Application of Observational Weather Data in Evaluating Resilience of Power Systems and Adaptation to Extreme Wind Events

Abstract

In Great Britain, 70% of wind-related faults on the transmission power network are attributed to the top 1% gusts. These faults cause outages to millions of customers and have extensive cascading impacts. This study illustrated the application of historical ground measured wind data in a multi-phase resilience analysis process by: (i) projecting an extreme wind event, (ii) assessing components’ vulnerabilities, (iii) analysing system’s response, (iv) quantifying baseline resilience, and (v) evaluating the effectiveness of selected adaptation measures. The extreme event was modelled as a ubiquitous 100-year return gust event impacting upon the operations of the Reduced Great Britain transmission network test case. The results show an unmet demand of about 569 GWh/Week. Adaptation measures were necessary for 60% of transmission corridors with responsiveness improving resilience by 70%, robustness by 55%, and redundancy by 35%. The study implies that resilience enhancement can be prioritized within high potency corridors and organisational resilience could prove to be more effective than infrastructural and operational resilience.

13.1 Introduction

Recent studies [1,2,3] have explored the conceptualisation and application of the resilience concept within power systems. The reasons vary but several studies [1, 2, 4] are motivated by the goal of developing power systems which are less vulnerable to extreme weather. This is because the resultant failure of power systems due to weather events have grave impacts on countries. For example, the ‘Great Ice Storm’ of 1998 that hit parts of Canada caused outages to 4 million people for over a month [5]. Up to 80% of power outages in USA are attributed to weather incidents affecting 22 million people annually [6].

In a study into Great Britain (GB) transmission system faults, it was reported that 50% of all faults were attributed to weather causes and that 30% of these were due to wind events [5]. Two-thirds of wind-related faults were caused by the top 1% of wind gusts [5]. Therefore, several studies [1, 3] have been conducted to assess GB transmission system resilience to extreme wind events but several gaps remain. Due to lack of long-term observations with wider coverage, previous studies [1, 7] used climate model, reanalysis, wind data to analyse and project extreme wind events. However, reanalysis data has been reported to be noisy, exhibits a wide range of biases and errors, and the assessment of its uncertainties is not well understood [8]. In addition, high intensity winds are rarely captured by climate models requiring several studies [1, 7] to arbitrarily scale up intensities for resilience analysis purposes. Moreover, several studies [1, 3] consider the effect of spatial variability of extreme weather events by dividing GB into large “weather regions” which are assigned homogeneous weather profiles. This is contrary to studies that have demonstrated that a met station’s record may not reliably represent weather of a location which is beyond 50 kms [5].

Therefore, this study’s aim was to assess the resilience of GB’s power transmission system and the effectiveness of selected adaptation measures against an extreme windstorm based on observed wind gusts. In particular, the study sought to model a ubiquitous 100-year wind gust event across GB, assess its impact on the network’s components, undertake a system response analysis, evaluate baseline resilience, and assess the effectiveness of redundancy, responsiveness, and robustness. Section 13.2 details the methods employed in determining and enhancing the system’s resilience. Section 13.3 presents and discusses the results whereas in Sect. 13.4, conclusions are drawn as well as implications and limitations of the study.

13.2 Methodology

This study builds upon a multi-phase approach implemented in several studies [1, 4]. As seen in Fig. 13.1, the process follows a five-phase modelling approach, namely: (i) weather threat characterization, (ii) components vulnerability analysis, (iii) systems response analysis, (iv) baseline resilience quantification, and (v) resilience enhancement. Prior to modelling, historical observed wind data was obtained from the Met Office Integrated Data Archive System [9]. The dataset was comprised of 173 met stations with data spanning 1949–2021. Two data types were retrieved: the hourly wind mean speeds and gusts.

Fig. 13.1

Phased resilience assessment simulation flow chart

13.2.1 Extreme Windstorm Characterization

Similar to previous studies [1, 10] which projected a probable cataclysmic wind scenario, this study assumed a high-impact event in which gusts of 100-year return duration would occur simultaneously across GB. Great Britain was divided into cells corresponding to having no more than one met station per cell. A total of 173 weather regions were created based on met-stations locations. Cells without a station were assigned data of a station nearest to their centroid. The Generalized Extreme Value (GEV) theory was used to estimate return gusts in each weather region. In particular, the block maxima method was employed as detailed by [11]. Annual maxima gust values $\left( {x \in {\mathbb{R}}} \right)$ were retrieved for each station. These were then used to fit the GEV cumulative probability distribution function for each station as seen in (13.1). $\mu \in {\mathbb{R}}$, $\sigma > 0$, $\xi \in {\mathbb{R}}$ are the location, scale, and shape parameters respectively. To fit the annual maxima data points to the GEV distribution, a numerical maximum log-likelihood function was used. The initial distribution parameters for each fitted curve of the station were considered as the mean $\left( \mu \right)$, standard deviation $\left( \sigma \right)$ and $\xi = 0.1$.

$$G\left( {x;~\mu ,\sigma ,\xi } \right) = \left\{ {\begin{array}{*{20}l} {\exp \left( { - \exp \left[ { - \left( {\left( {x - \mu } \right)/\sigma } \right)} \right]} \right)} \hfill & {,~\xi = 0} \hfill \\ {\exp \left( { - \left[ {1 + \xi \left( {\left( {x - \mu } \right)/\sigma } \right)} \right]^{{ - \frac{1}{\xi }}} } \right)} \hfill & {,1 + \frac{{\xi \left( {x - \mu } \right)}}{\sigma } > 0} \hfill \\ \end{array} } \right.$$

(13.1)

Given that there is no analytical solution for log likelihood function, the approximate solution was obtained from optimization by utilizing the Sequential Least Squares Programming method. To assess the goodness-of-fit of the optimized distribution parameters $\left( {\hat{\mu }, \hat{\sigma }, \hat{\xi }} \right)$, a coefficient of determination $\left( {R^{2} } \right)$ was derived for ordered empirical and modelled data probabilities. The 100-year return gust $\left( {\hat{x}_{100} } \right)$ for each weather region was then estimated using (13.2). The time, $t$, of return level occurrence was denoted as zero (0) and beyond $t = 0$, the windstorm temporal profiles at each met station were determined by (13.3) in which $\overline{x}_{0}$ is the station’s maximum value for the average hourly wind mean speeds and $\overline{x}_{t}$ are the subsequent mean wind speed values for a week $t \in \left[ {0,168} \right]$. This assumption is an inference from literature [12] in which significant reduction in intensity of windstorms were observed within one week. In the subsequent week of the model, the intensity was assumed to have a straight-line descent to ‘normal’ gusts.

$$\hat{x}_{100} = \hat{\mu } + \frac{{\hat{\sigma }}}{{\hat{\xi }}}\left[ {\left( { - {\text{log}}\left( {1 - 100^{ - 1} } \right)} \right)^{{ - \hat{\xi }}} - 1} \right]$$

(13.2)

$$\hat{x}_{{100_{t} }} = \frac{{\hat{x}_{100} \times \overline{x}_{t} }}{{\overline{x}_{0} }}$$

(13.3)

13.2.2 Vulnerability Analysis

The power system test case employed in this study is based on the Reduced Great Britain Network (RGBN) [13, 14]. RGBN comprises of 29 nodes, 24 of which have a total of 66 connected generators, 50 transmission corridors all with double circuit overhead lines (DC OHL) except one with a single circuit overhead line (SC OHL). Towers were assumed to be 350 m apart. The system has constant demand of 56.3 GW corresponding to peak winter consumption and available capacity of 75.3 GW. Only lines and towers were subjected to windstorms.

To determine the probability of failure, $P_{c} \left( {w_{i} } \right)$, of components with respect to the prevailing wind intensities, fragility curves employed in several studies [1, 7], were used. The highest intensity which an OHL would be subjected across all weather regions it spans, was considered to determine its probability of failure. Towers’ failure states were determined by cells in which they are located. Given the randomness of failures, a uniformly distributed random number, $r\sim U\left( {0,1} \right)$, was generated at every simulation step as proposed by [1] which was compared to the respective probability of failure of each component. If $r < P_{c} \left( {w_{i} } \right)$, the component was regarded permanently damaged. Failure of a single tower resulted in collapse of an entire corridor. Following a component’s failure, the Time to Repair $\left( {TTR} \right)$ was estimated as proposed by others [1, 7].

13.2.3 System Response and Baseline Resilience Evaluation

An AC OPF was run for every timestep whilst recording the Energy not served (ENS) until all corridors were restored. To quantify uncertainties inherent in the damage determination and repair processes, the model was run 1000 times. The mean of ENS values, expected energy not served (EENS), was used as an indicator for baseline resilience. The uncertainties were captured by a probability density function of ENS values.

13.2.4 Resilience Enhancement Modelling

This study adopted the Resilience Achievement Worth (RAW) index proposed by [3] to ascertain the criticality of corridors. The $RAW$ index quantifies the increment in resilience by a corridor when it is assumed to be unaffected by a disturbance. The corridors were then ranked in descending order of their criticality. Three adaptation measures were modeled as proposed by [1, 3]; robustness, responsiveness, and redundancy. Robustness was modelled by moving the fragility curves 20% to the right. This implies that the threshold hazard was increased leading to a delay of components’ outages. Redundancy was modeled by setting parallel corridors to existing ones. Responsiveness was modelled by assuming a constant TTR which is not contingent to the prevailing wind intensity. Each measure was then applied sequentially and cumulatively to groups of five corridors while recording the gains in resilience.

13.3 Results and Discussion

Figure 13.2b shows the expected 100-year gust returns for each weather region determined by the locations of met-stations in Fig. 13.2a. The proximity between each cell and the nearest met station is shown in Fig. 13.2c. 96% of cells are within 50 km of a met station. High altitude locations such as Cairngom Summit (85 m/s) have significantly higher return gusts than low altitudes sites such as Rochdale (27 m/s).

Fig. 13.2

a Location of met-stations, b 100-year return gusts, and c proximity of cells to the nearest met-station

The modelled temporal profile for return gusts can be seen in Fig. 13.3a and the proportion of OHLs and towers in-service can be seen in Fig. 13.3b and c. Up to 79% lines were damaged and about 6% of towers. Line states were observed to be highly fluctuating with sudden spikes and drops given that they are relatively sensitive to wind intensities and have considerably short repair durations. Failures from towers could have significant impact on the system considering their longer restoration (i.e., 500 h compared to 312 h for OHLs) and the fact that most of them carry multiple circuits. For example, 6% of damaged towers caused 36% of corridors to go out of service as seen in Fig. 13.4a.

Fig. 13.3

a Gust temporal profile, b impact on overhead lines, and c impact on towers

Fig. 13.4

a Corridor failure conditional to tower failure, b RGBN components c transmission corridors IDs

After evaluating 1000 instances of $ENS$ for RGBN (Fig. 13.4b and c), the corresponding minimum and maximum values were 396 and 825 GWh/week as seen in Fig. 13.5a. Resilience, $EENS$, was evaluated as 569 GWh/week with a standard deviation of 63 GWh/week. This EENS is about 28% of the weekly domestic demand for 2019 which translates into consumption of about 8 million households [15]. In comparison, [1] evaluated $EENS$ as 324 GWh/Week whereas [3] evaluated it as 690 GWh/Week. In both cases, climate model data were arbitrarily scaled to characterize windstorms and only 6 weather regions were considered for the entire GB.

Fig. 13.5

a Frequency plot and probability of exceedance of evaluated ENS values, b moving average of ENS per additional model run

Figure 13.5b shows that 1000 runs were sufficient in determining the EENS given that after 150 runs, the value deviates no more than ± 1%. Figure 13.6 shows the criticality of corridors based on the $RAW$ index. The corridors on the (bottom) horizontal axis are arranged in descending order of $RAW$ ranks, with corridor 41 being the most critical and 50, the least. The vertical segmented lines signify groups of five corridors which are considered simultaneously and cumulatively moving from left to right during the resilience enhancement process. It can be observed that 16 corridors have zero RAW, implying that adaptation measures may not improve system’s resilience to windstorms within these corridors. Of the three adaptation measures, responsiveness emerged to be the most effective compared to robustness and redundancy as seen in Fig. 13.7. The increase in resilience peaked at 70%, 55% and 35% respectively. All scenarios peaked after applying measures to the top 60% critical corridors.

Fig. 13.6

Criticality of corridors based on 100-year return gusts

Fig. 13.7

Level of resilience of RGBN under selected adaptation measures when applied to a cluster of transmission corridors

13.4 Conclusions

This paper presents a study of evaluating resilience of a power system against a projected extreme windstorm. Unlike previous studies that used reanalysis data and only had 6 weather regions, this study used historical ground observations from 173 met stations across the GB to characterize extreme wind threat with relatively high spatial resolution of weather regions.

The results show that a probable 100-year return gust event could have intensities ranging between 27 and 85 m/s. If such an event was to last a week, nearly 80% of OHL and 6% of towers could be damaged. This would result into loadshedding of 569 GWh/Week equivalent to consumption of about 8 million households. The study observed that responsiveness (70%) was a more effective adaptation measure than redundancy (55%) and robustness (35%). This is not conclusive considering that the study did not establish whether the assumptions made for the three measures were equally weighted. It was also observed that the level of criticality of corridors was dependent on the weather type and intensity, distribution of demand, network topology, and components’ vulnerabilities. The most vulnerable corridors are not necessarily the most critical in enhancing resilience. Moreover, organizational resilience could be more effective than infrastructural and operational resilience. Future work will seek to explore resilience of the system under a dynamic load and evaluation of the individual capacities of resilience (preparedness, absorptivity, and recovery).