Multi-Objective Decision-Making for an Island Microgrid in the Gulf of Maine

: Microgrid implementation often lacks economic and environmental efﬁciencies due to sub-optimal conﬁguration and operation. The current study aims to explore the optimal conﬁguration and operational strategies for a microgrid system with maximum life cycle economic and environmental co-beneﬁts. This study was inspired by a real microgrid optimization need for Shoals Marine Laboratory, a seasonal marine teaching and research ﬁeld station on Appledore Island, Maine. A system dynamic model was developed to simulate the microgrid operation, and a multi-criteria analysis was performed based on diesel electricity generation, equivalent annual costs, and carbon footprint under various system sizing and operation scenarios. This study found that an effective battery capacity of 120–165 kWh (400–550 kWh actual with 30% depth of discharge) and a solar capacity of 85–105 kW can effectively minimize all three objectives under an average daily demand of 265 kWh during the study period. Additionally, implementing an alternative system operation strategy can lead to a 12% reduction in diesel electricity generation.


Introduction
According to the International Energy Agency, nearly 775 million people, or approximately 10% of the world's population, are currently without physical or economic access to electricity [1].This percentage is typically very small or even negligible in many developed countries; however, in the US, around 14% of the US population (equivalent to approximately 46 million people) resides in rural areas [2,3].Many of these communities do not have cost-efficient means of developing, expanding, or maintaining centralized power infrastructure [4,5].Over the last two decades, microgrids have gained popularity as an alternative means to supply power [6].Microgrids are small-scale, localized, and autonomous energy systems that can operate either independently or in parallel with the centralized grid [7].They can be powered by a variety of energy resources, such as solar, wind, and diesel generators, or larger generators, such as gas turbines.There are currently 687 operational microgrids in the US, off-grid or grid-connected, with a total capacity of 4.4 GW supporting diverse communities, including universities, hospitals, and military bases, among others [6].The demand for microgrids continues to rise as entities and communities seek to use microgrids as supplementary power sources for enhanced energy resilience and reliability [8][9][10].Microgrids also offer promising sustainability benefits as renewable energy technologies become increasingly feasible and affordable [11].Despite the vast interest in microgrids and their potential to enhance energy accessibility, resilience, and sustainability, the implementation of microgrids has often been hampered by insufficient planning and coordination, resulting in sub-optimized solutions [12,13].There is, hence, a need to investigate microgrid designs for co-optimized technical, environmental, and economic benefits to guide its planning and implementation.
Previous investigations of the optimal design of microgrid systems have been primarily focused on a single objective, for instance, minimizing generation cost [14][15][16][17][18][19][20][21][22][23][24][25], increasing fossil fuel savings [26,27], or minimizing active power losses within the system [28].These studies often combine a process-based system simulation model (e.g., HOMER [29]) with an optimization algorithm (e.g., CPLEX embedded in GAMS [30,31]) to examine the optimal sizing or configuration of the energy generation and storage systems [18,22,24].Yet real-life microgrid decision-making is often based on multiple relevant considerations or factors, and our understanding of the potential trade-offs across the important decision factors to inform holistic decision support remains limited.Only a few studies conducted microgrid optimization considering multiple decision criteria.Hijjo et al. [32] and Anglani et al. [33] considered both fossil fuel consumption and battery life span when designing the optimal battery and renewable energy system sizing.Several other studies have sought to minimize both economic costs and environmental impact (e.g., greenhouse gas emissions or NO x and SO 2 emissions) when designing for the scheduling and control of the renewable generation systems embedded in the microgrids [34][35][36][37][38]. Several studies included objectives related to technical, economic, and environmental aspects in their optimization.For instance, El-bidairi et al. [39] included dependency on diesel generators, carbon emissions, levelized costs of electricity, and battery maintenance costs as optimization objectives.None of these studies, however, adopted a life cycle lens to assess the microgrid performance outcomes.Nagapurkar and Smith [40] included estimations of economic cost and carbon emissions from both construction operation and maintenance phases for their multi-objective optimization of an isolated microgrid.However, system optimization was ultimately focused only on economic cost minimization, and the trade-offs between cost and carbon emissions were not discussed.Bilich et al. [41] compared the life cycle environmental and energy impacts of three photovoltaic (PV) microgrids and other energy options for a model village in Kenya.Nevertheless, the three microgrids were pre-designed, and no system configuration optimization was performed.
Accordingly, this study seeks to investigate the optimal microgrid system design and operation strategies via a dynamic, lifecycle-based, multi-objective modeling framework.Three research questions were examined: (1) How do PV and battery system sizing influence the microgrid's diesel electricity generation, equivalent annual costs, and carbon footprint?(2) What are the trade-offs in these three objectives?(3) What is the PV and battery system sizing that co-optimizes the three objectives?The framework was applied to an island microgrid that consists of solar, wind, and diesel electricity generation systems and a battery storage system.

Case Study
The modeling framework was applied to Shoals Marine Laboratory on Appledore Island in the Gulf of Maine as a testbed.Appledore Island is the largest of nine islands in the Isles of Shoals, located six nautical miles off the east US coast at the border of Maine and New Hampshire [42].It hosts the Shoals Marine Laboratory (SML), jointly operated by the University of New Hampshire and Cornell University.The laboratory operates at full capacity seasonally only for about three months in the summer, from mid-June to mid-September.During these times, the island is inhabited by students, researchers, and staff taking courses or conducting research.All activities on the island are powered by the SML microgrid.We selected a study period between 3 July 2019 and 12 September 2019, which was during the last full field season before the nationwide COVID shutdown.During the study period, the microgrid contained 233 solar panels with a total nominal capacity of 68 kW, a Bergey Excel-R wind turbine with a rated power of 7.5 kW, two 27-kW diesel generators (only one used at a time), and an absorbed glass mat battery bank with a nominal capacity of 300 kWh.To extend service life, the battery bank is operated by SML only to 30% depth of discharge, resulting in an effective usable storage capacity of 90 kWh.The SML microgrid has grown organically over time, based on historic needs and equipment grants or donations, without formal system optimization efforts.The installation years of different system components are provided in Table S4 of the Supplementary Information (SI).SML has an ongoing sustainability initiative to upgrade the microgrid system to improve its environmental performance, especially in terms of reducing its diesel consumption and carbon emissions.This study is being conducted in part to aid in the decision-making process for upgrading the SML microgrid.
SML monitors its electricity demand, solar, wind, and diesel electricity generation, ambient temperature, and solar global horizontal irradiation (GHI) on a minute-by-minute basis [43].Wind speed data were obtained from the nearby IOSN3 station (42 • 58 2 N 70 • 37 24 W) of the National Data Buoy Center since it was not monitored directly at the site during the study period.To account for missing data, linear interpolation was used for periods lasting less than 10 min.For gaps that are longer than 10 min, the missing data were assumed to follow the trend of the previous day.None of the missing periods exceeded an hour in the 2019 dataset.Figure 1 shows the monitored daily renewable energy generation and electricity demand on the island over the study period.The total electric energy consumption during this period was 19,124 kWh, with an average daily consumption of 265 kWh.
generators (only one used at a time), and an absorbed glass mat battery bank with a no inal capacity of 300 kWh.To extend service life, the battery bank is operated by SML on to 30% depth of discharge, resulting in an effective usable storage capacity of 90 kWh.T SML microgrid has grown organically over time, based on historic needs and equipm grants or donations, without formal system optimization efforts.The installation years different system components are provided in Table S4 of the Supplementary Informati (SI).SML has an ongoing sustainability initiative to upgrade the microgrid system to i prove its environmental performance, especially in terms of reducing its diesel consum tion and carbon emissions.This study is being conducted in part to aid in the decisio making process for upgrading the SML microgrid.
SML monitors its electricity demand, solar, wind, and diesel electricity generati ambient temperature, and solar global horizontal irradiation (GHI) on a minute-by-m nute basis [43].Wind speed data were obtained from the nearby IOSN3 station (42°58 N 70°37′24″ W) of the National Data Buoy Center since it was not monitored directly the site during the study period.To account for missing data, linear interpolation w used for periods lasting less than 10 min.For gaps that are longer than 10 min, the missi data were assumed to follow the trend of the previous day.None of the missing perio exceeded an hour in the 2019 dataset.Figure 1 shows the monitored daily renewable ergy generation and electricity demand on the island over the study period.The total el tric energy consumption during this period was 19,124 kWh, with an average daily co sumption of 265 kWh.

Methods
In this study, a system dynamics model (SDM) was first developed and calibrated capture energy flows and balance in the studied microgrid system on a one-minute ti step (Section 3.1).SDM is a computational technique utilizing differential equations simulate complex systems over time [44].Vensim DSS V6.4a, developed by Ventana S tems Inc. in Harvard, MA, was employed for the purpose of system dynamics modeli Outputs from the SDM inform the overall diesel consumption over the study period, system's life cycle carbon emissions, and life cycle cost associated with different microg design scenarios (Section 3.2), which were used as the three decision criteria in this stud A production possibility frontier analysis was then performed to understand the synerg and the trade-offs across the three objectives and the system sizing that co-optimizes th three objectives (Section 3.3).We further examined the possibility of further improvi

Methods
In this study, a system dynamics model (SDM) was first developed and calibrated to capture energy flows and balance in the studied microgrid system on a one-minute time step (Section 3.1).SDM is a computational technique utilizing differential equations to simulate complex systems over time [44].Vensim DSS V6.4a, developed by Ventana Systems Inc. in Harvard, MA, was employed for the purpose of system dynamics modeling.Outputs from the SDM inform the overall diesel consumption over the study period, the system's life cycle carbon emissions, and life cycle cost associated with different microgrid design scenarios (Section 3.2), which were used as the three decision criteria in this study.A production possibility frontier analysis was then performed to understand the synergies and the trade-offs across the three objectives and the system sizing that co-optimizes these three objectives (Section 3.3).We further examined the possibility of further improving microgrid performance via an alternative dispatch strategy that is under consideration by the SML (Section 3.4).Last but not least, a sensitivity analysis was performed to evaluate the model's sensitivity to key input variables (Section 3.5).microgrid performance via an alternative dispatch strategy that is under consideration by the SML (Section 3.4).Last but not least, a sensitivity analysis was performed to evaluate the model's sensitivity to key input variables (Section 3.5).

Process-Based Modeling and Calibration of the Microgrid System
Figure 2 is a simplified schematic of the SDM developed in this study.The full model can be found at https://doi.org/10.6084/m9.figshare.23661798.v4(last accessed on 5 September 2023).The SDM comprises five components: (1) wind energy supply, (2) solar energy supply, (3) diesel energy supply, (4) energy demand, and (5) balance of the system.The solar energy supply was calculated based on local solar radiation, air temperature, and PV system specifications using equations obtained from Ren et al. (2020) [45] and Lilienthal (2005) [46] (Section S1 of the SI).Wind generation was calculated based on the manufacturer-provided power curve of the Bergey Excel 10 wind turbine, a recent replacement for the original Bergey Excel-R turbine (See Section S2 of the SI), with the wind speed at hub height being adjusted based on the wind profile power law using Equation (1) [47].
where Uz is the wind speed at hub height;  is the elevation at which the referenced anemometer is installed; ZH is the elevation at hub height;  is the monitored wind speed at the referenced point, and α is the power law exponent, which was assumed to be 1/7 based on Sutton [48].Diesel generation, when operating as a backup power source at the SML, was intentionally set to always have a 32% surplus over demand for charging the battery to reduce battery deterioration, according to the current practice.The battery state of charge was kept between 70% and 100% of the full capacity via a charge controller.
For each time step, if the renewable energy generation surpasses the demand and the

Energy Demand
Figure 2. A simplified illustration of the system dynamics model developed in Vensim DSS V6.4a for the Shoals Marine Laboratory's microgrid, which is comprised of solar, wind, and diesel energy supply, demand, and balance of the system.
The solar energy supply was calculated based on local solar radiation, air temperature, and PV system specifications using equations obtained from Ren et al. (2020) [45] and Lilienthal (2005) [46] (Section S1 of the SI).Wind generation was calculated based on the manufacturer-provided power curve of the Bergey Excel 10 wind turbine, a recent replacement for the original Bergey Excel-R turbine (See Section S2 of the SI), with the wind speed at hub height being adjusted based on the wind profile power law using Equation (1) [47].
where U z is the wind speed at hub height; Z re f is the elevation at which the referenced anemometer is installed; Z H is the elevation at hub height; U re f is the monitored wind speed at the referenced point, and α is the power law exponent, which was assumed to be 1/7 based on Sutton [48].Diesel generation, when operating as a backup power source at the SML, was intentionally set to always have a 32% surplus over demand for charging the battery to reduce battery deterioration, according to the current practice.The battery state of charge was kept between 70% and 100% of the full capacity via a charge controller.
For each time step, if the renewable energy generation surpasses the demand and the battery is not fully charged, the excess renewable energy will first fulfill the demand and then charge the battery.However, if the battery is charged to 100% of its full capacity, the surplus available renewable energy will not be used after fulfilling the demand.On the other hand, if renewable energy generation is insufficient to meet the demand, the gap between the demand and renewable energy generation will first be fulfilled by discharging the battery down to 70% of the battery capacity and then by diesel generation.Based on the current microgrid wiring and practice, once the diesel generator is on, an internal switch occurs so that the demand will be fully satisfied by diesel energy generation, while renewable energy will only be used to charge the battery.The diesel generator keeps operating until the battery state of charge reaches 78% of its full capacity, then it shuts off.
A calibration process was conducted to fine-tune certain parameters which can differ from their initial or rated values (i.e., solar PV module efficiency, wind energy conversion factor, and battery capacity) in the SDM by comparing the modeled and the monitored diesel, solar, and wind electricity generation data, as well as the battery state of charge.The Mean Squared Error (MSE) and/or R 2 were used as a calibration criterion based on suitability, where MSE indicates model error [49] and R 2 indicates trend similarity [50].The monitored solar energy generation data were first used to calculate an average solar PV module efficiency.SML has solar PV panels that were produced by different manufacturers and in different years, and installed with different tilting angles and azimuths.Since the PV array was treated as a whole in the model, the average module efficiency needed to be calibrated.The PV module efficiency was varied from 0.1 to 0.2 in increments of 0.01.The efficiency resulting in the lowest MSE was selected.The selected PV module average efficiency was 0.16, which resulted in an MSE of 8.15.Next, wind generation was calibrated by comparing simulated and monitored wind generation data.An energy conversion factor was introduced and varied from 0.1 to 1 in increments of 0.01.The wind energy conversion factor yielding the lowest Mean Squared Error (MSE), 0.94, was selected.Using the calibrated solar module efficiency and the wind energy conversion factor, we then further calibrated the actual battery storage capacity.The battery storage capacity at SML has degraded over time since its installation, and the actual remaining capacity is no longer known.In this calibration, the battery storage capacity was varied from 100 kWh to 300 kWh in increments of 1 kWh.The actual remaining capacity was determined by comparing the simulated and the actual battery state of charge and diesel electricity generation.To eliminate noises in simulated and real data, minute-based diesel generation data were aggregated to daily diesel electricity generation for comparison, while the battery state of charge was still compared on a minute basis.The MSE and R 2 of both battery state of charge and daily diesel generation were calculated for each battery storage capacity scenario.These MSE and R 2 values were then normalized by dividing each value by the maximum value of the respective criterion.This normalization process ensures comparability between the two calibration metrics.The normalized scores were then added with equal weights for each capacity scenario, and the storage capacity with the highest score was selected.The actual storage capacity found was 250 kWh (MSE and R 2 for daily diesel generation are 1216.8and 67.5%, respectively; MSE and R 2 for battery state of charge are 19.6 and 83.8%, respectively), which is a realistic value considering the battery age and the number of charge cycles.Note that a battery capacity of 250 kWh corresponds to an effective usable storage capacity of 75 kWh under a 30% depth of discharge operation.

Calculation of Decision Criteria
Three decision criteria were identified based on the key considerations of the SML decision makers: (1) Diesel electricity generation, (2) Equivalent annual cost (EAC), and (3) Carbon footprint (CF).Both EAC and CF included the construction/manufacturing and the use phases of the microgrid, while diesel electricity generation is only tied to the use phase.It should be noted that the construction/manufacturing of the wind system was not included as the SML was not considering adding more wind turbines due to its summer-focused operation.
The annual diesel electricity generation (E Diesel ) was computed as the total kWh of simulated diesel electricity generation over the study period.Minimization of diesel consumption has been an important consideration of the SML management team, given its sustainability implications as well as the difficulty in transporting large amounts of diesel to the SML.
EAC in 2019-dollar value was used as an indicator of the life cycle cost of the microgrid system, which provides a comprehensive view of the system's economic implications in the long term.It includes the capital (installation included) and the operation costs [51].End-of-life cost was not considered as the equipment is typically donated by the SML to other entities at the end of its expected lifespan.The authors acknowledge that this will not likely be common in other microgrid applications.Equation ( 2) describes the calculation of the EAC based on the discounted equivalent annual cost associated with solar PV and battery assets as well as the annual diesel cost [52].
where the annual discount rate is denoted by R, which was assumed to be 5%.P Battery is the capital cost of battery assets per kWh of battery capacity.It was estimated at $875.0 per kWh of battery capacity in 2019-dollar value, based on the local vendor's quote [53].S is the battery storage capacity in kWh; P PV is the capital cost of solar panels, which was estimated at $378.73 per panel (at 293-W capacity per panel) in 2019-dollar value based on the local vendor's quote [54].N PV is the number of installed panels, 233 panels; n is the battery lifespan, which was assumed to be 4000 charge cycles [55].A charge cycle was defined as a full charge and discharge of the actual battery capacity.m is the solar panel's lifespan, which was assumed to be 20 years [56].C Diesel is the annual diesel cost, which was calculated by Here, f is the diesel consumption conversion factor, which was assumed to be 0.0903 gallons of diesel per kWh of electricity generation [57].P Diesel is the average diesel cost in July 2019, $2.40 per gallon [58].
Carbon footprint (CF) is the life cycle greenhouse gas (GHG) emissions of the microgrid system, a commonly used metric to characterize an energy system's life cycle environmental impact.The carbon emission factors associated with the entire "supply chain" of different system components were calculated using the IPCC 2021 GWP100 method embedded in SimaPro 9.4, according to Equation (3).
where CF Battery is the unit amount of GHG emissions associated with manufacturing and installing battery storage system, estimated to be 92.5 kg CO 2eq /kWh of battery capacity based on the SimaPro data entry of {Battery cell, Li-ion {GLO}|market for|APOS, S}; CF PV is the unit amount of GHG emissions associated with manufacturing and installing solar panels, estimated to be 299 kg CO 2eq /panel based on the SimaPro data entry of {Photovoltaic panel, multi-Si wafer {GLO}|market for|APOS, S}.CF Diesel represents the unit amount of GHG emissions associated with diesel electricity generation, 0.0956 kg CO 2eq per MJ of diesel embodied energy based on the SimaPro data entry of {market for diesel, burned in diesel-electric generating set, 18.5 kW GLO}.C EE is the embodied energy conversion factor for diesel, which was estimated using the Cumulative Energy Demand 1.11 method embedded in SimaPro through {Diesel, burned in diesel-electric generating set, 18.5 kW {GLO}|market for|Cut-off, U}, 12.41 MJ of embodied energy/kWh.

Production Possibility Frontier Analysis
Optimal sizing of the PV and battery systems was identified based on either single or multiple decision criteria discussed in Section 3.2, namely annual diesel electricity generation, EAC, and CF.Battery capacity was changed in 50 kWh increments from 0 kWh to 1500 kWh, and the PV capacity was changed from 0 to 600 in 10-unit increments.The installation of additional wind turbines is currently not considered by the SML.A production possibility frontier (PPF) analysis was used to provide an analytical representation of choices and trade-offs among different decision criteria [59,60].PPF represented the pareto optimal or non-dominated solutions where none of the decision criteria could be improved without negatively impacting another [60,61].The PPFs in this study were identified using the "pareto2d" function coded in Python [62].Out of all pareto optimal solutions on the PPF, the balanced optimal solutions are those that balance the two or more competing decision criteria, which are typically the "turning points" of the PPF [63].The balanced optimal solutions can be identified through visual observation combined with stakeholder-defined constraints or thresholds in each decision criterion [64].In this study, a rough range of balanced optimal solutions between any two of the decision criteria was first identified through visual observations.These solutions were then overlaid to identify the balanced optimal solutions for all three criteria based on stakeholder-identified constraints of a CF of lower than 10,500 kg CO 2-eq , a diesel electricity generation of lower than 4000 kWh, and an EAC of lower than $35,000.

Alternative Dispatch Scenario Analysis
In the current system, once the diesel generator is on, it keeps operating until the battery reaches 78% of the full capacity, and the demand is solely met by diesel electricity generation during this time, while available renewable energy is used for charging the battery.While the approach allows the battery to be charged faster, it may not be the best way to reduce diesel consumption.An alternative dispatch strategy is to prioritize renewable energy to meet the demand while the diesel generator is still operating.The diesel generator adjusts its output and only satisfies the demand that is in excess of the renewable energy supply.The diesel generator turns off when the renewable generation exceeds the demand and the battery state of charge is above 70%.

Sensitivity Analysis
A sensitivity analysis was conducted to determine the outputs' sensitivity to selected input variables (Table 1) [65].We tested the input variables associated with technological advancement (i.e., solar PV, wind, and diesel generator efficiencies and lifespans, as well as system losses) [66], economic situation (i.e., discount rate, as well as diesel, PV and battery prices) [67], environmental impacts (i.e., diesel, PV, and battery environmental impacts), as well as parameters related to island specific characteristics (i.e., temperature, island demand load, PV azimuth, and PV tilting angle) [15].We changed each selected input parameter by ±5% [68].This range was selected considering the feasible range of each changing parameter.A sensitivity index was calculated using Equation (4) for comparing the sensitivity of different input parameters [44].The sensitivity index quantifies the variation in the relevant decision criteria under alterations in the input parameters.
where, f i denotes the system performance after the input was changed; f b is the base system performance value; SC i is the altered input value; and SC b is the base input value.

Simulation Results for Individual Objectives
When optimizing the battery sizing for the minimized diesel electricity generation, we found that increasing storage capacity up to 1000 kWh-while keeping PV capacity constant-can only decrease diesel electricity generation by 42.17%.This is because further diesel electricity generation reduction is restricted by solar energy generation.The change exhibits an exponential approaching pattern (Figure 3a).To further analyze the pattern, changes in the slope were calculated based on neighboring pairs of data points and the moving average of three slopes.The analysis revealed a turning point of 550 kWh of battery capacity.Below this value, each kWh increase in battery capacity results in an average of 8.2 kWh savings in diesel energy, while above this value, each kWh increase in battery capacity results in an average of only 0.7 kWh savings in diesel energy.We also investigated the effect of changing solar capacity on diesel electricity generation-while keeping battery capacity constant.No obvious turning point was identified within the range of the studied solar capacity.Changing solar capacity alone is also not feasible for achieving zero diesel generation, given the limited storage capacity (Figure 3b).It has to be noted that these findings are specific based on the SML-specific condition and may not be generalizable.It should also be noted that all stated battery capacities assume 30% depth of discharge operation, i.e., the effective storage capacity is 30% of stated values.investigated the effect of changing solar capacity on diesel electricity generation-while keeping battery capacity constant.No obvious turning point was identified within the range of the studied solar capacity.Changing solar capacity alone is also not feasible for achieving zero diesel generation, given the limited storage capacity (Figure 3b).It has to be noted that these findings are specific based on the SML-specific condition and may not be generalizable.It should also be noted that all stated battery capacities assume 30% depth of discharge operation, i.e., the effective storage capacity is 30% of stated values.Figure 4 presents the diesel electricity generation, CF, and EAC outcomes when battery and solar capacities are changed simultaneously.The results show that the SML is currently operating at a close-to-optimal state given the presently installed PV and battery capacity (highlighted as the red dots in Figure 4) with diesel consumption, CF, and EAC all within 30% of the largest value, although further improvements are feasible.A large battery capacity (750-1400 kWh) combined with a relatively large solar capacity (100-175 kW) can lead to zero diesel energy generation.Similarly, large battery (more than 1200 kWh) and solar (320-350 kW) capacities lead to minimized CF (about 40% of the current system's CF).However, net zero carbon emission was deemed unfeasible.A similar finding was also reported in Shezan et al. [69], Logenthiran et al. [70], and Pourmousavi et al. [71].As opposed to diesel electricity generation and CF, EAC minimization favors smaller battery and solar capacities.A three-fold increase in EAC was observed when zero diesel energy generation was achieved.

Multi-Objective Decision Making
Figure 5 presents the synergies and the trade-offs across the three studied objectives under various solar and battery sizing scenarios.The convex trend of the PPF between CF and EAC indicates that there is a trade-off between CF and EAC.Out of the optimized solutions for CF and EAC, solutions that could potentially balance these two objectives are between Points B and C1, with corresponding battery capacities of 50-550 kWh and solar capacities of 35.14-105.41kW (120-360 panels).Characteristics of these turning points are summarized in Table 2. Similarly, a convex PPF exists between diesel energy generation and EAC, emphasizing a similar trade-off between diesel energy generation and EAC.The balanced solutions were identified as between Points B and C2, with corresponding battery capacities of 50-550 kWh and solar capacities of 35.14-146.40kW (120-500 panels).CF and diesel energy generation, on the other hand, present a high collinearity, highlighting the dependence of CF on diesel consumption.A similar trend was also reported by Raj et al. [72] and Zhang et al. [73].While no PPF is observed between these two objectives, the optimal solutions with the lowest diesel electricity generation and CF were identified with a solar capacity of 93.70-102.48kW (320-350 panels) with a maximum possible battery capacity of 1500 kWh (red dots in Figure 5e,f).Solutions that co-optimize all three objectives are defined as these on the PPFs but with a diesel electricity generation of lower than 4000 kWh and a CF of lower than 11,000 Kg CO 2-eq .These co-optimized solutions have a solar capacity of 84.91-105.41kW (290-360 panels) and a battery capacity of 400-550 kWh (orange triangles in Figure 5).The optimal battery capacity is about 80% to 120% higher than the status quo, while the optimal PV capacity is about 42% to 54% higher than the status quo.This indicates that upsizing the current PV and battery systems at the SML has potential co-benefits in all criteria.These findings also indicate that achieving "win-wins" across the three objectives is possible.This aligns with findings from Litchy and Nehrir [74].capacity (highlighted as the red dots in Figure 4) with diesel consumption, CF, and EAC all within 30% of the largest value, although further improvements are feasible.A large battery capacity (750-1400 kWh) combined with a relatively large solar capacity (100-175 kW) can lead to zero diesel energy generation.Similarly, large battery (more than 1200 kWh) and solar (320-350 kW) capacities lead to minimized CF (about 40% of the current system's CF).However, net zero carbon emission was deemed unfeasible.A similar finding was also reported in Shezan et al. [69], Logenthiran et al. [70], and Pourmousavi et al. [71].As opposed to diesel electricity generation and CF, EAC minimization favors smaller battery and solar capacities.A three-fold increase in EAC was observed when zero diesel energy generation was achieved.optimized solutions have a solar capacity of 84.91-105.41kW (290-360 panels) and a battery capacity of 400-550 kWh (orange triangles in Figure 5).The optimal battery capacity is about 80% to 120% higher than the status quo, while the optimal PV capacity is about 42% to 54% higher than the status quo.This indicates that upsizing the current PV and battery systems at the SML has potential co-benefits in all criteria.These findings also indicate that achieving "win-wins" across the three objectives is possible.This aligns with findings from Litchy and Nehrir [74].

Comparison with an Alternative Dispatch Strategy
Figure 6 illustrates the potential changes in diesel consumption and CF as well as the number of charge cycles by implementing the alternative strategy.The new dispatch strategy is capable of reducing both diesel energy generation and CF of the system by 12.14% and 9.37%, respectively, compared to the current system setup.The highest reduction occurs when the battery capacity is at 285 kWh, holding solar capacity at the current size.Below this point, the diesel and carbon benefits diminish quickly with a decreased battery capacity.The highest diesel reduction is estimated to be 870 kWh, which equals 14.1% of the current diesel energy generation.The highest CF reduction is 1463 kg CO 2eq , which equals 10.6% of the current CF.This alternative strategy also reduces energy that goes unused by 22.5%.Battery charge cycles are also significantly reduced in the alternative strategy.The amount of charge cycle reduction is the most significant in smaller battery sizes.On the other hand, the alternative strategy increases the average daily diesel generator on and off cycles from 1.8 to 2.5, which may raise maintenance costs.Collectively, these findings show that the alternative dispatch strategy can be an effective approach to achieving enhanced environmental and economic benefits.However, the level of benefits that can be achieved is system size specific.It is also important to be aware of the potential trade-offs, such as an increased diesel generation on and off cycle.

Sensitivity Analysis
Table 3 represents the sensitivity indexes associated with a ±5% variation in selected variables for each objective.In terms of diesel energy generation, it exhibits the highest sensitivity to increased efficiency of the inverters, accompanied by the highest sensitivity index (S).Following that, an increase in electricity demand and an improvement in PV module efficiency also have notable effects.This highlights the significance of adopting advanced technology devices, such as newer PV panels and more efficient inverters, along with implementing demand management strategies and replacing energy-intensive devices with energy-efficient alternatives.
Regarding the CF, the most impactful factor is, again, the improvement in inverter efficiency.Additionally, improvements in diesel generator efficiency and reducing the carbon footprint of the diesel generator also contribute significantly.This emphasizes the importance of enhancing the efficiency of diesel generators and inverters to mitigate the environmental impact of the entire system.
In terms of the EAC, the highest sensitivity index is associated with improving diesel generator efficiency.This is followed by enhancing inverter efficiency and increasing the diesel price.These findings highlight that the life cycle costs of the system are highly sensitive to the efficiency of the diesel generator and inverter.Moreover, the cost of fuel plays a significant role after these factors in determining the overall EAC.

Sensitivity Analysis
Table 3 represents the sensitivity indexes associated with a ±5% variation in selected variables for each objective.In terms of diesel energy generation, it exhibits the highest sensitivity to increased efficiency of the inverters, accompanied by the highest sensitivity index (S).Following that, an increase in electricity demand and an improvement in PV module efficiency also have notable effects.This highlights the significance of adopting advanced technology devices, such as newer PV panels and more efficient inverters, along with implementing demand management strategies and replacing energy-intensive devices with energy-efficient alternatives.
Regarding the CF, the most impactful factor is, again, the improvement in inverter efficiency.Additionally, improvements in diesel generator efficiency and reducing the carbon footprint of the diesel generator also contribute significantly.This emphasizes the importance of enhancing the efficiency of diesel generators and inverters to mitigate the environmental impact of the entire system.
In terms of the EAC, the highest sensitivity index is associated with improving diesel generator efficiency.This is followed by enhancing inverter efficiency and increasing the diesel price.These findings highlight that the life cycle costs of the system are highly sensitive to the efficiency of the diesel generator and inverter.Moreover, the cost of fuel plays a significant role after these factors in determining the overall EAC.

Conclusions
This study investigated multi-objective decision-making of diesel electricity generation, CF, and EAC for an island microgrid located on Appledore Island, Maine.The analysis showed that adding storage capacity up to 1000 kWh while keeping PV capacity constant can reduce diesel electricity generation by 42.17%.While changing battery or solar capacity alone cannot achieve zero diesel energy generation, increasing both capacities simultaneously can.However, this will result in around a 70% increase in EAC compared to the status quo.The PPF analysis found high collinearity between diesel and CF, while both present a trade-off with the EAC.When EAC is co-optimized with either diesel or CF, the balanced optimal solutions as the turning points on the PPFs from the two decision-making schemes are similar.Solutions that can optimize all three studied objectives are found to involve utilizing 85-105 kW of solar PV capacity and 400-550 kWh of storage capacity (120-165 kWh of effective storage capacity considering the present 30% depth of discharge operating scenario).This shows that the currently installed system is working with approximately half of the optimal battery capacity and two-thirds of the optimal solar capacity.Adopting an alternative dispatch strategy that prioritizes renewable energy for satisfying the demand of overcharging the battery can potentially result in a 12.1% further saving in diesel energy generation, 9.4% saving in CF, and 23.9% reduction in battery charge cycles, with a trade-off of a 1.4-fold increase in diesel generator on and off cycles.Sensitivity analysis indicated that diesel energy generation and CF are the most sensitive to inverter efficiency improvement, while EAC is the most sensitive to diesel generator efficiency.This indicates that any technological advancements in diesel generators and system inverters can have a substantial impact on all three objectives examined in this study.Given the increased interest in microgrids for enhanced energy resiliency and sustainability, this study shows that proper planning and design can significantly increase the microgrid's environmental and economic performance.
There are several limitations to this study.Firstly, the microgrid under investigation was developed incrementally, resulting in variations in PV module angles, azimuths, and other characteristics.The analysis conducted in this study accounted for average system specifications but could benefit from further refinement in the model or in future research, enabling a more detailed examination of the microgrid's performance.Secondly, this study did not consider the potential impact of soiling and dirt accumulation on solar panels.These factors can reduce the efficiency of PV generation and should be considered in future studies for a more comprehensive analysis.Last but not least, this study did not include any demand side management of the energy consumption to focus on the system design.Given the isolated environment at the SML, water is currently supplied through an energyintensive seawater desalination process.In future studies, it is recommended to include the co-optimization of both the energy and water systems to achieve further environmental and economic benefits.

Figure 1 .
Figure 1.SML's daily renewable energy generation and electricity demand during the study peri

Figure 1 .
Figure 1.SML's daily renewable energy generation and electricity demand during the study period.

Figure 2 .
Figure 2.A simplified illustration of the system dynamics model developed in Vensim DSS V6.4a for the Shoals Marine Laboratory's microgrid, which is comprised of solar, wind, and diesel energy supply, demand, and balance of the system.

Figure 3 .
Figure 3.The single objective optimization focuses on the change in diesel electricity generation concerning the variations in battery capacity (a) and solar capacity (b).

Figure 4
Figure 4 presents the diesel electricity generation, CF, and EAC outcomes when battery and solar capacities are changed simultaneously.The results show that the SML is

Figure 3 .
Figure 3.The single objective optimization focuses on the change in diesel electricity generation concerning the variations in battery capacity (a) and solar capacity (b).

Figure 4 .
Figure 4. (a) Annual diesel costs, (b) CF, and (c) EAC of various solar capacities and battery capacities.The color scale represents the percentage of each objective relative to the highest value in each objective.(The red point highlights the current state at the SML).

Figure 5
Figure 5 presents the synergies and the trade-offs across the three studied objectives under various solar and battery sizing scenarios.The convex trend of the PPF between CF and EAC indicates that there is a trade-off between CF and EAC.Out of the optimized

Figure 4 .
Figure 4. (a) Annual diesel costs, (b) CF, and (c) EAC of various solar capacities and battery capacities.The color scale represents the percentage of each objective relative to the highest value in each objective.(The red point highlights the current state at the SML).

Figure 5 .
Figure 5. Production possibility frontiers (PPFs) between diesel energy generation, CF, and EAC.(a), (c), and (e) are colored based on the battery capacity, and (b), (d), and (f) are colored based on the solar capacity.The dashed red lines are the production possibility frontiers, indicating the optimized solutions based on two objectives.Orange triangles indicate the balanced optimal solutions for all three objectives identified through the PPF analysis.

Figure 5 .
Figure 5. Production possibility frontiers (PPFs) between diesel energy generation, CF, and EAC.(a), (c), and (e) are colored based on the battery capacity, and (b), (d), and (f) are colored based on the solar capacity.The dashed red lines are the production possibility frontiers, indicating the optimized solutions based on two objectives.Orange triangles indicate the balanced optimal solutions for all three objectives identified through the PPF analysis.

Sustainability 2023 , 17 Figure 6 .
Figure 6.Comparison of the current and the alternative dispatch strategies in terms of diesel consumption, CF, and battery charge cycles.The percentage change was calculated by dividing the improvement in the alternative strategy by the status quo.

Figure 6 .
Figure 6.Comparison of the current and the alternative dispatch strategies in terms of diesel consumption, CF, and battery charge cycles.The percentage change was calculated by dividing the improvement in the alternative strategy by the status quo.

Table 1 .
Sensitivity analysis scenarios for the 17 selected model variables.

Table 2 .
PPF turning points characteristics.Objective variables are normalized based on the highest possible value in each of the decision criteria.

Table 2 .
PPF turning points characteristics.Objective variables are normalized based on the highest possible value in each of the decision criteria.

Table 3 .
The sensitivity index (S) of each objective function under the change of each scenario.

Table 3 .
The sensitivity index (S) of each objective function under the change of each scenario.