Economic Consequences of Select Water-Energy Links : An Investigation of the Potential of Water-Energy Links Used to Improve the Economics and Added-Benefits of the Electrical System on Grand Cayman

(1)

i

Department of Thematic Studies Environmental Change

MSc Thesis (30 ECTS credits) Science for Sustainable development

Lewis James McNamee

Economic Consequences of Select Water-Energy Links

An Investigation of the Potential of Water-Energy Links Used

to Improve the Economics and Added-Benefits of the Electrical

System on Grand Cayman

(2)

ii

Copyright

The publishers will keep this document online on the Internet – or its possible replacement – for a period of 25 years starting from the date of publication barring exceptional circumstances. The online availability of the document implies permanent permission for anyone to read, to download, or to print out single copies for his/her own use and to use it unchanged for non-commercial research and educational purpose. Subsequent transfers of copyright cannot revoke this permission. All other uses of the document are conditional upon the consent of the copyright owner. The publisher has taken technical and administrative measures to assure authenticity, security, and accessibility.

According to intellectual property law the author has the right to be mentioned when his/her work is accessed as described above and to be protected against infringement.

For additional information about the Linköping University Electronic Press and its procedures for publication and for assurance of document integrity, please refer to its www home page: http://www.ep.liu.se/.

(3)

(4)

iv

1. Abstract

This investigation posits the hypotheses: 1) Renewable energy is a viable economic alternative to current electricity sources on Grand Cayman and 2) focus on the water-energy nexus reveals positive synergies in water and energy economics on Grand Cayman.

These were investigated by examining the water-energy links of wastewater as a resource, and water produced from a hydrogen fuel cell. Conditions were varied including cost and efficiency factors to understand the limits of both links.

The results show that both hypotheses can be confirmed, though not in all circumstances. Longer project lifetimes increase the viability of renewable energy. Short lifetimes favour fossil-fuelled energy. Generally, water-energy linked thinking is economically favourable when the water is considered an additional product. The economic benefit of the hydrogen fuel cell is near-negligible due to low water flow rate. The economic benefit of wastewater as a resource is large, offsetting much of the costs of any project, particularly at long lifetimes. Both links provide societal benefits in the form of increased water availability. This increase is small for the hydrogen fuel cell water link, and large for the wastewater link. The wastewater link is however limited both by availability of wastewater, and acceptance of the direct reuse of treated wastewater.

It was determined that further investigation of these and other links are justified. The economic value of water-energy links is proven over a wide range of variabilities. Renewable energy has also been shown to be economically viable for the island of Grand Cayman.

Keywords: Water-Energy Nexus; Grand Cayman; Renewable Energy; Water Resources; Islands

(8)

2

2. List of Abbreviations

BOD Biological Oxygen Demand

d Day

FC Fuel Cell

GC Grand Cayman

GHI Global Horizontal Irradiance

GIS Geographic Information Systems

GWh Gigawatt Hour

kW Kilowatt

kWh Kilowatt Hour

MCDM Multicriteria Decision Making (Assessment)

MWh Megawatt Hour

NIMBY Not in My Back Yard

NREL National Renewable Energy Laboratory

NSRDB National Solar Renewable Database

O&M Operating and Maintenance

PSM Physical Solar Model

TSS Total Suspended Solids

TWW Treated Wastewater

USD United States Dollar

W Watt

WEN Water-Energy Nexus

Wh Watt Hour

WW Wastewater

yr Year

(9)

3

3. Introduction

Climate change (CC) is regarded as one of the greatest threats facing humankind today. Significant effort is being invested globally in order to reduce greenhouse gas emissions, and to therefore mitigate CC. These actions take many forms, but one of the most significant involves transitioning energy systems to utilise renewable resources over the predominately fossil fuel-based systems that currently dominate.

In these transitions, there is a risk of undertaking ‘silo’ thinking (Abernethy, 2016). This could mean, for example, focusing on achieving sustainable energy, without consideration to other resources and areas of sustainability. This narrow perspective could then cause related negative impacts in these areas, that even negate the energy benefits. To avoid this, the water-energy nexus (WEN) approach has been proposed, whereby any efforts to improve one area should include study of synergies and trade-offs within the others. This has been successfully applied in a variety of situations, with a variety of strategies suggested, such as those suggested by Rasul and Sharma (2016) and reviewed by Dai et al. (2018). The WEN recognises the fact that these resources are interlinked, and therefore development of one will affect the other(s). This means the sustainable management of one resource requires understanding the manner in which it interacts with others to minimize negative trade-offs (WEF, 2011).

Highlighted in scientific literature on both CC mitigation and WEN are case studies on islands. It has been remarked “[on] islands global challenges become concrete” (Kueffer and Kinney, 2017, p.319). This is largely due to the well-defined boundaries which exist on islands, and the localised forms of governance which can closely replicate larger societies (Baldacchino, 2018). For these reasons, island studies are regularly employed to better characterise systems and changes which occur during transitions. Such studies include, e.g. the management of an energy transition on Samsø by Papazu (2015, 2016, 2018). The defined limits of the island in this case allowed Papazu to uncover the “storified” version of events on the island, and how they related to the actual events of the transition.

In this thesis, an island case study has been chosen to examine the relationship between selected water-energy links in renewable energy development. Grand Cayman (GC), the largest island of the Cayman Islands, within the Caribbean, relies heavily on desalination to produce water (CWA, 2019a). This process has high energy intensity. The Cayman Islands’ government has signified their interest in switching to an energy portfolio with a high renewable share (Cayman Islands Government, 2017). This makes GC a good case as it is typical of situations both on islands and otherwise; where energy intensive methods are utilised for water production and water (and sewerage) distribution is not well-developed (Crabb, 2009; CWA, 2019a). Additionally, its pursuit of low-carbon energy also matches global ambitions.

Due to the predominate conditions on GC, solar energy has been found the most plausible renewable energy source (CUC and Pace Global, 2017). The Caribbean Utilities Company (CUC and Pace Global, 2017) states however, that this would not be economical in the short term due to the limitations of energy storage. However, the storage examined in the 2017 study was limited to batteries. The potential of other energy storage methods in improving the economic outlook of solar energy has not been studied. One such method is the utilisation of hydrogen as an energy carrier, by using an electrolyser and hydrogen fuel cell (FC). In addition, as the FC reaction produces water, studies have suggested this could be utilised to reduce water stress (Hristovski et al., 2009; Kim, Lee and Park, 2011; Tibaquirá et al., 2011b, 2011a). By examining a hydrogen FC, both the viability of renewable energy on GC and WEN thinking may be examined simultaneously.

(10)

4

On GC, the majority of wastewater (WW) is treated using on-site septic tanks, of which there are significant concerns about related health effects. There is also concern about the impact on the sustainability of water resources. This arises due to failure of these septic systems to meet specified BOD/TSS limits, and that this discharged effluent may affect water resources on the island (Crabb, 2009). At the same time, many studies have suggested that WW utilised as a resource has significant benefits for energy (McCarty, Bae and Kim, 2011; Chen and Chen, 2013; Pfluger et al., 2020). The reuse of treated wastewater (TWW) can be utilised to replace energy-intensive forms of water abstraction, particularly desalination, for agriculture, industry, and direct and indirect recharge of potable water (Chua et al., 2009; Pedrero and Alarcón, 2009; Petousi et al., 2013; Mahasneh, 2014; Mcheik et al., 2017; Saliba et al., 2018).

3.1 The Water-Energy Nexus

The WEN is driven by an understanding that these resources are interlinked, and that these links must be understood and addressed to increase sustainability. This nexus is a subset of the water-energy-food nexus, which itself has many modifications (e.g. the water-water-energy-food-climate nexus). Subsets are often used in practical studies in order to simplify or focus the system. In such cases, an awareness of the interactions with other systems is still necessary to consider.

The nexus concept has found widespread usage and acceptance in many areas as a method to drive sustainability (e.g. Pacetti, Lombardi and Federici, 2015; Lechón, De La Rúa and Cabal, 2018). Much WEN literature focuses on high-level insight – i.e. the focus is on the benefits of nexus thinking as a whole (Dai et al., 2018). This suggests that there is room for a more detailed quantification of specific WEN techniques and their effects in the literature.

This thesis seeks to contribute to filling this gap by undertaking an analysis of WW as a resource and of the hydrogen FC water by-product, two WEN links proposed in literature. These links will be analysed in a case study system from an economic perspective. This approach has been selected because it is often necessary to prove the economic advantages of WEN approaches in order to secure funding for such developments (Guta et al., 2017). This study will provide information of the possibilities and drawbacks of using these two WEN links to increase renewable energy on GC.

3.2 Wastewater as a Resource

WW as a resource, one of the WEN links inspected in this study, contains two parts: the extraction of useful products from WW, as part of efforts to treat the water; and the reuse of TWW in place of abstracted water. This study examines both aspects of the use of WW as a resource. It inspects both the situation of net-positive energy generation through WW treatment, and the additional economic benefits which ensue through selling the TWW in place of fresh water.

The removal of contaminants is the objective of WW treatment, but this process also produces biogas, which is often utilised to offset the energy used in treating WW. However, there is an ongoing debate as to whether WW treatment can be net-positive in terms of energy. It is generally stated that 0.6 kWh of energy is required to treat 1m3_{of WW (McCarty, Bae and} Kim, 2011), though it is indicated this net energy requirement is likely to decrease in future. This 0.6 kWh includes the use of produced biogas to offset the energy costs of the process. However, TWW may also be used to avoid the abstraction of fresh water. Where this occurs, particularly where energy-intensive processes such as desalination are used, treating WW can have a net positive effect.

TWW is finding increasing acceptance in many applications. The most common use is perhaps within agriculture, on products for human consumption (Pedrero and Alarcón, 2009;

(11)

5

Maton et al., 2010; Aiello et al., 2013; Lonigro et al., 2016; Mcheik et al., 2017) and within non-consumable agriculture such as floriculture (Petousi et al., 2013; Uzen, Cetin and Unlu, 2016). Other uses include industrial activities, such as concrete production (Mahasneh, 2014; Asadollahfardi and Mahdavi, 2019) or as direct and indirect potable water, or for recharging of potable water reservoirs (Chua et al., 2009; Saliba et al., 2018). This study does not attempt to differentiate between the uses, nor the treatment required for each (i.e. it is assumed water is treated to the standard required for the highest-risk use).

3.3 Hydrogen Fuel Systems

Hydrogen fuel systems are a commonly utilised method for shifting renewable energy production to match demand, particularly in off-grid systems (e.g. Martins et al., 2007; Carapellucci and Giordano, 2012; Garcia et al., 2016). There is significant hope that in the future hydrogen will form a significant part of the energy system, particularly where electricity is limited; such as in transport (Kyriakarakos et al., 2011; Garcia et al., 2016).

When hydrogen reacts with oxygen (the reaction utilised in FCs), energy is released, and the sole chemical product is water:

2𝐻₂+ 𝑂₂ → 2𝐻₂𝑂 (3.1)

Due to the lack of other products, this water should be pure. There have therefore been investigations to examine if this water can be utilised, with a focus on human consumption. Several studies have confirmed that the purity of the produced water is high – with near distilled water quality (Hristovski et al., 2009; Kim, Lee and Park, 2011; Tibaquirá et al., 2011b, 2011a). There are however some risks, including increased corrosion of plumbing (mostly due to the purity of the water) and low levels of metal contamination, likely arising from the degradation of the materials of the FC (Hristovski et al., 2009). This water therefore has the potential to be suitable for human consumption, or for sale as a high-quality water product.

The variability of renewable energy demands an energy storage system, and hydrogen is selected for this purpose in this study. As there is potential for the water produced by FC to be utilised this will also be inspected in this study as one of the two WEN links examined. The intention is to understand the quantities of water produced and if this would be useful to reduce water stress on GC. Therefore, the amount of water that could be produced by such a system will be calculated, and how this could affect the economics of the electrical system, if it were sold as a product.

3.4 Aim and Research Questions

Often, young children are taught “electricity and water don’t mix”, to save them from potential consequence of touching electrical sources with wet hands. However, such thinking seems to pervade society, and it is this thinking that the WEN seeks to overturn. This study seeks to further investigate the WEN, and to add information as to whether electricity and water should be mixed. It accomplishes this by investigating the potential for establishing a renewable electricity system on GC, and the factors which could affect its economic viability. A particular focus is placed on energy-water links and how utilising these may aid the establishment of renewable energy on GC.

The following questions are investigated:

• Would solar energy in conjunction with a hydrogen energy carrier system be a viable economic alternative to meet the electricity needs of GC?

(12)

6

• To what extent would the water by-product of a hydrogen FC reduce water stress, and affect the economics of the electricity system?

These objectives are identified in order to answer the hypotheses:

• Renewable energy is a viable economic alternative to current electricity sources on GC • Focus on the WEN reveals positive synergies in water and energy economics on GC By answering the research questions, the study’s results will reflect the effect of different degrees of renewable energy on the economics of electricity generation on GC and will further scientific knowledge about the water-energy links in electricity generation.

(13)

7

4. Materials and Methods

4.1 Study Area

GC is the largest island in the British Overseas Territory of the Cayman Islands. The territory is located in the Caribbean, to the south of Cuba. GC can be considered the main island of the territory, hosting the majority of the population and economic activities. Cayman Brac and Little Cayman, the other islands in the territory, have been disregarded in this investigation due to their very small populations.

GC has a tropical wet and dry climate - Aw on the Köppen-Geiger classification (Peel, Finlayson and McMahon, 2007). The climate is dominated by a two-season year (wet and dry system) which is significant in terms of solar energy. The two-season year means that temperature and insolation are relatively constant throughout the year, providing a stable environment for solar energy.

4.2 Multicriteria Assessment of Solar Development Siting

A multicriteria decision making – GIS (MCDM-GIS) technique was utilised to investigate the extent and suitability of locations for the development of solar energy, based upon the methodologies described by Janke (2010) and Díaz-Cuevas, Domínguez-Bravo and Prieto-Campos (2019). The MCDM was chosen to highlight areas that could be developed for solar energy and which would be most preferable for development from a socio-economic perspective. The socio-economic factors (Table 4.1) are identified as being linked to resistance of the development of solar energy (Janke, 2010; Díaz-Cuevas, Domínguez-Bravo and Prieto-Campos, 2019). Resistance factors are those that would increase either cost or could cause social resistance to development. These factors were determined based upon those described in the studies by Janke (2010) and Díaz-Cuevas, Domínguez-Bravo and Prieto-Campos (2019). The reasons for the selection of these variables in given below.

Proximity to roads was considered as construction and maintenance costs would be lowered by increasing accessibility. Similarly, proximity to electrical infrastructure was also considered to decrease economic resistance, due to lowering transmission-related losses. Sites located close to urban areas were considered undesirable, as NIMBYism could increase social resistance in these cases. In this investigation, construction within urban areas was not considered possible, and hence these areas were discounted from the MCDM. Type of landcover would affect construction costs. For example, water bodies were considered impossible areas on which to develop for solar energy, and so were eliminated from the MCDM; wetlands and woods were regarded as undesirable as they are difficult to build on; and all other landcovers were assumed to have similar construction costs, and be cheaper than building on wetlands or woods, and therefore have lower economic resistance. Areas where the land was currently occupied were considered more expensive to develop and would have a social cost due to displacement of existing businesses. Protected areas (e.g. national parks) were eliminated from the study, as no development could take place. Map features of roads, electrical infrastructure, extent of urban areas, landcovers, water bodies, land-use and protected areas were downloaded from OpenStreetMap.com, distributed under the Open data Commons Open Database License (ODbL 1.0), with © OpenStreetMap contributors.

The definition of land not already utilised is derived from the data. As the data indicates no land use in these areas, this is what is utilised in this MCDM. It is recognised however that this may be erroneous as it is unlikely this land is completely unused. It may, for example, consist of informal agriculture or be barren. Available data does not clarify the current use, and so further investigation would be required to confirm its suitability for use.

(14)

8

It should be noted that, by considering urban areas as not being able to be developed, the development of for example rooftop solar has been determined to be impossible. The reason for not investigating this is because the economic impact of such developments is unclear on GC (CUC, 2017). This therefore means it is not certain if these developments increase or decrease economic resistance, and so inclusion could cause false results from the MCDM.

Overall scores indicating the potential of solar development were calculated with Equation 4.1, based upon several categories. Each category was scored according to the criteria in Table 4.1 where the scores from one to four refer to very low, low, high and very high potential in the category.

𝑆𝑢𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑆𝑐𝑜𝑟𝑒 = (𝑅 + 𝑃 + 𝑈1 + 𝐿𝐶1 + 𝐿𝑈)

5 ∙ 𝐿𝐶2 ∙ 𝑃𝐴 ∙ 𝑈2 (4.1)

The terms are as shown in Table 4.1.

The suitability score for each raster cell was calculated from Equation 4.1 and assigned to the relevant raster cell in a raster map. GIS analysis was undertaken using ArcMap 10.7.1, part of the ArcGIS suite by ESRI (Environmental Systems Research Institute). The maximum possible score is 3.2. This score would represent an area that could be regarded as the optimal area for development, according to the criteria used in this MCDM.

The area of all places which received the same suitability score were summed to give the total area of each suitability score. It also gave limits on the maximum areas that could be developed for solar energy dependent upon an acceptable minimum suitability. This maximum area could be used as a limit in the examination of solar energy – the maximal solar energy would equal to the maximal area acceptable for development. It should be noted that this is a theoretical maximum, as there may be other complicating factors which are not detected by the MCDM methodology. It is suggested that the area suitable for solar development found in this section be seen as a limit in modelling, and whilst there is high uncertainty, it would provide a basis for further investigation.

(15)

9

Table 4.1. Value Criteria for MCDM Assessment

Variable Description Values

R Proximity to roads 1: > 1500m

2: 1000 – 1500m 3: 500 – 1000m

4: 0 – 500m P Proximity to electrical infrastructure 1: > 1500m

2: 1000 – 1500m 3: 500 – 1000m

4: < 500m

U1 Proximity to urban areas 1: < 500 m

2: 500 – 1000m 3: 1000 – 1500 m

4: > 1500m

U2 Presence of an urban area 0: Within urban area

1: Outside urban area

LC1 Type of landcover 0: Water

1: Wetland or woods 2: Other land cover

LC2 Presence of water 0: Within water body

1: Outside water body

LU Existing land use 1: Land already utilised

2: Land not already utilised

PA Presence of protected area 0: Protected Area

(16)

10

4.3 Solar Potential Calculations

Due to the highly variable nature of the solar energy, it must be well defined in order to enable accurate representation of the limits, and the generation rates from solar panels. Therefore, this section describes study of these in the context of GC.

4.3.1 Solar Insolation Data

Solar insolation is the global horizontal irradiance (GHI) – the total irradiation received at the planet’s surface, which can be regarded as equivalent to the irradiation received by solar panels. The data in the study was drawn from the Physical Solar Model (PSM3) through the National Renewable Energy Laboratory’s (NREL) National Solar Radiation Database (NSRDB - Sengupta et al., 2018). The selected data is for 50 points which cover the entirety of GC, with hourly data (at the half-hour) for each point from 2009 – 2018 (inclusive) - the most recent 10 years of available data.

4.3.2 Spatial Variation of Average Solar Insolation

The spatial variance of solar insolation was investigated across GC utilising the data in Section 4.3.1. For each of the 50 points, the data was averaged to produce a decadal average. This decadal average was used as GHI is subject to influence by weather patterns, therefore a long-term average is more in line with the prevailing climate of the island.

The data was entered as points into a GIS vector layer and interpolated using inverse distance weighting to produce an averaged GHI raster image. This raster map was then reclassified based upon the ranges of GHI, to show the spatial variation of GHI. The spatial variation was so low that it was determined as negligible and hence not included in further calculations.

4.3.3 Solar Irradiance Profiles

To calculate the timing of solar irradiance, the 15th_{day of each month was selected as} representative of the solar profile for the month. Five of the 50 points were randomly selected and considered representative of values over the island.

For each point, the values for each hour and every year were averaged, giving a single value for each hour at each point representative of the 10-year period, 2009-2018. The five points were then averaged. This gave a set of values that were the average both of the decade, and the spatial variation across the island. These averages for each hour were then plotted, to create a 24-hour irradiance profile representative of each month. These profiles were used to calculate the average irradiation of solar panels.

4.3.4 Total Solar Potential Calculations

When calculating solar potential, the solar irradiance profiles were utilised as it was determined that there is little spatial variance in solar irradiance. Using hourly intervals, the curves were integrated using trapezoids:

∫ 𝑓(𝑥)𝑑𝑥 =1

2ℎ[(𝑦0+ 𝑦𝑛) + 2(𝑦1+ 𝑦2+ ⋯ + 𝑦𝑛−1)] 𝑥𝑛

𝑥0

(4.2) where 𝑦_𝑛 = 𝑓(𝑥_𝑛), ℎ represents the interval (1 hour)

Integration with this equation gave the total solar energy transferred to a 1m2 area in a day (Wh.m-2_d-1_{) for a representative day of a single month. This was then multiplied by the} number of days in the relevant month. The summation of these results gave the total energy

(17)

11

received by 1m2 of solar panel on the island in a year – the specific solar energy (𝑒_𝑆). Due to the previous assumption that the monthly profiles are representative of conditions across the island (due to narrow range of average GHI), this value is considered constant across GC. The additional day in February during leap years was not considered.

4.4 Wastewater to Energy Calculations

Net energy use can be calculated as the difference between the energy consumed to treat one cubic meter of water, and the avoided energy use if the TWW is used in place of abstracted water. It should also be noted that one cubic meter of WW does not produce one cubic meter of treated water, hence a conversion efficiency term can be introduced, yielding:

𝑒_𝑊𝑊 = 𝜀_𝑇𝑒_{𝐴𝑣𝑜𝑖𝑑}− 𝑒_𝑇 (4.3)

where 𝑒𝑊𝑊 is the specific energy “generation” of WW, 𝜀𝑇 is the volume ratio of TWW to untreated WW, 𝑒_{𝐴𝑣𝑜𝑖𝑑} is the specific energy in abstracting water and 𝑒_𝑇 is the specific energy to treat 1m3_{of WW.}

The net energy required to treat 1m3_{of WW (𝑒}

𝑇) was taken to be 0.6 kWh based upon figures given by McCarty, Bae and Kim (2011) and Pfluger et al. (2020). Inspection of tenders from the Cayman Water Authority (2018, 2019b), suggest their reverse osmosis desalination requires 3.2 kWh/m3 of water (𝑒_{𝑎𝑣𝑜𝑖𝑑}). The volume ratio (𝜀_𝑇) is taken to be 0.5.

Historic data on amounts of TWW per day (in central and onsite systems) in the Cayman Islands and corresponding populations were obtained from Crabb (2009). It was assumed that these population figures serve as representative of GC due to the low population of Cayman Brac and Little Cayman. It was also assumed that a linear relationship exists between population and WW treatment. Based on this, the volume of WW was extrapolated to current population estimates from the UN DESA (2019). It was further assumed that, in future, all WW will be treated centrally, and that TWW will find widespread use allowing all TWW to be used in place of abstracted water. Therefore, the maximum rates of WW treatment, and TWW generation were calculated.

The total amount of avoided electricity use when TWW is used in place of desalinated water would logically be limited by the amount of water generated by desalination as, if no further desalinated water existed to be replaced by TWW, there could be no additional avoided generation. There is no reliable data on the total water abstracted on Grand Cayman, and hence it is impossible to use this a limit in this model. In this case, the maximum available WW to utilise as a resource (as discussed above) is used to limit the energy that is avoided. In other words, it is assumed that the volume of WW that replaces water abstracted through desalination is less than or equal to that abstracted through desalination in all cases.

4.5 Electricity System Modelling

To investigate the most efficient distribution of resources, the electricity system and its associated economics are described by equations. These equations, when linked and with appropriate limits set, serve as a model of the real-world system.

4.5.1 The Electrical System

The overall electrical system must meet the total energy required by GC in a year. This is currently 692.9 GWh (CUC, 2020). Throughout the investigation, it is assumed this will not be subject to change. The total energy required in a year is the sum of electrical generation from all sources. This energy requirement is decreased by avoiding electricity usage by offsetting energy used in desalination using TWW, therefore:

(18)

12

𝐸_𝑇 − 𝐸_𝑊𝑊 = 𝐸_𝐷+ 𝐸_𝑁𝐺+ 𝐸_𝑆 (4.4)

where 𝐸𝑇 is the total energy consumed by GC in a year (i.e. equal to current yearly generation), 𝐸𝐷 is the electricity produced from diesel sources, 𝐸𝑁𝐺 is the electricity produced by natural gas sources, 𝐸_𝑊𝑊 is the net WW electrical “generation”, and 𝐸_𝑆 is the electricity produced by solar sources.

In the future, treatment of wastewater may produce more energy than it consumes, even neglecting avoided energy cost (McCarty, Bae and Kim, 2011). To ensure this model remains valid under such situations Equation 4.4 is rearranged:

𝐸_𝑇 = 𝐸_𝐷+ 𝐸_𝑁𝐺+ 𝐸_𝑊𝑊+ 𝐸_𝑆 (4.5)

Current electrical generation is assumed to be completely from diesel sources, equal to a maximum of 1410 GWh/yr based upon current capacity (CUC, 2020). However, due to the planned retirement of several generators (equal to a capacity of 38.3 MW), it is assumed that the maximum value for 𝐸_𝐷 is 1074 GWh/yr.

Natural gas has been proposed as a replacement for diesel generation on GC, both due to its lower and more stable cost, and lower carbon emissions (CUC and Pace Global, 2017). 𝐸_𝑁𝐺 represents the replacement of diesel with natural gas.

𝐸_𝑊𝑊 is calculated as:

𝐸_𝑊𝑊 = 𝑄_𝑊𝑊𝑒_𝑊𝑊 (4.6)

where 𝑄𝑊𝑊 is the average flowrate of WW to the treatment plant, and 𝑒𝑊𝑊 is calculated as in Equation 4.3.

𝐸_𝑆 represents the selection of solar energy sources. It is calculated as:

𝐸_𝑆 = 𝜀_𝑂𝐴_𝑆𝑒_𝑆 (4.7)

where 𝐴𝑆 is the total area dedicated to solar panels, and 𝜀𝑂 is the overall solar efficiency, consisting of:

𝜀𝑂 = 𝜀𝑃𝑉𝜀𝑆𝜀𝐹𝐶,𝑐𝑦𝑐𝑙𝑒 (4.8)

where 𝜀𝑃𝑉 is the individual efficiency of a solar panel, 𝜀𝑆 is the spacing efficiency of solar modules (the ratio of area of solar panel to area of ground) and 𝜀_{𝐹𝐶,𝑐𝑦𝑐𝑙𝑒} is the cyclic efficiency of the hydrogen system, calculated as:

𝜀_{𝐹𝐶,𝑐𝑦𝑐𝑙𝑒} = 𝜀_𝐹𝐶𝜀_𝐸𝑧 (4.9)

where 𝜀_𝐹𝐶 is the efficiency of the hydrogen FC, and 𝜀_𝐸𝑧 is the efficiency of the electrolyser.

The solar electrical system as described above represents a situation where all solar energy passes through the hydrogen system. Though this is unlikely in a real system (and therefore it leads to larger solar area, electrolyser, and FC estimates), it could be selected as a running mode to gain more water by-product from the FC.

Through these equations a balance of electrical sources can be determined, subject to the limits determined through the methodology detailed in Sections 4.2 – 4.4.:

𝐸_𝑇 = 692.9 𝐺𝑊ℎ 0 ≤ 𝐸_𝐷 ≤ 1074 𝐺𝑊ℎ

0 ≤ 𝐸_𝑁𝐺

(19)

13

0 ≤ 𝐴𝑆 ≤ 149.4 𝑘𝑚2

These restrict the model to the limits currently placed upon the real system. Through the use of these combined equations, the model sets the mix of electrical systems.

4.5.2 The Hydrogen System (Fuel Cell, Electrolyser and Tank)

The hydrogen system is an implicit part of the electrical system – it supports solar generation but is not part of the calculation of energy share. However, to ensure levelling of the solar system it must be properly sized, and this affects the economics of the system.

A transient analysis is the most appropriate manner in which to size the hydrogen components (e.g. Carapellucci and Giordano, 2012; Janghorban Esfahani et al., 2016; Vivas et

al., 2017). However, as this study uses steady-state analysis it will be related to the solar

generation. It should be noted that this leads to an oversizing of these components, and as a result, a lower economic viability for solar energy.

The energy output of the FC must be equal to that of the total solar energy (representing a situation where there is no solar energy generated). As the FC has an associated efficiency, this would mean that the capacity of the FC would be related to this through its efficiency:

𝐶𝑃_𝐹𝐶 = 𝐶𝑃𝑆

𝜀_𝐹𝐶 (4.10)

where 𝐶𝑃_𝐹𝐶 is the capacity of the FC and 𝐶𝑃_𝑆 is the total solar capacity.

The electrolyser must be capable of utilising the entire available solar energy to prevent any curtailment of generation if load demand does not utilise any solar energy. Therefore, the capacity of the electrolyser is:

𝐶𝑃𝐸𝑧 = 𝐶𝑃𝑆 (4.11)

where 𝐶𝑃_𝐸𝑧 is the capacity of the electrolyser.

Without utilising transient analysis, the hydrogen tank is impossible to accurately size. However, in literature there are examples of hydrogen-renewable hybrid systems, and an empirical correlation for hydrogen tank size based upon variable energy generation can be derived. Based on several locations studied by Prieto-Prado et al., (2018) and Abdin and Mérida (2019) a power equation is derived:

𝐶𝑃_𝑇 = 175.44𝐸_𝑆0.85 (4.12)

where 𝐶𝑃_𝑇 is the capacity of the hydrogen tank (in kg) and 𝐸_𝑆 is the yearly solar energy (in GWh).

4.5.3 Water-Energy Links

The following equations describe the first water-energy link, the use of WW as a resource. The equations in Section 4.5.1 already account for the net “generation” of utilising WW. However, it must also be considered that the TWW may be sold as an additional product, therefore it is necessary to calculate the production of TWW. Previously, 𝜀𝑇 has been defined as the ratio of volume of TWW to WW fed to a treatment plant. Therefore:

𝑄_𝑇𝑊𝑊= 𝜀_𝑇𝑄_𝑊𝑊 (4.13)

(20)

14

The second water-energy link is the water by-product of the hydrogen FC. This is directly related to the total hydrogen created by the electrolyser and consumed by the FC. The hydrogen produced by the electrolyser can be calculated as:

𝑚̇_𝐻2 =8.76 ∙ 10 6_𝐶𝑃

𝐸𝑧𝜀𝐸𝑧

𝐹_𝐸𝑧 (4.14)

where 𝑚̇_𝐻2 is the mass flow rate of hydrogen in kg/yr, and 𝐹_𝐸𝑧 is the energy (in kWh) to produce 1kg of hydrogen. James et al. (2013) suggest this would be 50kWh/kg.

Equation 3.1 gives the chemical equation for the reaction occurring in the FC. Utilising this, the water produced by the FC is given by:

𝑚̇𝐻2𝑂 = 𝑚̇𝐻2𝜀𝐹𝐶 𝑀_𝐻2𝑂

𝑀𝐻2

(4.15) where 𝑚̇_𝐻2𝑂 is the mass flow rate of water, and 𝑀𝐻2𝑂

𝑀𝐻2 is the ratio of molar masses of

water and hydrogen.

To convert the mass flow rate to volumetric flow rate: 𝑄_𝐹𝐶 =𝑚̇𝐻2𝑂

𝜌_𝐻2𝑂 (4.16)

where 𝑄_𝐹𝐶 is the volumetric flow rate of water from the FC and 𝜌_𝐻2𝑂 is the density of water, taken as 1000 kg/m3.

4.6 Economic Modelling

4.6.1 Capital Costs

Capital costs are assessed at a strategic level. To do so installed costs per capacity are used, except for the WW treatment plant, as given in Table 4.2. Unless otherwise noted, monetary values are given in United States Dollars (USD).

Table 4.2. Capital Costs per Unit Capacity

Equipment Capital Cost per Unit

Capacity ($USD) Capacity Unit Source Solar Panels 1100 kW Fu et al. (2017)

Fuel Cell 3000 kW Steward et al. (2009)

Electrolyser 850 kW Saur (2008)

Hydrogen Tank 623 kg Steward et al. (2009)

Natural Gas 2095 kW US EIA (2013)

The capital cost of any diesel system is assumed to be zero, because diesel generators already exist on the island, and therefore investment is not necessary to install new ones (CUC and Pace Global, 2017).

(21)

15

The capital cost for each electricity source can therefore be calculated as:

𝐶𝐶𝑖 = 𝐶𝑃𝑖∙ 𝐶𝐹𝑖 (4.17)

where 𝐶𝐶_𝑖 is the capital cost for any electricity source (e.g. for natural gas), 𝑖; 𝐶𝑃_𝑖 is the capacity of electricity source 𝑖 (in its capacity units, e.g. kW) and 𝐶𝐹_𝑖 is the capital cost per unit capacity (e.g. $1100USD/kW for solar) as given in Table 4.2.

The exception to this is the WW treatment plant, for which both the cost of the plant and the civil works must be considered. Both costs are non-linearly linked to population due to discounting at increased scale. The cost functions given by Pinheiro et al. (2018), for extended aeration activated sludge with disinfection have been used. Therefore:

𝐶𝐶𝑊𝑊 = 𝑃(4895𝑃−0.415+ 19063𝑃−0.552) (4.18) where 𝐶𝐶_𝑊𝑊 is the capital cost for the WW works, and 𝑃 is the population the plant will have the capability to service, calculated as a proportion of the maximum potential WW flowrate:

𝑃 = 𝑄𝑊𝑊 𝑄_{𝑊𝑊,𝑚𝑎𝑥} =

𝑄𝑊𝑊

10846000 (4.19)

As Equation 4.18 yield values in Euros, the exchange ratio to USD was taken as 1.10, hence:

𝐶𝐶𝑊𝑊$ = 1.1𝐶𝐶𝑊𝑊= 1.1𝑃(4895𝑃−0.415+ 19063𝑃−0.552) (4.20)

4.6.2 Ongoing Costs

The yearly costs that are incurred through the running of the generation facilities are the operating and maintenance (O&M) costs, and fuel costs (where applicable). Asset depreciation is not considered in this analysis.

The costs for the solar panels, WW system, FC and electrolyser are given by:

𝑂𝐶_𝑖 = 𝐶𝑃_𝑖𝑂𝑀_𝑖 (4.21)

where 𝑂𝐶_𝑖 is the ongoing cost for the electrical system, 𝑖, and 𝑂𝑀_𝑖 is the O&M cost per unit capacity as given in Table 4.3.

Table 4.3. O&M Costs per Unit Capacity

Equipment O&M cost per Unit

Capacity ($USD) Capacity Unit Source Solar Panels 10 kW Abdin and Mérida

(2019)

Fuel Cell 27 kW Steward et al. (2009)

Electrolyser 20 kW Abdin and Mérida (2019)

(22)

16

The ongoing cost of the hydrogen tank is assumed to be negligible. The costs for diesel and natural gas generation are described by:

𝑂𝐶𝑖 = 𝐹𝐶𝑖 + 𝑉𝑂𝑀𝑖+ 𝐹𝑂𝑀𝑖 (4.22)

where 𝐹𝐶_𝑖 is the fuel cost of 𝑖, 𝑉𝑂𝑀_𝑖 is the variable O&M cost of 𝑖, and 𝐹𝑂𝑀_𝑖 is the fixed O&M cost of 𝑖.

These are calculated as:

𝐹𝐶𝑖 =

𝑐_{𝑓𝑢𝑒𝑙,𝑖}𝐸_𝑖 𝜀𝑖

(4.23) where 𝑐_{𝑓𝑢𝑒𝑙,𝑖} is the cost of fuel per unit of chemical energy of fuel 𝑖, 𝐸_𝑖 is the yearly energy produced by 𝑖 and 𝜀𝑖 is the electrical efficiency of the generator.

𝑉𝑂𝑀𝑖 = 𝑣𝑜𝑚𝑖𝐸𝑖 (4.24)

where 𝑣𝑜𝑚_𝑖 is the variable O&M costs per unit of produced energy.

𝐹𝑂𝑀𝑖 = 𝑓𝑜𝑚𝑖𝐸𝑖 (4.25)

where 𝑓𝑜𝑚_𝑖 is the fixed O&M costs per unit of capacity.

The values used for these calculations are shown in Table 4.4. It should be noted that in this investigation, biofuel replacements for both diesel and natural gas are not considered. These would change the values given in Table 4.4 for the fuel costs (and potentially the capital and other ongoing costs). Biofuels have not been considered as the growth of fuel crops can increase water stresses, in contradiction to WEN principles (Dalla et al., 2011).

Table 4.4. Values for Diesel and Natural Gas O&M Calculations

Variable Value Units Source

cfuel,D 75.9 $USD/MWh CUC (2017)

cfuel,NG 12.97 $USD/MWh CUC (2017)

εD 0.4 - Krarti (2018)

εNG 0.37 - Krarti (2018)

vomD 2.71 $USD/MWh CUC (2017)

vomNG 6.78 $USD/MWh US EIA (2013)

fomD 44.52 $USD/kW CUC (2017)

fomNG 31.79 $USD/kW US EIA (2013)

4.6.3 Modifications for Water-Energy Links

Modifications to the cost equations are made to understand the economic benefits that may exist for the additional WEN links. The potential economic value of water produced by the hydrogen FC, and the treatment of WW is calculated:

(23)

17

𝐼_𝑇𝑊𝑊 = 𝑐_{𝑤𝑎𝑡𝑒𝑟}𝑄_𝑇𝑊𝑊 (4.26)

where 𝐼𝑇𝑊𝑊 is income from TWW, 𝑐𝑤𝑎𝑡𝑒𝑟 is the cost of water, assumed to be 0.45 $USD/m3 based upon current water costs on GC (CWA, 2019c).

𝐼_𝐹𝐶 = 𝑐_{𝑤𝑎𝑡𝑒𝑟}𝑄_𝐹𝐶 (4.27)

where 𝐼𝐹𝐶 is income from water produced by the FC.

These values are incorporated into the ongoing costs of the respective systems, to represent a cost offset:

𝑂𝐶𝑊𝑊 = 𝐶𝑃𝑊𝑊𝑂𝑀𝑊𝑊− 𝐼𝑇𝑊𝑊 (4.28)

𝑂𝐶_𝐹𝐶 = 𝐶𝑃_𝐹𝐶𝑂𝑀_𝐹𝐶− 𝐼_𝐹𝐶 (4.29)

These are modified versions of Equation 4.21 and are used in comparisons involving the considered economic benefit of the water-energy links.

4.6.4 Combination of Capital and Ongoing Costs

In order to understand the total cost of the choices made in the electrical system, the capital costs and ongoing costs must be combined. The total cost of the system is used to calculate the cost per unit of electricity, which represents the cost to the operator to generate one unit of electricity (normally one kWh), which is often used to set customer pricing.

The total cost equation is:

𝑇𝐶_𝑖 = 𝐶𝐶_𝑖+ 𝑂𝐶_𝑖𝑡 (4.30)

where 𝑇𝐶𝑖 is the total cost of 𝑖, and 𝑡 is the expected lifetime of the system. Therefore, the total cost of the electrical system is the sum of these:

𝑇𝐶_𝑇 = ∑ 𝑇𝐶_𝑖 = 𝑇𝐶_𝑆+ 𝑇𝐶_𝑊𝑊+ 𝑇𝐶_𝐷+ 𝑇𝐶_𝐹𝐶+ 𝑇𝐶_𝐸𝑧+ 𝑇𝐶_𝑇 (4.31) where 𝑇𝐶_𝑇 is the total cost of the portfolio, over the lifetime of the system.

4.6.5 Objective Function

The objective function of the optimization is intended to minimize the cost per unit of electricity. It is:

𝑐𝐸𝑙𝑒𝑐 = 𝑇𝐶_𝑇 𝑡 ∙ 𝐸𝑇

(4.32) where 𝑐𝐸𝑙𝑒𝑐 is the cost per unit energy.

Minimization of 𝑐_{𝐸𝑙𝑒𝑐} through this function would represent the most economic situation for the given parameters. Therefore, this is a desirable quantity to know for planning decisions and will indicate which energy generation choices lead to most economically desirable electrical system. It also allows comparison between scenarios where water-energy links are considered and not. A full list of input, decision and calculated variables is given in Section 10.1 (Appendix I).

To optimise, initial values are assigned to the decision variables: 𝐸𝐷 = 1 𝐺𝑊ℎ, 𝐸𝑁𝐺 = 1𝐺𝑊ℎ, 𝐴𝑆 = 8420𝑚2, 𝑄𝑊𝑊 = 1000000𝑚3/𝑦𝑟, corresponding to 1GWh of generation from each source. All input variables are assigned their respective variables. The system is then optimised by a generalised reduced gradient solver with multi-start (𝑛 = 500) to find the

(24)

18

minimum value of the cost per unit electricity (𝑐_{𝐸𝑙𝑒𝑐}, see Lasdon, Fox and Ratner, 1974). The use of multi-start prevented the presence of local optima over global optima, with initial values selected to encourage exploration of each source by the algorithm. The generalised reduced gradient solver attempts to minimize the cost per unit electricity by altering the decision variables (as given in Appendix I). With fixed input variables, provided based on the assumptions in this section, the combination of fixed and decision variables calculates the calculated variables which contribute to the final calculation of the decision variable.

The effect on the value of 𝑐𝐸𝑙𝑒𝑐 is investigated through introducing the energy-water modifications shown in Section 4.6.3, with these modifications compared to the original results as in Section 5.6.

4.6.6 Sensitivity Analysis

As there is uncertainty in many of the variables, due to reasons of location, time, etc. sensitivity analysis on selected variables was performed to show to what degree the changes affect the results. This also gives indication as to what degree changes which may occur in the future (i.e. through research) might have on the results. In particular, the most sensitive values could become foci for further research.

The variables selected for sensitivity analysis are the capital cost factor of solar (𝐶𝐹_𝑆) fuel costs of diesel and natural gas (𝑐𝑓𝑢𝑒𝑙,𝐷, 𝑐𝑓𝑢𝑒𝑙,𝑁𝐺), the cost price of water (𝑐𝑤𝑎𝑡𝑒𝑟), the net energy to treat WW (𝑒_𝑇), the efficiencies of the electrolyser and FC (𝐸_𝐸𝑧, 𝐸_𝐹𝐶) and the WW treatment efficiency (𝜀_𝑇).

(25)

19

5. Results

5.1 Multicriteria Assessment of Solar Sites

The MCDM assessment of sites shows which areas of the island are suitable (and preferable) for development for solar power. The results of the MCDM are divided into three categories regarding the development of solar power (Figure 5.1). Areas with a score of zero are considered completely incompatible with any solar development, either for reasons of geography (e.g. water bodies) or for reasons of social or environmental important (e.g. protected natural areas). Areas with a score of one could be developed but are less desirable as they may be costlier to develop or would be met with a higher degree of social resistance. It should be noted that the optimal score is 3.2.

Figure 5.1. MCDM Score Locations

The total area of GC is 195.2 km2, of which approximately 149.4 km2 of land is suitable for development (76.5% of the island). An area of 128.1 km2_{received the higher score of two} (65.6% of the island) and 21.3 km2 received the lower score of one (10.9% of the island). This means the majority of the island is suitable for solar development. The total area suitable for development of solar energy (149.4 km2_{) may be used as a limit to the area of solar panels. This} value is treated as a purely theoretical maximum, based upon the datasets utilised. It is suggested that Figure 5.1 be used as a starting point for further examination of the suitability of each area.

5.2 Average Solar Insolation

Solar insolation varies on GC (Figure 5.2). The highest insolation is found on the Eastern and Northern tips of the island, and the lowest in the South. Middling values fall in a band between these areas. However, there is a relatively narrow range of solar insolation values across the island. For this reason, in all analyses, it has been assumed that an average of a random sample of points serves as representative of solar insolation across the island.

(26)

20

Figure 5.2. Solar Irradiation at Ground Level Across Grand Cayman

5.3 Monthly Solar Insolation Profiles

The derived solar irradiation profile for the representative day of each month is shown in Figure 5.3.

Figure 5.3. Hourly Irradiance Profiles for Representative Day

There are similar profiles for each month due to the relatively stable climate of the Cayman Islands (Figure 5.3). Peak insolation occurs around midday. The highest peak value is 911.2 W/m2 in May, the lowest peak is 652.8 W/m2 in December. The shortest day has approximately nine hours of daylight and the longest 11 hours.

(27)

21

5.4 Total Solar Potential

The total yearly potential is shown in Table 5.1, derived from the profiles in Figure 5.3.

Table 5.1. Monthly Solar Potential

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Daily Insolation

(Wh.m-2_d-1₎ 4323 5249 5779 6325 6901 5887 6817 6175 6006 5383 4846 4333 Monthly Potential

(kWh.m-2₎ 134 147 179 190 214 177 211 191 180 167 145 134

The total yearly potential is 2070 kWh/m2. The month with greatest daily insolation is May (6900.7 Wh.m-2d-1), and the month with least is January (4322.8 Wh.m-2d-1). The month with the greatest potential is May (213.9 kWh.m-2_{) and the month with least is January (134.0} kWh.m-2).

Assuming the total area available for solar development includes locations scoring one and two from the MCDM (Section 5.1), this suggests the maximum solar energy available in a year is 309250 GWh.

5.5 Wastewater Potential

The WW potential represents the potential energy that can be avoided by the use of TWW in place of using desalination as a water source. This is a function of the WW available and the treatment efficiency (𝜀_𝑇). Table 5.2 shows this under the assumed treatment efficiency for this study.

Table 5.2. Volume of Wastewater Treated and Net Energy

Available Wastewater (1000m3/yr) εT Avoided Abstraction (1000m3/yr) Avoided Energy (GWh/yr) 10846 0.5 5423 10.85

There is 10.85 GWh/yr of potential energy savings in utilising WW in this manner, under the assumption that all TWW may be used. For comparison, net energy generation was 692.9 GWh in 2019 (CUC, 2020).

5.6 Comparison of Basic and Water-Energy Scenarios

This section details the results of the basic scenario and the water-energy scenario. In the basic scenarios, WW is considered as an energy source (through the net energy avoided in its use), and the hydrogen system as energy storage. The water-energy scenarios differ by inspecting the volume of water available as a by-product and considering the price it may be sold for – referred to here as the cost price of water. This difference in the scenarios enables inspection of the

(28)

22

economic benefits when water-energy links are considered. The volume of water made available in each case is also examined, to quantify the societal good (increased water availability) which the water-energy links may also produce.

Different project lifetimes (i.e. the expected lifetime of equipment) are considered under both scenarios, as this can have a significant effect on the viability of different electricity sources.

5.6.1 Comparison of Cost of Electricity.

Figure 5.4 shows the cost per unit electricity and the corresponding electrical mix for varying project lifetimes. The total electricity consumed is 692.9 GWh/yr, as discussed in Section 4.5. The bar graph demonstrates the proportions of each electricity source contributing to meeting this consumption.

Figure 5.4. Cost of Electricity Under the Basic Scenario Considering Different Project Lifetimes, Showing the Corresponding Electricity Mix

Only under very short project lifetimes (3 years) are fossil fuels preferred. Natural gas is preferable economically to the existing fuel, diesel, despite the new investment which would be required to convert to this fuel source. This is shown by the lack of diesel in the energy share under any lifetime. As the expected lifetime of the project increases solar energy becomes the most economically viable electricity source. Longer lifetimes also decrease the cost per unit electricity. It can also be seen that without considering the water-energy links, the avoided energy use through the use of WW is not a preferable electricity “source” – this means that avoiding the energy use in desalination is uneconomic compared to generating more electricity from other sources.

Figure 5.5 shows the same scenario but considering the cost price of water (i.e. when the water is sold as a product).

(29)

23

Figure 5.5. Cost of Electricity Considering Cost Price of Water and Different Project Lifetimes, Showing the Corresponding Electricity Mix

As can be seen, if water is sold, WW becomes preferable under all the project lifetimes - though it only makes up a small portion of the electricity mix due to the relatively small amount of WW available as a resource. The rest of the electricity supply is made up of the same sources as in Figure 5.4.

The cost of electricity is slightly lower when the water prices are considered (Table 5.3).

Table 5.3. Comparison of Cost of Electricity Under Each Scenario

Lifetime (Years) 3 7 10 15 20 25 Celec ($/kWh) Basic Scenario 0.125 0.074 0.055 0.04 0.032 0.028 Water Link Scenario 0.124 0.072 0.052 0.037 0.03 0.025

The cost of electricity does decline when considering the water cost, though the difference is small.

5.6.2 Comparison of Produced Water

The water produced under each scenario above (Figure 5.4 and Figure 5.5) are shown in Table 5.4, for all of the lifetimes.

(30)

24

Table 5.4. Comparison of Water Produced Under Each Scenario from Each Source

Lifetime (years) 3 7 10 15 20 25 Basic Scenario Water from FC (1000m3_/yr) 0 52 52 52 52 52 Treated WW (1000m3_/yr) 0 0 0 0 0 0 Total Water (1000m3_/yr) 0 52 52 52 52 52 Water Links Scenario Water from FC (1000m3_/yr) 0 52 52 52 52 52 Treated WW (1000m3_/yr) 5423 5423 5423 5423 5423 5423 Total Water (1000m3_/yr) 5423 5475 5475 5475 5475 5475

Water is produced where solar power is used (from the FC reaction) and/or where WW is treated. The production from the FC is much lower than that produced by treating WW. The daily domestic consumption per person in the United States is approximately 307 litres per person per day (112 m3_{/yr - Dieter and Maupin, 2017) and this number has been used for GC,} and is considered a reasonable estimate for GC due to a comparable standard of living. This suggests that the water from the FC reaction could meet the water needs of 464 people, and the TWW 48 420 people. The population of Grand Cayman is approximately 65 000 people.

5.6.3 1 GWh Basis Comparison

The total cost for each electrical source, solar, WW, diesel and natural gas on a 1GWh/yr basis is shown in Figure 5.6. Diesel, despite not requiring new capital investment, has a high ongoing cost (shown by a steep gradient), meaning it rapidly becomes uneconomical with lifetimes longer than 2 years. Natural gas has a shallower gradient of increase, meaning it may become more competitive as lifetimes increase, though it too becomes uneconomical from a 7-year lifetime. WW has the largest capital investment, yet also displays a shallow gradient of increase. This means that it is not economical under a short lifetime and where water is not sold, only becoming more economical than diesel from a 16-year lifetime, though other sources remain cheaper over all lifetimes. Solar energy has a capital investment cost that is in the middle of the options considered, which makes it uneconomical initially. However, due to the low ongoing costs of solar energy it is the most economical option from a 7-year lifetime. If one factors in the water cost price, the results for WW and solar are altered.

(31)

25

Figure 5.6. Comparison of Total Costs on a 1GWh/yr Basis

Figure 5.7. Comparison Under Each Scenario on a 1GWh/yr Basis for Wastewater Treatment

Including water costs drastically affects the economics of WW treatment as an electricity source (Figure 5.7). In this case, the gradient of the line becomes negative, implying that this source becomes profitable based upon the sale of water alone. In other words, the sale of water acts to pay off the capital cost and operation of the WW plant. The payoff period of the wastewater plant is 13 years (i.e. a 13-year lifetime) when TWW is sold as a product.

(32)

26

Figure 5.8. Comparison Under Each Scenario on a 1GWh/yr Basis for Solar Energy

The solar energy graph demonstrates little change when water price is factored in (Figure 5.8). This is likely due to the relatively low volume of water produced by the FC, as shown in Table 5.4. This therefore suggests there is very little economic benefit in extracting the water by-product from the FC.

5.7 Sensitivity Analysis

As many of the values used in this investigation are subject to variation, both with time (for example as technology advances, or due to global pricing trends) and location. The degree to which variations in input variables influence outcomes is demonstrated in this section.

5.7.1 Capital Cost of Solar

The capital cost of solar panels is highly variable, and work seeks to further decrease these costs. The degree to which price changes affect the viability of solar energy in the different time periods, with inclusion and exclusion of water costs is shown in Figure 5.9. The electricity mix for each point is shown in Section 10.2 (Appendix II).

(33)

27

Figure 5.9. Effect of the Solar Cost Factor on celec for Lifetimes of a) 3 years, b) 7 years, c) 10

years, d) 15 years, e) 20 years, f) 25 years

As with the general scenarios (Figure 5.4 and Figure 5.5), increasing project lifetimes decreases the cost of electricity, as does considering water prices. The decrease by considering water prices is a very small amount, hence the lines demonstrating when water prices are considered, and when they are not, appear near coincident.

For a 3-year lifetime, solar energy does not feature in the electricity mix, hence the capital cost has no effect on the cost per unit of electricity. For 7 and 10-year lifetimes, the kinks in the line (at 1500 and 2500 $/kW respectively) represent a change in the electricity mix. Prior to the kink, solar energy is favoured, and hence changes in 𝑐𝑒𝑙𝑒𝑐 are directly proportional to changes in the capital cost of solar energy. Following this, the line becomes flat as natural gas replaces solar capacity, and hence is unaffected by changes in the capital cost of solar energy. For 15, 20 and 25-year lifetimes, solar energy is the dominant electricity source, and is affected by the capital cost.

When compared to the general scenarios presented in Section 5.6, a change in the capital cost of solar energy over the values covered does not affect the selection of this energy source for lifetimes of 15 years or greater, nor does it improve the selection for a lifetime of 3 years. Within 10 and 15-year lifetimes, the capital cost is significant to the use of solar as an energy source.

The selection of WW as an energy source is not affected by the capital cost factor of solar energy, depending solely on the consideration of water prices. As in the general scenarios (Figure 5.4 and Figure 5.5), considering water prices causes the model to select WW as an electricity source to its greatest potential which however causes only a small effect on the price per unit electricity.

a. b.

c. d.

(34)

28

5.7.2 Fuel Cost of Diesel

The cost of fuel for diesel generators is subject to large fluctuations, with fossil fuel prices being particularly unstable (Wilber et al., 2019). The effect these changes in fuel price would have on the cost of electricity is demonstrated in Figure 5.10.

Figure 5.10. Effect of the Fuel Cost of Diesel on celec for Lifetimes of a) 3 years, b) 7 years

The effect of diesel pricing on the cost of electricity is somewhat limited. Diesel is only selected at low prices and on a short lifetime, replacing natural gas as the favoured energy source in a 3-year lifetime, when the cost of fuel is below 50 $/MWh. As the lifetime is increased to 7 years, solar energy is competitive with both prices and becomes the dominant energy source. It should be noted that it is only under these conditions that diesel is selected as an electricity source, not appearing in the general scenarios in Section 5.6. For this reason, only 3 and 7-year lifetimes are considered in this analysis.

As found previously, the selection of WW as an energy source depends solely on if the cost of water is taken into consideration. If it is included, it is utilised to its full potential and results in a small decrease in the cost of electricity, again with the lines showing each appearing near coincident.

5.7.3 Fuel Cost of Natural Gas

As with diesel, the cost of natural gas is subject to uncertainty and fluctuations. The sensitivity of the cost of electricity to changes in its cost is demonstrated in Figure 5.11.

Figure 5.11. Effect of the Fuel Cost of Natural Gas on celec for Lifetimes of a) 3 years, b) 7

years, c) 10 years, d) 15 years

a. b.

(35)

29

The fuel cost of natural gas has a significant impact on the cost of electricity. For a 3-year lifetime where natural gas dominates in the general scenarios, natural gas is preferred over all lifetimes examined here. A proportional relationship exists between the cost of natural gas and the cost of electricity. For 7 and 10-year lifetimes, natural gas is selected at low prices, instead of solar energy as in the general scenarios (Figure 5.4 and Figure 5.5). For a 15-year lifetime natural gas is not selected across any of the values, hence longer lifetimes are not inspected. This suggests that natural gas is economically viable over 3-10-year lifetimes as long as the fuel price is low.

The cost of natural gas does not affect the selection of WW as an electricity source, rather this depends solely on if the cost price of water is taken into consideration. In this case, WW narrowly decreases the cost of electricity (with the lines appearing near coincident as previously), up to the maximum potential of WW on the island.

5.7.4 Cost Price of Water

As has been shown in the previous sections, the selection of WW as an electricity source depends solely on the cost price of water. The effect of changing the cost price of water on the cost of electricity is shown in Figure 5.12.

Figure 5.12. Effect of the Cost Price of Water on celec for Lifetimes of a) 3 years, b) 7 years, c)

10 years, d) 15 years, e) 20 years, f) 25 years

For a 3-year lifetime, WW as an electricity source is only considered where the cost price of water is above 0.45 $/m3. For longer lifetimes, a cost price of 0.1 $/m3 is the only value at which the cost of water leads to a situation where WW as an electricity source is not selected. If the price is higher, WW is utilised to its fullest extent. Higher cost prices of water lead to greater decreases in the cost of electricity, though over the values considered there is still a cost to generating electricity.

a. b.

c. d.

(36)

30

5.7.5 Net Energy to Treat Wastewater

The net energy required to treat WW is a subject of ongoing debate (McCarty, Bae and Kim, 2011; Pfluger et al., 2020). As this net energy affects the net potential energy per unit of WW (through avoiding abstraction and net power to treat), this will change the maximum energy which may be obtained from the same WW supply. The net energy to treat 1m3 of WW is shown in Figure 5.13. Pfluger et al., (2020) suggests that the maximal energy contained in domestic WW is 1.8 kWh/m3, this is taken as a maximum to the net energy to treat WW (i.e. assuming it requires no energy to treat, and the full energy is extracted). In future, it is likely that the net energy to treat WW will continue to decrease, potentially allowing more energy to be extracted than is required to treat the WW which will turn the net energy requirement, 𝑒𝑇, negative.

Figure 5.13. Effect of the Net Energy to Treat One Cubic Metre of Wastewater on celec for

Lifetimes of a) 3 years, b) 7 years, c) 10 years, d) 15 years, e) 20 years, f) 25 years

For all lifetimes, decreasing net energy to treat 1m3 of WW decreases the cost of electricity by greater amounts when the cost of waster is considered. This change is still small compared to the overall cost of electricity due to the limited amount of WW. Under the lowest net energy (1.8 kWh/m3), the maximum electricity from WW is 36.9 GWh/yr (compared to 10.8 GWh for the default value). As previously, the inclusion of water costs slightly decreases the cost per unit electricity, though the lines mostly appear coincident.

5.7.6 Electrolyser Efficiency

The efficiency of electrolysers affects the production of water from the FC, hence variation in the efficiency affects the cost of electricity when water price is considered. This relationship is shown in Figure 5.14.

a. b.

c. d.

Economic Consequences of Select Water-Energy Links : An Investigation of the Potential of Water-Energy Links Used to Improve the Economics and Added-Benefits of the Electrical System on Grand Cayman

Lewis James McNamee

Economic Consequences of Select Water-Energy Links

An Investigation of the Potential of Water-Energy Links Used

to Improve the Economics and Added-Benefits of the Electrical

System on Grand Cayman

Copyright

Table of Contents

1. Abstract

2. List of Abbreviations

3. Introduction

3.1 The Water-Energy Nexus

3.2 Wastewater as a Resource

3.3 Hydrogen Fuel Systems

3.4 Aim and Research Questions

4. Materials and Methods

4.1 Study Area

4.2 Multicriteria Assessment of Solar Development Siting

4.3 Solar Potential Calculations

4.4 Wastewater to Energy Calculations

4.5 Electricity System Modelling

4.6 Economic Modelling

5. Results

5.1 Multicriteria Assessment of Solar Sites

5.2 Average Solar Insolation

5.3 Monthly Solar Insolation Profiles

5.4 Total Solar Potential

5.5 Wastewater Potential

5.6 Comparison of Basic and Water-Energy Scenarios

5.7 Sensitivity Analysis