Development of a Tool for Optimizing Solar and Battery Storage for Container Farming in a Remote Arctic Microgrid

High transportation costs make energy and food expensive in remote communities worldwide, especially in high-latitude Arctic climates. Past attempts to grow food indoors in these remote areas have proven uneconomical due to the need for expensive imported diesel for heating and electricity. This study aims to determine whether solar photovoltaic (PV) electricity can be used affordably to power container farms integrated with a remote Arctic community microgrid. A mixed-integer linear optimization model (FEWMORE: Food–Energy–Water Microgrid Optimization with Renewable Energy) has been developed to minimize the capital and maintenance costs of installing solar photovoltaics (PV) plus electricity storage and the operational costs of purchasing electricity from the community microgrid to power a container farm. FEWMORE expands upon previous models by simulating demand-side management of container farm loads. Its results are compared with those of another model (HOMER) for a test case. FEWMORE determined that 17 kW of solar PV was optimal to power the farm loads, resulting in a total annual cost decline of ~14% compared with a container farm currently operating in the Yukon. Managing specific loads appropriately can reduce total costs by ~18%. Thus, even in an Arctic climate, where the solar PV system supplies only ~7% of total load during the winter and ~25% of the load during the entire year, investing in solar PV reduces costs.


Introduction
Remote communities in Alaska pay some of the highest prices for electricity in the United States, often in excess of $1/kWh [1]. These high costs are due to the communities' isolation from Alaska's electric grid and its road system. Communities must instead operate and maintain their own diesel generators to provide electricity via a self-contained electric grid, also known as an islanded microgrid. Diesel fuel must be imported over a long distance by plane or boat. Electricity is subsidized for residential use in many communities, but subsidies are not available for commercial operations including for agriculture [1].
Alaskan remote communities are therefore more similar to energy-insecure areas worldwide than they are to the rest of the United States [2]. Most people worldwide facing energy insecurity live in rural areas. For over 70% of them, microgrids provide the best solution to addressing energy insecurity due to the logistical challenges of extending a centralized grid [2,3]. Microgrids can also help to reduce climate change damage, air pollution, and land degradation [4]. used, given their ability to solve problems at speed with necessary detail, as state-of-the-art in energy system modeling [16].
Commercial tools have been built to bridge this gap of complexity and performance with speed and accessibility in designing renewable energy microgrids. For example, the default tool for analyzing microgrids is HOMER (Hybrid Optimization of Multiple Energy Resources), originally developed at the National Renewable Energy Laboratory (NREL). HOMER has been used widely for modeling remote islanded microgrid systems [17]. Singh et al. [18] compares the hybrid PV-wind-biomass-storage optimization in HOMER with an evolutionary algorithm approach, which has better performance. Shoeb and Shafiullah [19] use HOMER to optimize operation of water pumps in a microgrid with solar PV. Tapia [20] implemented a HOMER model to study hybrid renewable energy optimization of a container farm; however, the load profile was assumed fixed and no load flexibility was implemented in this analysis.
Still, other microgrid design tools have been developed by government labs and organizations. NREL has developed ReOpt (Renewable Energy Integration and Optimization) Lite as an open-source tool for optimizing solar and storage capacity for a specific load, and is based on the more complex ReOpt software; however, it is not possible to manipulate the load profile to analyze DSM of specific loads [21]. NREL has also developed RPM (Resource Planning Model) to analyze the value of flexibility of battery storage and interruptible loads, but it is used at a large-scale for capacity expansion modeling [22].
Numerous microgrid models have also been developed that use demand-side management. Neves et al. compare a self-built economic dispatch model that uses genetic algorithms with the capabilities of HOMER for modeling demand response [23]. They emphasize that there is a significant challenge in using commercial tools for demand response modeling and have found that most models using DSM are self-built. An optimization framework must also balance long-term investment planning with short-term dispatch strategies [24]. HOMER cannot schedule specific loads as part of an overall demand profile in hourly increments with custom dispatch strategies, and instead distributes flexible load operations evenly across a day [23].
A model has not yet been developed that optimizes the capacity and dispatch of novel food-energy-water controllable loads for demand-side management as part of a container farm in islanded renewable microgrids. Most models also do not account for thermal energy requirements or optimization, which is more typically suited for energy models for buildings. Numerical models for operating container farms have been developed, though these do not include energy optimization strategies with renewable energy systems [25]. Other tools have been designed around the food-energy-water nexus, but optimize the size of a greenhouse-not a container farm or individual loads-with a solar PV array [26]. This paper's contribution, then, is the development of a tool, FEWMORE: Food-Energy-Water Microgrid Optimization with Renewable Energy, to optimize the capacity and operations of a solar PV and battery system in order to power optimally-scheduled loads of a container farm within a remote islanded microgrid. Additionally, for modeling flexible loads, it is critical to have a tool tailored to specific constraints and system dynamics of which no energy optimization model is currently articulated for container farms. The model also balances electric and thermal (both sensible and latent) energy requirements.
The rest of the paper is structured around container farming description, modeling methodology, and energy simulation results and conclusions.

Container Farming
Container farms have been introduced in the Arctic due to their modular nature, ease of transport and siting, and ability to grow food year-round indoors in a well-insulated unit [27]. Shipping containers are already a relatively common method of transporting goods to Alaskan villages. These containers are generally retrofitted with hydroponic growing systems, in which plants are grown in trays of circulated nutrient-rich water. In addition to being highly productive, this system does not use soil, which can be advantageous in Arctic areas without access to fertile soil [28]. An example of a container farm is a CropBox unit, which can produce 5400 kg (12,000 lbs) per year of herbs and greens [10]. Based on an analysis of a CropBox, the cost of growing this produce (in a typical location) is $6.34/kg ($2.88/lb) including all energy, labor, and miscellaneous costs [12]. Table 1 provides the typical characteristics of a hydroponic growing container used for this analysis [29]. All heating, ventilation, and air-conditioning (HVAC) are assumed to be electric. There are also accessory loads including those for carbon dioxide (CO 2 ) pumping, nutrient pumping, and sensors that have negligible electric requirements, and therefore are not included. The loads are assumed to be well optimized in size within an energy-efficient container. Loads that are on at all times or baseloads include air circulation fans and water pumps for the hydroponic growing trays. These total approximately 1 kW of instantaneous power. They can, in theory, be shut off for a period if there is a lack of renewable power; however, in reality, this may lead to a decline in produce quality, so were not considered for the DSM. All equipment results in heat gain, which must be removed via cooling if the unit exceeds its interior temperature range.
Due to its opaque envelope, a container farm substitutes natural sunlight with LED grow lights at a relatively high energy demand. LED arrays provide lighting for 18 h per day at 4.5 kW (or 81 kWh per day). While LED lighting is relatively efficient, this still implies that nearly all of the 4.5 kW of electricity is dissipated as heat to the indoor environment, leading to a potentially high cooling load. Lights are assumed to operate continuously during the 18-h block, but can be scheduled to be on during any time of day.
Dehumidification is also a significant load. Plants transpire, resulting in an accumulation of humidity in the indoor space, or latent heating load. Plants also reduce the sensible heat load due to the evaporative cooling effect of evapotranspiration, thus offsetting some heat gains from lighting and other equipment. These effects occur primarily during lighting hours; it was assumed that the ratio of transpiration during the plants' day to night was 3:1 [30]. The container farm operates at an optimal 65-75% relative humidity (RH); we assumed the RH was fixed at 70% [29]. If this level is exceeded and moisture is not removed, then fungal growth and disease may occur; alternatively, if too much moisture is removed, plants may desiccate and reduce yield. A dehumidifier, rated at 1.5 kW, was assumed to operate continuously during the baseline operation of a container farm [31] (See Appendix C.3. for additional energy modeling detail). However, this load may be dispatched accordingly, as long as the RH is managed using ventilation.
Ventilation can be used, especially in an Arctic climate to balance sensible and latent thermal loads by exhausting warm, moist indoor air and replacing it with cold, dry ambient air, respectively. The cost of carbon dioxide pumping must also be accounted for when considering ventilation, given that plants have higher yields at elevated CO 2 levels and excessive ventilation would increase costs due to the high price of replacing compressed CO 2 [32]. However, during winter, when there is significant potential to use ventilation for cooling due to the high temperature and humidity difference between the indoor and ambient air, no CO 2 pumping is used given the reliance on outdoor air exchanges in the baseline operation. There is also a minimum number of continuous air exchanges in the container farm, assumed to be 0.5 air changes per hour, due to the combined effects of infiltration and ventilation [33] (See Appendix C.2).
Heating and cooling are provided via an electric fan-coil unit. This unit cycles throughout the day and requires~2 kW. In the baseline case, it is assumed to operate for half the time in a given day (See Appendix A for technology modeling parameters). Thermal energy flows include sensible and latent heat balances. During the vast majority of a year in the Arctic, the ambient temperature is colder outside than the balance point temperature set by the thermostat (20 • C). Sensible heat loss occurs via conduction through the container envelope, infiltration, and ventilation of outside air, and evaporative cooling from plants. Sensible heat gains result from mechanical equipment, and from exterior conduction and infiltration on warm summer days (See Appendix C.1). Latent heat must also be balanced due to the plants' emitted moisture as well as the latent component of infiltration and ventilation air flows (See Appendix C.3).

Methods
The FEWMORE model is applied to a community in Interior Alaska that is interested in local food production and renewable energy, and does not currently have a container farm. This analysis uses collected data from an operating CropBox container farm in Whitehorse, Yukon. These data are used within the FEWMORE model to analyze a control case, named the Base Case, of optimizing solar PV and battery storage with container farm loads in the status quo. Then, the FEWMORE model is used to optimize solar and storage while allowing the prior container farm load profile to be flexible and optimally dispatched, named the Dispatchability Case. In this section, the collected data are analyzed, the FEWMORE model is summarized, and a model simulation procedure is presented.

Container Farm Load Data
A year of power consumption data was collected for the CropBox unit operating in Whitehorse, Yukon, Canada. The data contains the total energy consumption values at 5-min temporal resolution from November 2018 to October 2019, which have been processed to align with a calendar year and averaged to hourly resolution. Averaged diurnal load profiles for each season are shown in Figure 1.

Methods
The FEWMORE model is applied to a community in Interior Alaska that is interested in local food production and renewable energy, and does not currently have a container farm. This analysis uses collected data from an operating CropBox container farm in Whitehorse, Yukon. These data are used within the FEWMORE model to analyze a control case, named the Base Case, of optimizing solar PV and battery storage with container farm loads in the status quo. Then, the FEWMORE model is used to optimize solar and storage while allowing the prior container farm load profile to be flexible and optimally dispatched, named the Dispatchability Case. In this section, the collected data are analyzed, the FEWMORE model is summarized, and a model simulation procedure is presented.

Container Farm Load Data
A year of power consumption data was collected for the CropBox unit operating in Whitehorse, Yukon, Canada. The data contains the total energy consumption values at 5-min temporal resolution from November 2018 to October 2019, which have been processed to align with a calendar year and averaged to hourly resolution. Averaged diurnal load profiles for each season are shown in Figure 1. . Electricity use is greatest overnight along with a midday peak when all loads (lighting, heating/cooling/ventilation, dehumidification) are operating. Reductions in electric use occur in the mid-morning hours, which can be attributed to reduced heating, cooling, and dehumidification as well as late afternoon and evening hours when lighting is turned off. Summer electricity use is generally highest, given substantial cooling required to exhaust waste heat from operating electric loads, which are nearly sufficient to heat the opaque container in the winter. . Electricity use is greatest overnight along with a midday peak when all loads (lighting, heating/cooling/ventilation, dehumidification) are operating. Reductions in electric use occur in the mid-morning hours, which can be attributed to reduced heating, cooling, and dehumidification as well as late afternoon and evening hours when lighting is turned off. Summer electricity use is generally highest, given substantial cooling required to exhaust waste heat from operating electric loads, which are nearly sufficient to heat the opaque container in the winter.
Electricity use in the container farm follows a relatively similar daily profile from season to season. Consumption is fairly constant over a day, peaking at 8 kW when all loads are operating, typically overnight and in the middle of the day. During the late afternoon and early evening, approximately 3 pm-9 pm, lighting is shut off. In the mid-morning hours, there is also a reduction in energy use due to less HVAC and dehumidification operation. The profile is slightly shifted later in the day during the fall and winter, presumably due to daylight savings time and later sunrises. In November 2018, during system initialization, there was slightly less energy use, with a peak power demand of 6.5 kW.

Model Summary
The FEWMORE model is a mixed-integer linear program built in the Julia/JuMP optimization language. The modeling framework has been chosen to reduce computational expense while preserving necessary modeling complexity. Optimization is performed hourly for energy operations and DSM, over an annual capacity planning horizon. The single-year output was extrapolated with perfect foresight to a 20-year project lifetime, subject to a discounted cash flow analysis. The FEWMORE model output was also ultimately compared with HOMER.
The objective of FEWMORE is to minimize the total net present cost of the project, namely capital and lifetime operational costs of powering a container farm (See Appendix B for model form detail). The final objective cost is also divided by the total amount of greens grown over the lifetime to estimate an energy cost per unit of crop production. Assuming the container itself is already purchased, the total project cost includes purchasing, installing, and maintaining the solar PV, battery storage, and power conversion infrastructure to couple directly with the container, in addition to buying electricity from the community microgrid. Grid electricity is purchased at an unsubsidized rate of $0.67/kWh, and prices are assumed to escalate annually at a real rate of 3% [34]. Capital costs include the solar array, with a 20-year lifetime, and a battery and inverter with a 10-year lifetime, replaced at a real discount rate of 3%. Operational costs include a solar PV maintenance cost of $50/kW/yr and a variable cost of battery system maintenance of 0.5 cents per kWh throughput.
The model inputs included the container farm electric load profile and solar yield profile. To determine a synthetic thermal load profile, the ambient temperature and humidity were also used for the specific Interior Alaska climate. The model output the optimal capacity of additional infrastructure (solar PV, battery storage, and inverter) as well as an hourly dispatch of all technologies (battery charging/discharging and DSM of select loads) (See Appendix A for all model inputs and outputs). The dispatch of flexible loads including ventilation fans and dehumidifiers were constrained by physical requirements and optimized for lowest operating cost (See Appendix B).

List of Model Simulation Cases
Two sets of simulations were performed, one with the collected electric load data named the Base Case, and the other with a flexible, synthetic electric load profile known as the Dispatchability Case, as shown in Table 2. The synthetic load profile was derived from typical patterns in the collected electric load data in order to disaggregate specific loads and optimally dispatch them as part of DSM strategies. Lighting was fixed in the synthetic profile to operate coincident with the solar noon. The synthetic load profile also included a sensible heat and latent heat thermal load profile, derived from profiles of ambient temperature and ambient humidity, respectively, to model the optimal operation of the HVAC and dehumidifier units. For each of the two sets of simulation cases, the Base Case and Dispatchability Case, the same three simulations were initially performed. The first simulation (named Baseline simulation) analyzed the container farm operations when all loads were powered by the community microgrid at the unsubsidized electricity rate. In the next simulation (Solar simulation), the amount of solar PV capacity to be added to the container farm was optimized. The solar array generated electricity to be used directly by the container farm, thus potentially reducing the amount of energy purchased from the microgrid, and any excess solar generation beyond the farm load was curtailed. In the Solar & Storage simulation, the amount of battery storage capacity and inverter power capacity were optimized including hourly charging and discharging strategies, in addition to solar PV optimization.
The next simulations (Lighting with Solar, and Lighting with Solar & Storage) were performed only for the Base Case. The lighting schedule was modified from the collected load data, which included lighting operating for an 18-h block somewhat parallel with solar daylight hours (approximately two hours misaligned from solar noon), to a schedule that was perfectly centered around peak solar PV output. The rest of the load profile was assumed to be the same. Then, solar PV capacity and solar PV plus battery storage capacities were optimized for the two respective cases.
The final simulations were performed only for the Dispatchability Case, using a synthetic load profile to analyze DSM strategies of specific loads. The first simulation, named Ventilation, optimized the operation of the ventilation system by determining the number of air changes per hour to perform, given constraints on replacing CO 2 and thermal load requirements. The next simulation, named Dehumidification, optimized how the dehumidifier should operate, in addition to the ventilation system. The dehumidifier was optimized to turn on and off, given that it was assumed to run at a single maximum power setting when operating.

Results and Discussion
The results of the model simulations outlined in Table 2 are presented first for the Base Case (Section 4.1), with the collected load profile, and second for the Dispatchability Case (Section 4.2), with the synthetically derived load profile.

Baseline Simulation
In the baseline simulation, all energy use, or 58.4 MWh per year, was met by purchases from the diesel powerhouse of the community microgrid. The energy cost of operating the farm was $39 k per year, or $783 k for the entire 20-year lifetime. Dividing by the total production of greens over the lifetime resulted in an energy cost per unit of crop produced of $7.17/kg ($3.26/lb).

Solar and Storage Simulations
The model determined that the optimal nameplate capacity of solar PV alone (Solar simulation) to be added to the container farm was 17.1 kW. The solar capacity was approximately 33% higher than the container farm's peak load of 12.8 kW. The total solar electric energy generated was 18.9 MWh/yr, of which 4.8 MWh (~25%) was curtailed (no battery storage is assumed for this simulation). The overall project cost decreased by $106 k compared with the baseline case, or a 13.5% reduction due to adding solar PV. The energy cost of crop production was $6.20/kg ($2.82/lb).
In the Solar & Storage simulation, a battery storage system was added and optimized for its energy capacity and inverter power. The model added a very small battery system of 1.2 kWh/0.5 kW of energy and power capacity, respectively; thus, the total objective cost was nearly the same as in the solar PV-only simulation. The optimal solar PV capacity was 17.5 kW and a total solar electric energy generation of 19.4 MWh/yr with 4.9 MWh curtailed. Similar to the Solar simulation, the energy cost per unit of crop production was $6.20/kg. The battery was used to extend the solar day slightly as shown in Figure 2, in which some excess solar energy was used to charge the battery in the early morning and late afternoon, and then was discharged in the early evening once solar PV output had declined below the container farm load. The vast majority of excess solar energy was otherwise curtailed. The overall project cost decreased by $106 k compared with the baseline case, or a 13.5% reduction due to adding solar PV. The energy cost of crop production was $6.20/kg ($2.82/lb).
In the Solar & Storage simulation, a battery storage system was added and optimized for its energy capacity and inverter power. The model added a very small battery system of 1.2 kWh/0.5 kW of energy and power capacity, respectively; thus, the total objective cost was nearly the same as in the solar PV-only simulation. The optimal solar PV capacity was 17.5 kW and a total solar electric energy generation of 19.4 MWh/yr with 4.9 MWh curtailed. Similar to the Solar simulation, the energy cost per unit of crop production was $6.20/kg. The battery was used to extend the solar day slightly as shown in Figure 2, in which some excess solar energy was used to charge the battery in the early morning and late afternoon, and then was discharged in the early evening once solar PV output had declined below the container farm load. The vast majority of excess solar energy was otherwise curtailed. summer, and (c) fall. In spring, a small amount of excess solar was used to charge the battery at the beginning and end of the solar day with even smaller amounts of charging necessary during the summer, given that more solar energy is available from day to day. Any excess solar generation, beyond the load and charging to the battery, was curtailed. When the battery had energy in storage, it was fully discharged in the early evening hours. In late fall and winter, solar energy output was less than the container farm load.
As shown in Figure 2, given the small size of the recommended battery capacity, it did not provide substantial benefit to the system in terms of dispatching energy. The 0.5 kW rated power of the battery is only about 6% of the farm's peak load. Given 1.2 kWh of storage capacity and discharged at the maximum rate of 0.5 kW, the battery can provide 6% of load for 2.4 h. Thus, while the solar array could meet the container farm load for approximately half of a day during spring and summer, the battery system offered comparatively negligible autonomy. Over the course of a year, only 1.5% of solar generation was used to charge the battery. The low utilization of battery optimization by FEWMORE can be attributed to the relatively high battery storage and power conversion costs ($1000/kWh, $1000/kW) assumed for the Interior Alaska region; in less remote areas with lower costs, the battery capacity may increase.
The solar PV array, with the small battery energy storage system, provided 25% of the power In spring, a small amount of excess solar was used to charge the battery at the beginning and end of the solar day with even smaller amounts of charging necessary during the summer, given that more solar energy is available from day to day. Any excess solar generation, beyond the load and charging to the battery, was curtailed. When the battery had energy in storage, it was fully discharged in the early evening hours. In late fall and winter, solar energy output was less than the container farm load.
As shown in Figure 2, given the small size of the recommended battery capacity, it did not provide substantial benefit to the system in terms of dispatching energy. The 0.5 kW rated power of the battery is only about 6% of the farm's peak load. Given 1.2 kWh of storage capacity and discharged at the maximum rate of 0.5 kW, the battery can provide 6% of load for 2.4 h. Thus, while the solar array could meet the container farm load for approximately half of a day during spring and summer, the battery system offered comparatively negligible autonomy. Over the course of a year, only 1.5% of solar generation was used to charge the battery. The low utilization of battery optimization by FEWMORE can be attributed to the relatively high battery storage and power conversion costs ($1000/kWh, $1000/kW) assumed for the Interior Alaska region; in less remote areas with lower costs, the battery capacity may increase.
The solar PV array, with the small battery energy storage system, provided 25% of the power needs of the container farm over the course of the entire year, as shown in Figure 3. Electricity from the solar array met the load first and any excess was stored or curtailed. In the winter, only 7% of load was met by solar plus storage, with the rest provided by purchases from the community microgrid and its diesel powerhouse. In the summer months (June through August), 38% of load was met by renewable energy. Spring (March through May) resulted in a similar amount of renewable energy penetration compared to summer, as relatively high sun angles and reflectance from snow cover can lead to improved solar performance.
Energies 2020, 13, x FOR PEER REVIEW 9 of 17 Figure 3. Amount of load met by solar and storage in each hour of the year. Only 7% of load was met by the renewable energy system in the winter months, and the rest was provided by community microgrid purchases. In the summer months, 38% of load was met by solar plus storage.

Lighting Simulations
Two simulations were performed in which the lighting schedule in the collected load profile was modified to be perfectly symmetric around the solar PV generation peak output. Originally in the collected electric load profile, lighting did not operate during late afternoon and early evening hours. The Lighting with Solar and Lighting with Solar & Storage simulations were performed for the optimization of solar PV and solar PV plus battery energy storage, respectively. However, given the results for the solar PV-only and solar PV-plus-battery energy storage simulations were quite similar, only results with respect to the solar PV-only (Lighting with Solar) simulation are presented.
The optimal solar PV array power capacity increased marginally from 17.1 to 17.3 kW when the lighting schedule was modified to be symmetric around solar noon in the Lighting with Solar simulation. Thus, the collected data profile was already relatively optimal, given lighting was scheduled for most of the peak solar PV generation hours, approximately 10 am-4 pm. Solar PV power capacity increased, albeit slightly, given the larger amount of load coincident with solar hours. The energy cost of crop production declined marginally by two cents per kilogram from $6.20/kg to $6.18/kg because a larger percentage of the load was met directly by solar PV.
The simulations using FEWMORE in Section 4.1.1-4.1.3 were repeated using HOMER, with the results displayed in Table 3 for comparison. The HOMER model was developed using the same assumptions as the FEWMORE model. The total cost objectives varied ~4-7% between the two models. The HOMER model resulted in an energy cost per unit of crop production of $6.64/kg ($3.02/lb) for the Solar simulation.
HOMER recommended a smaller solar array of ~1.5-2 kW generally across the simulations compared to the FEWMORE model. While this was a ~9% difference in solar capacity compared to Figure 3. Amount of load met by solar and storage in each hour of the year. Only 7% of load was met by the renewable energy system in the winter months, and the rest was provided by community microgrid purchases. In the summer months, 38% of load was met by solar plus storage.

Lighting Simulations
Two simulations were performed in which the lighting schedule in the collected load profile was modified to be perfectly symmetric around the solar PV generation peak output. Originally in the collected electric load profile, lighting did not operate during late afternoon and early evening hours. The Lighting with Solar and Lighting with Solar & Storage simulations were performed for the optimization of solar PV and solar PV plus battery energy storage, respectively. However, given the results for the solar PV-only and solar PV-plus-battery energy storage simulations were quite similar, only results with respect to the solar PV-only (Lighting with Solar) simulation are presented.
The optimal solar PV array power capacity increased marginally from 17.1 to 17.3 kW when the lighting schedule was modified to be symmetric around solar noon in the Lighting with Solar simulation. Thus, the collected data profile was already relatively optimal, given lighting was scheduled for most of the peak solar PV generation hours, approximately 10 am-4 pm. Solar PV power capacity increased, albeit slightly, given the larger amount of load coincident with solar hours. The energy cost of crop production declined marginally by two cents per kilogram from $6.20/kg to $6.18/kg because a larger percentage of the load was met directly by solar PV.
The simulations using FEWMORE in Sections 4.1.1-4.1.3 were repeated using HOMER, with the results displayed in Table 3 for comparison. The HOMER model was developed using the same assumptions as the FEWMORE model. The total cost objectives varied~4-7% between the two models. The HOMER model resulted in an energy cost per unit of crop production of $6.64/kg ($3.02/lb) for the Solar simulation.
HOMER recommended a smaller solar array of~1.5-2 kW generally across the simulations compared to the FEWMORE model. While this was a~9% difference in solar capacity compared to FEWMORE in the Solar simulation, the resulting changes in total objective cost were smaller. For example, if the HOMER results for solar capacities are given to the FEWMORE model as fixed inputs, the objective cost of the FEWMORE model changes by less than 0.1% compared to the optimal FEWMORE solar capacity. Thus, differences in solar capacity have less of an effect than other parameters, as highlighted in Section 4.1.4.

Sensitivity Analysis for FEWMORE Solar Simulation
A sensitivity analysis was performed around certain parameters for the Solar simulation using FEWMORE. The energy cost per unit of crop production of $6.20/kg in Table 3 resulted from the model assumptions of a 3% real discount rate and 3% escalation rate (accounted for inflation). Instead, varying the escalation rate from 1-5% (with a fixed discount rate at 3%) resulted in costs of $5.21 to $7.39/kg ($2.37-$3.36/lb) and solar capacity of 14.2 kW to 25.7 kW. For a fixed escalation rate of 3%, varying the discount rate from 2-6% resulted in costs of $6.80 to $4.82/kg ($3.09-$2.19/lb) and solar capacity from 18.9 kW to 13.5 kW.
Thus, the financial parameters of investing in container farm energy infrastructure may have a relatively substantial effect on optimal infrastructure sizing within the FEWMORE model. Reducing the discount rate by one percent increased the size of the solar array by 2 kW (~11%), and increasing the grid escalation rate by one percent increased the solar PV array size by 6 kW (~35%). A sensitivity analysis with respect to solar capital expenditure ($/kW), solar operating expenditure ($/kW/yr), battery energy storage capital cost ($/kWh), and inverter capital cost ($/kW) resulted in comparatively insubstantial changes compared to the sensitivity analysis on discount and grid escalation rates.

Dispatchability Case
Compared to the Base Case, which used collected electric load profile, simulations in the Dispatchability Case were performed using a synthetically-derived profile of electric and thermal loads. The purpose of this study was to determine if the operations of the HVAC and dehumidification loads could be optimized to reduce costs and improve energy flexibility, while maintaining temperature and humidity constraints on plant growth.

Baseline Simulation
The FEWMORE model was modified slightly for use of a flexible, synthetic electric load profile. Beginning with the Baseline simulation, the model had the following collective assumptions: baseloads were always on; fixed heat gains from dehumidification and lighting were constant; lighting was symmetric around solar noon; no ventilation was optimized aside from fixed minimum ventilation and infiltration; and the dehumidifier was always on to meet the latent heating load. The HVAC system operation was optimized and must heat if there is a net heat loss, and cool if there is a net heat gain in each time step.
The baseline for the synthetic profile resulted in an energy cost of crop production of $7.55/kg ($3.43/lb), with the full results displayed in Table 4. This was about 5% higher than the collected profile baseline, given that the synthetic load profile used about 6% more energy than the baseline profile. A notable insight of the model was that no hours of heating were required, given substantial heat gain from mechanical equipment, especially that of the dehumidifier. Table 4. Summary of results using a synthetic load profile in the FEWMORE model to analyze dispatchability of ventilation and dehumidification systems. Optimizing the dispatch of the ventilation system, in addition to adding a solar array, reduced costs by~18%. Managing the demand of the dehumidification system, in addition to the ventilation system, did not provide any benefit.

Solar and Storage Simulations
Compared to the Baseline simulation, optimizing solar PV alone (Solar simulation) led to a 21.5 kW array and a 15% decrease in cost, as shown in Table 4. The energy cost per unit of crop production was $6.47/kg ($2.94/lb). Even with the option to add battery energy storage (Solar & Storage simulation), the model did not optimize for storage; thus, this result was not displayed. Therefore, solar PV alone was optimal given that most of the electric load (primarily lighting) occured during daytime hours.

Demand-Side Management (DSM)
Ventilating excess heat optimally may allow for a more cost-effective method of operating the container farm. Ventilation may be used for cooling during most of the year, given there are only 178 h of the year during which the ambient temperature exceeds 20 • C in northern Alaska. In the Ventilation simulation, the model optimized when to ventilate and the number of air changes per hour (ACH) to perform. Thus, the cooling system was allowed to turn off to some extent, compared to the Baseline simulation, assuming the same sensible and latent thermal load profiles. The dehumidifier was assumed to operate at all times at its full power capacity, in order to examine the effects of adding only one dispatchable load at a time (the ventilation exhaust fan first). The dehumidifier could modify its moisture removal rate from 30-100% of its rated specification while maintaining the same power draw [31].
The results of using ventilation as a dispatchable load are shown in the Ventilation simulation in Table 4. Overall cost declined by 4.5% compared to the Solar simulation, with a $6.18/kg ($2.81/lb) energy cost. The optimal solar array size was slightly smaller at 21.3 kW and no storage system was recommended. Given no utilization of CO 2 during winter was allowed, and thus no subsequent pumping cost compared to the rest of the year, ventilation was performed exclusively during winter.
The model optimized for ventilation to occur at greater rates during times of high demand for cooling and also when the ambient temperature was only modestly cold (>0 • C).
In the final simulation (Dehumidification in Table 4), the dehumidifier was optimized to turn on and off to minimize energy costs while maintaining sensible and latent thermal energy balance. Given that a dehumidifier emits a significant amount of heat during operation, when it is off the HVAC system must provide heat to the unit. With the opportunity to optimize dispatch of the dehumidifier, the model chose only to interrupt its operation 3% of the time. This yielded similar results to the prior Ventilation simulation and an energy cost of crop production of $6.23/kg. Therefore, operating the dehumidifier, which provides sensible heat addition and latent heat removal, is in general preferable to requiring heat addition from the HVAC system and latent heat removal via ventilation of ambient dry air. Dehumidification was turned off primarily during moderately cold weather and very dry ambient air conditions, given that supplemental heating was less necessary during those times and the most benefit of latent heat removal via dry ambient air can be realized.

Conclusions
This paper provides an initial planning tool for Arctic communities interested in container farms to understand their overall energy use, as well as strategies to modify them appropriately for islanded renewable microgrids. A tool (FEWMORE) has been developed specifically to optimize container farm loads together with solar and battery nameplate capacities when all three are connected to the existing local microgrid.
Adding approximately 15-17 kW of solar PV nameplate capacity to power the container farm was optimal based on a collected electric load profile of an experimental farm. Battery energy storage did not provide substantial benefits, and is not justified. FEWMORE recommended adding 17.1 kW of solar PV, slightly higher than the optimal result of 15.6 kW from the HOMER model. Using a synthetically-derived load to allow for optimizing demand-side management of loads, namely ventilation fans and a dehumidifier, resulted in reductions in energy cost of up to 18% from the baseline. The subsequent cost of energy delivered per unit of crop production was reduced from $7.55 to $6.18/kg ($3.43-$2.81/lb). Analyzing other forms of energy storage, modeling at a higher temporal resolution, and studying additional integration with a community microgrid, such as modeling benefits in frequency regulation or export of excess energy, are left to future work. This paper presents an initial modeling framework, and the control strategy and assumptions on container farm operations and specific loads have not been experimentally validated. The study builds on early stages of installing a CropBox container farm at the Kluane Lake Research Station (KLRS) in Yukon Territory, Canada. Future work will utilize the KLRS system year-round for expanded data analysis and experimental operation of the strategies recommended here. There are numerous other demand-side management techniques, such as shifting baseload and thermal storage, that can also be incorporated in the future. 0 < E in/out,t < I (A5) • Sensible thermal energy must be balanced at all times: where Q mech,t is the heat gain of all equipment in time step t; Q cond,t is the heat loss due to conduction through the container envelope; Q vent/inf,t is the heat loss due to ventilation and infiltration; and Q ET,t is the heat loss due to evaporative cooling from plant evapotranspiration (See Appendix C).
• Latent thermal energy must be balanced at all times by balancing moisture flows in the container: where L ET,t is the moisture, in liters of water, emitted by plants; L dehum,t is the moisture removed by the dehumidifier; and L vent/inf,t is the moisture added or removed via air exchanges with the ambient environment.
$0.21. The container farm is assumed not to use CO 2 during the winter (December through February) given operator preference to employ a high degree of ventilation for cooling and dehumidification.

Appendix C.3. Evapotranspiration
The container farm must maintain an optimal humidity level for plant growth; thus, moisture flows must be balanced. In the container farm, moisture is added by plants, removed by a dehumidifier, and either added or removed via ventilation depending on the outdoor humidity level. Each of these components are described below.
Plants emit moisture into the container growing space via evapotranspiration. They absorb water through their roots from the hydroponic growing trays and emit water vapor through openings in their leaves, or stomata. The amount of moisture emitted via evapotranspiration (E) can be determined using the Priestly-Taylor method, assuming that the evaporation rate is energy supply limiting (assuming constant optimal indoor humidity and minimal convection), as defined below with subsequent descriptions of each variable: The variable ∆ is the saturation vapor pressure gradient (pressure per degree temperature). It is defined as: ∆ = 4098*e s /(237.3 + T) 2 where e s is the saturation vapor pressure (2310 Pa at standard conditions) and T is temperature in degrees Celsius. The value γ is the psychrometric constant given by: where c p is the specific heat of air (1005 J/kg-K), p is the air pressure (101,000 Pa at sea level), and l v is the latent heat of vaporization (2.45 * 10 6 J/kg at 20 • C).
The variable E R is the water evaporation rate dictated by an energy-supply limited process defined as: E R = R n /(ρ*l v ) = 6.12*10 −8 [m/s], where R n is the net radiation (W/m 2 ), or total light power (4500 W) per growing area, A, and ρ is the density of water (1000 kg/m 3 ). Using Equations (A11)-(A13) into Equation (A10) results in an evaporation rate, E, of plants in the container farm of 5.8 L/hr (5.4 × 10 −8 m/s at given volume) when lights are on. This is approximately similar to rated capacities of dehumidifiers in typical container farms. Given the latent heat absorbed to evaporate this much water, this yields 1.3 or 3.9 kWh of evaporative cooling due to plants (Q ET ) in each hour, depending on if lights are off or on, respectively, as calculated in Equation (A14): Q ET = E*l v /(3.6*10 6 J/kWh). (A14) In order to meet the specifications of the container farm, a typical dehumidifier rated for such conditions is chosen and uses 1.5 kW of electric power when on and emits 3.2 kW of thermal power (11,000 Btu/hr) when operating [31].
Lastly, the humidity of outdoor air must be accounted for in ventilation and infiltration air flows. The outdoor air in an Arctic climate is typically drier than the interior humidity set point, leading to moisture removal when ambient air replaces indoor humid air. The amount of moisture (in kg of water) lost from the container farm due to replacing indoor air with dry ambient air is modeled in Equation (A15): L vent/inf = H in -ρ*H amb,t *V*ACH t .
where H in is the interior humidity ratio setpoint equal to 0.011 kg of water per kg of dry air (equivalent to 70% relative humidity at optimal growing conditions); ρ is the density of air at room conditions (1.2 kg/m 3 ); H amb,t is the ambient humidity ratio of outdoor air; and ACH is the amount of air changes to perform in each time step.