Alternative to Absorption Chillers

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An alternative to absorption chillers are the adsorption chillers which use a solid sorption material rather than liquid solutions. However they come in relatively small sizes up to 500kW, have a relatively low COP (0.6) and given that the market for them is not fully developed, prices are higher than for absorption chillers (Solair, 2009), and as such they were not considered in the present study. In case of absorption chillers, the working solution is a pair of refrigerant-absorbent which for temperatures in the region of 4C is water-lithium bromide. If lower temperatures are required, such as in cooling storage applications, ammonia-water pair is used instead. Plant comes in various sizes, between 18kW and 11MW, and they are available in two configurations: single-stage and two-stage. Single-stage works at lower input temperatures (around 100C) while two-stage works at higher input temperatures. The latter are commonly used with exhaust heat from CHPs. Table 7 shows the cost and performance of different sizes and configurations of absorption chillers as of 2016.

1.1.1        Market Status for Absorption Chillers

The growth in absorption refrigeration market is closely linked to the growth in CHP uptake and according to Future Market Insights (2018) the growth in absorption chiller market in Europe is expected to be driven by increasing demand from the frozen food sector. Additionally, the UK government perceives good quality CHP (such as CCHP) systems as a key technology in delivering the carbon targets and play a vital role in ensuring cost-effective and secure energy supply, particularly for industry, hence continued support for these technologies is expected in the future (DECC, 2011).

1.1.2        Support Mechanisms

There are no specific support mechanisms for absorption chillers in the UK, however when coupled with CHP, the increase in efficiency would facilitate CHPQA standard accreditation. The system would then be eligible for the financial benefits discussed in Section 2.2.2.

1.2         Fuel Cells

A fuel cell is an electrochemical device that converts the energy of the chemical reaction between oxygen and hydrogen into electricity and heat, with water as a by-product, without direct combustion (DECC, 2013). There are different types of fuel cells, used in stationary (CHP) and transportation applications, however this paper will discuss only those that are applicable to CHP. The four primary fuel cell types in this case are: phosphoric acid (PAFC), molten carbonate (MCFC), solid oxide (SOFC) and proton exchange membrane (PEMFC). Table 8 shows the advantages and disadvantages of the different types of fuel cells used in CHP applications, Table 9 shows the performance and costs of those technologies and finally Table 10 summarises the advantages and disadvantages of deploying fuel cells in the retail sector.

1.2.1        Market Status for Fuel Cells

Price reduction lead to a doubling of installed capacity between 2009 and 2013 and as of 2013 there were 200 MW of fuel cell capacity installed globally, MCFC and PEMFC being the most common technologies followed by SOFC (EPA, 2017). In Europe, there is increasing support form governments via subsidies to leverage deployment of fuel cell technologies and develop the market, and it is expected that this trend will continue in the future, since hydrogen is often seen as an essential component of the future energy system (Hart et al., 2016). Increased production capacity from 100 to 10,000 units/year has the potential to reduce costs by approximately 30% (Battelle Memorial Institute, 2016), and manufacturers argue that this increase is essential to reduce the price of fuel cells to the point where they become competitive with other DES technologies (Hart et al., 2016). Finally, an important aspect to consider is the significant effect of economies of scale on the final price per kW of the system. A 250 kW system is approximately 20% cheaper per unit of output compared to a 100 kW (Hart et al., 2016).

1.2.2        Support Mechanism

Fuel cell CHPs are eligible for the same support mechanisms as conventional CHPs and those are described in Section 2.2.2.

1.3         Distributed Energy Storage

Energy storage is an established concept for balancing the mismatch between supply and demand for heating or cooling and it is a versatile way to generate additional cost savings by shifting building energy demand or by providing grid services. At a high level, storage can be divided into bulk (pumped hydro), distributed (batteries) and fast (supercapacitors), each of them providing a different level of flexibility to the energy system (Strbac et al., 2012).  Although energy can be stored in multiple forms, this paper analysed thermal and electrochemical (batteries) at a distributed level, as these are more suitable and realistically feasible in the retail sector. These are technologies that tend to be smaller in nature relative to bulk storage, and have short duration storage capability:

  • Storage batteries: lithium-ion, lead-acid, sodium-sulphur, vanadium-redox
  • Thermal storage as sensible heat: hot/cold water tank, ground storage (borehole)

Table 11 shows the advantages and disadvantages of installing energy storage devices in the retail sector, Table 12 compares different storage technologies, and finally Table 13 shows the cost and performance of different technologies.

It should be noted that in case of thermal storage, O&M and replacement costs have not been considered in the analysis since both options have very long lifetimes relative to other technologies and require very little maintenance. Estimates indicate that on an annual basis operation and maintenance costs represent 0.25% and 1% of the CAPEX (Mangold et al., 2010).

1.3.1        Market Status for Energy Storage

Approximately 400,000 hot water tanks are sold in the UK per annum, with an installed base of approximately 11 million. In the commercial sector there is a stable market for tank energy storage and it is expected that deployment will continue to grow. In growth scenarios, studies indicate that uptake of ground storage in the commercial sector will increase. The most common application for ground energy storage is in commercial buildings that have heating demands in winter and cooling loads in summer, but at present there are very few installations in the UK (Delta Energy & Environment Ltd, 2016). On the other hand, sensible heat storage technologies are unlikely to see major cost reductions in the future since they are based on very well established technologies and materials, and are mass produced. In case of batteries, cost of lithium-ion batteries is expected to decrease at a rate of 12% per year all the way through 2020, followed by a slowdown (Balu and Raja, 2016). Decrease in costs are expected for the other battery technologies as well, as they reach maturity and develop a market base.

1.3.2        Support Mechanisms

Although there are no specific support mechanisms for energy storage technologies, there are different potential sources of revenue, which were discussed below.

Bill Management/Energy Arbitrage

Large consumers such as the retail sector are faced with variable electricity prices, also known as Time of Use (ToU) tariffs. Storage technologies allow the operator to charge the system during times of low prices and discharge it during peak prices, hence significantly reducing their energy expenditure (Balu and Raja, 2016).

Reduced Demand-Based Charges

National Grid charges consumers for the maximum capacity they require (peak demand). Energy storage can be used to reduce the peak demand, hence ensuring lower charges (Balu and Raja, 2016).

Frequency Response

It is an immediate power response as a result of a change in grid frequency, to avoid spikes and dips when it deviates from 50 Hz (Mariaud et al., 2017), employed by National Grid to help balance supply and demand on a second by second basis. As the value of balancing will increase in the future with the introduction of more intermittent renewables into the mix, frequency response can become a significant source of revenue (Balu and Raja, 2016).

1.4         Heat Pumps

Heat pumps are a group of technologies that transfer heat from a low temperature heat source to a high temperature heat sink and they have been widely used to provide space heating, hot water or cooling (in heat driven refrigeration cycles) (Herold, Radermacher and Klein, 2016). The most common technologies in the UK are ground-source heat pumps (GSHP) and air-source heat pumps (ASHP) and they will be those analysed in this paper. In case of GSHP the heat source/sink can be either the ground or water, and can be categorised into the following: horizontal (closed-loop), vertical (closed-loop), pond/lake (closed-loop) and open-loop (Wu, 2009). While horizontal and vertical designs strictly refer to how the ground drilling is being carried out (with vertical boreholes taking less space, going deeper, and inherently more expensive), the closed/open systems refer to how the fluid is circulated in the system. In a closed system the fluid is circulated in a closed loop and absorbs the heat from the source, while in an open-loop water from the source is pumped into the heat pump, heat exchanged with it, and then pumped back into the reservoir (Wu, 2009). Table 14 shows the considerations of installing heat pumps in commercial buildings, Table 15 shows the comparison between GSHP and ASHP and Table 16 shows the cost and performance of the two technologies.

In should be noted that given that maintenance costs are low for heat pumps, they were not included in this analysis. Running costs, on the other hand are highly variable and depend on electricity prices.

1.4.1        Market Status for GSHP & ASHP

Heat pumps are a mature technology, despite relatively low market penetration in the UK compared to the rest of Europe (DECC, 2016). Out of all technologies, the most common type installed in the UK is the ASHP (Frontier Economics and Element Energy., 2013). On the other hand, GSHPs represent less than 1% of heating technology sales in domestic and commercial environments; and that is because GSHP face difficult barriers from the market, installer and manufacturer base perspectives, essentially making it hard to compete against the cheaper, easily retrofittable ASHP. There is potential for driving GSHP costs down and estimates indicate approximately 18% total cost reduction potential, however this would likely happen as the UK market becomes more mature and confident in the technology, but this is not expected to change significantly by 2020 (DECC, 2016).

1.4.2        Support Mechanism

Renewable Heat Incentive (RHI)

The RHI is a government support mechanism meant to leverage deployment of renewable heat in the UK. Eligible installations receive quarterly payments for 20 years, tariff adjusted in line with CPI. GSHP and ASHP are eligible subject to a set of conditions (Ofgem, 2017):

  • Must have a COP of at least 2.9 and a SPF of at least 2.5.
  • Electrical input into the pump must be measured.
  • Reversible heat pumps measure only heating not cooling.
  • GSHP capacity to be specified based on design conditions.
  • Microgeneration certification required for schemes less than 45 kWth.

In case of ASHP, rates are applicable to all capacities and as of October 2017 they were 2.61 p/kWhth. In case of GSHP, Ofgem introduced a tier system which pays the higher rate (tier 1) of 9.09 p/kWhth for the first 1,314 hours (15% of the year) of operation, and for the rest the lower (tier 2) of 2.71 p/kWhth, regardless of system size (Ofgem, 2016, 2018c).

1.5         Organic Rankine Cycle (ORC)

ORC is a way to generate electricity by using a working fluid with a low boiling temperature that enables the use of low grade heat in the process (Carbon Trust, 2010). It is based on the same working principle as the steam Rankine Cycle, the expansion of a high pressure liquid to low pressure, generating mechanical work. Although more than 70% of ORC installed capacity is aimed at power generation from geothermal brine, waste heat recovery is an emerging field, accounting for approximately 14% of the market (376 MW). At present however, it is being done for small scale applications (<150 kWe) (Tartière and Astolfi, 2017). Table 17 shows the advantages and disadvantages of ORC systems relative to steam turbines and Table 18 shows estimates of performance and costs associated with ORCs.

1.5.1        Market Status for ORC

Manufacturers of ORC have been on the market since the 80’s and the technology has been growing almost exponentially since and it is expected that this trend will continue in the future (Quoilin et al., 2013). As of 2017 there were 2,701 MW of installed ORC capacity globally (Tartière and Astolfi, 2017). Low capacity systems are under development or in the demonstration stage and it is essential that niche markets begin industrial production to develop the market and reduce costs. Current R&D is focusing on improving the efficiency of the system aiming for above 20% by improving the cycle architecture and fluid selection. In the UK, as of 2016, the total installed capacity or plants under construction was around 20 MWe, entirely used in biomass combustion heat recovery (Tartière and Astolfi, 2017).

1.5.2        Support Mechanisms

There are no specific support mechanisms for ORC systems in the UK, however when coupled with CHP, the increase in efficiency would facilitate CHPQA standard accreditation. The system would then be eligible for the financial benefits discussed in Section 2.2.2.

1.6         Barriers to DES Implementation in Commercial Organisations

Literature has identified a myriad of barriers to change in the industrial sector from an energy efficiency perspective, but they can relate directly to the commercial sector and DES adoption in particular. A comprehensive review of those barriers was carried out by Cagno and Trianni (2014). They classified barriers as external and internal. External barriers can be, for instance, the lack of interest or knowledge from the consumers or from the investors, and it has been pointed out that companies have little ability to overcome those (Lozano, 2013).  Internally, barriers can be more complex such as people behaviour and organisational issues. Cagno et al. (2013) have synthesised those barriers based on the aforementioned categories and their origin (internal or external), and their findings are presented in Table 19 below.

2           System Modelling

Section 2.7 presented the various technologies that can act as viable, long-term solutions to the energy problem facing the UK retail sector. Each technology was shown to have different advantages and disadvantages, and there is no right solution to all applications and scenarios.

In their study, Liu, Pistikopoulos and Li, (2010) distinguished between different types of measures that can be implemented in a supermarket: energy saving, conversion and generation technologies. They realised that energy saving measures such as sun pipes or motion sensors, do not compete with other technologies and that they are always beneficial on site. On the other hand energy conversion, such as LED lighting, although they have competition, they dominate the selection. Finally, energy generation, such as the technologies described in this paper, compete against each other and while they may be good in a certain scenario, they would fail in a different one. This highlights the fact that each building, in this case each supermarket, should be analysed and modelled separately and a generalisation is sometimes not possible.

This leads to decision makers having to face the difficult task of selecting the most suitable technology from a technical perspective, operating it as efficiently as possible, while achieving the desired outcome from their investment in a profitable manner, while being constraint by a tight budget. Computer simulations and different optimisation techniques have been used to assist decision-makers in this endeavour and those were discussed in the following sections.

Figure 3 shows a typical schematic of a polygeneration system meant to supply different services in a building. Polygeneration refers to the generation of different energy carriers (electricity, chilled water, hot water, etc.), in a single integrated process.

2.1         Optimisation Problems

Optimisation problems are arguably some of the most common ways engineers and scientists approach real-world problem solving (Cui et al., 2017). According to Omu, Choudhary and Boies (2013), literature around optimisation of energy resources has been trying to answer four distinct questions: 1. What is the technical, economic and environmental performance of the system?, 2. What are the long-term impacts of a specific energy system under different scenarios?, 3. How would energy supply, demand, pricing change in the future at a national scale?, and 4. What is the optimal way to integrate, operate and dispatch generation technologies? (typically at a district or building scale). The latter is the focus of this present research. In this case, there is also a lot of diversity in terms of how literature has been framing the problem. Some studies only deal with a single technology and/or fuel (Mago and Chamra, 2009; Ghadimi, Kara and Kornfeld, 2014). Most recent studies however, have a diverse portfolio of technologies and analyse the optimum distribution and operation of technologies under the given scenario (Ren et al., 2010; Acha et al., 2018). The technologies that are being modelled also vary slightly, but there are some that are part of almost any optimisation model. Table 20 shows a distribution of technologies from the literature that was investigated (14 peer reviewed articles). It is by no means exhaustive but it is meant to give an indication of the share of technologies present in the optimisation literature.

A typical optimisation problem consists of one or more objective functions (the scope of optimisation), decision variables (the variables that determine the result of the objective function), and equality and/or inequality constraints (to set the boundaries for the values the decision variables can take). According to the number of objective functions, optimisation problems can be classified into single or multi-objective optimisation problem (MOP). Typical objectives for optimisation were described by Toffolo and Lazzaretto (2002) as thermodynamic (maximum efficiency, minimum fuel consumption, minimum irreversibility), economic (minimum cost, maximum profit) and environmental (minimum emissions). Some typical decision variables can be existence, numbers and sizes of energy devices, operation status, energy rates; and they can be binary (1 or 0 representing the status on/off or exists or not) or continuous. Finally, the typical constraints found in DES optimisation are design constraints, operation constraints and energy balance (Somma et al., 2017).

Increasing complexities associated with modern energy systems, the myriad of parameters and variables that impact appropriate sizing and operation of an energy system has led to an evolution of the techniques employed to solve those problems. Nowadays, most optimisation problems are solved using mixed-integer linear programming (MILP), mixed-integer nonlinear programming (MINLP), stochastic optimisation (SO), and genetic algorithms (GA) (Moussawi, Fardoun and Louahlia-Gualous, 2016). In case of MOP, two or more functions have to be solved simultaneously. A problem arises when the objective functions are contradictory to each other, meaning that the optimal solution for one function leads to a less than optimal result for the other function(s), and it is hard, if not impossible to find a solution that leads to general optimality (Cui et al., 2017), which brings the concept of Pareto optimality. In this case, the solution is not an unique combination but instead, a set of optimal arrays, and those points constitute a Pareto set or Pareto front. Each point on the Pareto front is an optimum solution in its own sense, providing planners with information around trade-offs between alternatives when selecting a suitable compromise solution (Ren et al., 2010; Abdollahi and Meratizaman, 2011). A summary of the typical methods used in DES optimisation is presented in Table 21.

It is worth mentioning that MILP problems focus on two aspects regarding energy supply: design of the system taking into account the different technologies available and the operation of the selected technologies (Iturriaga et al., 2017). For example, Mehleri et al. (2012) aimed to optimise the selection for district-scale DES for minimum annualised investment and operating costs, while on the other hand (Bischi et al., 2014) looked at the most cost-effective operation of a CCHP plant, taking into account time varying loads and costs. There are also papers such as that of Wang, Jing and Zhang (2010) who acknowledge that the technical, economic and environmental performance of a CCHP is not only linked to a suitable design but also to an optimum operation strategy. From a system operation perspective, different strategies have been proposed, especially aimed at CHP and CCHP, in light of their good dispachability characteristics (Andrianopoulos, Acha and Shah, 2015). Two of the most common strategies are thermal and electrical load following. Cardona and Piacentino (2003) investigated the benefits of CCHP over CHP under those two strategies in the hotel sector and argue that both technologies should be operated to satisfy the thermal loads, on the basis that if there is any excess electricity, it can be exported to the grid. Although the aforementioned strategy is better than constant load operation, Cho et al. (2008) argues that significantly more savings can be achieved by having an optimum dispatch algorithm that optimises the objective function at each step in the simulation.

2.2         Typical Problem Formulation

2.2.1        Simulation Periods

Simulation time is usually represented at three levels, half-hourly/hourly, days and years and days are generally grouped based on day types (seasonal, period of the week) (Alvarado et al., 2016). Some papers ran the model based on and hourly – daily – monthly basis with a small number of days selected as representative for each season (Cho et al., 2009; Ren et al., 2010; Somma et al., 2017). The simulation is ran for a relatively small number periods to keep the computational power requirements to reasonable levels, however, as highlighted by Alvarado et al. (2016), data should be analysed beforehand to understand how representative the simplification is.

2.2.2        Objective Functions

It was described above that the objective function F(x) can be the formulation of a single objective f1(x) or multiple objectives as shown below:

Where

f1xcan be the discounted costs of the system which the model aims to minimise, as described by (Alvarado et al., 2016). They sum all the costs incurred for a period of 1 year and then they use a present value multiplier to extrapolate the costs to the entire period of the analysis; in addition, the initial CAPEX was spread throughout the lifetime of the project and discounted to present value (

CC). A similar formulation was done for the maintenance (

Cm), operational (

Co)and emissions costs (

CGHG), with the only difference that the maintenance cost was assumed as fixed, the operational cost is dependent on the energy cost incurred minus the revenue of exported electricity and the cost of emissions is calculated as the total emissions resulting from the energy used. The cost of carbon offset from electricity export was not included. (

CC) and (

Cm)were calculated for each technology for the whole year, while (

Co)and (

CGHG)is done for each time step, regardless of technology.

Such formulations are typical in the literature reviewed, and the differences may consist in the level of detail the model goes. For instance, the model developed by Alvarado et al. (2016) is the only one found to be accurately modelling electricity prices in real-time depending on a UK-regional basis. Generally, models use fixed prices over the period of the analysis (Kong, Wang and Huang, 2004; Somma et al., 2017).

In case of an environmental objective (i.e.

f2x), the scope is to minimise the total emissions over the period of the analysis. In order to do this, an accounting for the amount of fuel used by all generators as well as electricity from the grid is needed, and then multiplied by the emission factor of each fuel. In case the amount of fuel is not known, the product (electricity, heat, cooling) can be used and divided by the efficiency of the generator.

A support function (i.e.

f3x) was used by Somma et al. (2017) that adds weighting factors (i.e.

 1and (1-

 1)) to the cost and environmental functions. These factors are user defined and allow for a single solution to be found. The weighting can then be shifted to understand trade-offs.

Finally, an exergetic objective (i.e.

f4x) was described by Somma et al. (2017) where they aimed to maximise the overall efficiency of the system. For sake of clarity, exergy is the maximum theoretical useful work that can be obtained as a system interacts with a state of equilibrium and more practically, it highlights where losses occur and their magnitude (Yucer and Hepbasli, 2011).  This was done by calculating the ratio between the total annual exergy input to the total annual exergy output (what it is required to supply the loads). Since demand is known, the exergy output is known. Exergy input (

Exi)was calculated for every energy carrier (i), every hour (h) of every day (d), with the aim of minimising it, taking into account the exergetic efficiency of the generating equipment.

In their study, Liu, Pistikopoulos and Li (2010) preformed a multi-objective optimisation, taking into account cost and environmental criteria, for different combinations of energy technologies, for a commercial building. The result of their analysis is in the form of a Pareto frontier (shown in Figure 4), where configuration A leads to the highest amount of CO2eq emissions but yields the lowest cost. At the other end of the spectrum, configuration D is the most environmentally friendly by comes at the highest cost.

Using continuous variables, it ensures that the electricity demand at each simulation period is met by on-site energy technology (et), imported (eg) or from battery discharging (ed) and any surplus exported to the grid (ee) if no storage charging (ec) is required (6). Similarly, the heat and cooling demand are met by the simulated technologies (ht and

ct), with any waste heat released to the atmosphere (7,8). Finally, a constraint was put to limit the generation to the maximum capacity of the technology (9). Some works in the literature, most notably Rezvan, Gharneh and Gharehpetian (2013), took a slightly different approach, in the sense that they did not constrained the problem such that the loads are met, and instead they added a penalty cost for unmet heating or cooling demands. However it is believed that this method has two fundamental problems: choosing the cost of unmet heating and cooling demands is not only subjective but also difficult to estimate for the given context, and the fact that a relatively low penalty compared to the cost of installing or operating the system may lead to deliberate undersizing of the system, which is not something that it is done in practice.

An example of the effect of this constraint is shown in Figure 5 where supply from different technologies modelled meets the demand for different services at each simulated time interval.

Additionally, inequality constraints can be added to reflect the limits imposed by the studied building. For instance, the capacity of solar PV panels that can be installed is limited by the roof space that is available (Liu, Pistikopoulos and Li, 2010).

2.2.3        Model Considerations

An important aspect that requires consideration is the computational limitations and accessibility of a model. Optimising an energy system with high temporal resolution for long durations 1 year or longer in half-hourly or hourly time granularity, leads to complicated mathematical procedures that take a long time to solve (Milan et al., 2015). A solution are simplifications, but they can sometimes adversely impact the model accuracy (Bianchi et al., 2014). A review of literature carried out by Milan et al. (2015) revealed that one of the most common simplifications relates to the efficiency of generating technologies, which most of the time is treated as a constant. Framing the mathematical system as a set of linear equations is meant to keep computational time and costs to an accessible level. This is a problem however, especially in terms of CHP, whose economic performance, in the end, is heavily reliant on the conditions under which it is operated, and which changes significantly at partial-load conditions (Wu and Wang, 2006), the range of thermal and electrical efficiencies being very significant, (10-30% and 40-90% respectively (Bianchi et al., 2014) or even higher (Kayo, Hasan and Siren, 2014)) at maximum thermal power recovery. Figure 6 shows a typical ICE-CHP electrical efficiency curve at different load levels.

Since CHP load changes based on demand, so does the efficiency of the plant and hence it is important to model the system taking this time-variation into account for a more realistic assessment, however this turns the simplistic linear problem into a non-linear. In this case the problem would be solved as a MINLP, however there is a risk that the solution would not be a global optimum. In case of commercial buildings where demand remains relatively constant throughout the year, the inherent loss of accuracy from linearizing may not change the results significantly, which is explained by Milan et al. (2015), who have developed a model in which they analyse two methods to convert the non-linearity character of efficiency to a linear function, making it suitable for use in MILP algorithms. The first is using two binary variables, one to select the capacity and one to select the efficiency at every simulation time-step, from a pre-made table. This method was also used by Alvarado et al. (2016) in their model. However, it poses some disadvantages, since the model can only extract a single value from the table, without any possibility for interpolation between variables for both capacity and efficiency. The second method is to use special-order-set variables and it was proposed by Beale and Tomlin (1970). This method adds flexibility to the tabulated values in the sense that it allows for interpolation between load levels and also allows for separate constraints to be easily included, such as minimum load. It should be noted that this method although more accurate and flexible than the first, it adds complexity, does not work with all MILP solvers and requires additional user intervention.

Finally, Milan et al. (2015) drew two conclusions of particular interest, the fact that when variable efficiencies are considered, the role of storage increases in importance, particularly heat storage, and the fact that constant efficiency CHP models are a reasonable approximation of the system efficiency and they do not change the investment decision significantly, however they become important when establishing the optimum operational strategy. This in line with the study of Ghadimi, Kara and Kornfeld (2014) who have found that there is an optimum-cost size system for each operational strategy. The size of a CHP is mainly determined by the shape of the external temperature duration curve, the base temperature set-point of the building, the benefit from economy of scale, and the variation of the CHP part-load efficiencies (Gelegenis and Mavrotas, 2017). Thermal storage allows the operation of the CHP at full load and results in higher optimal capacities. Another interesting finding is that the optimal size of CHP is not influenced by electricity and gas prices, but by the plant efficiency, directly linked to the selected operational strategy. This finding has implications for the investment decision by removing part of the uncertainty, especially in volatile energy markets. In addition, according to Kong, Wang and Huang (2004), highlighted that the operational strategy is determined by the electricity-to-gas-ratio, and when it is low it may not be economical to run the CHP and when it is higher than a threshold (specific to each system) the operational strategy is independent of the energy cost.

Finally, according to Alvarado et al. (2016), energy prices and demands “should be represented as accurately as possible to what occurs in real-life, most importantly by considering their variability”. Additionally, projections of costs is important and other parameters that tend to vary in time are essential for greater confidence and accuracy of results.

3           Uncertainty Analysis

Uncertainty has always been a factor that determines whether an investment will take place or not. In case of DES, uncertainties can arise from variables such as energy demand, price of fuel, cost of investment, discount rate and regulations, and consequently these have a great influence on the project ROI (Rezvan, Gharneh and Gharehpetian, 2013). It is therefore important to understand the impact of those uncertainties on the financial returns of an investment, and provide decision-makers with a comprehensive tool to direct effort and capital. This section discussed different methods to analyse uncertainty, examples of where those have been applied in energy system design and planning and finally the financial metrics used to quantify the viability of the investment.

3.1         Methods to Analyse Uncertainty

According to the review done by Ioannou, Angus and Brennan (2017), methods to analyse risk can be grouped into quantitative and semi-quantitative. Quantitative methods deal with risk factors that can be described by probability distributions (such as solar resource or price fluctuations), and they are: Sensitivity Analysis (SAN), Mean-Variance Portfolio (MVP), Real Options Analysis (ROA), Stochastic Optimisation (SO) and Monte-Carlo Simulations (MCS). Semi-quantitative methods can be used with both statistical and non-statistical risks (i.e. policy/economic instability, space availability), and they are: MCDA (Multi-Criteria Decision Analysis) and Scenario Analysis (SA).

3.1.1        Sensitivity Analysis

SAN is a classical technique used to examine the effect of changing an independent variable (in case of DES that can be energy prices, subsidies, etc.) on a dependent variable (i.e. payback period). It is different from SA in the sense that it isolates each variable and records the outcome, whereas SA starts from a scenario and variables are aligned to match that scenario; as such, the two methods complement each other (Investopedia, no date). Brun and Lambert (2018) did a comparative analysis between installing CHP-ICE and fuel cell CHP in a commercial building. They used sensitivity analysis on the key parameters affecting the annual savings and payback period, the gas and electricity prices, to understand if the investment decision between the two technologies would change. They found that CHP-ICE is a better options and conducted a second sensitivity analysis to understand what would make fuel cell CHP more competitive by varying its efficiency and capital cost. They found that the because fuel cells are already very efficient, increasing it more does not impact the returns and the key aspect for improvement is the capital cost. Acha and Brun (2018) carried out a sensitivity analysis to understand the impact of changing the average electricity and gas prices, average electricity and gas demand and the efficiency on the viability of CHP investments. By changing the value of the input parameters, they found that electricity price and installation costs have the highest influence, followed by electricity and gas demand, with CHP efficiency and gas price having almost no influence. This can be seen from the slope of the trends shown in Figure 7.

As shown by Acha and Brun (2018), a global sensitivity analysis can also be carried out using variance-based sensitivity analysis, also known as Sobol Indices. This attributes the variance of the result to each input parameter. In their model, they found that in case of CHP, the largest cause of variance in the output is the annual gas demand (Figure 8).

3.1.2        Mean Variance Portfolio

MVP refers to the diversification of investment portfolio (mix of generating assets) in order to minimise risk and maximise expected return. Risk is minimised by increasing energy security and reducing the threat from fluctuating energy prices, while maximisation of return is achieved by grouping generation technologies, which, analysed separately may not be financially viable (Ioannou, Angus and Brennan, 2017). In the literature, the standard deviation of IRR by varying energy prices and subsidies was used to quantify return risk of a portfolio (Muñoz et al., 2009). On the other hand, it is also argued that from an investor perspective diversification may not bring significant value due to correlation between gas, electricity and carbon prices (Awerbuch, Bazilian and Roques, 2008). MVP is useful for both policymakers for a country/regional scale energy planning, and for private investors to understand their potential returns within a confidence level (Ioannou, Angus and Brennan, 2017).

3.1.3        Real Options Analysis

ROA is a particularly effective method for analysing the impact of investment decisions when there is flexibility in timing. This enables the investor to take an action when more information on the market is available and risk is reduced. ROA supplements discounted cash flow analysis and relies on the principle that an investor can postpone a decision, to make a more informed decision at a future point in time in a dynamic way with market conditions (Awerbuch, Bazilian and Roques, 2008). Literature commonly applied this method to understand the impact of changing policies or to understand the timing and capacity for generation projects (Boomsma, Meade and Fleten, 2012) from a private investor perspective, but it also has applications in policymaking, however they are outside the scope of this work.

3.1.4        Monte Carlo Simulation

MCS involves random sampling of probability distributions of input parameters in order to produce multiple scenarios, with the sampling being carried out such that the distributions reflect the shape of the output distribution. This leads to the output being the combined probability distribution of the possible outcomes (Vose, 2008). An example of application of this method in the literature was to evaluate the risk of investing in an energy project under variable equipment cost, maintenance cost, policy and market conditions, with the NPV and final energy cost being the dependent variables (Pereira et al., 2014). Urbanucci and Testi (2018) have used MCS in stochastic optimisation in order to establish the optimal design and operation (for lowest cost) of a CHP under long-term uncertainty of load demand, for a hospital. In order to integrate the demand uncertainty, they generated a random sample for the annual cost of energy under the form of a probability density function (PDF), and for each sample they ran the simulation under a different size of CHP and different operational strategy. They also formulated the problem as a multi-objective with Pareto efficiency constructed between the average value of cost saving from the PDF and the worse-case cost-saving scenario of the PDF. This will indicate which sizes of CHP are likely to provide higher possible profits at higher risks as opposed to lower profits even in the worse-case scenarios. Finally, they found out that in case of disregarding the long-term demand fluctuations, the model overestimates the size of the CHP by 30% and the cost saving from using the CHP by 10%.  Another studied carried out by Acha and Brun (2018) around optimal investment in CHP under uncertainty in the retail sector used MCS by varying the electricity and gas prices, electricity and gas demand, installation costs and plant efficiency and presented the results using the Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) indicators. After they selected appropriate distributions for the aforementioned parameters, they combined them into distributions for the ROI and payback period. Based on the values for ROI and payback demanded by the commercial organisations, they calculated the VaR and CVaR of the distributions. Results for a single store are presented in Figure 9.

3.1.5        Stochastic Optimisation

This method has widely been used for energy mix planning and design, energy storage management, and other various areas, and consists of introducing uncertainty in one or more input parameters (Ioannou, Angus and Brennan, 2017). Some uncertainties can be energy prices, energy demand, technology performance. This method would be used by an investor to minimise cost (or maximise revenue) by minimising costs, under a set of constraints from a policy, technology, budget or risk-acceptability perspective (Thangavelu, Khambadkone and Karimi, 2015). Rezvan, Gharneh and Gharehpetian (2013) developed a model to assess the optimum size of a CHP/CCHP – boiler/electric chiller system in a hospital under uncertain demand. The mathematical formulation is shown below:

minC × X+f(X,h(ω))

(10)

Where C is a vector of capacities, X is a vector of costs, h is a random vector that is being generated and the function

fdescribes the operational costs of the system. Their study revealed that an increase in energy demand uncertainty leads to a lower optimal capacity of CHP/CCHP to avoid the risk of overcapacity, while the capacity of boilers and chillers increases in order to meet the peak loads. Results are presented in Figure 10.

3.1.6        Multi-Criteria Decision Analysis

Typically used as a decision making tool for evaluating alternative energy sources, based on multiple stakeholder criteria, using a ranking structure (Kolios, Read and Ioannou, 2016). Common, in decision making under uncertainty, it has also been used to define the optimum design of a specific option, similar to a multi-objective optimisation. A particularly interesting study done by Zeng et al. (2015) investigated a cost-risk multi-objective problem for an utility-scale investment in generation portfolio, in an attempt to develop a decision making algorithm that can output the technologies with the lowest cost per kWh at minimum risk. They also suggested that such optimisation can be done purely economical, in the sense that a monetary value can be assigned to each risk and the optimisation be run for the lowest overall cost. The difficulty however arises in assigning this value.

3.1.7        Scenario Analysis

The viability of an investment can be analysed using discounted cash flow analysis under different potential future scenarios, each with their own characteristics (energy/carbon/technology costs, policies, etc.). Usually SA is being used to highlight investment options under best-worst case scenario or under scenarios that are most likely to occur (Kosow and Gaßner, 2008). An example of application of this method in the literature was to generate an energy investment portfolio under future market development of several technologies (Chen et al., 2009).

3.1.8        Summary of Methods to Analyse Uncertainty

Table 22 shows the summary of methods to analyse uncertainty that were discussed in this section, discussing their advantages, disadvantages and how common they are based on the review paper of Ioannou, Angus and Brennan (2017).

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