11 Energy resilience is a vital consideration for ensuring the survivability of modern 12 infrastructure systems. Achieving 100% resilience, however, is often impractical and 13 economically burdensome. In this paper, we propose a smart investment framework 14 that enables decision-makers to determine optimal investments in energy resilience 15 based on available resources and desired levels of resilience. To illustrate the effect- 16 iveness of this framework, we present a case study of a campus microgrid research 17 and testing facility. Using a real-time simulation approach conducted with Typhoon 18 HIL, we evaluate the performance of the microgrid system over 24 hours following 19 four historically significant hurricanes that have affected Louisiana in the past few 20 years. The microgrid is designed to power local loads during outages, providing an 21 effective solution for enhancing energy resilience. Real solar data collected from our 22 1.1Megawatt(MW)solarfacilityontheUniversityofLouisianaatLafayettecampus 23 is integrated into the simulation, enabling a realistic evaluation of the system’s per- 24 formance under hurricane-induced disruptions. By employing the proposed smart 25 investment framework, decision-makers can better identify and address resilience 26 challenges. The framework facilitates informed investment decisions by consider- 27 ing available resources and aligning them with the desired level of resilience. This 28 approach avoids over-investment in unnecessary redundancy while ensuring critical 29 systems are adequately protected. Our research contributes to the field by demon- 30 strating the practicality and benefits of a smart investment framework for energy 31 resilience in a real-world scenario. The case study of the campus microgrid research 32 1 facility provides valuable insights for decision-makers in similar contexts, highlight- 33 ing the potential of this framework to guide resilient energy infrastructure planning 34 and investment strategies. 35 1. Introduction 36 Energy resilience assessment is becoming a critical part of contemporary power & energy 37 systems at the design and operation levels, considering the increasing climate change im- 38 pacts and natural disasters. Natural disasters can spread quickly, which affects the power 39 grids heavily and creates a negative impact on society and the economy Bhusal et al., 40 2020; Dugan et al., 2021; Mukhopadhyay & Nateghi, 2017. These unwanted weather con- 41 ditions are the main reasons for the major power outages, which cost billions of dollars as 42 modern civilizations depend on the continuous utilization of power and energy. Different 43 important sectors of the current civilization depend on the availability of electricity Dugan 44 et al., 2021; Hossain et al., 2021. The expenditure of natural disasters is around $25 to 45 $70 billion per year of the President. Council of Economic Advisers, 2013. According 46 to the National Oceanic and Atmospheric Administration (NOAA), 20 natural disasters 47 affected the USA in 2021, and each disaster’s financial damage was over $1 billion ‘NOAA 48 National Centers for Environmental Information (NCEI)’, 2022. Due to natural disasters, 49 power outages have happened more frequently in recent times, for instance, Hurricane 50 Sandy, which occurred in 2012 and caused 8.5 million people to go out of power of the 51 President. Council of Economic Advisers, 2013, the Hokkaido blackout of 2018 caused by 52 an earthquake, blackouts in California in 2019, and the infamous Texas power outages in 53 2021 due to the winter storm Dugan et al., 2021; Kenward, Raja et al., 2014. In 2021, the 54 National Oceanic and Atmospheric Administration (NOAA) named 2020 as the year of 55 extremes. Within the past six years, five major hurricanes have hit Louisiana, including 56 Nate (2017), Laura (2020), Delta (2020), Zeta (2020), and Ida (2021). These hurricanes 57 left thousands of people out of power from a few hours to several days or even months 58 Arora & Ceferino, 2023. In different sets of literature, increasing outages across the US 59 are reported largely as a result of outdated infrastructure and grid consolidation. Despite 60 this fact, replacing the grid anytime soon is highly unlikely, considering it would impose 61 several trillion dollars on the US economy. Therefore, research around responsive and 62 corrective approaches is of great importance to improve the grid’s resilience. 63 Resilience is a fairly new concept in power systems. Although there are different 64 definitions of resilience from various perspectives Arghandeh et al., 2016, a more general 65 definitionofresiliencereferstotheabilityofapowersystemtowithstandandabsorbhigh- 66 impact, low-probability (HILP) disturbances and quickly recover from those eventsAli et 67 al., 2023. Withstanding severe disturbances (e.g., hurricanes) is mainly discussed under 68 infrastructure resilience through hardening and related risk assessment activities Moglen 69 et al., 2023; Schweikert & Deinert, 2021. On the other hand, operational resilience is 70 2 linkedtoresponsiveandcorrectivecontrolschemesaswellasresourceadequacyAbianeh& 71 Ferdowsi, 2020; Ferdowsietal., 2019. Inordertoimproveresilience, ithastobequantified 72 first. There are several methods reported in the literature for resilience quantification. 73 This paper puts an emphasis on operational resilience rather than infrastructure. These 74 two categories are well discussed in Hamidieh & Ghassemi, 2022. 75 Resilience metrics are required as the first step of the investigation to improve re- 76 silience. Several works have been done, and different resilience metrics and approaches 77 are presented in the recent literature. Available resilience metrics can be classified into 78 three main categories: attribute-based, performance-based, and general Daeli & Moha- 79 gheghi, 2023. Attribute-based resilience metrics mainly concentrate on the behavior of 80 a system. Determining this type of metric requires reviewing the system’s performance 81 to measure the degree of the attributes held within it Vugrin et al., 2017. This type 82 of resilience metric basically provides qualitative assessments. Performance-based met- 83 rics can be utilized to evaluate the efficiency of different types of reinforcement tactics 84 installed in the system Vugrin et al., 2017. Performance-based metrics consist of two 85 subcategories metrics: performance metrics and consequence metricsRaoufi et al., 2020; 86 Vugrin et al., 2017. System performance metrics can model the behavior of the power 87 system in accordance with the natural disasters, whereas consequence metrics concentrate 88 on the impacts of power outages and can be quantified in the form of financial impacts, 89 social impacts, and security impacts Raoufi et al., 2020; Vugrin et al., 2017. Several 90 types of performance-based performance resilience metrics are available in the literat- 91 ureRaoufi et al., 2020. Attribute-based metrics are comparatively easier to model as they 92 depend on qualitative or semi-quantitative knowledge and analysis. However, this type of 93 metric cannot analyze the benefits achieved from potential resilience enhancements and 94 the effectiveness of investments. Hence, they are not as explanatory in comparison to 95 performance-based metrics for grid resilience planning and investment strategies Vugrin 96 et al., 2017. Performance-based metrics can be very complex and generally require a 97 large amount of data to model as they model different stages of operation, disruption, 98 and recovery Daeli & Mohagheghi, 2023. However, performance-based metrics are more 99 dynamic than attribute-based metrics: not only can they be utilized to analyze the resili- 100 ence of the system to previous events, but they can also simulate how the system will be 101 affected by future events. General metrics can be utilized to portray different aspects of 102 performance, functionality, impacts, etc. The Figure of Merit (FOM) curve is a common 103 resilience assessment tool in dynamic systems, not necessarily power systems. FOM rep- 104 resents the functionality of a system in terms of the quantity/quality of services delivered 105 by the system. The FOM has been used in different sets of literature for resilience ana- 106 lysis in different engineering systems such as transportation Janić, 2018 and energy Das 107 et al., 2020. In some literature, FOM metric/curve is referred to as trapezoid Force et al., 108 2022 or triangle curve Panteli et al., 2017. The resilience curve and advanced trapezoidal 109 resilience curve can be utilized as a general metric as they both can express different 110 3 dimensions of performance or consequences Daeli & Mohagheghi, 2023. In Fig. 1, the 111 resilience curve shows the changes in the resilience of the power network with respect to 112 time. The quality indicator of the resilience curve can be based on attribute-based or 113 performance-based metrics. Although it is very easy to interpret these types of curves, 114 these curves are unable to collect all the different dynamic resilience dimensionsPanteli 115 et al., 2017. 116 Figure 1: Traditional Resilience Curve Bie et al., 2017; Daeli & Mohagheghi, 2023; Lei et al., 2018; Mishra et al., 2020 While it is very important to measure the resilience of an existing system, it is also 117 very important to investigate the enhancement of the resilience of the system as well 118 as the necessary investment in comparison to the benefits and value it generates to the 119 whole systemAnderson et al., 2020. It is neither practical nor economical to have an 120 energy system that can fully withstand and absorb a wide range of disturbances with a 121 very high level of robustness and continue its service with no interruption. Therefore, 122 effective investment in the area of achievable resilience is of great importance in power 123 systems. In order to achieve a more resilient power system, microgrids with the capability 124 of operating in islanded mode are locally impactful if they can quickly respond to the loss 125 of the main grid and feed the local loads. The extent to which a microgrid can contribute 126 to serving the local loads after the main grid goes down depends on 1) the microgrid’s 127 resourcefulness and 2) the energy management strategy, assuming microgrid assets have 128 survived the severe event. Microgrid is proposed in many academic studies and industry 129 reports as a promising solution to expedite the restoration process Igder et al., 2022 130 and mitigate the duration/frequency of outages Khodayar et al., 2012 and/or impacts of 131 outages Lin et al., 2022. Some of the commonly proposed improvement methods include 132 4 prediction Mohammadian et al., 2021, load shedding Li et al., 2017; Sedzro et al., 2018, 133 reconfiguration Choobineh & Mohagheghi, 2015; Ding et al., 2020, and mobile resources 134 Lei et al., 2016. These improvement strategies are more tied to microgrid planning. From 135 the operation’s standpoint, resilience-oriented energy management techniques have been 136 proposed in some research works recently Gholami et al., 2016; Liu et al., 2020. However, 137 the proposed energy management techniques are more in the form of optimization-driven 138 scheduling in microgrids. When it comes to energy resilience, planning and operation are 139 complementary, which is not well discussed in the existing literature. Furthermore, energy 140 planners and decision-makers need to have an insight into the cost of resilience so they can 141 better invest to meet certain requirements and needs. The relationship between resilience 142 improvement and necessary cost is not well investigated in the literature. In Benallal et 143 al., 2023, Bayesian inference-based energy management was proposed to supply priority- 144 based loads in a hybrid microgrid environment. In Ali et al., 2023, authors investigated 145 the comparison between their proposed grid-connected system and renewable energy- 146 based ad-hoc microgrid to supply critical loads (local hospital). Although these research 147 studies investigated supplying the critical load and presented economic analysis using 148 HOMER, the authors did not provide an in-depth analysis of the resilience enhancement 149 on the variation of investment considering multiple natural disasters. A practical long- 150 term planning strategy should be investigated to enhance the resilience of power systems. 151 This research work studies resilience-enabling resource adequacy using resilience met- 152 rics from planning and operation perspectives. High-fidelity real-time simulations are 153 conducted using Typhoon Hardware In Loop (HIL). The case study is the microgrid facil- 154 ity at the University of Louisiana at Lafayette, USA. The cost of resilience is estimated, 155 andoperationallimitationsareidentifiedindifferentscenariosofmultiplehurricanes. This 156 paper serves as a practical guideline for decision-makers, especially for community energy 157 systems. Our proposed planning scheme will give decision-makers a better insight into 158 what investment is required to improve resilience by a certain level. Resilience studies are 159 always scenario-dependent. Therefore, as step zero, a high-impact, low-frequency event 160 must be identified as the disturbance scenario affecting the system. It largely depends on 161 the geographical area for weather-related events. This paper assumes for every scenario 162 of all the hurricanes that the main power grid is down, and the microgrid is expected to 163 serve the loads solely until the main power grid is restored locally. 164 So, the main contributions of this paper are given below: 165 •Introducing a novel framework for optimal energy resilience investments, aligning 166 resources with desired resilience levels to avoid unnecessary redundancy. 167 •Utilizing a high-fidelity real-time simulator evaluating a campus microgrid’s per- 168 formance in powering local loads during outages, with a focus on resilience enhance- 169 ment. 170 •Quantitatively investigating the cost of improving resilience, providing insights into 171 5 balancing economic considerations with desired energy infrastructure resilience. 172 Therestofthepaperisorganizedasfollows. Insection(2), resiliencemetrics, technical 173 analysis, andeconomicanalysismethodsarediscussed. Section(3)describesthemicrogrid 174 as the case study. Results are presented in section (4). Conclusions and future works are 175 presented in sections (5) and (6). 176 2. Case Study 177 Figure 2: Overview of the UL-Cleco AC/DC Microgrid Facility The case study in this investigation is a microgrid shown in Fig. 2. Load data from 178 a real distribution feeder is scaled and utilized for three different load categories of this 179 microgridsystem. Tosupplytheloaddemandbasedontheirpriority, threeloadcategories 180 are classified as critical load 1, critical load 2, and critical load 3. Here, critical load 1 181 represents the highest priority for load serving, also labeled as priority load 1; critical load 182 2 represents the moderate priority for load serving, also labeled as priority load 2; critical 183 load 3 represents the lowest priority for load serving, also labeled as priority load 3. For 184 24 hours, the total load demand for priority load 1, priority load 2, and priority load 185 3 is 681.762 kW, 957.701 kW, and 638.475 kW, respectively. The 24-hour load profiles 186 for different priorities are shown in Fig. 3. The simulation has been done considering 187 24-hour power outages for four hurricanes that hit Louisiana in the past six years. Those 188 hurricanes are Nate (2017), Laura (2020), Zeta (2020), and Ida (2021). For the hurricanes 189 6 Laura (2020), Zeta (2020), and Ida (2021), it is considered that the power outages started 190 at12amandranfor24hours. Toinvestigatefromadifferentdimension, thepoweroutage 191 for Hurricane Nate (2017) is considered to start at 7 am and run for the next 24 hours. 192 To make the investigation more realistic, the solar radiation data corresponding to every 193 hurricane occurring day is collected from the University of Louisiana at Lafayette’s 1.1 194 MW solar PV plant facility Veerendra Kumar et al., 2022. The normalized solar power 195 profile corresponding to each Hurricane day is shown in Fig. 4. 196 Figure 3: Different Priorities Load Data Figure 4: Solar Radiation Data (Normalized) The microgrid simulation for every hurricane contains three scenarios utilizing three 197 different configurations of solar PV plant and battery energy storage system (BESS). For 198 7 Table 1: Configuration of Three Scenarios for Every Hurricanes Scenario PV SizeBESS Size (kW)BESS capacity (kWh) 150kW 50kW 100kWh 2150kW 150kW 300kWh 3250kW 250kW 500kWh scenario (I), the solar PV plant is 50 kW, whereas the rating of BESS is 50 kW and 100 199 kWh. For scenario (II), the solar PV plant is 150 kW, whereas the rating of BESS is 150 200 kW and 300 kWh. For scenario (III), the solar PV plant is 250 kW, whereas the rating 201 of BESS is 250 kW and 500 kWh. Table 1 contains the simulation configurations of the 202 three scenarios for every hurricane. 203 The selection of three different PV sizes helps to investigate in detail for enabling three 204 different PV penetration environments. Solar PV penetration is calculated as the ratio 205 of the peak solar photovoltaic power to the peak load apparent power on the feeder Hoke 206 et al., 2012; Ullah et al., 2021. 207 PV Penetration =Peak PV Power Peak Load Apparent Power(1) Three PV plant sizing is 50kW, 150 kW, 250 kW, and the peak load apparent power 208 is 161.90 KVA. So, using the equation 1, three scenarios of this study represent 30.88%, 209 92.64%, and 154.41% PV penetration, respectively. For battery capacity, the optimal 210 BESS profit can be generated with 2 kWh of storage capacity per kilowatt peak (kWp) of 211 solar PV system Lund, 2018. So, for three scenarios, BESS size is selected to 100 kWh, 212 300 kWh, and 500 kWh, respectively. The maximum and minimum state of charge (SOC) 213 for BESS are selected as 90% and 10%, respectively. As we know the probable hurricane 214 arriving day from the weather forecast, it is considered that the BESS is charged and the 215 BESS SOC is 90% when the simulation starts. 216 To investigate the real-time performance of the microgrid, Typhoon HIL real-time 217 simulator is used to model and analyze the proposed algorithm. 218 3. Methodology 219 3.1 Resilience Metrics 220 During weather-related power outages, it takes several hours to days to restore the main 221 power grid. The formation of microgrids is an effective solution to provide support during 222 power outages. It is realistically impossible to supply all the loads when the main power 223 grid is not operational. Therefore, the loads can be classified based on their priority. 224 Considering 24 hours of power outage for every natural disaster, the served critical loads 225 8 Figure 5: Flowchart of The Microgrid Operation Algorithm can be calculated and investigated to find out the resilience level of the microgrid. 226 In our proposed resilience metric, resilience will be evaluated based on the amount 227 of energy supplied to the loads, concentrating on the most critical loads. All the loads 228 will be divided into three categories, where the load groups 1, 2, and 3 will be known 229 as priority load 1, priority load 2, and priority load 3. Here, priority load 1 is the most 230 critical load, priority load 3 is the least critical load, and priority load 2 stays in between 231 them. Researchersinvestigatedresilienceenhancementusingthevalueoflostload(VoLL), 232 considering critical loads and non-critical loads. Several recent research studies Gao et al., 233 2017; Nazemi et al., 2021; Yao, Wang & Zhao, 2018; Yao, Zhao et al., 2018; Yao et al., 234 2019, 2020 emphasized five times more weight on the most critical loads in comparison to 235 the least critical loads. As priority load 1 is the most critical load and priority load 3 is the 236 least critical load in this study, the weighted factors 5, 2.5, and 1 are assigned for priority 237 load 1, 2, and 3, respectively. So, our proposed resilience metrics can be calculated using 238 the following equation. 239 Resilience, R = 5α1+ 2.5α2+α3 (2) In (2), α1represents conditions of the served load for priority load 1. If priority load 240 1 is served for a time interval, α1will be considered as 1 whereas, α1will be considered 241 9 as 0 if the load is not served. Likewise, α2,α3will be 1 or 0 for priority load 2, and 3, 242 respectively. As α1,α2,α3maximum value can be 1, the maximum resilience that can 243 be achieved is 8.5. Using our proposed resilience metrics, we can evaluate the resilience 244 level of a power grid (concentrating on the amount of energy served on the most critical 245 loads). 246 3.2 Technical Analysis 247 Our proposed algorithm is provided as a flowchart in Fig. 5. The algorithm is designed 248 to satisfy the loads during an outage, concentrating on the most critical load category. 249 This microgrid case study consists of a solar PV plant and battery energy storage system 250 (BESS)tosupplydifferentprioritiesofloads. Duringthepoweroutage, thesolarPVplant 251 and BESS will coordinate to supply the critical loads effectively for a longer duration of 252 hours. During the mid-day or when the solar radiation remains higher for a longer time 253 horizon, it tends to be a more efficient approach to charge the battery to a certain level at 254 first instead of satisfying the less critical load so that the microgrid achieves the ability to 255 supply the critical load 1 during the greater amount of power outage hours. The proposed 256 control system will continuously analyze the solar PV generation, battery state of charge 257 (SOC), and load demands and will take steps accordingly. When there is any solar PV 258 generation, the control system will check the battery SOC conditions and satisfy the load 259 demands based on the battery’s SOC. If the battery SOC is greater than 70%, all the load 260 demands will be fulfilled by solar PV and BESS. If solar PV generation is higher than 261 all the load demands, solar PV will satisfy the power demands by itself, and the extra 262 generated PV power will go to the battery for its charging. If the solar-generated power 263 is less than the power demands of all the loads, solar PV and battery storage systems will 264 satisfy the load demands together. When the battery SOC remains in the range between 265 70% to 40%, only priority loads 1 and 2 will be served, and priority load 3 will be cut 266 off. If solar PV generation is higher than the demands of priority loads 1 & 2, solar PV 267 will satisfy the power demands by itself, and the extra generated PV power will go to 268 the battery for its charging. Otherwise, solar PV and battery storage systems will satisfy 269 the load demands together. When the battery SOC remains between 40% to 10%, only 270 priority load 1 will be satisfied, whereas priority loads 1 & 2 will be curtailed. If solar 271 PV generation is higher than the demands of priority loads 1, solar PV will satisfy the 272 power demands by itself, and the extra generated PV power will go to the battery for its 273 charging. Otherwise, solar PV and battery storage systems will satisfy the load demands 274 together. If the battery SOC is less than 10%, all the priority loads will be curtailed, and 275 the battery will go to charging mode solely. 276 When there is no solar PV generation, the battery will satisfy the loads. If the battery 277 SOC remains higher than 80%, all the loads will be supplied. If the SOC stays between 278 80% to 50%, only the priority loads 1 & 2 will be supplied while priority load 3 will be 279 cut off. When the SOC remains in the range of 50% to 10%, only priority load 1 will be 280 10 served, whereas priority loads 2 & 3 will not be satisfied. If the battery SOC go below 281 10%, all the loads will be curtailed. 282 3.3 Economic Analysis 283 This research studies the economic assessment from different perspectives of economic 284 indicators. 25 years is considered as the average life duration of solar PV panels Anusuya 285 et al., 2023; Chowdhury et al., 2020; Tan et al., 2022. A solar PV power generation-based 286 project consists of design, building, and operation of a solar PV power plant for a time 287 period of 20-30 yearsCurtis et al., 2021. In this study, a 24-year time horizon is selected 288 for the economic assessment of this microgrid studyUllah et al., 2023. The time duration 289 of solar PV inverter and BESS is 12 years and 10 years, respectivelyMongird et al., 2020; 290 Ramasamy et al., 2022. In this investigation, 8 years is selected as the time duration 291 of the solar PV inverter and BESS as the advanced features (i.e., Volt-VAR control, 292 Volt-Watt control, etc.) shorten the inverter’s conventional lifetime Gandhi et al., 2018. 293 Cost analyses are provided for all three scenarios of the four hurricanes. Furthermore, the 294 investigation is also extended to analyze the impact of the increased number of Hurricanes 295 in a 24-year time horizon (considering 4 hurricanes in 1 set). 296 The revenue is produced from the selling of solar plus storage power to the priority 297 loads 1, 2, and 3. Using 3, the revenue, Rcan be found where Eirepresents the energy 298 supplied to the priority loads in kWh, and αis the selling price of solar plus storage energy 299 in $/kWh. Inflation factor, dis considered as 2.5% for this investigation Ramasamy et 300 al., 2022. During the hurricane days emergency supply, the value of αis considered as 301 $10/kWh, $5/kWh, and $2/kWh for priority load 1 (most critical load), priority load 2 302 (medium critical load), and priority load 3 (least critical load), respectively Nazemi et al., 303 2021; Yao, Wang & Zhao, 2018; Yao, Zhao et al., 2018; Yao et al., 2019, 2020. For all the 304 remaining regular days, the value of αis considered as $0.10/kWh in this case study. 305 R=nX i=1Ei·α·(1 +d)i−1(3) Equation 4 calculates the expenditure of the solar PV system which is the algebraic 306 summation of the market price of the solar PV panel, CMAR PV, operation and maintenance 307 cost of the solar, COM PV, and salvage value of the solar PV, CSAL PV. Equation 5 calculates 308 the expenditure of the solar PV inverter, which is the algebraic summation of the market 309 price of the inverter, CMAR INV, operation and maintenance cost of the inverter, COM INV, salvage 310 valueofthesolarinverter, CSAL INV. Equation6isusedtocomputetotalinverterexpenditure 311 for 24 years time period where SINVis the rating of the inverter in kVA, dis the inflation 312 factor, and TINV Ris the lifetime of the inverter. 313 CPV=CMAR PV +COM PV−CSAL PV (4) 11 β=CMAR PV,INV +COM PV,INV −CSAL PV,INV (5) CPV,INV =nX j=1SINV·β·(1 +d)(TINV R 2)(j−1)(6) The BESS expenditure is calculated based on its power and energy ratings using 314 equation 7 and 8, respectively. Equation 7 is used to determine the BESS cost for power 315 rating, γ, which is the algebraic summation of the market price of BESS for power rating, 316 CMAR BESS,P, O&M cost of the BESS for power rating, COM BESS,P, and the salvage value of 317 BESS for power rating, CSAL BESS,P. Equations 8 is used to calculate the BESS cost for 318 energy rating, η, and this calculation follows the same approach of the equation 7. ηis319 determined using the market price of BESS for energy rating, CMAR BESS,E, O&M cost of the 320 BESSforenergyrating, COM BESS,E,andthesalvagevalueofBESSforenergyrating, CSAL BESS,E.321 In equation 9, BESS cost for 24 years is calculated where the BESS lifetime, TBESS R, is 322 considered as 8 years, and pis the BESS depreciation rate for each year, 2%. PBESS,323 andEBESSrepresent the power capacity and energy capacity of the battery, respectively. 324 To calculate the battery inverter cost, equation 10 is utilized where the cost of the BESS 325 inverter is the algebraic summation of the market price of the BESS inverter, CMAR BESS,INV ,326 operation and maintenance cost of the BESS inverter, COM BESS,INV , salvage value of the 327 BESS inverter, CSAL BESS,INV . 328 γ=CMAR BESS,P +COM BESS,P −CSAL BESS,P (7) η=CMAR BESS,E +COM BESS,E −CSAL BESS,E (8) CBESS =nX k=1[γ·PBESS +η·EBESS]·(1−p)(TBESS R−1)(k−1)(9) δ=CMAR BESS,INV +COM BESS,INV −CSAL BESS,INV (10) CBESS,INV =nX j=1SBESS,INV ·δ·(1 +d)(TINV R 2)(j−1)(11) Intable2, alltheinputparametersofeconomicanalysisandtheircorrespondingvalues 329 are included. Here, we presented some economic indicators that measure the benefit of 330 solar plus storage systems in power distribution systems for 24 years operation horizon. 331 1.Total cost : the Total cost, C, is the summation of costs for solar PV panel, solar 332 PV inverter, BESS, and BESS inverter expressed in 12. 333 C=CPV+CPV,INV +CBESS +CBESS,INV (12) 12 2.Gained profit by solar system’s owner : The profit, Pis the difference between 334 the revenue and the total cost calculated using the equation 13. The revenue, R,335 expressed in the equation 3. 336 P=R−C. (13) 3.NetProfitMargin : Thenetprofitmargin NPM, orsimplynetmargin, represents 337 how much net income or profit is generated as a percentage of revenue made by solar 338 system owner. The ratio represents the net profit to revenue for the owner of a solar 339 system facility. 340 NPM =P R(14) 4.Net Present Value : Two terms characterize the net present value ( NPV), the 341 present discounted value of costs PDCin (16) and the present discounted value 342 of revenues PDRin (15) by NPV =PDR −PDC. If we consider Rito be the 343 (undiscounted) revenues (benefits) of the solar system project during the year iand 344 we consider Cito be the (undiscounted) costs of the solar system project during the 345 year i, afterward, we can calculate NPVusing equation (17). When the NPVis346 more than zero, the investment plan is considered as profitable from the investor 347 side. 348 PDR =TX i=1Ri (1 +d)i−1(15) PDC =TX i=1Ci (1 +d)i−1(16) NPV =TX i=1(Ri−Ci) (1 +d)i−1(17) 5.Revenue-Cost Ratio : The revenue-cost ratio is the ratio of PDRtoPDCwhich 349 is mentioned in (18). When the RCRis greater than one, the investment plan will 350 make revenue for the investor. 351 RCR =PDR PDC=PT i=1Ri (1+d)i−1 PT i=1Ci (1+d)i−1(18) 13 Table 2: Different Input Parameters of Economic Analysis Parameters Value Reference α 10, 5, 2, 0.1 ($/kWh) Nazemi et al., 2021; Yao, Wang & Zhao, 2018; Yao, Zhao et al., 2018; Yao et al., 2019, 2020 d 2.5% Ramasamy et al., 2022 CMAR PV 400 ($/kW) Ramasamy et al., 2022 COM PV 1% ($/kW) Deotti et al., 2020 CSAL PV 10% ($/kW) Humphreys & Brown, 1990 CMAR INV 60 ($/kW) Ramasamy et al., 2022 COM INV 1% ($/kW) CSAL INV 10% ($/kW) Humphreys & Brown, 1990 CMAR BESS,INV 50 ($/kW) Ramasamy et al., 2022 COM BESS,INV 1% ($/kW) CSAL BESS,INV 10% ($/kW) Humphreys & Brown, 1990 CMAR BESS,P 628 ($/kW) Ramasamy et al., 2022 COM BESS,P 10 ($/kW) Mongird et al., 2020 CSAL BESS,P 10% ($/kW) Humphreys & Brown, 1990 CMAR BESS,E 157 ($/kW) Ramasamy et al., 2022 COM BESS,E 0.003 ($/kW) Mongird et al., 2020 CSAL BESS,E 10% ($/kW) Humphreys & Brown, 1990 EBESS 100, 300, 500 (kWh) PBESS 50, 150, 250 (kW) p 2% SINV 55, 162, 275 kVA TINV R 8 Years TBESS R 8 Years 4. Results and Discussion 352 In this section, the results of the resilience metrics, technical analysis, and economic 353 analysis are presented and analyzed. All the simulation results are collected from the 354 real-time simulator Typhoon HIL for its high-fidelity characteristics. 355 4.1 Resilience Metrics 356 After the completion of microgrid simulation for all the scenarios considering all power 357 outages caused by the hurricanes, the resilience curve of all scenarios for all the power 358 outages is plotted for 24 hours. In Fig. 6, the resilience curve for three scenarios is 359 plotted for a 24-hour power outage due to Hurricane Laura, which runs from 12 am to 360 12 am. From 2 am to 8:45 am and 6:45 pm to 12 am, the resilience value remains zero 361 for scenario 1; during these time intervals, solar PV and BESS cannot serve any load at 362 all. From 12 am to 2 am and 8:45 am to 6:45 pm, different priority loads are satisfied in 363 scenario 1. It is important to mention that scenario 1 resilience value remains zero for a 364 longer period of time in comparison with scenario 2 & 3 (scenarios 1, 2, 3 configuration 365 is already provided in Table 1). Although scenario 2 contains a resilience value of zero 366 from 6 am to 8:15 am and from 9 pm to 12 am, it shows a resilience value of zero for 367 5.25 hours whereas scenario 1 shows it for 12 hours. Scenario 3 shows a higher resilience 368 14 trend than scenario 1 and scenario 2 for the significant time duration during the 24-hour 369 time horizon. The resilience values of scenario 3 also show that energy is supplied to the 370 most critical load during the whole 24 hours without curtailing any priority load 1. The 371 lowest resilience value of scenario 3 is 5, whereas the lowest resilience values of scenario 372 1 and scenario 2 stay zero for 12 and 5.25 hours, respectively. Scenario 3 shows the best 373 resilience curve where the solar PV and BESS successfully served the most critical load 374 for a 24-hour time horizon. The results show the extent to which resilience is improved 375 with a certain investment in resources. 376 Figure 6: Resilience evaluation for the hurricane Laura In Fig. 7, the resilience value for three scenarios is plotted for a 24-hour power outage 377 due to Hurricane Zeta. From 2 am to 9 am and from 6.15 pm to 12 am, the resilience 378 value remains zero for scenario 1. Moreover, scenario 1 resilience value remains zero 379 for maximum outage hours among all three scenarios. Although scenario 2 contains a 380 resilience value of zero from 6 am to 8:45 am and from 9:15 pm to 12 am, it shows zero 381 resilience value for only 5.5 hours whereas scenario 1 holds zero resilience value for 12.75 382 hours, indicating more than 50% improvement in scenario 2. Scenario 3 shows a higher 383 resilience trend than scenario 1 and scenario 2 for the significant time of the 24-hour time 384 horizon. The resilience values of Scenario 3 also show that energy is supplied to the most 385 critical load almost all 24 hours except from 8 am to 8:30 am and from 23:45 pm to 12 AM 386 when the resilience value of scenario 3 becomes 0. It is worth mentioning that scenario 387 3 configuration of solar PV and BESS also served priority loads 2 & 3 much better than 388 scenario 1 & 2. 389 In Fig. 8, the resilience value for three scenarios is plotted for a 24-hour power outage 390 due to Hurricane Ida. From 2 am to 8:45 am and from 6 pm to 12 am (except the in- 391 between time duration of 7:45 pm to 8 pm), the resilience value remains zero for scenario 392 15 Figure 7: Resilience evaluation for the hurricane Zeta 1. Moreover, scenario 1 resilience value remains zero for maximum outage hours among 393 all three scenarios. Although scenario 2 contains a resilience value of zero from around 394 6 am to around 8:15 am and from 8:30 pm to 12 am, it shows a resilience value of zero 395 for only 5.75 hours, whereas scenario 1 shows 12.75 hours. Scenario 3 shows a higher 396 resilience value characteristics than Scenario 1 and Scenario 2 for the significant time of 397 the 24-hour time horizon. The resilience values of scenario 3 also show that energy is 398 supplied to the most critical load for all 24-hour power outages without any curtailment 399 of the most critical load. 400 Figure 8: Resilience evaluation for the hurricane Ida 16 In Fig. 9, the resilience value for three scenarios is plotted for 24-hour power outages 401 due to Hurricane Nate. From 8 am to 9 am and from 6.15 pm to 7 am, which represents 402 13.75 hours of the 24-hour time period, the resilience value remains zero for scenario 1. 403 Moreover, the scenario 1 resilience value remains zero for the maximum number of outage 404 hours among all the scenarios. Although scenario 2 contains a resilience value of zero 405 from 9 pm to 7 am, it contains a resilience value of zero for 10 hours, whereas scenario 406 1 has zero resilience values for 13.75 hours . Scenario 3 shows a higher resilience value 407 than scenario 1 and scenario 2 for the significant time of the 24-hour time horizon. The 408 resilience values of Scenario 3 also show that energy is supplied to the most critical load 409 successfully from 7 AM to 12 AM, whereas from 12:15 am to 7 am, for 6.75 hours, the 410 resilience value of scenario 3 remains 0. Although scenario 3 of Hurricane Nate could not 411 supply energy to the most critical load for 6.75 hours, which is the worst performance 412 among all scenarios 3 of four hurricanes, still scenario 3 configuration of the power outages 413 caused by Hurricane Nate shows better performance in serving the most critical load 7 414 hours more than scenario 1 and 3.25 hours more than scenario 2. 415 Figure 9: Resilience evaluation for the hurricane Nate 4.2 Technical Analysis 416 In this section, the served amount of different critical loads for all the scenarios of power 417 outages will be described and analyzed. In Fig. 10, the served load of Priority Loads 1, 418 2, and 3 are illustrated for all three scenarios of power outages due to Hurricane Laura. 419 For priority load 1, 35.89% of loads are served in scenario 1, whereas 70.07% loads are 420 served in scenario 2. In scenario 3, all the 100% priority load 1 is served successfully 421 during the whole 24 hours. For priority load 2, 16.15% loads are served in scenario 1, 422 whereas 34.09% loads are served in scenario 2. In scenario 3, 43.25% of priority load 2 is 423 17 Figure 10: Served Loads for the Hurricane Laura (In Percent) Figure 11: Served Loads for the Hurricane Zeta (In Percent) served. For priority load 3, 4.83%, 20.11%, and 24.93% of loads are served in scenarios 424 1, 2, and 3, respectively. During all three scenarios, there is a trend of increasing served 425 load for all the priority loads. Most importantly, the amount of served loads of priority 426 18 Figure 12: Served Loads for the Hurricane Ida (In Percent) Figure 13: Served Loads for the Hurricane Nate (In Percent) load 1 doubled in scenario 2 in comparison to scenario 1, whereas scenario 3 shows the 427 best performance by satisfying 100% priority load 1, which is the most critical load. 428 In Fig. 11, the served load of Priority Loads 1, 2, and 3 are depicted for all three 429 19 Figure 14: Serving Time Duration of Most Critical Load (In Percent) scenarios of power outages caused by Hurricane Zeta. For priority load 1, 31.84% loads 430 are served in scenario 1, whereas 69.28% loads are served in scenario 2. In scenario 3, 431 96.55% priority load 1 is served during the whole 24 hours. For priority load 2, 17.37% 432 loads are served in scenario 1, whereas 29.12% loads are served in scenario 2. In scenario 433 3, 39.93% of priority load 2 is served. For priority load 3, 8.94%, 17.76%, and 22.05% of 434 loads are served in scenarios 1, 2, and 3, respectively. During all three scenarios, there 435 is also a similar trend of increasing served load for all the priority loads, like Hurricane 436 Laura. For priority load 1, the amount of served loads of priority load 1 is more than 437 doubled in scenario 2 in comparison to scenario 1, whereas scenario 3 shows the best 438 performancebyserving96.55%priorityload1, whichisthemainobjectiveofourproposed 439 control system. For the outage caused by Hurricane Zeta, the solar PV plant received 440 solar radiation 45 minutes later in the early morning in comparison to the power outages 441 caused by Hurricane Laura, which is the major reason for satisfying 96.55% most critical 442 load. If the solar radiation would come earlier in the morning, the solar PV plant could 443 start generating solar PV power earlier, and BESS could also go into charging mode, 444 which could help to achieve 100% satisfaction of most critical loads like the previous case 445 study of power outages by Hurricane Laura. 446 In Fig. 12, the served load of Priority Loads 1, 2, and 3 are drawn for all three 447 scenarios of power outages caused by Hurricane Ida. For priority load 1, 32.23% loads 448 are served in scenario 1, whereas 66.53% loads are served in scenario 2. In scenario 3, all 449 the 100% priority load 1 demand is satisfied successfully during the whole 24 hours. For 450 priority load 2, 7.34% loads are served in scenario 1, whereas 30.77% loads are served in 451 scenario 2. In scenario 3, 39.32% of priority load 2 is served. For priority load 3, 0.9%, 452 10.14%, and 20.50% of loads are served in scenarios 1, 2, and 3, respectively. During 453 all three scenarios, there is a trend of increasing served load for all the priority loads. 454 20 Most importantly, the amount of served loads of priority load 1 is more than doubled in 455 scenario 2 in comparison to scenario 1, whereas scenario 3 shows the best performance 456 by satisfying 100% of the most critical load demand. For the outage caused by Hurricane 457 Ida, the solar PV plant received earlier solar radiation than Hurricane Zeta but later than 458 Hurricane Laura. So, this helped in satisfying 100% of the most critical load in scenario 459 3, like Hurricane Laura. Although the most critical load is satisfied 100% in scenario 3 460 of Hurricane Ida, the satisfaction of priority load 3 is lowest in comparison to Hurricane 461 Laura and Hurricane Zeta. In comparison to Hurricane Laura and Hurricane Zeta, the 462 lower peak value of solar radiation throughout the power outage caused by Hurricane Ida 463 is the main reason for the lower satisfaction of priority load 3. 464 In Fig. 13, the served load of Priority Loads 1, 2, and 3 are drawn for all three 465 scenarios of power outages caused by Hurricane Nate. For priority load 1, 31.01% loads 466 are served in scenario 1, whereas 53.77% loads are served in scenario 2. In scenario 3, 467 70.6% priority load 1 demand is satisfied. For priority load 2, 10.27% loads are served in 468 scenario 1, whereas 33.83% loads are served in scenario 2. In scenario 3, 43.35% of priority 469 load 2 is served. For priority load 3, 1.64%, 16.53%, and 24.63% of loads are served in 470 scenarios 1, 2, and 3, respectively. During all three scenarios, there is a trend of increasing 471 served load for all the priority loads like all the other hurricanes. Most importantly, the 472 amount of served loads of priority load 1 is 22% higher in scenario 2 in comparison to 473 scenario 1, whereas scenario 3 shows the best performance by satisfying 70.6% priority 474 load 1 demand, which is almost double in comparison to scenario 1. Although the solar 475 PV plant received early solar radiation in morning and received moderate peak solar 476 radiation throughout the power outages caused by Hurricane Nate, the different approach 477 (investigating from 7 am to 7 am next day, unlike the previous 3 hurricanes time duration 478 from 12 am to 12 am next day) played the major reason for satisfying the lowest amount of 479 most critical load among all the four hurricanes. The power outages caused by Hurricane 480 Nate occurred from 7 am to 7 am the next day for 24 hours. Although BESS stays in a 481 healthy condition from 7 am to 7 pm, it can not get any charging opportunities in the 482 next 12 hours. On the other hand, all the previous 3 hurricanes, BESS discharges from 483 12 am to 7 am(when there is no solar PV generation) and gets opportunities for charging 484 for the next 12 hours(from 7 am to 7 pm), which essentially helps BESS to supply in the 485 dark hours(when there is no sunlight, from 7 pm to 12 am). 486 Our proposed algorithm fully prioritizes satisfying the priority load 1 (most critical 487 load) throughout the time horizon. In Fig. 14, the time duration of the served most 488 critical load is presented. For Hurricane Laura, the most critical load is satisfied for 50% 489 hours of the 24 hours in scenario 1, whereas the most critical load is served in scenario 490 2 for 78.13% hours of the 24 hours. Scenario 3 shows the best performance by satisfying 491 the most critical load for the whole 24 hours. For Hurricane Zeta, the most critical load 492 is satisfied for 46.88% hours of the 24 hours in scenario 1, whereas the most critical load 493 is served in scenario 2 for 77.08% hours of the 24 hours. Scenario 3 shows the best 494 21 performance by satisfying the most critical load for around 96.88% time of the whole 24 495 hours. For Hurricane Ida, the most critical load is satisfied for 46.88% hours of the 24 496 hours in scenario 1, whereas the most critical load is served in scenario 2 for 76.04% hours 497 of the 24 hours. Scenario 3 shows the best performance by satisfying the most critical 498 load for the whole 24 hours. For Hurricane Nate, the most critical load is satisfied for 499 around 42.71% hours of the 24 hours in scenario 1, whereas the most critical load is served 500 in scenario 2 for 58.33% hours of the 24 hours. Scenario 3 shows the best performance 501 by satisfying the most critical load for 71.88% hours of the 24 hours. Among all the 502 hurricanes, Scenario 3 shows best performance in comparison to Scenario 1 & 2. 503 In Fig. 15, Fig 16, Fig 17, and Fig18, the battery SOC profiles for all the scenarios 504 of the hurricanes are presented. In Fig. 15, the battery SOC for all three scenarios is 505 provided for Hurricane Laura. In scenario 1, the battery SOC stays at 10% for around 10 506 hours, which is the maximum duration of hours in all the scenarios. 10% SOC indicates 507 that no loads are served during that time horizon. In scenario 2, the battery SOC shows 508 better characteristics, and SOC stays at 10% for around 4 hours. The SOC stays at 90% 509 for around 6 hours, indicating that all the loads are served during that time. In scenario 510 3, the minimum SOC never reaches 10% ,and the minimum SOC is 12.05%, which shows 511 that at least priority load 1 is served for the whole 24 hours. The SOC remains 90% for 512 more than 6 hours, indicating that all the loads are served during that time. 513 Figure 15: Battery SOC for the Hurricane Laura In Fig. 16, the battery SOC for all three scenarios is provided for Hurricane Zeta. In 514 scenario 1, the battery SOC stays at 10% for around 11 hours, which is the maximum 515 duration of hours in all the scenarios. In scenario 2, the battery SOC shows better 516 characteristics, and SOC stays at 10% for around 5 hours. The SOC stays at 90% for 517 around 5 hours, indicating that all the loads are served during that time. In scenario 3, 518 the minimum SOC reaches 10% for less than an hour in the whole 24 hours, which shows 519 22 that at least priority load 1 is served for almost all 24 hours. The SOC stays 90% for 520 more than 5.5 hours, indicating that all the loads are served during that time. 521 Figure 16: Battery SOC for the Hurricane Zeta In Fig. 17, the battery SOC for all three scenarios is provided for Hurricane Ida. In 522 scenario 1, the battery SOC stays at 10% for more than 9 hours, which is the maximum 523 duration of hours in all the scenarios. In scenario 2, the battery SOC shows better 524 characteristics, and SOC stays at 10% for around 5.5 hours. The SOC stays at 90% for 525 around 2 hours, indicating that all the loads are served during that time. In scenario 3, 526 the minimum SOC never reaches 10%, and the minimum SOC is 11.25%, which shows 527 that at least priority load 1 is served for the whole 24 hours. The SOC remains 90% for 528 around 3 hours, indicating that all the loads are served during that time. 529 In Fig. 18, the battery SOC for all three scenarios is provided for Hurricane Ida. In 530 scenario 1, the battery SOC stays at 10% for around 13 hours, which is the maximum 531 duration of hours in all the scenarios. After 1 hour from starting at 7 am, the SOC reaches 532 a maximum of around 60%. In scenario 2, the battery SOC shows better characteristics, 533 and SOC stays at 10% for around 10 hours. The SOC stays at 90% for around 3 hours, 534 indicating that all the loads are served during that time. In scenario 3, the minimum 535 SOC to reaches 10% for less than 7 hours, which shows the best performance among all 536 the three scenarios. The SOC remains 90% for more than 4 hours, indicating that all the 537 loads are served during that time. 538 4.3 Economic Assessment 539 Table 3 presents the investment required for 24 years considering scenarios 1, 2, and 3, 540 respectively. Scenario 1 requires 147.95 thousand US dollars, whereas Scenario 2 requires 541 381.97 thousand dollars, which is more than 2.5 times the investment of Scenario 1. 542 23 Figure 17: Battery SOC for the Hurricane Ida Figure 18: Battery SOC for the Hurricane Nate Scenario 3 requires the maximum investment among all three scenarios, 739.75 thousand 543 dollars. 544 Table 4 provides the profit produced during 24 years time duration for all three scen- 545 arios considering different numbers of hurricane sets. For one hurricane set (considering 546 4 hurricanes in 1 set) in 24 years, the profit of scenarios 1, 2, and 3 is 280.81, 716.29, and 547 769.29 thousand US dollars, respectively. For five hurricane sets (considering 4 hurricanes 548 in 1 set) in 24 years, the profit of scenarios 1, 2, and 3 is 340.27, 844.45, and 946.85 thou- 549 sand US dollars, respectively. It is visible that the monetary profit is increasing with the 550 increasing number of hurricane sets for all three scenarios, and scenario 3 is the leading 551 24 profit generator among all the hurricane sets. 552 Table 3: Investment for Three Scenarios (in thousands US $) Scenario 1 Scenario 2 Scenario 3 Investment 147.95 381.97 739.75 Table 4: Profit for Three Scenarios of Different Hurricane Sets (in thousands $) Hurricane SetsScenario 1 Scenario 2 Scenario 3 1 280.81 716.29 769.29 2 293.16 742.91 806.17 3 307.05 772.86 847.66 4 322.68 806.55 894.34 5 340.27 844.45 946.85 For the in-depth analysis of the impacts of different numbers of hurricane sets in all 553 three scenarios, three economic indicators, NPV, NPM, and RCR, are utilized for all 554 three scenarios considering the number of hurricane sets from 1 to 5. In Fig. 19, NPV is 555 increasing for all three scenarios with the increasing number of hurricane sets. Among all 556 the hurricane sets, scenario 1 has the lowest NPV in all three scenarios. Although scenario 557 2 has the highest NPV for hurricane sets 1, 2, 3, and 4, scenario 3 achieves almost identical 558 NPV of scenario 2 for hurricane sets 5. In Fig. 20, NPM curves portray the net profit 559 margin for different hurricane sets. For all the different hurricane sets, NPM gradually 560 increases for all three scenarios. Furthermore, scenario 1 is leading scenarios 2 and 3 for 561 all the hurricane sets. Also, NPM curves for scenarios 1 and 2 are close which indicates 562 that both scenarios are generating similar profits relative to their revenues. In Fig. 21, 563 RCR graphs are presented for all three scenarios of different numbers of hurricane sets. 564 For all the hurricane sets, all three scenarios have RCR value greater than 1, and the 565 RCR value increases with the increasing number of hurricane sets. 566 5. Summary and conclusions 567 In conclusion, this manuscript introduces a pioneering Smart Investment Framework, em- 568 powering decision-makers to optimize energy resilience investments by aligning resources 569 with desired resilience levels. Through a real-time simulation of a campus microgrid us- 570 ing Typhoon HIL, the study demonstrates the framework’s practicality, showcasing the 571 microgrid’s effectiveness in powering local loads during outages. A quantitative analysis 572 of resilience improvement costs adds economic depth to the framework, aiding decision- 573 makers in balancing the economic burden with resilience goals. This research contributes 574 25 Figure 19: Net Present Value (NPV) Figure 20: Net Profit Margin (NPM) valuable insights for resilient energy infrastructure planning, offering a cost-effective ap- 575 proach to enhance resilience without unnecessary redundancy. The case study serves as 576 a valuable guide for decision-makers in similar contexts, emphasizing the framework’s 577 potential in real-world applications. 578 6. What is Next 579 The current framework is entirely cost-driven. As a prospective avenue for further re- 580 search, there is an opportunity to enhance the framework by integrating considerations 581 26 Figure 21: Revenue-Cost Ratio (RCR) of energy equity. This exploration could involve evaluating how the proposed investment 582 framework can be adapted to ensure fair and equitable distribution of energy resources, 583 addressing social and economic disparities. This extension would contribute to a more 584 comprehensive understanding of energy resilience, aligning with broader sustainability 585 goals and promoting inclusivity in resilient energy infrastructure planning. 586 Acknowledgements 587 This research work is partially supported by the Louisiana Board of Regents, ITRS pro- 588 gram as well as Cleco Power under the grant# LEQSF(2022-25)-RD-B-05 589