Reducing microgrid availability to reduce costs for coastal Puerto Rican communities

Renewable microgrids are sustainable, resilient solutions to mitigate and adapt to climate change. Making electric loads nearly 100% available (i.e., power remains on) during outages increases cost. Near 100% availability is required when human life or high-cost assets are involved, but availability can be reduced for less consequential loads leading to lower costs. This study analyses costs for photo-voltaic and lithium-ion battery microgrids with availability ranging from 0–99%. We develop a methodology to analyse three Puerto Rican coastal communities. We consider power outage effects for hurricanes, earthquakes, and everyday outages. The results show cost versus availability from 0–99%. There is 27–31% cost reduction at 80% availability in comparison to 99% availability. A regression model of microgrid availability versus three ratios: 1) the annual generation to demand ratio, 2) storage to interruption energy ratio, and 3) peak storage to load ratio produced a coefficient of determination of 0.99949 with 70% of the data used for training and 30% for testing. The results can therefore be extended to other coastal Puerto Rican communities of varying sizes that have ratios within the ranges analysed in this study. This can empower decision makers to rapidly analyse designs that have availabilities well below 100%.


Introduction
A microgrid is an electric network that is capable of functioning on its own when the electric grid experiences an outage (Dagar, Gupta, and Niranjan 2021).Microgrids can contribute to solving the present climate crisis if sustainable technologies are used in their design (ASHRAE 2021;Hoummadi et al. 2023).Alternatively, they can increase emissions if they are fossil fuel dependent.Microgrids can therefore be an important part of adapting to increases in frequency, intensity, and duration of extreme temperature, precipitation, hurricanes, and fires (IPCC 2021).Such adaptations will decrease human suffering and death due to climate change (Vicedo-Cabrera et al. 2021).This is especially true for isolated islands such as Puerto Rico.
Puerto Rico faced a double strike from historically record-breaking hurricanes Irma and Maria in 2017, resulting in the longest disaster response recovery in the history of the United States (U.S.) (Sayers et al. 2023).An estimated 2,975 persons lost their lives as a result, making Maria one of the deadliest hurricanes in U.S. history (George Washington University 2018).As a result, significant efforts are being made to assure that Puerto Rico's infrastructure will be more resilient in the future.Microgrids are an important part of this.A multi-objective approach is needed to integrate microgrids effectively.Several factors such as cost, resilience, and environmental considerations need to be included (Petrelli et al. 2021;Jeffers et al. 2023;Broderick et al. 2021).While some microgrids may be damaged during a disaster, many will survive.As a result, such microgrids can increase the probability that Puerto Rico's electric infrastructure will perform better during and in the aftermath of future disasters (Kwasinski et al. 2012).Microgrids are therefore a key component of achieving resilience in energy master planning for Puerto Rican communities (Jeffers et al. 2020;Shandiz et al. 2020).
Unfortunately, current U.S. microgrids are highly dependent on fossil fuels.The U.S. Department of Energy (DOE) Combined Heat and Power (CHP) Microgrid Database indicates that 60% of 461 microgrids across the U.S. have dependence on fossil fuel (CHP-MG-DB 2021).The database indicates that 45% of generation is dependent on fossil fuels, 10% on renewables, 42% on CHP, and 24% on unknown other sources.Also, microgrids are expensive, with project costs collected by a National Renewable Energy Laboratory (NREL) study ranging from 0.3 to 13 million U.S. dollars (USD) per MW (Giraldez et al. 2018).The cost is highly dependent on what combination of technologies are used, how many kinds of technologies are used, and the total size of microgrid installed.The majority of the microgrids include fossil fuels generation so that reliability can be achieved when renewables and energy storage fail to meet load (Hoummadi et al. 2023).First costs are high if 100% renewable generation is required with high reliability during power outages because of the need for large amounts of energy storage.Even so, 100% renewable microgrids can have higher net present values if generation by renewables offsets high electricity costs (Villa et al. 2023a).
Many microgrids are designed for high-consequence applications such as hospital life support (NFPA 2021) and military command centers (Booth et al. 2019).Such critical missions serviced by microgrids must not be compromised because human life is likely to be lost should they fail.Therefore, they are created to be available 99-99.9999% over the required outage operation.Here, availability is a metric equal to the percentage of the load energy demand served by the microgrid during power outages, not including the startup period.For example, the 2017 U.S. Navy requirement is 99.9886% availability (Booth et al. 2019, 2).This availability must be maintained across the range of design basis threats (DBTs) considered in microgrid design.DBTs are events that could disrupt or disable microgrid operations.DBTs can be divided into naturally caused events (Kwasinski et al. 2012) and human-induced events.Naturally caused DBTs include events like earthquakes, hurricanes, tornadoes, and heat waves.Human-induced DBTs include physical attacks, cybersecurity breaches (Gaggero, Girdinio, and Marchese 2021), and human errors (Wicaksana, Wibowo, and Ketut Aryani 2021).
There is a growing market for less critical applications such as community microgrids (Tomin et al. 2022).Unlike critical applications, the residential, community, and commercial sectors are likely to cause inconvenience rather than fatalities if a microgrid fails during a DBT.This reduction of consequence also makes 100% renewable energy with relatively limited storage a more probable solution even though availability will not be as high.
This study focuses on reducing first costs by analyzing photovoltaic (PV)-battery microgrids that do not support high availability.Such microgrids may not continue to provide power during extended cloudy periods.Even so, if designed properly, such systems will reinitiate electric coverage regardless of grid status when the sun begins to shine again.PV-battery microgrids will simultaneously increase resilience and sustainability of the Puerto Rican grid.Also, though coverage from a PV-battery microgrid will not be as good as a microgrid with fossil fuel generators, such an approach has been shown by Tosado et al. (2021) to lead to increases in availability of refrigeration for medication and prescribed diets, asthma therapy, inflatable mattresses for bedsores, and sleep apnea machines for residential situations where critical medical protection was needed during power outages.The renewables approach has the advantage that no fuel is needed for the power provided in postdisaster scenarios.
Our motivation for conducting this study is therefore focused on cases where communities are committed to having 100% clean energy generation while also needing an increase in resilience (Wallsgrove et al. 2021).For such cases we hypothesize that PV-battery microgrids with low availability will be affordable to a larger section of Puerto Rico's population.We think adoption of such microgrids will produce a higher combined sustainability and resilience in comparison to high-availability microgrids that either are costly because they are 100% renewable or are dependent on fossil fuels.
This study seeks to answer the following two research questions: (1) How much first cost can be avoided by implementing low-availability 100% solar PV-battery microgrids for noncritical loads in Puerto Rico's coastlines?(2) How sensitive are these cost savings to variations in climate along the coast of Puerto Rico?To answer these questions, an analysis using a building energy modeling (BEM) tool called Tiered Energy in Buildings (TEB) (Villa 2021), the System Advisory Model (SAM) for solar PV generation (SAM 2020), and the Microgrid Design Toolkit (MDT) (Eddy, Miner, and Stamp 2017;Eddy and Gilletly 2020) is conducted.Three coastal locations that have the largest variations in temperature and solar radiation are analysed to demonstrate sensitivity to different locations along the Puerto Rican coast.These locations also have significant differences in the frequency and magnitude of damaging hurricanes and earthquakes.et al. (2018) provide an island-wide perspective for Puerto Rico with recommendations for hundreds of locations where microgrids will have the greatest resilience benefits.Aros-Vera et al. (2021) perform another island-wide study of Puerto Rico and how microgrids could increase infrastructure resilience.Both studies call for cost-benefit analysis of microgrids in Puerto Rico.We complement these studies through investigating how first costs of PV-battery microgrids can be reduced for three locations on the Puerto Rican coast.Lisa Cohn (2022) interviewed microgrid industry experts and identified five strategies for reducing costs: (1) optimize the energy resources for maximum benefits, (2) tweak designs, (3) avoid overengineering, (4) use standard packages, and (5) finance with no down payment.Our approach of designing with low availability falls into strategies 2 and 3.

Jeffers
Cost reduction strategies fall into the broader category of overcoming barriers to microgrid deployment.Norouzi et al. (2022) provide a multidisciplinary review on sociotechnical barriers to deployment of microgrids.Jord an, O'Neill-Carrillo, and L opez (2016) provide a specific look at community-scale microgrids in Puerto Rico, like our study, but with a focus on seamless integration to the grid rather than first costs.Ullah et al. (2021) broaden this community scale to a review of community-level net-zero case studies globally.
Recent microgrid cost studies include the work of Villa and Henao (2022), which shows how oversizing microgrids for small communities with loads less than 100 kW is an optimal strategy for cost recovery for several locations in Colombia.Many studies are available that look at how complex interactions between controllers, markets, and design sizing affect initial and operation costs.For example, Wang et al. (2021) provide a recent study that looks at how uncertainty in renewables, energy storage systems, and demand management in an electrical market as a mix affect optimal microgrid design.Shirdar and Ghafouri (2022) show such an analysis with a mixture of controllable and uncontrollable loads in an isolated rural setting.Lake et al. (2022) investigate how individual homeowners might avoid energy costs using a home-level microgrid.Several other studies provide further examples of cost optimization strategies (Haidar, Fakhar, and Helwig 2020;Murty and Kumar 2020;Beyazit et al. 2022).None of these focuses on first costs, though.
Studies that point toward microgrid benefits besides cost for Puerto Rico are abundant.For example, Mango, Casey, and Hern andez (2021) show that home-based electricity resilience measures can protect vulnerable, low-income populations during outages.Tormos-Aponte, Garcia-Lopez, and Painter (2021) and Sotolongo, Kuhl, and Baker (2021) show how vulnerable populations can be more likely to receive slow recoveries from power outages.Even so, studies showing quantitative strategies for reducing first costs of microgrids in Puerto Rico are lacking.This gap needs to be filled so that alternative design strategies can be thoroughly investigated for specific cases.
This study is an extension of our original conference paper that looked at initial cost reductions achieved by lowering availability for a New Mexico community in Albuquerque (Villa et al. 2022).The work stemmed from the question of how a residential developer in New Mexico could profitably deploy a neighborhood with a direct current (DC) renewable microgrid.The study showed that significant initial cost savings could be achieved by reducing availability requirements.Targeting 80% availability led to 50% cost savings in comparison to a 99% available DC microgrid.The neighborhood would still have significant resilience benefits from the DC microgrid's presence at 80% availability.We extend this work to Puerto Rico, where reducing up-front costs is also important.This study also uses the TEB BEM tool that we previously developed and documented in another conference paper focused on reducing microgrid costs in Puerto Rico (Villa et al. 2023a).Our tiered circuits approach shows promise through providing loads that can be dropped when energy storage is low.This study uses the TEB BEM tool but does not focus on tiered circuits.
After searching the literature, we conclude that our concept of reducing availability to reduce first costs for Puerto Rican coastal communities is unique.Most studies assessing DBTs are focused on microgrids that require high availability (e.g., Kwasinski 2020; Krishnamurthy and Kwasinski 2016).Investigation concerning reductions in first costs for low-availability microgrids are therefore needed.

Outline
This article starts with elaborating the methods used.A description of the three locations analysed is given, followed by a brief description of the TEB BEM tool used to generate electric load profiles.The specifications of the solar generation analysis and MDT are given.The methods section continues with specification of the DBTs and ends with definitions for three dimensionless ratios used to generalize availability results.A description of how the MDT analysis was run for the three locations analysed is then given.This is followed by presentation of the analysis results, which highlight how cost is directly a function of availability.We then provide discussion of the results, assumptions, and implications of the analysis.The article ends with conclusions including the need for creating low-availability PVbattery microgrid designs.

Methods
The flow of data and tools used in our analyses is summarized in Figure 1.The analyses used hourly weather data from three locations in Puerto Rico to run the TEB software for electric demand loads.Solar generation profiles were calculated using SAM.Analyses were also conducted to assess how hurricanes, earthquakes, and normal power interruptions would affect the three locations.All these results were used to run the MDT software.Elaboration of the details for the analysis is provided in the following subsections.

Locations analysed
Weather data for global Typical Meteorological Years X (TMYx) for the 2007-2021 timeframe were used for Aguadilla, San Juan Metro Area (SJMA), and Penuelas, as seen in Figure 2 and Table 1 (Crawley and Lawrie 2019).The TMYx monthly analysis follows the same TMY/International Organization for Standardization (ISO) 15927-4:2005 methodologies used for the TMY3 dataset (Wilcox and Marion 2008;ISO 2005).The TMYx dataset is improved, though, using more recent years and more accurate sources for solar radiation.We distinguish between SJMA and the city of San Juan because our analysis considers issues for the greater area around San Juan.

Building energy modeling
The BEM demand loads are calculated using an open-source tool called Tiered Energy in Buildings (TEB) (Villa 2021).The development of TEB was driven by the need for a fast BEM tool that could be used alongside MDT.TEB uses a resistive capacitive (RC) model obtained from another opensource tool called the RC Building Simulator (Jayathissa et al. 2017;Jayathissa 2022) with five resistive elements and one capacitive element in conformance with ISO standard 13790 (ISO 2008).The models from the RC Building Simulator were wrapped into TEB.The final model includes dynamics for solar gains, sun angle, windows, infiltration, heat flow to ground, occupant sensible thermal loads, internal dehumidification via wall air conditioning (A/C) units, heat gains from electric loads, hourly weather boundary conditions for humidity and temperature, and heat capacitance of cinder block/prefab concrete panel construction typical for Puerto Rico.For thermodynamic relationships used in psychrometric calculations, the National Institute of Standards and Technology (NIST) REFPROP database (Lemmon et al. 2018) is used, alongside an equation for vapor pressure found in the literature (Buck 1981).

Community description
The inputs to TEB are extensive for the community analysed.
Table 2 gives the top-level inputs to the entire TEB input deck.The residential building types are in columns.
Table 2 has several additional configurations that include separate issues in each housing unit, such as home medical device use, the presence or absence of wall A/C units, and presence or absence of an electric vehicle.Each building type was run and then scaled to the total area of the community.The total area of the community is 24,988 m 2 of space with 5,415 m 2 of commercial, 5,914 m 2 of institutional, and 12,416 m 2 of residential space.
Each residential unit was assumed to have a full-size refrigerator, with 30% of homes having a mini-split capable of cooling a single room, modeled according to Meissner et al. (2014).Meissner's model includes inefficient modes of operation in hot-humid conditions typical of Puerto Rico.The total energy use intensity (EUI) was compared to the Residential Energy Consumption Survey (RECS) and the Commercial Building Energy Consumption Survey (CBECS) for the U.S. southern region (EIA 2018).For residential spaces, RECS data for spaces less than 93 m 2 were used.Adjustments were intuitively made based on significantly lower use of A/C in Puerto Rico.The same TEB buildings configuration was used in this study as in our tiered circuit effects study for a Puerto Rican community (Villa et al. 2023a).The only difference to the community at each of the three sites analysed for this article was use of different TMYx weather files.Also, the additional outputs provided by tiered circuits were not used.Only the full demand load of the community was used as the input to MDT.

System Advisory Model
The System Advisory Model (SAM) was used to calculate the production of electric energy from solar panels (Blair et al. 2014, SAM 2020).An array of 12 strings of 21 400-W panels was used to create a 100-kW array of panels with a DC to alternating current (AC) ratio of 1.12.The characteristics of the PV array are provided in Table 3.The same TMYx files were used to drive the SAM simulation except that albedo was given a constant value of 0.2.All other inputs were retained as the defaults in SAM.This 100-kW increment was then used in the MDT analysis.Suk and Hall 2020).We provide a summary of MDT's capabilities here.MDT's inputs include (1) generation assets, (2) electric loads, (3) optimization parameters, (4) reliability definitions, and ( 5) DBTs (e.g., probability of power outage events).In MDT, complex networks of electric grid elements are linked to demand loads.Each grid element can be static or can be a design variable.An example of a design variable is for a PV solar array to be able to be three different size arrays (100 kW, 200 kW, 300 kW).An analysis can include several DBTs.
At each time step, the load and generation/storage states are assessed, the possibility of component failures is considered, and the beginnings of DBT events are initiated accordingly.The combination of load-generation balance, failures, and DBTs produces resilience metrics within a Monte Carlo study.In this study, energy availability was used as a performance metric, defined as the percentage of the load energy served by the microgrid during power outages, not including the startup period.Availability is useful because it gives a measure of what percentage of energy a microgrid design can provide under DBTs.An optimization routine in MDT tracks the designs that have the Pareto optimal cost and availability.Our previous work on a New Mexico neighborhood gives a good example of another application of MDT (Villa et al. 2022).

Design basis threats
The DBTs addressed in this study are for hurricanes, earthquakes, and day-to-day grid reliability issues.Two exponential distributions were used for each DBT.The first was for the frequency of the DBT.An average time between DBT events was estimated for this first distribution.The second exponential distribution was for the duration of DBT events.
The duration in this study is strictly for the length of power outage caused by the event and is not associated with the duration of the actual event.No other effects of the DBT are modeled besides loss of electrical power.The DBT event duration distribution was characterized by estimation of the average power outage event duration, expressed in days.The following subsections summarize the approach for the three DBTs analysed: hurricanes, earthquakes, and normal power outages.

Hurricanes
The time between hurricanes was derived from the HURDAT2 database (Landsea and Franklin 2013).A hurricane was counted as a strike if it made landfall (i.e., the eye of the storm touched land) or was at its closest approach to a coastline at a distance less than 200 km from the three sites analysed.All storms from 1982 to 2022 were included.This avoids the lack of data for earlier dates.
For hurricane power outage duration, the maximum wind speed for qualifying events was assumed to be exponential.Even though there were only small samples, the best fit exponential distribution fits were used.The Kolmogorov-Smirnov test statistic p values lead to acceptance of the null hypothesis that the random sample of hurricane velocities are exponentially distributed at 95% confidence (i.e., p > 0.05) except for SJMA, as seen in the right-hand column of Table 4.The value of 0.040 is acceptable given the fact that no more data can be collected, the sample size is small, and the other two fits were statistically significant.The alternative of trying other distributions is not desirable because the phenomenon being modeled is likely to have an exponential distribution since the other two geographically corelated locations obtained statistically significant fits.
We then used the peak wind speed of Hurricane Maria of 135 knots to linearly scale the estimated average length of power outages from Rom an et al. ( 2019) to the average wind speed.The analysis clearly indicates that SJMA is at significantly higher risk of severe hurricanes with prolonged power outages.
For all three locations, the hurricane DBT events also include a period of complete cloudiness (i.e., no solar PV electricity generation) with an exponential distribution for Science and Technology for the Built Environment which the average is 36 h.This approximates the cloudy period brought in by a hurricane system during which the sun does not shine for an extended period.

Earthquakes
Earthquakes are less of a threat to Puerto Rico's power infrastructure than hurricanes but are still capable of producing significant damage.Like hurricanes, they are an inevitable part of Puerto Rico's natural disasters (Hunter 2020).
Less information is available for power outages due to earthquakes because such events are less frequent than hurricanes and structural damage to buildings is emphasized (Wikipedia 2023a).Hundreds of earthquakes occur each year, but most are not a threat.We rely on the average incidence of major earthquakes provided by Woods Hole Oceanographic Institution (WHOI), that major earthquakes likely to cause significant power outages strike once every 50 years (WHOI 2005; Brink and Lin 2004) for each site.National Aeronautics and Space Administration (NASA) data show that the power outages tend to be on the order of a couple of days (NASA 2020).We qualitatively assigned longer power outages to the southern portion of the Puerto Rican coast, which is estimated to be more vulnerable based on the recent earthquake swarm that has occurred there (Wikipedia 2023b).The values chosen are shown below in the two lefthand rows of Table 5.We neglect the possibility of a major earthquake that could disrupt the entire island.

Day-to-day outages
In June 2021 LUMA energy took control of the Puerto Rican grid.We use the LUMA energy baseline System Average Interruption Duration Index (SAIDI) and System Average Interruption Frequency Index (SAIFI) to model day-to-day outages that are not caused by severe weather or earthquakes.These are important because this study looks at low-availability systems for which the performance may quickly degrade for shorter more frequent outages.The 2020 baseline values are average SAIDI of 1,307 min/yr of interruption and an average SAIFI of 9.8 outages/yr for all of Puerto Rico (LUMA 2021).We used these values to estimate mean time between outages and mean outage duration as seen in the right two columns of Table 5 with an exponential distribution.

Nondimensional ratios
The availability of a PV-battery bank microgrid is more easily understood when compared to three ratios.The first is the annual generation to demand ratio (AGDR), which is equal to the total amount of solar production in energy per year divided by the total amount of demand in energy per year: where EPI is the energy production intensity for the solar PV array in energy per year per area of PV installed.The results from a SAM analysis can be used to derive this for a specific location.Results for different size systems can then be evaluated by multiplying by the area of the PV array for a given design A PV : The EUI is the energy use intensity for the entire community of buildings and A buildings is the total floor area of all buildings (conditioned and unconditioned).
The second ratio is the storage to interruption energy ratio (SIER), which is equal to the battery energy divided by the average energy consumed by a community during the average duration of an outage: where E b is the total energy capacity of the battery bank for a design.The average power P avg is the mean of annual power output for BEM results of a location and the average duration, D avg , is the weighted average of DBTs for a location where the weights are the frequency of occurrence of each DBT.The last ratio is the peak storage to load ratio (PSLR): where P max b is the maximum power output of the battery bank and P max c is the peak power demand of the community.High-availability microgrid requirements make it necessary that all three of these ratios be greater than one.We investigate cases where they are less than one.

MDT analyses description
The same MDT model was used for all three locations.First cost and energy availability are the comparative metrics used in MDT.At the core of each model is the representative load for each location, which is defined in the model by a year-long hourly demand load produced by the TEB BEM tool previously described.As seen in Figure 3, this load was connected to the microgrid via a switch.For each hour, the switch is kept closed if the PV and batteries can meet the load (i.e., no partial load service).Otherwise, the switch is kept open, which causes a power outage for the community.
The three DBTs for each location (hurricanes, earthquakes, and normal utility outages) were entered for each location model as previously described.In MDT, the DBTs are defined in terms of time between occurrences and duration.The exponential distribution was applied to both settings for all DBTs in the models.MDT does not have a provision to only allow hurricane DBTs to occur during the Atlantic hurricane season.We therefore assume a hurricane can strike at any time in the year.The relative uniformity of Puerto Rico's seasons makes this an acceptable assumption.Also, our time between events includes all times where hurricanes do not occur, such that the frequency of hurricane strikes is accurate even if the timing is off-season.
Figure 3 illustrates the general model structure utilized for the three locations.There is a central bus to which the load (black rectangle next to the switch) is connected.This splits to two busses that are connected to the PV systems (green backdrops), and battery units (blue backdrops).The PV and battery systems consist of two clusters each-the ones on the left are fixed assets and the ones on the right are design variables.To produce results that spanned across energy availabilities from 0 to 99%, it was necessary to adjust the number of fixed assets for each location, while the design variables were always given 12 values.For PV each increment was 100 kW, corresponding to the SAM analysis array.For battery units the increment was 100 kW peak load with 400 kWh of energy.The sizing of the units dictates the granularity in the results, as they represent the incremental sizing options that can be chosen by the simulation.
Failure rates can be assigned to all components in an MDT model, such as generators and lines.Since the models were not based on actual infrastructure layouts, and to allow for consistent comparison between locations, both the topography and the equipment complexity were minimized.No line failures were defined for any of the conductors, and there were no transformers or other equipment defined.Failure rates for the PV and battery units were implemented, per Table 6, where two exponential distributions were applied: the first for mean time between failures, and the second for mean time to repair after failure.The first costs for PV and batteries are also listed.Continuous maintenance and repair costs were not included in the analysis since our emphasis is first costs.
The simulation length for each design was set to 500 years, which allows for thorough cycling of the DBTs throughout the year.The length of 500 years does not convey actual passage of time.Otherwise, complete replacement of the systems would be necessary many times over.Rather 500 years is a repeated application of statistically similar years such that the distribution of possible outcomes stabilizes for each design.Five hundred years captures all the 878 Science and Technology for the Built Environment coincidences between load demand and PV output for each design, which then appropriately sizes the battery and reports robust statistics for each design option evaluated.At a 500-year simulation length, the hurricane DBTs ($37-71 days duration) would be cycled approximately 112-162 times, and earthquakes ($1-3 days duration) approximately 10-12 times, depending on the specific location frequencies and durations for each DBT.The normal utility outage DBT was defined the same for each location, and would occur almost 5,000 times within the 500 years, at a smaller duration average of 2.4 h.

Results
Nine runs of MDT were required for each location.Three runs were required per location with different availability targets in MDT and three runs were executed per availability target to assure that variations between stochastic runs were captured.Variation between repeated stochastic runs was less than 0.1%, proving that 500 years simulation time provides sufficient convergence.The following subsections provide tables and figures of the important outputs of the study.

BEM and solar power
The TEB analysis EUI comparison to CBECS and RECS is shown in Table 7.The comparisons are for order-of-magnitude confirmation only.The lower EUI for the TEB model of 142.0 kWh/m 2 is desired since A/C loads are known to be smaller in Puerto Rico.
For the three locations, the SAM 100-kW system analysis only exhibited minor differences in power production, with Penuelas producing 1.9% more power than Aguadilla and 2.6% more power than SJMA. Figure 4 shows monthly aggregates of the hourly timeseries input into the MDT analysis.The legend gives the annual sum of each site.
Several metrics for calculating AGDR, SIER, and PSLR derived from SAM and TEB analyses are provided in Table 8.The average energy consumed during an outage is calculated by (1) taking the average of power outage duration weighted by frequency (i.e., reciprocal of time between  events) for all three DBTs (hurricanes, earthquakes, and dayto-day outages) and (2) multiplying the average power outage duration by the average load derived from the EUI and community floor space area.The average energy consumed during an outage in SJMA is much higher, making it more expensive to cover with a microgrid.This is intuitively correct because of SJMA's lower solar irradiance and higher average temperature, as displayed in Table 1.The combination of SJMA's DBTs is the larger factor, though, making SJMA have much higher (i.e., $2.5 times greater) average energy consumption requirements during the longer outages expected.The other two sites have much more similar metrics.

First costs versus availability
The MDT analyses Pareto fronts for 1033 designs derived from 3 repeated runs of MDT are shown in Figure 5.The variation between locations is distinct but not large, with SJMA clearly requiring higher cost than the other two locations and Aguadilla costing the least for most availabilities.A 15th-order polynomial fit of availability versus the natural logarithm of cost is shown in the graph with a line that is the same color as the markers for each dataset.The coefficients for the polynomial for each location are provided in Table 9 along with the coefficient of determination (i.e., R 2 value) that gives a measure of the goodness of fit.This function was chosen for empirical reasons only and is intended to convey a smooth fit to the scatter of data.The variations in cost versus availability between the polynomial fits for the three locations have a maximum of 12%.This is a relatively small difference in cost in comparison to the percent difference in total DBT power outage durations.The highest availability analysed for each dataset for Aguadilla, Penuelas, and SJMA was 99.64%, 99.60%, and 99.36%, respectively.Values higher than these should not be analysed using the results of this study.
The results displayed in Figure 5 clearly show that availability has a strong relationship to first costs and that variations along Puerto Rico's coast are significant but small.The cost rises in a roughly linear way from 60 to 95% availability and then quickly rises as it approaches 100% availability.The cost variation of 15% in the 60-95% availability range shows that an 80% available renewables microgrid is likely to cost 27% to 31% less than a 99% available microgrid.
The first costs are a compound function of the total PV installed, battery energy, and battery power of the microgrid.The plots on the left side of Figure 6 show the results set of availabilities as a function of total generation capacity, total battery energy, and battery power.The plots on the right side show the corresponding dimensionless ratios previously introduced that normalize for energy use and DBT severity.Though not easily fitted by analytic functions, the multivariable relationship between availability, AGDR, SIER, and PSLR was captured by a random forest regression algorithm (Pedregosa et al. 2011).Seventy percent of the data was

Discussion
Observation of Figure 5 clearly answers our research questions.The least-squared optimal cost reduction percentage can be calculated for one of the three locations by using the coefficients in Table 9.The small variation between the three cases indicates that coastal regions will have variations of about 12% in costs due to differences in weather and DBTs.Aguadilla and Penuelas almost break even exactly.Aguadilla has milder hurricane and earthquake conditions leading to fewer DBT outages, but Penuelas has higher solar radiation and lower average temperature than Aguadilla.SJMA clearly requires higher costs to meet a specific availability, though.This is primarily due to its higher frequency and greater severity hurricane strikes, but higher EUI and lower EPI also contribute to this.The reduction in costs attainable by reducing availability requirements provides strong evidence that new design strategies on noncritical loads are worthwhile in Puerto Rico.Our previous work (Villa et al. 2023a) shows that properly designed renewables systems can quickly pay for themselves in Puerto Rico even though they have higher up-front costs than fossil fuel solutions.This is due to the high cost of electricity in Puerto Rico.Further reductions in cost through reducing availability requirements could lead to quicker deployment of renewables and microgrids than would occur for high availability PV-battery microgrids applied to noncritical loads.Our proposed strategy could therefore lead to a win-win situation for both sustainability and resilience.Our results must be used in economic assessments to quantify how much advantage can be gained by the reductions in first costs shown.
Even so, there are several limitations to this study that should be noted to assure the results of this study are used correctly.First, our work in this article does not address what microgrid design changes would be needed to properly run a low-availability microgrid.Additional costs not included in this analysis are likely.Further work is therefore needed to understand the redesign issues needed for realizing an efficient, low-availability microgrid.Regardless, for this study we assume that the high-level design parameters used by MDT reflect a low-availability microgrid design.A study like the work of Haidar et al. (2020) or Amupolo et al. (2022) that works out design issues in unique conditions is therefore needed case by case to understand how lowering availability may help a specific situation.Designs would need to maximize capacity to repeatedly restart without any help from the external grid.Added components to assure robustness of such restarts would therefore become a priority.
Second, this analysis constrains solutions to a solar PVbattery design.Introducing small amounts of fuel-based generation can significantly change the availability curves presented here.If the fuel-based generation is incidental for emergency purposes or is a fuel with clean emissions like hydrogen, such alternatives are equally viable and warrant investigation for coastal Puerto Rican communities considering implementing a microgrid.
Lastly, even though the DBT analysis performed here is a robust stochastic approach, the historical record for DBTs and the single set of TMYx weather used do not cover the breadth of uncertainty possible.Future studies should consider including climate change projections concerning how cloud cover and solar irradiance change for Puerto Rico.Such capabilities are active areas of research and represent a gap in the capacity to assess how microgrids are likely to perform in future conditions.Also, the effects of climate change on hurricanes have not been included.Analysis methods for doing this are emerging and compilations of hurricane results enable shifts in hurricane characteristics (Jewson 2023;Knutson et al. 2020).Even so, such assessments have much less certainty than changes to extreme heat, which are unequivocal (IPCC 2021).There is a lack of scientific consensus, with studies predicting increases, decreases, and no change to many kinds of hurricane metrics (Roca-Flores et al. 2023;Balaguru et al. 2023;Schenkel et al. 2023;Knutson et al. 2022).Including climate change projections for North Atlantic hurricanes is therefore still scientifically questionable, and increases of population along coastlines are a much larger driver of potential damages (Landsea and Knutson 2022).
The results from this study show much less sensitivity than our previous study for the same topic applied to New Mexico (Villa et al. 2022).For example, at 80% availability the New Mexico residential community was estimated to have 50-70% cost savings for the baseline cases, whereas this study estimates 27-31% cost savings.This is due to the New Mexico case having much milder DBTs than this study (70-min outage once per year and a 48-h outage once every 10 years).A secondary factor is the much higher swings in temperature that occur in New Mexico's climate in comparison to Puerto Rico.These differences show that the results of this study should not be extended to other climates.Even the inland portions of Puerto Rico must be analysed separately since the mountainous regions have different climates.
The small variation in results between the three locations stands out to provide confidence that the cost to availability trade-off is similar for most coastal locations in Puerto Rico.We have captured a strong variation in hurricane strike frequency in our DBT analysis and have varied sites across the maximum range of solar radiation.Even so, our analysis does not include the possibility that a DBT would significantly damage and require costly repairs to a microgrid design.There are likely to be sharper differences in cost performance at different locations if such issues are analysed.
The SIER metric seen in the middle plot of the righthand side of Figure 6 exhibits a marked difference for SJMA in comparison to Aguadilla and Penuelas.This is due to SJMA having a much larger (i.e., 2.5 times greater) power consumption during an average power outage (Table 8).This large difference does not lead to an equivalent factor of 2.5 for cost, though.The much smaller difference in cost is due to the use of renewable sources of energy that serve the load during DBTs when the sun is shining.We therefore observe that for Puerto Rican coastal locations, renewable microgrids have significant advantages over nonrenewable microgrids that can run out of fuel.If battery storage can meet the normal cloudy periods of Puerto Rico, the SIER does not have a very strong effect on availability.This is not the case for fuel-based microgrids, where the long DBT periods present in this analysis would make large storage containers of fuel a costly requirement and environmental hazard.
Finally, returning our attention to the TEB model and the EUI comparison in Table 7, we note that Puerto Rican power consumption data are not available by the categories needed to make strong calibration targets possible.In general, Puerto Ricans consume less energy due to higher prices, among other factors (EIA 2023).We therefore set our target below the RECS and CBECS values deliberately.Even so, the grocery store was left at a much less efficient state because of its small size, and commercial spaces were assumed to use significantly less energy.The overall EUI of 142 versus the comparative 172.3 from CBECS and RECS is a satisfactory result and is the main driver for the MDT analysis.

Design basis threats
Our assessment of hurricane damage is likely to become overly conservative as Puerto Rico hardens its aging grid to hurricane strikes.The more recent hurricane strike by Fiona with 74-knot maximum wind speeds led to longer than desired power outages but with a much quicker recovery time than our model would suggest (NASA 2022).We retain the longer power outage periods because good forecasts of how quickly Puerto Rico will harden infrastructure were not available.Future work may seek to overcome this by breaking hurricanes into more than one DBT and by performing an analysis that extrapolates future performance of the grid to hurricanes.
Data for normal outages in Puerto Rico are difficult to obtain.Even though the LUMA 2020 baselines are used in this study, local conditions can be much different and customers experience can be much worse than the number published (Rosenburg 2022).On the other hand, LUMA has indicated that it has improved outage statistics 30% since its contract was awarded.Regardless, the outages due to hurricanes by far outweigh other factors, making higher precision in this small factor less important.
Finally, the lack of a 95% confidence fit for SJMA hurricane DBT in Table 4 is not desirable.Regardless, the p value of 0.04 nearly meets the 95% confidence level, and the MDT analysis proved to be less sensitive to cost variations, as seen in Figure 5.

Conclusion
This study has shown that the first costs of a solar PV-battery microgrid can be reduced significantly by reducing microgrid availability for three locations in Puerto Rico.The results from Figure 5 and Table 9 can be used to estimate reductions in cost of similar microgrid systems for other analyses of coastal regions in Puerto Rico.This extends our previous study (Villa et al. 2022) showing a more detailed relationship for a new location.The large differences in results between the two studies indicate that a broad geographic investigation of reduced cost versus availability is needed to understand the intersection between climate and DBTs for microgrids in different locations.Such a study will require significant investment to understand how reliable the electric grid is for a broad range of locations.
The reduced costs quantified by our study provide a rationale for creating engineering designs that cost less, turn off during disasters, and restore power quickly once the sun starts shining again.Our results can be used for cost-benefit analysis of designs by any coastal Puerto Rican community.If the AGDR, SIER, and PSLR for a design are within the ranges analysed in our study, an availability can be estimated from the random forest relationship calculated from the data.The close fit produced by the random forest regression shows that availability can be precisely predicted as a function of these three ratios within the DBT and climate fluctuations analysed for the three locations.
Continuation of our work could include consideration for climate change, projections of Puerto Rico's grid reliability, more detailed investigation of localized DBT effects, and fragility curves for PV and battery systems for hurricanes and earthquakes.Also, studies of inland Puerto Rican climates could extend applicability to the entire island.Finally, this study could be significantly enhanced by taking a stochastic approach to the hurricanes and solar/cloud cover through a weather generator like our work with heat waves (Villa et al. 2023b).

Fig. 1 .
Fig. 1.Flow diagram for data (ovals) and tools (boxes) used in the study.

Fig. 2 .
Fig. 2. Geographic locations with numbers corresponding to left side of Table 1.Colors correspond to elevation from the U.S. Geological Survey (USGS 2023).

Fig. 4 .
Fig. 4. SAM model monthly aggregates for solar PV energy produced for the three coastal locations.
used for training and the remaining 30% produced a coefficient of determination (R 2 value) of 0.99949 for predictions.The tight fit indicates that use of the AGDR, SIER, and PSLR to interpolate our results provides an accurate predictive model.Such a predictor can be used in place of MDT.Other coastal locations in Puerto Rico or other locations that have very similar DBTs and climactic conditions can therefore be analysed.The fit is only valid in the range of PSLR, SIER, and AGDR coordinates evaluated, though, making it necessary to verify that a given PSLR, SIER, and AGDR point is close to the dataset.

Fig. 6 .
Fig. 6. Results vs. three cost variables and three corresponding dimensionless ratios.The vertical axis is percent availability.The same legend in the upper left plot applies to all six plots.

Table 2 .
Top level inputs to TEB building types in the community.

Table 1 .
Summary statistics for coastal locations analysed.

Table 3 .
SAM design specifications for 100-kW increment used in MDT.

Table 4 .
Cyclone DBT analysis results.Used data are for nearby Mayaguez on the same side of the island.2Theactual San Juan city limits had much better recovery times on average.

Table 5 .
Earthquake and day to day outages DBT values.
Fig. 3. General MDT model layout used for all sites.

Table 6 .
PV and battery failure and first costs used.

Table 8 .
Summary results for SAM and TEB metrics.

Table 9 .
Polynomial coefficients to the natural logarithm of cost C ¼ expð