c,t}$ as:10δc,ts=0,ifmini∈IjsDci−ωisΔt>Δc1,ifmini∈IjsDci−ωisΔt<Δc\begin{equation} \delta ^s_{c,t}= {\begin{cases} 0, & \text{if}\nobreakspace \min \limits _{i \in I^s_j} D_{c}^{i} - \omega _i^s \Delta t &gt; \Delta c \\ 1, & \text{if}\nobreakspace \min \limits _{i \in I^s_j} D_{c}^{i} - \omega _i^s \Delta t &lt; \Delta c \end{cases}} \end{equation}where Δt=t−t∗=t$\Delta t = t- t^*= t$ (t∗=0$t^*=0$) is the potential duration of the wildfire spread, Dci$D_{c}^{i}$ is the Euclidean distance from the potential ignition point i to the grid component c, and ωisΔt$\omega _i^s \Delta t$ is the spreading radius of the wildfire from its ignition point. Note that Equation (10) considers potential wildfire ignition with spread closest to component c, since multiple ignition points can possibly occur in a scenario s, which was reportedly the case in the infamous Campfire. Also, when a component is on outage (δts=1$\delta ^s_t=1$), we assume it continues to be out until the end of the considered operation horizon. The value of Δc$\Delta _c$ can be adapted from numerical determination of the acceptable safety distance [39], which furnishes a detailed thermodynamics of wildfire effect on system components, informed by flame characteristics and a vulnerability threshold. The safety distance is informed by flame characteristics and a vulnerability threshold, and is the distance between the transmission line and the fire at which the thermal radiative flux is less than a given threshold, Φthresh$\Phi _{\text{thresh}}$. The threshold value is set to the vulnerability of transmission lines. The safety adapted distance is determined by the following correlation:11Dx(opt)=D|1−exp−pthresh2Llf,\begin{equation} D_{x} (\text{opt}) = D^{|} {\left(1-{\rm exp} {\left(-p_{{\rm thresh}} \frac{2L}{l_{{\rm f}}} \right)} \right)}, \end{equation}where pthresh is a pre‐determined empirical parameter for each Φthresh, lf is the flame length, 2L is the width of fire, and12D|=lfcosγ−4Φthresh2+(BTf4ετ)22Φthresh+Ifsinγ,\begin{align} D^{| } = \frac{l_{{\rm f}} \text{cos} \gamma \sqrt {-4 \Phi _{{\rm thresh}}^{2} + (BT_{{\rm f}}^{4}\varepsilon \tau )^{2}}}{2 \Phi _{{\rm thresh}}} + I_{{\rm f}} \text{sin} \gamma , \end{align}where τ is the atmospheric transmissivity, ε represents flame emissivity, B is the Boltzmann constant, and Tf is the average temperature of the flame.5FIGUREWildfire‐induced outage scenario generationMetrics for power grid wildfire risk assessmentThe following metrics are developed to aid utility decision making process and operational strategies in the wake of a wildfire threat. Note, since the metrics are used for a particular operation day j of the grid, we omit the notation j from hereon for simplifying the notation.The critical response time (Δt¯$\overline{\Delta t}$)This metric furnishes the time period within which utility operators can make operational changes to minimise economic damages before power shutoff is absolutely necessary. It is a function of the distance from the potential wildfire ignition point i to power system component c (see Figure 5), and the wildfire rate of spread ωis$\omega ^{\rm s}_i$ as follows:13Δt¯=min∀i∈Is,s∈SDci−Δcωis.\begin{eqnarray} \overline{\Delta t} = \min \limits _{\forall i\in I^{\rm s}, s \in \mathcal {S}} \dfrac{D_{c}^{i} - \Delta _ c}{\omega ^{\rm s}_i}. \end{eqnarray}Note the importance of this metric since aspects of vegetation, fuel, and velocity of wildfire spread, based on the spreading model in Equation (8), is incorporated into a time measure for optimising utility actions pre‐wildfire. The metric inadvertently provides a time estimate before the potential ignition will pose a risk, and serves in two ways depending on application. First, if Δt¯$\overline{\Delta t}$ is <<$&lt;&lt;$ threshold (utility defined, associated with Δc$\Delta _c$), then ignitable location is close to the power system component, ignition is possible within Δc$\Delta _c$ and components should be de‐energised to avoid being sources of ignition for endogenous wildfires. Secondly, if Δt¯$\overline{\Delta t}$ is >>$&gt;&gt;$ threshold, i.e. distance of potential ignition is far enough from component, the utility can afford to wait pre‐wildfire and not cut off power to customers, say H hours before actual ignition, which is mainly where revenue is lost during wildfire threats [10]. Also for the latter depending on the critical time, utilities can operate and strategise before any potential exogenous wildfire fronts induce component outages.The scenario based damage costThe operational damage cost of a particular scenario s is the result of the optimal response of the power grid against the realised outage scenario. The operational damage cost includes losses in revenue accruing to the power utility due to lost opportunity costs arising from load curtailment, including power shutoff to customers and intended unavailability of power components, e.g. power lines, from wildfire threats. In the case of the power transmission grid, such scenario based damage cost can be defined as the optimal value of the following security constrained optimal power flow as below:14costs=min∑t∈T∑b∈BVOLLb,tLCb,ts.\begin{eqnarray} \mbox{cost}_s = \min \quad \sum _{t\in T} \sum _{b \in \mathcal {B}} \mbox{VOLL}_{b,t} \mbox{LC}_{b,t}^s. \end{eqnarray}15s.t.Pl,ts=θb,ts−θb′,tsxl(1−δl,ts),∀l=bb′∈L\begin{eqnarray} \text{s.t.} \quad P^s_{l,t} = \dfrac{{\left[\theta ^s_{b,t}- \theta ^s_{b^\prime , t}\right]}}{x_{l}} (1-\delta ^s_{l,t}), \nobreakspace \forall l = bb^\prime \in \mathcal {L} \end{eqnarray}16Pg,b,ts−Pd,b,t+LCb,ts=∑bb′∈LPbb′,ts,\begin{eqnarray} P^s_{g,b,t} - P_{d,b,t} + \mbox{LC}_{b,t}^s = \sum \limits _{bb^\prime \in \mathcal {L}} P_{bb^\prime ,t}^{s}, \end{eqnarray}170≤LCb,ts≤Pd,b,t,∀b∈B,∀t∈T\begin{eqnarray} 0 \le \mbox{LC}^s_{b,t} \le P_{d,b,t},\nobreakspace \forall b \in \mathcal {B}, \forall t \in \mathcal {T} \end{eqnarray}18(1−δg,b,ts)P̲g,b≤Pg,b,ts≤(1−δg,b,ts)P¯g,b,∀g∈G,∀b∈B,∀t∈T\begin{eqnarray} (1-\delta ^s_{g,b,t}) \underline{P}_{g,b} \le P_{g,b,t}^s \le (1-\delta ^s_{g,b,t}) \overline{P}_{g,b},\nobreakspace \nonumber \\ \forall g \in \mathcal {G}, \forall b \in \mathcal {B}, \forall t \in \mathcal {T} \end{eqnarray}19−(1−δl,ts)P¯l≤Pl,ts≤(1−δl,ts)P¯l,∀l∈L,∀t∈T\begin{eqnarray} -(1-\delta ^s_{l,t}) \overline{P}_{l} \le P^s_{l,t} \le (1-\delta ^s_{l,t}) \overline{P}_{l}, \nonumber \\ \forall l \in \mathcal {L}, \forall t \in \mathcal {T} \end{eqnarray}20θ̲b≤θb,ts≤θ¯b∀b∈B,∀t∈T,\begin{eqnarray} \underline{\theta }_{b} \le \theta ^s_{b,t} \le \overline{\theta }_{b} \quad \forall b \in \mathcal {B}, \forall t\in \mathcal {T}, \end{eqnarray}21Pg,b,ts−Pg,b,t−1s≤RUg,b,∀g∈G,∀b∈B,∀t∈T,\begin{eqnarray} P^s_{g,b,t} - P^s_{g,b,t-1} \le RU_{g,b},\nobreakspace \forall g \in \mathcal {G}, \forall b \in \mathcal {B}, \forall t \in \mathcal {T}, \end{eqnarray}22Pg,b,t−1s−Pg,b,t≤RDg,b,∀g∈G,∀b∈B,∀t∈T.\begin{eqnarray} P^s_{g,b,t-1} - P_{g,b,t} \le RD_{g,b},\nobreakspace \forall g \in \mathcal {G}, \forall b \in \mathcal {B}, \forall t \in \mathcal {T}. \end{eqnarray}where B$\mathcal {B}$, L$\mathcal {L}$, G$\mathcal {G}$, and T$\mathcal {T}$ denote the set of transmission buses b, transmission lines l, generators g, and time slots t. The objective function (14) is to minimise the load curtailment cost over all the sets of buses and the scheduling horizon where LCb,ts$\mbox{LC}^s_{b,t}$ denotes the load curtailment in bus b in time t in scenario s and VOLLb,t$\mbox{VOLL}_{b,t}$ denotes the value of loss load. The optimisation is subject to the following constraints. The DC power flow constraints of the transmission lines l connecting bus b and b′$b^\prime$ is captured in Equation (15) where the scenario based outage status of the line l is represented by a binary parameter δl,ts$\delta ^s_{l,t}$. In particular, if the line is potentially damaged by the modelled wildfire, i.e. δl,ts=1$\delta ^s_{l,t}=1$, there is no power flow on the line. Power balance constraint in bus b is captured in Equation (16) where the power Pg,b,ts$P^s_{g,b,t}$ generated by g in b, minus the bus power demand Pd,b,t$P_{d,b,t}$, plus load curtailment LCb,ts$\mbox{LC}^s_{b,t}$, equals the total power flowing out of b. Additionally, the load curtailment at any bus must remain within the limitations of the total demand at that bus, which is presented in Equation (17). The power generated by g is constrained by its minimum and maximum capacity as in Equation (18). The power flow over the line l is constrained by its thermal capacity P¯l$\overline{P}_l$ as in Equation (19). On a similar note, the upper and lower limit constraints of the bus phase angle θb,ts$\theta ^s_{b,t}$ are described in Equation (20). Furthermore, the limitations RUg,b,RDg,b$RU_{g,b}, RD_{g,b}$ of the generators' ramping up and down rates are furnished in Equations (21) and (22) respectively. Note that our framework can also apply to power distribution network where DC power flow constraints are replaced by the DisTFlow model considering line outage status [40].The expected power system damage costThe expected damage cost of power systems [41] for a given set of wildfire motivated outage scenarios S is calculated as:23ECOST=∑s∈Sπs×costs,\begin{eqnarray} \text{ECOST} = \sum _{s \in \mathcal {S}} \pi _s \times \mbox{cost}_s , \end{eqnarray}where costs is obtained by solving the optimal response of the power grid against the wildfire motivated outage scenario s, e.g. solving optimisation problems (14)–(22) for the case of transmission networks. Hence, the ECOST$\text{ECOST}$ metric, in addition to estimated infrastructure damage costs, can aid utility decisions of wildfire mitigation vs. restoration, i.e. informing the important question: should the utility use the “let‐burn” strategies, since oftentimes the utility is burdened with the economic decision of either fighting wildfires or employing the “let‐burn strategy” where the wildfire is allowed to burn and damages are rebuilt/restored [42]. If the firefighting costs are greater than the expected damage costs (operational, infrastructural and otherwise), the utility could utilise the “let‐burn” strategy.NUMERICAL RESULTSSimulation setupWe consider an area covering approximately 200km2$200\text{ km}^{2}$ in Northern California and spanning latitudes 38∘49′17.616′′N$38^{\circ } 49^{\prime } 17.616^{\prime \prime }\text{ N}$ to 40∘46′7.14′′N$40^{\circ } 46^{\prime } 7.14^{\prime \prime }\text{ N}$, and longitudes 120∘11′52.8′′W$120^{\circ } 11^{\prime } 52.8^{\prime \prime }\text{ W}$ to 122∘43′55.2′′W$122^{\circ } 43^{\prime } 55.2^{\prime \prime }\text{ W}$. The chosen area reflects homogeneous climate yet spatially diverse in fuel and vegetation as illustrated in Figure 15 detailed in Appendix A.3. The STWIP was trained and validated using a 70% and 30% split training data of 10,900 samples, and compared to other data‐based conventional baselines [43, 44] including decision tree, boosted decision tree, and linear regression. We first provide the wildfire estimation results over the studied area to illustrate the effectiveness of the first stage of the framework, i.e. the STWIP model.Wildfire estimation analysisThe performance analysis in Figure 6 shows the average accuracy for training and validation of the STWIP was (98.31% and 97.0%), while the boosted decision tree was (93.27% and 92.0%), both outperforming other baselines. Also, the proposed STWIP achieves the best performance with an area under the receiver operating characteristic curve (AUC) of 0.995. Note that the AUC describes the model trade‐off in terms of sensitivity and specificity. This performance is followed again by the boosted + tree algorithm with an AUC of 0.965 and the regression with an AUC of 0.903 respectively.6FIGUREAccuracy of baselinesNext, we test STWIP with the 2018 year, comparing results with the actual wildfire occurrence currently available in ref. [45]. In the test data we use the 15th day of the month as it is representative of its wildfire characteristics. Thus, we seek to obtain similar patterns of spatial density and temporal distribution.Results in Figure 7 show that predicted hotspots are similar to the actual historical test year, clustered between latitudes and longitudes (39° 30′ 00′′$^{\prime \prime }$ N , 122° 30′ 00.0000′′$^{\prime \prime }$ W) and (39° 30′ 00.0000′′$^{\prime \prime }$ N , 121° 30′ 00.0000′′$^{\prime \prime }$ W). The central valley area of northern California has less ignition clusters, which is attributed to limited elevation and fuel.7FIGURETest year: actual (left) vs. predicted spatial ignition patternSimilarly, the temporal results are analysed monthly as furnished in Figure 8, showing that the estimated temporal distribution well follows the test year's actual temporal wildfire distribution (approximately Gaussian). Hence, by employing the STWIP for analysis as opposed to the conventional utility predefined fire threat areas and fire threat levels as detailed in Appendix A.7, power systems can further improve wildfire forecast and analysis towards actual expectations.8FIGURETest year: actual(left) vs. predicted temporal ignition patternThe percentage weighted impact of WPVs on the wildfire ignition status is presented in Figure 9. In particular, the WPVs are evaluated based on their weighted influence on wildfire occurrence. Terrain and temperature, and cloud type and historical ignition, have the highest and least influence, respectively. Also, humidity seemingly influenced daily wildfire ignition maps produced by the predictor especially in the central valley of northern California. This suggests which measurement types (sensors in monitoring corridors) that the power utility should invest for enhancing situational awareness against wildfire. The performance of STWIP is further underlined as linear methods such as regression do not well capture terrain which is indeed a high impact feature [46].9FIGUREInfluence of wildfire predictor variables: STWIP captures the magnitude of this influence better than the widely utilised linear regression. For instance, the influence of land‐use and terrain which are well known influential factors in wildfire occurrenceIllustrating wildfire aware power grid operation analysisConventionally, utility often uses region‐scale and deterministic threat level analysis as discussed in Section 1.1 and detailed in Appendix A.7.In this situation as further illustrated by Figure 10, as seen in the “conservative” utility case, the utility will have an extreme alert in the red area since there are more wildfire threats as opposed to the elevated threat area (orange highlight). The customers in the area with extreme alert will have their power shut off for the duration of the wildfire threat, including customers up north (relatively farther) from the wildfire threat cluster. The magnitude of the shut off can be visualised given the size of the predefined threat areas in a sample utility wildfire awareness issue as shown in Figure 18 in Appendix A.7. However, the potential ignition map and spread parameters provided by the first stage estimation model can be used to analyse the risk of over de‐energisation motivated by power component failure‐ignited wildfires and the risk of outages induced by exogenous wildfire. With the granularity in spatial detail of the wildfire potential probability maps, the spread model, and the proposed risk assessment, the utility can optimise the time before shut off is necessary in exogenous fires, and also emulate the distance between a potential ignition location (ignitable location) and the power equipment in endogenous/equipment‐induced wildfires.10FIGUREIllustration of the casesThe analysis is conducted on a 24‐bus test system mapped to span the length and breadth of the studied area as detailed in Appendix A.6, however, this analysis can be done on any transmission or distribution system given complete system details. We consider two case studies which deviate from the power system normal operation when there are no wildfire threats. In Case 1, the test system is simulated with the current conventional “conservative” utility approach of threat area and levels discussed in the Section 1.1 and detailed in Appendix A.7. In this case, all the power components located in the pre‐defined elevated threat area as illustrated in Appendix A.7 are intentionally outaged whether or not they are in the direct vicinity of high wildfire potential. This simulates current utility procedure to prevent endogenous wildfires [10]. In Case 2, the wildfire analysis and test system de‐energisation is based on the wildfire potential ignition map produced by STWIP as described in Section 4 aiming to improve spatial granularity and optimise (shorten) the time span of utility de‐energisation. The data used in simulation is based on November 10, 2018. The value of lost load is set to 1000 $/MWh. Details of the components that are out of service in the three case studies are shown in Table 2.2TABLEWildfire motivated de‐energisationCase studyTransmission line outagesGenerator outagesCase 1L1‐4, L6‐8, L14, L19, L24‐33G1‐4, G15‐29Case 2L4, L8, L19, L23‐24, L28, L31‐33NoneAssessing risk of outages induced by exogenous wildfireFor exogenous wildfire induced outage risk analysis, the probabilistic ignition map is used to generate wildfire ignition scenarios and simulated spreading pattern, thus modelling exogenous wildfire‐induced damages on power grid components. The expected damage cost, ECOST, as illustrated in Figure 11, represents the aggregate analysis for one operational year of the test system in the studied area. It shows that the power system is highly vulnerable during summer time from June to September, and quite low during winter time from December to March. However, the risk of wildfire induced outage still exists during non‐summer times, which can be explained by the impacts of the time independent WPVs such as land‐use and terrain. Hence, an efficient allocation of utility wildfire monitoring resources should be based on spatio‐temporal analysis of wildfire occurrence, e.g. monitoring grid and vegetation should be done more frequently during high risk period.11FIGUREExpected damage cost over the period of 1 year: showing sustained wildfire risk during non‐summer monthsEnhancing de‐energisation decision for mitigating power component failure‐ignited wildfiresWildfires can be ignited by electric power line faults that cause arcing in a high‐heat release of energy. Such incidents are majorly caused by ignitable vegetation contacting power lines. Indeed, the correlation between the wildfire ignition probability map and electric power failures motivates the use of proactive de‐energisation of equipment as a preventive measure [28]. We aim to illustrate the improvements in de‐energisation using the proposed STWIP, which is more granular and stochastic, over conventional utility approach.The proposed framework aids in enhancing de‐energisation and estimating the potential cost of wildfire occurrence as detailed further.The total system energy consumption, total loadshed, and loadshed‐bus localisation of the three cases are shown in Figure 12. The total energy demand of the system is 54,358.679 MWh, with Case 1 supplying 29,449.051 MWh due to large amounts of load shedding, 45.8%, resulting from the conventional threat area and threat level methods. Relative to Case 2, the power grid response avoids a large amount, 19,798 MWh, of unnecessary load shedding. Hence, a more detailed wildfire potential ignition map provided by the proposed granular analysis results in less conservative shutoff, i.e. only components in the high wildfire vicinity are proactively de‐energised to prevent component failure‐caused wildfire [28].12FIGUREDemand served and load shedding for Cases 1 and 2: illustrating that a detailed wildfire potential ignition map provided by the proposed power grid wildfire risk assessment model results in less conservative proactive de‐energisationTable 3 presents load shedding cost, and generation cost for all cases. For the normal system operation, there are no load shed costs and generation costs are $568,084.40 The total costs for Case 1 is high due to the amount of load shed and the increase in production of expensive online generators.3TABLECosts for Cases 1 and 2 ($)Load shedding cost ($)Generation cost ($)Case 1181,591.25537,969.01Case 237,263.75537,991.32In addition, the framework aids improve the resilience of the system by spatio‐temporally informing the disaster progression phase of the resilience trapezoid as illustrated in Figure 13, hence reducing the “dip” in the resilience curve [47].13FIGUREProfile of load served in the system. The proposed power grid wildfire risk assessment model aids in enhancing system robustness and hence resilience, as evident in Case 2 as opposed to Case 1Specifically, in Case 1, a large and sudden drop of the percentage load served (performance indicator) is observed. This is because without spatio‐temporal analysis, the utility performs conservative forced outages as soon as a wildfire threat is observed in their pre‐defined regional threat areas, which in this simulation is set to the beginning of the scheduling horizon at t∗=0$t^{*}=0$. The percentage load served in Case 2 is observed to reduce over time. This is possible due to the improved granularity provided by spatio‐temporal analysis where expectations of wildfire parameters such as distance, spread rate, and the critical response time have been pre‐estimated as discussed in Section 4.2.1. Hence, with a grasp of the expected critical response times, the utility operations have increased and informed time flexibility in forcing component outages.CONCLUSIONThis paper proposed a comprehensive spatio‐temporal framework for power system wildfire risk analysis. The framework includes two sequential models, where the first model estimates the granular and spatio‐temporal potential wildfire probability and spread based on influential parameters such as vegetation and fuel, wind speed, geographical, and meteorological variables, while the second model leverages the estimated probabilistic ignition maps in order to analyse system risk from exogenous wildfire and to enhance power system de‐energisation in mitigating endogenous fires induced by power equipment failures. Numerical results show that lower forced electricity outages to customers can be achieved by increased granularity in spatial locations in utility service areas. Hence, the framework significantly improves utility de‐energisation decision compared to the current “conservative” threat area approach In addition, the framework aids to improve system resilience and utility revenue and prioritise resource allocation given increased localisation of high wildfire potential. Future work will entail using the proposed model as a base in proposing a self‐sufficient model for complete wildfire prediction and detection for electric power utilities using recent state‐of‐the‐art sensor developments and designs in wildfire detection. Part of these future studies are already formulated but not included in this paper to enable a concise and clear exposition.CONFLICT OF INTERESTThe authors declare no conflict of interest.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.REFERENCESCouncil of Economic Advisers: Economic Benefits of Increasing Electric Grid Resilience to Weather Outages The Council, Executive Office of the President, The White House, Washington, D.C. (2013)https://www.iii.org/table‐archive/21424. Accessed 29 March 2022Ramsey, M. 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Accessed 2 April 2022Calviño‐Cancela, M., Chas‐Amil, M.L., García‐Martínez, E.D., Touza, J.: Interacting effects of topography, vegetation, human activities and wildland‐urban interfaces on wildfire ignition risk. For. Ecol. Manage. 397, 10–17 (2017)Umunnakwe, A., Huang, H., Oikonomou, K., Davis, K.: Quantitative analysis of power systems resilience: standardization, categorizations, and challenges. Renewable Sustainable Energy Rev. 149, 111252 (2021)https://www.academia.edu/13981064/Data_for_the_IEEE_24_bus_Reliability_Test_System. Accessed 2 April 2022Carbon, K., DAgostino, B.: Catastrophic Risk Mitigation through Analytics: Wildfire Threat Index. Sempra Energy and San Diego Gas & Electric, San Diego, CA (2015)San Diego Gas & Electric Company Fire Prevention Plan, pp. 1–44 (2018). https://www.sdge.com/sites/default/files/documents/SDGE_Fire_Prevention_Plan_2018.pdf. Accessed 29 March 2022AAPPENDIXA.1  Spatial features detailsWe assume that land‐use data contains information on fuel type, fuel load, fuel continuity as illustrated in Table 1 while terrain informs the topography of the ecoregion. The land‐use and terrain are examples of spatial features and usually do not change significantly over the short‐term, hence the name static. Land‐use refers to the natural vegetation and the various ways in which humans make use of and manage the land and its resources. The terrain represents the topography of the geographical area. Hence, input features employed are not exhaustive but motivated from wildfire studies.A.2  Same climate assumptionIn this work, we assume same climate distribution over the period which we collect historical data for analysis. This assumption is enabled by similar distribution in spatial and temporal data. In the said period, the latter is approximately Gaussian, while the former is as furnished in Figure A.1.A.1FIGURESame climate assumption: dimilar distribution of historical data‐points latitude and longitudeA.3  Spatio‐temporal wildfire estimation model: setupLand‐use was obtained from the NOAA's HRRR model and ranges from evergreen needleleaf forest to barren tundra, assigned values [1, 20], while Terrain input gives insight into the topography and elevation of the area with values in the range [6, 2603] m as shown in Figure A.2. Temporal variables were obtained from the Open Weather Map database by building an application programming interface scrapper in python, to make data requests to the open weather map online weather database using the http protocol. Requested meteorological data includes temperature levels, rain, humidity, cloud, atmospheric pressure, visibility, month, and sunshine hours, where numerical values are assigned to qualitative features, for instance, the daily weather types (clear, cloudy, hazy, drizzly, rainy) are assigned real values in the ratio [0.1, 0.3, 0.5, 0.7, 0.8] respectively. Historical wildfire ignition records were obtained for the multi‐year period of analysis (1996–2016,2018) from the U.S. Geographical Survey database and provides the samples of the training and test data, respectively.A.2FIGUREThe spatial features of studied geographical area: terrain (left) and land‐use (right)A.4  Temporal probability detailsThe temporal probabilities of wildfire ignition is also calculated from historical data with the assumption of a same climate period as shown in Figure A.3.A.3FIGUREWeekly temporal distribution of historical wildfire occurrenceA.5  The STWIP algorithm1ALGORITHMBatch learning based STWIP1:Given a training set (x1,y1),…,(xn,yn)$({\bf x}_{1}, y_{1}), \ldots, ({\bf x}_{n}, y_{n})$ with features in instances xi${\bf x}_{i}$ ∈Rn$\in R^{n}$, with label yi$y_{i}$ ∈ {0,1}$\lbrace 0, 1 \rbrace$2:Input(X,Y): A set of labelled input features [temp, ..., month], of training samples θ, batch size b3:Output: the spatio‐temporal ignition probability maps.4:Hyper‐parameter selection5:function Predictor_Training$Predictor\_Training$X, Y6:Shuffle ← enabled7:count_max ← θb${\frac{\theta }{b}}$8:count ← 09:while count < count_max do10:for batch b in θ do11:STWIP ← DNN learns (b×$b\times$[temp, ..., month])12:count ++$++$13:end for14:end while15:Compute accuracies16:Compute the ROC AUC metrics17:Apply STWIP to test samples18:returnWildfire potential ignition maps of πi,j$\pi _{i,j}$19:end FunctionThe trained STWIP, as presented in Algorithm 1, is then validated and utilised in the prediction for unlabelled test samples for a future period j. When the algorithm ends, the probability map of potential ignitions, πi,j$\pi _{i,j}$, is returned.A.6  Mapping bulk power grid to the wildfire potential mapThe IEEE 24‐bus reliability test system [48] that includes 24 buses, 38 lines, and 33 generating units is aligned to the ignition probability map as shown in Figure A.4. Also, to illustrate conventional power utility wildfire practices, the grid is divided into fire threat areas with extreme, elevated, and normal threat levels, while spatio‐temporal analysis employs the most probable generated scenarios.A.4FIGUREIEEE 24‐bus mapping into three wildfire threat areasA.7  Utility‐employed predefined fire threat areas and levelsElectric power utilities have carried out ground breaking work in modelling wildfire occurrence, including developing analytical tools such as the FPI and more [49].These indices, for instance the FPI, calculated at district level corresponding to three levels of wildfire threat alert, as shown in Fig. A.5, are efficient for planning decisions, however, they start to fall short in the day to day operational decisions for utilities as spatio‐temporal granularity is lost in these methods, i.e. the use of pre‐defined wide threat areas and few (extreme, elevated, normal) threat levels.A.5FIGUREA sample SDG&E wildfire awareness issueIn particular, the challenges posed by current utility techniques include the use of fire threat areas (FTAs), fire threat levels (FTLs), the independent analysis of the WPVs, and the exclusion of adequate past wildfire characteristics in analysis.As stated by Brian D'Agostino, SDG&E's director of fire science and climate adaptation: “we need to understand what the weather is doing in every canyon, every ridgetop all across the backcountry to really bring that level of customer safety and customer service”. Thus, the use of FTAs and FTLs can introduce ambiguity in utility analysis, such as the over allocation of resources, excess load shedding in risk assessment, and lengthened forced outages to customers, since the pre‐defined area may not be granular enough for operational wildfire analysis.Furthermore, the independent analysis of wildfire predictor variables introduces errors in estimation due to the exclusion of the effects of the interactions between these variables. For instance, for utility operations, when certain conditions (e.g. relative humidity ⩽15%, sustained winds and gusts ≥25 and 35 mph respectively, for a duration ≥6 h) are met, operational decisions, e.g. all reclosers being turned off, sensitive relay settings being enabled [50], are taken. However, these assessments of environmental conditions are made independently, leaving little room for evaluating how the interactions between variables drive wildfire potential. Moreover, data obtained from historic events provide increased information on spatial wildfire characteristics as demonstrated in this work. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "IET Generation, Transmission & Distribution" Wiley

Data‐driven spatio‐temporal analysis of wildfire risk to power systems operation

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© 2022 The Institution of Engineering and Technology.
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10.1049/gtd2.12463
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Abstract

INTRODUCTIONThe increasing magnitude and frequency of power outages induced or motivated by wildfires affects the operation of critical services and leads to lost opportunity costs [1]. The California Department of Forestry and Fire Protection estimates damages from the 2018 Woolsey and Camp fires to be about $4 and $11 billion respectively [2], with Campfire responsible for about 84 deaths [3]. Additionally, wildfire threats in October 2018 and 2019 led Pacific Gas and Electric (PG&E) to shut off power to a sizeable number of customers in extreme risk areas of northern California leading to lost opportunity costs when no wildfires occurred [4]. Subsequently, the 2020 Zogg fire saw PG&E facing 31 criminal charges, including manslaughter, for the utility's role in the fire that claimed 4 lives and destroyed more than 200 building properties [5]. More recently, the 2021 Dixie fire was caused by the blowing of two fuses when a Douglas fir fell on a PG&E line [6]. The fire gulped more than $630 million in suppression efforts and led to tangible losses including damages to approximately 1500 residential and commercial property, injuries, and fatalities [7].Background and motivationIn response to wildfire threats, utilities have significantly invested on wildfire monitoring systems and analytical tools, which generally rely on observations from remote automated weather stations to evaluate current weather conditions [8] that are disseminated and retrieved [9] from many sources such as Synoptic's Mesonet API. These data are then used to estimate and strategise for optimal operation in the face of wildfire threats, but with room for improvements. In fact, the decisions of a utility to shut off power to more than sixty thousand northern California customers in 2018 and nearly a million in 2019, was controversial [10]. It may be, however, impossible to assess if this was an overestimation of impact and utility resources (“conservative”), but the passing of the California Senate Bill 901 required states investor‐owned utilities with the California Public Utilities Commission to file wildfire mitigation plans, increasing research on the topic [11].Conventionally, electric power utilities have often performed fundamental analysis to indicate wildfire threat alert on coarse resolutions of spatial areas while not utilising the richness of historical data, evident in indices such as the fire potential index (FPI) [12]. This index, for instance, utilises a linear summation of present weather variables and fuels to provide threat levels (extreme, elevated, normal) for predefined regional‐scale threat areas. This may arguably lead to over‐estimation of risk, over‐allocation of operational resources, and consequently “conservative” risk analysis for utilities.Literature reviewStudies on wildfire prediction and estimation [13–15] have mainly focused on numerical quantification [16] and fire scale [17], often using techniques such as regression [18], in an effort to aid mitigation. In ref. [19], wildfire variables are studied to predict spatial patterns of ignition producing national‐level ignition risk maps. To aid pre‐wildfire planning, ref. [20] implements fire danger mapping system based on numerical weather prediction and derived moisture content of live fuels. Historical data for vegetation, climate, and locational features have been utilised in ref. [21] to predict the risk of wildfire ignition. However, these region‐specific wildfire models are simply aggregated over space or time with approximated/linear and spatially constant effects [22]. Hence, their accuracy can be affected by the limited integration of the non‐linear influence of variables, and similarly, do not fully utilise recent wildfire monitoring investments of grid utilities. Wildfire risk prediction has also been done where model performance using machine learning approaches have been evaluated [23]. Artificial intelligence techniques have also been effective for wildfire analysis and outperform conventional statistical methods [24–26]. Additionally, interactive maps have been garnering literary and industry application to supply information on wildfires in real‐time. For instance, in ref. [27], a real‐time fire prediction system is developed for visualising wildfire risk at specific locations based on a machine learning model. Although these methods prove effective, they generally have not been designed to integrate with the power grid operations.The effect of this on the power system side is the assumption of already progressing wildfires, while geographical uncertainties of spatio‐temporal variables are often assumed [28] and not investigated. For instance in ref. [29], energy dispatch is optimised assuming an already progressing wildfire. The same progressing wildfire assumption is applied in ref. [30] to dynamically change thermal ratings of power lines and in ref. [15] to optimise resource preparation.Approaches, contributions, and paper structureThis paper develops a deep learning based framework for analysing the expected spatio‐temporal impacts of stochastic wildfire threat on the power grid. The proposed framework, as shown in Figure 1, integrates a detailed spatio‐temporal wildfire analysis model to evaluate system risk. The model incorporates information from real databases towards potential wildfire ignition maps, as the spatio‐temporal wildfire “readiness” of a location does not necessarily imply an ignition until a fire source is applied. Therefore, a model is proposed to estimate the spatio‐temporal probability of a potential wildfire ignition which can be applied to power transmission and distribution systems. The advantage in modelling potential ignitions pre‐wildfire is to prepare for critical scenarios and proceed with optimal strategies to better mitigate risks arising from extreme wildfire events, thereby reducing the propensity of outages and power shutoff to customers. As wildfires can be caused by power system failure or by exogenous causes (human, natural events), the applications of the estimation result are twofold. First, it provides spatio‐temporal risk for proactive de‐energisation against potential power system failure‐induced wildfire [28]. Second, it generates a spatio‐temporal spreading model for optimal grid operations against potential exogenous wildfires [15]. Depending on the application, risk metrics quantifying potential wildfire operational impact, power utility response time for mitigation, and strategy‐enabling metrics for mitigation vs. restoration, are developed in the second‐stage.1FIGUREStructure of spatio‐temporal wildfire risk assessment modelIn summary, the main paper contributions are as follows:We develop a comprehensive spatio‐temporal wildfire risk analysis framework using a data‐driven deep learning approach that efficiently incorporates publicly‐available historical wildfire and GIS data for estimating wildfire ignition risk and its impact on power grid.Novel quantitative risk metrics that capture potential effects of fuel, vegetation, and wind speed, on wildfire propagation are proposed, while the weighted impacts of wildfire predictive variables are furnished to serve utility operations and stakeholder strategies.The framework can provide information to power utilities towards optimising the grid operation, i.e. the proactive de‐energisation to prevent endogenous power system failure induced wildfire and the response strategy, e.g. “let‐burn”, against exogenous wildfire threats.The rest of the paper is organised as follows: overview of the proposed spatio‐temporal framework is outlined in Section 2 where the geographical formulation and data requirements are also discussed. In Section 3, the wildfire estimation model is discussed and the result utilised in the power grid risk assessment model as presented in Section 4, which also develops the quantitative power system risk metrics. Simulations are conducted and numerical results are illustrated on the IEEE 24‐bus test system as presented in Section 5, while the conclusions are drawn in Section 6.OVERVIEW OF THE PROPOSED MODELWildfires are influenced by a number spatial and temporal factors that can be unique in different geographical locations which can lead to inaccuracies in specified mathematical models. Hence, the objective of the proposed framework is to drive operational strategy with data‐driven situational awareness to wildfire. As in Figure 1, the framework consists of two sequential stages. First, the spatio‐temporal wildfire estimation model predicts the probability of potential wildfire ignition, utilising the spatio‐temporal wildfire ignition probability predictor model (STWIP), and estimates potential wildfire spread, producing important parameters such as ignition probability maps and the rate of spread of potential ignitions to critical power components. These parameters are then passed to the proposed power grid wildfire risk assessment model, which aims to optimise power system operations and risk assessment such that outage cost is minimised. The risk assessment model optimises power system operations by GIS‐enabled mapping of these parameters to the power network and generating wildfire threat scenarios. Part of the risk assessment model also includes proposed power system‐wildfire metrics that enable optimal operational strategies such as choosing mitigation vs. restoration (“let‐burn”). Both Stage 1 and 2 models incorporate effective wildfire analysis, enhancing power system resilience, reduction in customer outages, and hence, operational cost during wildfire threats.The rest of this section discusses the structure of the proposed model and data requirements, while the spatio‐temporal wildfire estimation and power grid wildfire risk assessment models are discussed in detail in the next two sections.Geographical structure of the modelA spatial location is a point i with geospatial coordinate i.loc$i.loc$ defined by a latitude and longitude (lat,lon) at any location in a grid cell. The grid cells here are 3 km × 3 km polygons which have uniform past spatio‐temporal wildfire characteristics and a centroid. Each grid centroid also has geospatial coordinates gc.loc$g_{c}.loc$. For instance, the past spatio‐temporal characteristics of a historical sample ignition occurred in i is obtained by its association with gc.loc$g_{c}.loc$ of the grid cell g∈G$g \in G$ in which it is situated, since the centroid is processed to bear the characteristics of g. Each grid has a set of historical wildfire ignition events with geospatial coordinates i.loc$i.loc$. These historical events, which form sample points in the training data, have a set of variables, x=[x1,x2,…,xD]${\bf x} = [x_{1}, x_{2}, \ldots, x_{D}]$, obtained for their unique i.loc$i.loc$ and dates of ignition. Here, D denotes the dimensionality. These wildfire‐informative variables are referred to as wildfire predictor variables (WPVs) and are usually sourced from weather stations geographically situated at locations of interest. Their interactions and correlation can be modelled towards wildfire prediction. They can vary spatially and/or temporally, are indicative of wildfire occurrence, and are often called explanatory variables [31].Data requirementsThe proposed framework proceeds with data pre‐processing and integration (solid green arrows), feature extraction and training the predictor (solid black arrows), these precursors are as illustrated in Figure 2 and discussed as follows.2FIGURESpatio‐temporal wildfire prediction modelData pre‐processingThis stage proceeds with obtaining the grid centroids together with spatial data, e.g. land‐use and terrain data, from databases such as the National Oceanic and Atmospheric Administration's High Resolution Rapid Refresh (HRRR) model [32].The temporal probabilities, πj$\pi _{j}$ of wildfire ignition, as shown in Appendix A.4, are also calculated in this stage from the US Geological Survey historical ignition data and can be used as a feature to improve estimation. This assumption of a same climate period is enabled by the similarity in the data distribution over the historical period of analysis as illustrated in Appendix A.2, Figure 14. Also in this phase, the python scrapper is coded to request and clean meteorological data for unique spatial locations on days of interest. These days of interest depend on user applications but for this work, meteorological variables on historical ignition and non‐ignition days are duely processed for training/validation of the predictor while forecasted meteorological variables are requested for days that wildfire potential is to be predicted.Data integrationThe next phase is data integration which proceeds in two levels. The first is the spatial integration, where i.loc$i.loc$ of historical ignitions are associated to gc.loc$g_{c}.loc$ to obtain the past ignition characteristics of g. The goal here is to enable spatial locations in the training data inherit wildfire attributes of the grid cell in which they are located. The second occurs after feature extraction during integration into python's pandas dataframes in preparation for training. This dataframe is a two dimensional data structure with columns of multivariate data. The month in which the training ignition sample occurred is incorporated as a feature to account for temporal relation of features, and is also critical to the utilisation of only one fundamental deep network.Feature extractionPast spatio‐temporal ignitionThis feature captures sequential changes in characteristics of spatial wildfire ignition over time and is crucial in the capability of the predictor to use one fundamental deep network. It is calculated from the historical wildfire database and is the initial (historical) ignition probability of a spatial location in the same climate period. To this end, we compute the past wildfire ignition probability mg,j$m_{g,j}$ of a grid cell g in period j of our comprehensive year. Since this attribute is inherited by all i in grid cell g, we refer to this attribute as mi,j$m_{i,j}$. Specifically, because the climate pattern of the multiple‐year‐dataset is assumed constant, the conditional probability of an ignition occurring in grid cell i given the study area, is used to calculate mi,j$m_{i,j}$ given that grid cells are a subset of the studied geographical area as in Equation (1).1mi,j≈ng,jN,\begin{eqnarray} m_{i,j} \approx \dfrac{n_{g,j}}{N}, \end{eqnarray}where ng,j$n_{g,j}$ is the total number of wildfires occurred in cell g in period j, and N is the total number of wildfires that occurred in the multiple year period. Assuming constant climate, the multi‐year period (e.g. 1996–2016) can be modelled as a comprehensive year. As mentioned earlier, in order to enhance the computation of mi,j$m_{i,j}$ considering the scarcity of historical ignitions in some grid cells, the Monte Carlo population technique is employed in pre‐processing the original dataset to further populate grid cells.Temporal (meteorological) featuresWildfire occurrence is influenced by non‐linear and complex meteorological features which are temporally related. Temporal meteorological input includes temperature, rain, humidity, sunshine hours. The choice of these features are informed by indices such as the Angstrom, Nesterov, and Canadian Forest Fire Weather Index as well as the US Fire Danger Rating System [33].Spatial (static) featuresThese features characterise spatial locations for same climate periods and are influential to wildfire occurrence [34]. Spatial data of land‐use and terrain can be obtained from sources such as the HRRR model which have standard grid points that can serve as grid centroids and enable division of the studied geographical area into grid cells with the same spatial and spatio‐temporal features. Historical ignition events that fall within a grid cell are used to obtain mi,j$m_{i,j}$ of the respective cells which are in turn inherited by the sample points i within g, during training.In addition, the past ignition probability and ignition month are also included as spatio‐temporal and temporal features respectively. Additional details can be found in Appendix A.1 and A.3.Data constructionHere, we discuss the logic behind constructing the training data as there is little to none pre‐existing for wildfire analysis. Since training samples are based on historical ignition/non‐ignition days, the dates (dd/mm/yy) and corresponding i.loc$i.loc$ are extracted from the historical ignition database and are utilised to automatically request training sample variables. Once the features are extracted from obtained variables, this training sample point is assigned with a classification label 1, meaning the historical status of ignition was active for the sample. Next, the feature data are requested for the same i.loc$i.loc$ and another (dd/mm/yy) prior to the active ignition date, when no wildfire ignitions were reported to have occurred and this is labelled a 0, meaning that the historical status of ignition was inactive for the sample. In particular, the ignition label for a training sample is defined as:2Ign=1,ifign(j)recorded0,ifign(j−n)¬recorded\begin{equation} Ign = {\begin{cases} 1, & \text{if}\nobreakspace \quad ign_{(j)}\nobreakspace \text{recorded} \\ 0, & \text{if}\nobreakspace \quad ign_{(j-n)} \nobreakspace \lnot \text{recorded} \end{cases}} \end{equation}where Ign$Ign$ is the historical wildfire ignition status in day j, and n={1,2,…,30}$n = \lbrace 1,2,\ldots,30\rbrace$ depending on any day in the given month and year where an ignition was not recorded. This process constitutes the dataframe for training the STWIP. For the 0‐labelled samples, dates prior to ignition (1‐labelled sample) of an i.loc$i.loc$, are chosen since historical ignition could have significantly tampered with temperature, fuel and vegetation, rendering later dates deceptive for use as 0‐labelled training samples. It is worth noting that although we assume true absence points, these 0‐labelled samples are pseudo‐absence points since it is unknown if ignition could not occur (there was no potential for ignition) or simply did not occur (there was no source of ignition) in that historical date and i.loc$i.loc$.SPATIO‐TEMPORAL WILDFIRE ESTIMATION MODELAfter data construction, the dataframe is fed into STWIP as input data following some transformations discussed herein. The input data is cleaned, missing values are filled with an average of their nearest neighbours. A major part of training data processing includes rescaling the features to have the properties of a standard normal distribution (μ=0,σ=1$\mu = 0, \sigma = 1$). The need for rescaling arises as features are multivariate with different units. Also, since feature magnitudes in instance xi${\bf x}_{i}$ play a role in the updates applied to the weights during gradient descent, rescaling becomes important. This standardisation is implemented using the Z‐score as follows:3z=x−μσ.\begin{eqnarray} z = \dfrac{x - \mu }{\sigma }. \end{eqnarray}Then STWIP predicts the expected ignition potential of a spatial location in period j as discussed further.Spatio‐temporal wildfire ignition probability predictorThe aim is to train a neural network with the problem objective formulated as follows. Given a collection of sample points i with geospatial coordinates i.loc$i.loc$ of (lat,lon) ∈ historical ignition data, where features of the sample point i are known, we aim to predict the potential of a wildfire ignition at periodic intervals. We propose a model based on supervised learning of spatial, spatio‐temporal and temporal features to capture complex and non‐linear interactions between WPVs using a deep neural network (DNN).The DNN is the prediction algorithm of the STWIP and unlike traditional methods of wildfire estimation with simple logistic regression [18, 35], the DNN is capable of modelling non‐linear correlations between the WPVs as illustrated in Equation (4), and can update the network's basis functions in specific input space directions.4ŷ=σ∑h=1HwohTh∑i=1DwhiT∗xi+wh0+wo0,\begin{eqnarray} \widehat{y} = \sigma {\left(\sum _{h=1}^{H} w_{oh}^{T} h{\left(\sum _{i=1}^{D} w_{hi}^{T} * x_{i} + w_{h0} \right)} + w_{o0} \right)}, \end{eqnarray}where w is the vector of adjustable weight parameters, with input variables xi$x_{i}$, σ is a threshold function, and {i,h,o}$\lbrace i, h, o \rbrace$ represent the input, hidden, and output layers. By adjusting the weight vector through different training epochs the predicted labels are mapped closer to the target labels, estimating the probability of potential wildfire ignition, πi,j$\pi _{i,j}$, as follows:5πi,j=f(x).\begin{eqnarray} \pi _{i,j} = f({\bf x}). \end{eqnarray}The STWIP architecture is a three layer fully connected network as shown in Figure 3, utilising the Adam optimiser, ReLU activation, and softmax activation at the output layer.3FIGUREInputs and predicted outputThe hidden layers' (12,3) neurons, respectively, are chosen to avoid over‐fitting and enhance prediction accuracy. The data input, x, is fed into the input layer. The output layer consists of two neurons that output probabilities of potential ignition/non‐ignition in one hot encoded format. The network is trained and minimised over the cross‐entropy loss. The trained STWIP is illustrated in Algorithm 1 in Appendix A.5.Wildfire spread estimationIn modelling wildfire behaviours including spread, software such as Prometheus and Burn‐P3 have been developed, but however, may require predefined inputs such as initial ignition grids from all historical fires, the different ecoregions, percentage of escaped fires and more, which may not be readily available to the user. In literature, models such as the FLAME [36] have been developed to rely on observable field assessments to consider areas of high fire spread rates. In refs. [37, 38], the developed model seeks to attain the fire front using a variation of the Thomas Equations shown in Equations (6) and (7).6Vf=k(1+Vw)ρb\begin{align} &V^{\rm f} = \frac{k(1+V_{\rm w})}{\rho _{\rm b}} \end{align}7ri,j,ω,tf=ri,j,ω,t−1f+Vω,tfΔtcos(ϕi,j,ω,tw)\begin{align} &r_{i,j,\omega ,t}^{\rm f} = r_{i,j,\omega ,t-1}^{\rm f} + V^{\rm f}_{\omega ,t} \nobreakspace \Delta t\nobreakspace \text{cos}(\phi ^{\text{w}}_{i,j,\omega ,t}) \end{align}where Vw is wind speed, k is fire‐type parameter, ρb is the bulk density, rf is the radius from the initial ignition point to the fire boundary, and ϕw is wind direction.However, if a wildfire ignites in a cell i in period j, its spread rate depends on surrounding fuel types and wind speed, which can be captured by the wildfire‐fuel spread characteristics. Hence, we adapt an approximate radial spread rate using the fireline assessment method [36], that can be determined by assessing the fuel type and wind speed at each HRRR grid point nearest to the potential wildfire ignition location. In this paper, instead of arbitrary values of spread rates, practical datasets that adapt the considered geographical area to different fuel types is utilised.The study area is mapped, by a consulted fire expert, Robert Ziel, to three common fuel types namely crown, litter, and grass as illustrated in Table 1 which also shows the coverage of each fuel type in our study area in northern California. Hence, this paper considers three common vegetation/fuel types (crown, litter, and grass) with spread rates modelled as a function of wind speed, W, as in Equation (8) and as shown in Figure 4. Note that in the case of multi‐fuel types such as litter and crown, the fuel type with higher spread rate was chosen. Constant but atypical wind speed directed towards the power system components is assumed, in order to account for the worst case scenarios of wildfire spread in the spatio‐temporal assessment.8ωgrass=14.4(W)1.232,ωcrown=4.87(W)1.146,ωlitter=1.03(W)1.213.\begin{eqnarray} \omega _{\sf grass} = 14.4(W)^{1.232},\nobreakspace \nonumber \\ \omega _{\sf crown} = 4.87(W)^{1.146},\nobreakspace \nonumber \\ \omega _{\sf litter} = 1.03(W)^{1.213}. \end{eqnarray}Armed with the potential rate of spread of the wildfire, utilities are able to optimise operations based on parameters such as expected distance and the time it takes a potential ignition to reach critical grid components.1TABLERelating the land‐use features to fuel typeValueLabelFuelStudy area coverage1Evergreen needleleaf forestLitter/crown46.139%2Evergreen broadleaf forestLitter/crown0.000%3Deciduous needleleaf forestLitter0.000%4Deciduous broadleaf forestLitter0.000%5Mixed forestLitter/crown0.000%6Closed shrublandsLitter/crown0.000%7Open shrublandsLitter/crown0.000%8Woody savannasGrass11.611%9SavannasGrass14.306%10GrasslandsGrass9.583%11Permanent wetlandsBarrier0.000%12CroplandsBarrier/grass17.028%13Urban and built‐upBarrier0.722%14Cropland/natural vegetation mosaicBarrier/grass0.000%15Snow and iceBarrier0.000%16Barren or sparsely vegetatedBarrier0.028%17WaterBarrier0.583%18Wooded tundraLitter/crown0.000%19Mixed tundraGrass0.000%20Barren tundraBarrier0.000%4FIGURERate of spread as a function of wind speed (1 ch/h = 0.005588 m/s)POWER GRID WILDFIRE RISK ASSESSMENT MODELThis section presents the proposed model for the power grid risk assessment, utilising the outputs of wildfire estimation model presented in Section 3. The wildfire potential ignition map (ignition probability map), produced by the STWIP, aids in proactive de‐energisation to prevent endogenous fires caused by power system failure [28] while the spread estimation aids improvement in adaptive operation of power grid against exogenous wildfires [15]. Specifically, a set of grid component outage scenarios are first generated by incorporating the output parameters of the first stage estimation model with GIS information of the power grid. In particular, given πi,j$\pi _{i,j}$, scenarios are sampled given the distribution of the wildfire potential ignition map and potential ignition locations, generating expected scenarios for the power system risk assessment model. Note that the granularity of πi,j$\pi _{i,j}$ can be improved to hourly depending on user application. In this paper, we estimate the hourly probabilities from πi,j$\pi _{i,j}$ as follows:9(1−pi,h)H=(1−πi,j)\begin{equation} (1-p_{i,h})^{H} = (1-\pi _{i,j}) \end{equation}where pi,h$p_{i,h}$ is the hourly probability of potential wildfire ignition in i, and H is the cardinality of hours in day j. Based on these scenarios, three risk metrics, namely, critical response time, scenario based damage cost, and the expected damage cost are calculated to assess risk.Power grid outage scenario generationWe aim to generate the outage scenario of grid component c at time t of operational day j of the year. Assume that the wildfire ignition happens at time t∗=0$t^*=0$, and we aim to assess the operation of power grid for the subsequent 24 h after the potential incident. In other words, the utility operator's thought process is: “if the potential wildfire occurs given scenario, s, and I have knowledge of the spread rates given s, I should estimate what component outages can be induced or motivated by this fire so I can be better prepared for such scenarios”.Let πs$\pi _{s}$ denote the probability of occurrence of scenario s corresponding to a set Ijs$\mathcal {I}^s_j$ of potential ignition locations of day j. The spreading rate ωis$\omega _i^s$ of the ignition in location i in scenario s is obtained by using the spread model presented in Section 3.2 with the corresponding values of forecast wind speed and fuel types around i. The GIS data of the power grid is mapped into the considered area. The characterisation of a wildfire induced (exogenous) grid outage scenario is illustrated in Figure 5. In particular, the component (e.g. transmission line) is assumed to be damaged if the potential fire crosses its safety zone defined by Δc$\Delta _c$ and the status of power grid component c is characterised by a scenario dependent parameter δc,ts$\delta ^s_{c,t}$ as:10δc,ts=0,ifmini∈IjsDci−ωisΔt>Δc1,ifmini∈IjsDci−ωisΔt<Δc\begin{equation} \delta ^s_{c,t}= {\begin{cases} 0, & \text{if}\nobreakspace \min \limits _{i \in I^s_j} D_{c}^{i} - \omega _i^s \Delta t &gt; \Delta c \\ 1, & \text{if}\nobreakspace \min \limits _{i \in I^s_j} D_{c}^{i} - \omega _i^s \Delta t &lt; \Delta c \end{cases}} \end{equation}where Δt=t−t∗=t$\Delta t = t- t^*= t$ (t∗=0$t^*=0$) is the potential duration of the wildfire spread, Dci$D_{c}^{i}$ is the Euclidean distance from the potential ignition point i to the grid component c, and ωisΔt$\omega _i^s \Delta t$ is the spreading radius of the wildfire from its ignition point. Note that Equation (10) considers potential wildfire ignition with spread closest to component c, since multiple ignition points can possibly occur in a scenario s, which was reportedly the case in the infamous Campfire. Also, when a component is on outage (δts=1$\delta ^s_t=1$), we assume it continues to be out until the end of the considered operation horizon. The value of Δc$\Delta _c$ can be adapted from numerical determination of the acceptable safety distance [39], which furnishes a detailed thermodynamics of wildfire effect on system components, informed by flame characteristics and a vulnerability threshold. The safety distance is informed by flame characteristics and a vulnerability threshold, and is the distance between the transmission line and the fire at which the thermal radiative flux is less than a given threshold, Φthresh$\Phi _{\text{thresh}}$. The threshold value is set to the vulnerability of transmission lines. The safety adapted distance is determined by the following correlation:11Dx(opt)=D|1−exp−pthresh2Llf,\begin{equation} D_{x} (\text{opt}) = D^{|} {\left(1-{\rm exp} {\left(-p_{{\rm thresh}} \frac{2L}{l_{{\rm f}}} \right)} \right)}, \end{equation}where pthresh is a pre‐determined empirical parameter for each Φthresh, lf is the flame length, 2L is the width of fire, and12D|=lfcosγ−4Φthresh2+(BTf4ετ)22Φthresh+Ifsinγ,\begin{align} D^{| } = \frac{l_{{\rm f}} \text{cos} \gamma \sqrt {-4 \Phi _{{\rm thresh}}^{2} + (BT_{{\rm f}}^{4}\varepsilon \tau )^{2}}}{2 \Phi _{{\rm thresh}}} + I_{{\rm f}} \text{sin} \gamma , \end{align}where τ is the atmospheric transmissivity, ε represents flame emissivity, B is the Boltzmann constant, and Tf is the average temperature of the flame.5FIGUREWildfire‐induced outage scenario generationMetrics for power grid wildfire risk assessmentThe following metrics are developed to aid utility decision making process and operational strategies in the wake of a wildfire threat. Note, since the metrics are used for a particular operation day j of the grid, we omit the notation j from hereon for simplifying the notation.The critical response time (Δt¯$\overline{\Delta t}$)This metric furnishes the time period within which utility operators can make operational changes to minimise economic damages before power shutoff is absolutely necessary. It is a function of the distance from the potential wildfire ignition point i to power system component c (see Figure 5), and the wildfire rate of spread ωis$\omega ^{\rm s}_i$ as follows:13Δt¯=min∀i∈Is,s∈SDci−Δcωis.\begin{eqnarray} \overline{\Delta t} = \min \limits _{\forall i\in I^{\rm s}, s \in \mathcal {S}} \dfrac{D_{c}^{i} - \Delta _ c}{\omega ^{\rm s}_i}. \end{eqnarray}Note the importance of this metric since aspects of vegetation, fuel, and velocity of wildfire spread, based on the spreading model in Equation (8), is incorporated into a time measure for optimising utility actions pre‐wildfire. The metric inadvertently provides a time estimate before the potential ignition will pose a risk, and serves in two ways depending on application. First, if Δt¯$\overline{\Delta t}$ is <<$&lt;&lt;$ threshold (utility defined, associated with Δc$\Delta _c$), then ignitable location is close to the power system component, ignition is possible within Δc$\Delta _c$ and components should be de‐energised to avoid being sources of ignition for endogenous wildfires. Secondly, if Δt¯$\overline{\Delta t}$ is >>$&gt;&gt;$ threshold, i.e. distance of potential ignition is far enough from component, the utility can afford to wait pre‐wildfire and not cut off power to customers, say H hours before actual ignition, which is mainly where revenue is lost during wildfire threats [10]. Also for the latter depending on the critical time, utilities can operate and strategise before any potential exogenous wildfire fronts induce component outages.The scenario based damage costThe operational damage cost of a particular scenario s is the result of the optimal response of the power grid against the realised outage scenario. The operational damage cost includes losses in revenue accruing to the power utility due to lost opportunity costs arising from load curtailment, including power shutoff to customers and intended unavailability of power components, e.g. power lines, from wildfire threats. In the case of the power transmission grid, such scenario based damage cost can be defined as the optimal value of the following security constrained optimal power flow as below:14costs=min∑t∈T∑b∈BVOLLb,tLCb,ts.\begin{eqnarray} \mbox{cost}_s = \min \quad \sum _{t\in T} \sum _{b \in \mathcal {B}} \mbox{VOLL}_{b,t} \mbox{LC}_{b,t}^s. \end{eqnarray}15s.t.Pl,ts=θb,ts−θb′,tsxl(1−δl,ts),∀l=bb′∈L\begin{eqnarray} \text{s.t.} \quad P^s_{l,t} = \dfrac{{\left[\theta ^s_{b,t}- \theta ^s_{b^\prime , t}\right]}}{x_{l}} (1-\delta ^s_{l,t}), \nobreakspace \forall l = bb^\prime \in \mathcal {L} \end{eqnarray}16Pg,b,ts−Pd,b,t+LCb,ts=∑bb′∈LPbb′,ts,\begin{eqnarray} P^s_{g,b,t} - P_{d,b,t} + \mbox{LC}_{b,t}^s = \sum \limits _{bb^\prime \in \mathcal {L}} P_{bb^\prime ,t}^{s}, \end{eqnarray}170≤LCb,ts≤Pd,b,t,∀b∈B,∀t∈T\begin{eqnarray} 0 \le \mbox{LC}^s_{b,t} \le P_{d,b,t},\nobreakspace \forall b \in \mathcal {B}, \forall t \in \mathcal {T} \end{eqnarray}18(1−δg,b,ts)P̲g,b≤Pg,b,ts≤(1−δg,b,ts)P¯g,b,∀g∈G,∀b∈B,∀t∈T\begin{eqnarray} (1-\delta ^s_{g,b,t}) \underline{P}_{g,b} \le P_{g,b,t}^s \le (1-\delta ^s_{g,b,t}) \overline{P}_{g,b},\nobreakspace \nonumber \\ \forall g \in \mathcal {G}, \forall b \in \mathcal {B}, \forall t \in \mathcal {T} \end{eqnarray}19−(1−δl,ts)P¯l≤Pl,ts≤(1−δl,ts)P¯l,∀l∈L,∀t∈T\begin{eqnarray} -(1-\delta ^s_{l,t}) \overline{P}_{l} \le P^s_{l,t} \le (1-\delta ^s_{l,t}) \overline{P}_{l}, \nonumber \\ \forall l \in \mathcal {L}, \forall t \in \mathcal {T} \end{eqnarray}20θ̲b≤θb,ts≤θ¯b∀b∈B,∀t∈T,\begin{eqnarray} \underline{\theta }_{b} \le \theta ^s_{b,t} \le \overline{\theta }_{b} \quad \forall b \in \mathcal {B}, \forall t\in \mathcal {T}, \end{eqnarray}21Pg,b,ts−Pg,b,t−1s≤RUg,b,∀g∈G,∀b∈B,∀t∈T,\begin{eqnarray} P^s_{g,b,t} - P^s_{g,b,t-1} \le RU_{g,b},\nobreakspace \forall g \in \mathcal {G}, \forall b \in \mathcal {B}, \forall t \in \mathcal {T}, \end{eqnarray}22Pg,b,t−1s−Pg,b,t≤RDg,b,∀g∈G,∀b∈B,∀t∈T.\begin{eqnarray} P^s_{g,b,t-1} - P_{g,b,t} \le RD_{g,b},\nobreakspace \forall g \in \mathcal {G}, \forall b \in \mathcal {B}, \forall t \in \mathcal {T}. \end{eqnarray}where B$\mathcal {B}$, L$\mathcal {L}$, G$\mathcal {G}$, and T$\mathcal {T}$ denote the set of transmission buses b, transmission lines l, generators g, and time slots t. The objective function (14) is to minimise the load curtailment cost over all the sets of buses and the scheduling horizon where LCb,ts$\mbox{LC}^s_{b,t}$ denotes the load curtailment in bus b in time t in scenario s and VOLLb,t$\mbox{VOLL}_{b,t}$ denotes the value of loss load. The optimisation is subject to the following constraints. The DC power flow constraints of the transmission lines l connecting bus b and b′$b^\prime$ is captured in Equation (15) where the scenario based outage status of the line l is represented by a binary parameter δl,ts$\delta ^s_{l,t}$. In particular, if the line is potentially damaged by the modelled wildfire, i.e. δl,ts=1$\delta ^s_{l,t}=1$, there is no power flow on the line. Power balance constraint in bus b is captured in Equation (16) where the power Pg,b,ts$P^s_{g,b,t}$ generated by g in b, minus the bus power demand Pd,b,t$P_{d,b,t}$, plus load curtailment LCb,ts$\mbox{LC}^s_{b,t}$, equals the total power flowing out of b. Additionally, the load curtailment at any bus must remain within the limitations of the total demand at that bus, which is presented in Equation (17). The power generated by g is constrained by its minimum and maximum capacity as in Equation (18). The power flow over the line l is constrained by its thermal capacity P¯l$\overline{P}_l$ as in Equation (19). On a similar note, the upper and lower limit constraints of the bus phase angle θb,ts$\theta ^s_{b,t}$ are described in Equation (20). Furthermore, the limitations RUg,b,RDg,b$RU_{g,b}, RD_{g,b}$ of the generators' ramping up and down rates are furnished in Equations (21) and (22) respectively. Note that our framework can also apply to power distribution network where DC power flow constraints are replaced by the DisTFlow model considering line outage status [40].The expected power system damage costThe expected damage cost of power systems [41] for a given set of wildfire motivated outage scenarios S is calculated as:23ECOST=∑s∈Sπs×costs,\begin{eqnarray} \text{ECOST} = \sum _{s \in \mathcal {S}} \pi _s \times \mbox{cost}_s , \end{eqnarray}where costs is obtained by solving the optimal response of the power grid against the wildfire motivated outage scenario s, e.g. solving optimisation problems (14)–(22) for the case of transmission networks. Hence, the ECOST$\text{ECOST}$ metric, in addition to estimated infrastructure damage costs, can aid utility decisions of wildfire mitigation vs. restoration, i.e. informing the important question: should the utility use the “let‐burn” strategies, since oftentimes the utility is burdened with the economic decision of either fighting wildfires or employing the “let‐burn strategy” where the wildfire is allowed to burn and damages are rebuilt/restored [42]. If the firefighting costs are greater than the expected damage costs (operational, infrastructural and otherwise), the utility could utilise the “let‐burn” strategy.NUMERICAL RESULTSSimulation setupWe consider an area covering approximately 200km2$200\text{ km}^{2}$ in Northern California and spanning latitudes 38∘49′17.616′′N$38^{\circ } 49^{\prime } 17.616^{\prime \prime }\text{ N}$ to 40∘46′7.14′′N$40^{\circ } 46^{\prime } 7.14^{\prime \prime }\text{ N}$, and longitudes 120∘11′52.8′′W$120^{\circ } 11^{\prime } 52.8^{\prime \prime }\text{ W}$ to 122∘43′55.2′′W$122^{\circ } 43^{\prime } 55.2^{\prime \prime }\text{ W}$. The chosen area reflects homogeneous climate yet spatially diverse in fuel and vegetation as illustrated in Figure 15 detailed in Appendix A.3. The STWIP was trained and validated using a 70% and 30% split training data of 10,900 samples, and compared to other data‐based conventional baselines [43, 44] including decision tree, boosted decision tree, and linear regression. We first provide the wildfire estimation results over the studied area to illustrate the effectiveness of the first stage of the framework, i.e. the STWIP model.Wildfire estimation analysisThe performance analysis in Figure 6 shows the average accuracy for training and validation of the STWIP was (98.31% and 97.0%), while the boosted decision tree was (93.27% and 92.0%), both outperforming other baselines. Also, the proposed STWIP achieves the best performance with an area under the receiver operating characteristic curve (AUC) of 0.995. Note that the AUC describes the model trade‐off in terms of sensitivity and specificity. This performance is followed again by the boosted + tree algorithm with an AUC of 0.965 and the regression with an AUC of 0.903 respectively.6FIGUREAccuracy of baselinesNext, we test STWIP with the 2018 year, comparing results with the actual wildfire occurrence currently available in ref. [45]. In the test data we use the 15th day of the month as it is representative of its wildfire characteristics. Thus, we seek to obtain similar patterns of spatial density and temporal distribution.Results in Figure 7 show that predicted hotspots are similar to the actual historical test year, clustered between latitudes and longitudes (39° 30′ 00′′$^{\prime \prime }$ N , 122° 30′ 00.0000′′$^{\prime \prime }$ W) and (39° 30′ 00.0000′′$^{\prime \prime }$ N , 121° 30′ 00.0000′′$^{\prime \prime }$ W). The central valley area of northern California has less ignition clusters, which is attributed to limited elevation and fuel.7FIGURETest year: actual (left) vs. predicted spatial ignition patternSimilarly, the temporal results are analysed monthly as furnished in Figure 8, showing that the estimated temporal distribution well follows the test year's actual temporal wildfire distribution (approximately Gaussian). Hence, by employing the STWIP for analysis as opposed to the conventional utility predefined fire threat areas and fire threat levels as detailed in Appendix A.7, power systems can further improve wildfire forecast and analysis towards actual expectations.8FIGURETest year: actual(left) vs. predicted temporal ignition patternThe percentage weighted impact of WPVs on the wildfire ignition status is presented in Figure 9. In particular, the WPVs are evaluated based on their weighted influence on wildfire occurrence. Terrain and temperature, and cloud type and historical ignition, have the highest and least influence, respectively. Also, humidity seemingly influenced daily wildfire ignition maps produced by the predictor especially in the central valley of northern California. This suggests which measurement types (sensors in monitoring corridors) that the power utility should invest for enhancing situational awareness against wildfire. The performance of STWIP is further underlined as linear methods such as regression do not well capture terrain which is indeed a high impact feature [46].9FIGUREInfluence of wildfire predictor variables: STWIP captures the magnitude of this influence better than the widely utilised linear regression. For instance, the influence of land‐use and terrain which are well known influential factors in wildfire occurrenceIllustrating wildfire aware power grid operation analysisConventionally, utility often uses region‐scale and deterministic threat level analysis as discussed in Section 1.1 and detailed in Appendix A.7.In this situation as further illustrated by Figure 10, as seen in the “conservative” utility case, the utility will have an extreme alert in the red area since there are more wildfire threats as opposed to the elevated threat area (orange highlight). The customers in the area with extreme alert will have their power shut off for the duration of the wildfire threat, including customers up north (relatively farther) from the wildfire threat cluster. The magnitude of the shut off can be visualised given the size of the predefined threat areas in a sample utility wildfire awareness issue as shown in Figure 18 in Appendix A.7. However, the potential ignition map and spread parameters provided by the first stage estimation model can be used to analyse the risk of over de‐energisation motivated by power component failure‐ignited wildfires and the risk of outages induced by exogenous wildfire. With the granularity in spatial detail of the wildfire potential probability maps, the spread model, and the proposed risk assessment, the utility can optimise the time before shut off is necessary in exogenous fires, and also emulate the distance between a potential ignition location (ignitable location) and the power equipment in endogenous/equipment‐induced wildfires.10FIGUREIllustration of the casesThe analysis is conducted on a 24‐bus test system mapped to span the length and breadth of the studied area as detailed in Appendix A.6, however, this analysis can be done on any transmission or distribution system given complete system details. We consider two case studies which deviate from the power system normal operation when there are no wildfire threats. In Case 1, the test system is simulated with the current conventional “conservative” utility approach of threat area and levels discussed in the Section 1.1 and detailed in Appendix A.7. In this case, all the power components located in the pre‐defined elevated threat area as illustrated in Appendix A.7 are intentionally outaged whether or not they are in the direct vicinity of high wildfire potential. This simulates current utility procedure to prevent endogenous wildfires [10]. In Case 2, the wildfire analysis and test system de‐energisation is based on the wildfire potential ignition map produced by STWIP as described in Section 4 aiming to improve spatial granularity and optimise (shorten) the time span of utility de‐energisation. The data used in simulation is based on November 10, 2018. The value of lost load is set to 1000 $/MWh. Details of the components that are out of service in the three case studies are shown in Table 2.2TABLEWildfire motivated de‐energisationCase studyTransmission line outagesGenerator outagesCase 1L1‐4, L6‐8, L14, L19, L24‐33G1‐4, G15‐29Case 2L4, L8, L19, L23‐24, L28, L31‐33NoneAssessing risk of outages induced by exogenous wildfireFor exogenous wildfire induced outage risk analysis, the probabilistic ignition map is used to generate wildfire ignition scenarios and simulated spreading pattern, thus modelling exogenous wildfire‐induced damages on power grid components. The expected damage cost, ECOST, as illustrated in Figure 11, represents the aggregate analysis for one operational year of the test system in the studied area. It shows that the power system is highly vulnerable during summer time from June to September, and quite low during winter time from December to March. However, the risk of wildfire induced outage still exists during non‐summer times, which can be explained by the impacts of the time independent WPVs such as land‐use and terrain. Hence, an efficient allocation of utility wildfire monitoring resources should be based on spatio‐temporal analysis of wildfire occurrence, e.g. monitoring grid and vegetation should be done more frequently during high risk period.11FIGUREExpected damage cost over the period of 1 year: showing sustained wildfire risk during non‐summer monthsEnhancing de‐energisation decision for mitigating power component failure‐ignited wildfiresWildfires can be ignited by electric power line faults that cause arcing in a high‐heat release of energy. Such incidents are majorly caused by ignitable vegetation contacting power lines. Indeed, the correlation between the wildfire ignition probability map and electric power failures motivates the use of proactive de‐energisation of equipment as a preventive measure [28]. We aim to illustrate the improvements in de‐energisation using the proposed STWIP, which is more granular and stochastic, over conventional utility approach.The proposed framework aids in enhancing de‐energisation and estimating the potential cost of wildfire occurrence as detailed further.The total system energy consumption, total loadshed, and loadshed‐bus localisation of the three cases are shown in Figure 12. The total energy demand of the system is 54,358.679 MWh, with Case 1 supplying 29,449.051 MWh due to large amounts of load shedding, 45.8%, resulting from the conventional threat area and threat level methods. Relative to Case 2, the power grid response avoids a large amount, 19,798 MWh, of unnecessary load shedding. Hence, a more detailed wildfire potential ignition map provided by the proposed granular analysis results in less conservative shutoff, i.e. only components in the high wildfire vicinity are proactively de‐energised to prevent component failure‐caused wildfire [28].12FIGUREDemand served and load shedding for Cases 1 and 2: illustrating that a detailed wildfire potential ignition map provided by the proposed power grid wildfire risk assessment model results in less conservative proactive de‐energisationTable 3 presents load shedding cost, and generation cost for all cases. For the normal system operation, there are no load shed costs and generation costs are $568,084.40 The total costs for Case 1 is high due to the amount of load shed and the increase in production of expensive online generators.3TABLECosts for Cases 1 and 2 ($)Load shedding cost ($)Generation cost ($)Case 1181,591.25537,969.01Case 237,263.75537,991.32In addition, the framework aids improve the resilience of the system by spatio‐temporally informing the disaster progression phase of the resilience trapezoid as illustrated in Figure 13, hence reducing the “dip” in the resilience curve [47].13FIGUREProfile of load served in the system. The proposed power grid wildfire risk assessment model aids in enhancing system robustness and hence resilience, as evident in Case 2 as opposed to Case 1Specifically, in Case 1, a large and sudden drop of the percentage load served (performance indicator) is observed. This is because without spatio‐temporal analysis, the utility performs conservative forced outages as soon as a wildfire threat is observed in their pre‐defined regional threat areas, which in this simulation is set to the beginning of the scheduling horizon at t∗=0$t^{*}=0$. The percentage load served in Case 2 is observed to reduce over time. This is possible due to the improved granularity provided by spatio‐temporal analysis where expectations of wildfire parameters such as distance, spread rate, and the critical response time have been pre‐estimated as discussed in Section 4.2.1. Hence, with a grasp of the expected critical response times, the utility operations have increased and informed time flexibility in forcing component outages.CONCLUSIONThis paper proposed a comprehensive spatio‐temporal framework for power system wildfire risk analysis. The framework includes two sequential models, where the first model estimates the granular and spatio‐temporal potential wildfire probability and spread based on influential parameters such as vegetation and fuel, wind speed, geographical, and meteorological variables, while the second model leverages the estimated probabilistic ignition maps in order to analyse system risk from exogenous wildfire and to enhance power system de‐energisation in mitigating endogenous fires induced by power equipment failures. Numerical results show that lower forced electricity outages to customers can be achieved by increased granularity in spatial locations in utility service areas. Hence, the framework significantly improves utility de‐energisation decision compared to the current “conservative” threat area approach In addition, the framework aids to improve system resilience and utility revenue and prioritise resource allocation given increased localisation of high wildfire potential. Future work will entail using the proposed model as a base in proposing a self‐sufficient model for complete wildfire prediction and detection for electric power utilities using recent state‐of‐the‐art sensor developments and designs in wildfire detection. Part of these future studies are already formulated but not included in this paper to enable a concise and clear exposition.CONFLICT OF INTERESTThe authors declare no conflict of interest.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.REFERENCESCouncil of Economic Advisers: Economic Benefits of Increasing Electric Grid Resilience to Weather Outages The Council, Executive Office of the President, The White House, Washington, D.C. (2013)https://www.iii.org/table‐archive/21424. Accessed 29 March 2022Ramsey, M. 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Accessed 29 March 2022AAPPENDIXA.1  Spatial features detailsWe assume that land‐use data contains information on fuel type, fuel load, fuel continuity as illustrated in Table 1 while terrain informs the topography of the ecoregion. The land‐use and terrain are examples of spatial features and usually do not change significantly over the short‐term, hence the name static. Land‐use refers to the natural vegetation and the various ways in which humans make use of and manage the land and its resources. The terrain represents the topography of the geographical area. Hence, input features employed are not exhaustive but motivated from wildfire studies.A.2  Same climate assumptionIn this work, we assume same climate distribution over the period which we collect historical data for analysis. This assumption is enabled by similar distribution in spatial and temporal data. In the said period, the latter is approximately Gaussian, while the former is as furnished in Figure A.1.A.1FIGURESame climate assumption: dimilar distribution of historical data‐points latitude and longitudeA.3  Spatio‐temporal wildfire estimation model: setupLand‐use was obtained from the NOAA's HRRR model and ranges from evergreen needleleaf forest to barren tundra, assigned values [1, 20], while Terrain input gives insight into the topography and elevation of the area with values in the range [6, 2603] m as shown in Figure A.2. Temporal variables were obtained from the Open Weather Map database by building an application programming interface scrapper in python, to make data requests to the open weather map online weather database using the http protocol. Requested meteorological data includes temperature levels, rain, humidity, cloud, atmospheric pressure, visibility, month, and sunshine hours, where numerical values are assigned to qualitative features, for instance, the daily weather types (clear, cloudy, hazy, drizzly, rainy) are assigned real values in the ratio [0.1, 0.3, 0.5, 0.7, 0.8] respectively. Historical wildfire ignition records were obtained for the multi‐year period of analysis (1996–2016,2018) from the U.S. Geographical Survey database and provides the samples of the training and test data, respectively.A.2FIGUREThe spatial features of studied geographical area: terrain (left) and land‐use (right)A.4  Temporal probability detailsThe temporal probabilities of wildfire ignition is also calculated from historical data with the assumption of a same climate period as shown in Figure A.3.A.3FIGUREWeekly temporal distribution of historical wildfire occurrenceA.5  The STWIP algorithm1ALGORITHMBatch learning based STWIP1:Given a training set (x1,y1),…,(xn,yn)$({\bf x}_{1}, y_{1}), \ldots, ({\bf x}_{n}, y_{n})$ with features in instances xi${\bf x}_{i}$ ∈Rn$\in R^{n}$, with label yi$y_{i}$ ∈ {0,1}$\lbrace 0, 1 \rbrace$2:Input(X,Y): A set of labelled input features [temp, ..., month], of training samples θ, batch size b3:Output: the spatio‐temporal ignition probability maps.4:Hyper‐parameter selection5:function Predictor_Training$Predictor\_Training$X, Y6:Shuffle ← enabled7:count_max ← θb${\frac{\theta }{b}}$8:count ← 09:while count < count_max do10:for batch b in θ do11:STWIP ← DNN learns (b×$b\times$[temp, ..., month])12:count ++$++$13:end for14:end while15:Compute accuracies16:Compute the ROC AUC metrics17:Apply STWIP to test samples18:returnWildfire potential ignition maps of πi,j$\pi _{i,j}$19:end FunctionThe trained STWIP, as presented in Algorithm 1, is then validated and utilised in the prediction for unlabelled test samples for a future period j. When the algorithm ends, the probability map of potential ignitions, πi,j$\pi _{i,j}$, is returned.A.6  Mapping bulk power grid to the wildfire potential mapThe IEEE 24‐bus reliability test system [48] that includes 24 buses, 38 lines, and 33 generating units is aligned to the ignition probability map as shown in Figure A.4. Also, to illustrate conventional power utility wildfire practices, the grid is divided into fire threat areas with extreme, elevated, and normal threat levels, while spatio‐temporal analysis employs the most probable generated scenarios.A.4FIGUREIEEE 24‐bus mapping into three wildfire threat areasA.7  Utility‐employed predefined fire threat areas and levelsElectric power utilities have carried out ground breaking work in modelling wildfire occurrence, including developing analytical tools such as the FPI and more [49].These indices, for instance the FPI, calculated at district level corresponding to three levels of wildfire threat alert, as shown in Fig. A.5, are efficient for planning decisions, however, they start to fall short in the day to day operational decisions for utilities as spatio‐temporal granularity is lost in these methods, i.e. the use of pre‐defined wide threat areas and few (extreme, elevated, normal) threat levels.A.5FIGUREA sample SDG&E wildfire awareness issueIn particular, the challenges posed by current utility techniques include the use of fire threat areas (FTAs), fire threat levels (FTLs), the independent analysis of the WPVs, and the exclusion of adequate past wildfire characteristics in analysis.As stated by Brian D'Agostino, SDG&E's director of fire science and climate adaptation: “we need to understand what the weather is doing in every canyon, every ridgetop all across the backcountry to really bring that level of customer safety and customer service”. Thus, the use of FTAs and FTLs can introduce ambiguity in utility analysis, such as the over allocation of resources, excess load shedding in risk assessment, and lengthened forced outages to customers, since the pre‐defined area may not be granular enough for operational wildfire analysis.Furthermore, the independent analysis of wildfire predictor variables introduces errors in estimation due to the exclusion of the effects of the interactions between these variables. For instance, for utility operations, when certain conditions (e.g. relative humidity ⩽15%, sustained winds and gusts ≥25 and 35 mph respectively, for a duration ≥6 h) are met, operational decisions, e.g. all reclosers being turned off, sensitive relay settings being enabled [50], are taken. However, these assessments of environmental conditions are made independently, leaving little room for evaluating how the interactions between variables drive wildfire potential. Moreover, data obtained from historic events provide increased information on spatial wildfire characteristics as demonstrated in this work.

Journal

"IET Generation, Transmission & Distribution" – Wiley

Published: Jul 1, 2022

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