B. Resultados
VII. Conclusiones
systems
This study uses the terms 𝑚𝐶𝑂𝑐𝑜𝑔2
(𝑟) and 𝐶𝑐𝑜𝑠𝑡𝑐𝑜𝑔(𝑟) to refer to the CO2 emissions and cost of
a given cogeneration system during the rth year of its lifetime. These values are calculated
as follows: 𝑚𝐶𝑂𝑐𝑜𝑔2(𝑟) = ∑ (𝑄𝑓𝑢𝑒𝑙𝑐ℎ𝑝 (𝑞) +𝑄 𝑝𝑏(𝑞) 𝑡ℎ𝑏 ) 𝑁ℎℎ𝑦 𝑞=1 𝑓𝑒𝑚𝑛𝑔 + (𝑄𝑒𝑙𝑖𝑚𝑝(𝑞) − (𝑄𝑒𝑙𝑒𝑥𝑝(𝑞))) 𝑓𝑒𝑚𝑔𝑟(𝑞, 𝑟) kgCO2 3.31 𝐶𝑐𝑜𝑠𝑡𝑐𝑜𝑔(𝑟) = (𝑡𝑜ℎ𝑐ℎ𝑝𝑐𝑚𝑐ℎ𝑝) ∑ 𝑄𝑓𝑢𝑒𝑙𝑐ℎ𝑝(𝑞) 𝑁ℎℎ𝑦 𝑞=1 𝑐𝑛𝑔𝑖𝑚𝑝(𝑟) + (𝑄 𝑝𝑏(𝑞) 𝑡ℎ𝑏 ) (𝑐𝑛𝑔 𝑖𝑚𝑝(𝑟) + 𝑐 𝑚𝑏) + (𝑄𝑒𝑙𝑖𝑚𝑝(𝑞) − (𝐾𝑒𝑥𝑝𝑄𝑒𝑙𝑒𝑥𝑝(𝑞))) 𝑐𝑒𝑙𝑖𝑚𝑝(𝑟) £ 3.32
Table 3-6 lists all of the parameters used in the equation 3.31 and 3.32. This study calculates the CO2 emissions based on half-hourly time step because this duration
corresponds to the dispatch resolution of grid’s power plants. The term q is used to index each half hour of a calendar year. Furthermore, this study assumes that the boiler efficiency is constant.
The second bracket in equation 3.31 calculates the emissions from electrical energy exchanged with the grid. The terms 𝑄𝑒𝑙𝑖𝑚𝑝
, 𝑄𝑒𝑙𝑒𝑥𝑝 represent the amount of electricity imported from and exported to the electricity grid, respectively. This study calculates the export revenues by multiplying the export cost coefficient (𝐾𝑒𝑥𝑝) with the cost of
importing electricity (𝑐𝑒𝑙𝑖𝑚𝑝(𝑟)). In Chapter 5, the impact of export rates over the cost and
CO2 savings of the cogeneration systems is discussed.
Table 3-6 key parameters in calculating the cost and CO2 emissions of cogeneration systems
Parameter Unit Description Value
𝑚𝐶𝑂𝑐𝑜𝑔2(𝑟) kgCO2 Mass of saved CO2 emissions Equation 3.31
𝐶𝑐𝑜𝑠𝑡𝑐𝑜𝑔(𝑟) £ Cost savings Equation 3.32
𝑁ℎℎ𝑦 -- Number of half-hours per year 17520
r -- Year index 1-15
q -- Half hour index 1-17520
𝑄𝑓𝑢𝑒𝑙𝑐ℎ𝑝(𝑞) kWh CHP’s fuel consumption Equation 3.8
𝑄𝑝𝑏(𝑞) kWh Peak boiler’s heat output Equation 3.28
𝑄𝑒𝑙𝑖𝑚𝑝(𝑞) kWh Imported electricity Equation 3.29
𝑄𝑒𝑙𝑒𝑥𝑝(𝑞) kWh Exported electricity Equation 3.30
𝑓𝑒𝑚𝑔𝑟(𝑞, 𝑟) kgCO2/kWh CO2 intensity of the imported electricity See Chapter 4
𝑓𝑒𝑚𝑛𝑔 kgCO2/kWh CO2 intensity of the natural gas 0.184
𝑡ℎ𝑏 -- Boiler’s efficiency 0.8
𝑡𝑜ℎ𝑐ℎ𝑝 Hours/year Annual operating period
𝑐𝑚𝑐ℎ𝑝 £/hour CHP’s maintenance cost Table 3-7
𝑐𝑚𝑏 £/kWh Boiler maintenance cost 0.004 [74]
𝑐𝑛𝑔𝑖𝑚𝑝(𝑟) £/kWh Cost of importing natural gas Figure 3.9 𝑐𝑒𝑙𝑖𝑚𝑝(𝑟) £/kWh Cost of importing electricity Figure 3.9
𝐾𝑒𝑥𝑝 -- Export cost coefficient See 5.3.3
The term 𝑓𝑒𝑚𝑔𝑟
represents the CO2 intensity of the electricity delivered by the grid. The
methodology which is used to calculate this value is discussed in Chapter 4.
According to a CHP maintenance contractor in the UK [75], the maintenance costs of the CHP units are calculated based on their operating hours, regardless of their output. The hourly maintenance costs were calculated by dividing the maximum number of hours per service over the cost of each maintenance service. Table 3-7 lists the calculated hourly maintenance costs of the selected CHP units.
Table 3-7 Maintenance costs of selected CHP units [75] Parameter Units 6 𝑘𝑊𝑒 9 𝑘𝑊𝑒 15 𝑘𝑊𝑒 20 𝑘𝑊𝑒 Service Interval Hours 10000 10000 8500 6000 Service cost £s 1450 1495 1525 1840
𝑘𝑚𝑐ℎ𝑝 £
ℎ𝑜𝑢𝑟𝑠 0.145 0.16 0.179 0.306
Figure 3.9 shows the future estimates of the prices of natural gas and electricity in the UK’s retail price. These values are imported from the Annex M of the annual energy and emissions projection report which is published by the UK’s government [76]. The values shown in Figure 3.9 correspond to the reference scenario explained in [76].
Figure 3.9 Estimated retail prices of importing a unit of natural gas and electricity[76] In case of the conventional system, the heat demand (𝑄𝑡ℎ𝑑 ) is entirely covered by the
boilers and the electrical demand(𝑄𝑒𝑙𝑑)is imported from the grid. The terms 𝑚 𝐶𝑂2
𝑐𝑜𝑛𝑣 (𝑟)and
𝐶𝑐𝑜𝑠𝑡𝑐𝑜𝑛𝑣(𝑟) represent the cost and CO2 emissions which results from operating a given
conventional system. These values are calculated in equation 3.33 and equation 3.34. Table 3-6 explains the rest of the parameters used in the below equations.
𝑚𝐶𝑂𝑐𝑜𝑛𝑣2 (𝑟) = ∑ (𝑄𝑡ℎ 𝑑 (𝑞) 𝑡ℎ𝑏 ) 𝑁ℎℎ𝑦 𝑞=1 𝑓𝑒𝑚𝑛𝑔+ 𝑄𝑒𝑙𝑑(𝑞)𝑓𝑒𝑚𝑔𝑟(𝑞, 𝑟) 𝑘𝑔𝐶𝑂2 3.33 𝐶𝑐𝑜𝑠𝑡𝑐𝑜𝑛𝑣(𝑟) = ∑ ( 𝑄𝑡ℎ𝑑(𝑞) 𝑡ℎ𝑏 ) 𝑁ℎℎ𝑦 𝑞=1 𝑐𝑛𝑔𝑖𝑚𝑝(𝑟) + 𝑄𝑒𝑙𝑑(𝑞)𝑐𝑒𝑙𝑖𝑚𝑝(𝑟) £ 3.34
It worth highlighting the assumption made in terms of calculating the economic feasibility of cogeneration systems. In broad terms, the economic case for cogeneration systems is from the fact that CHPs consume natural gas and cogenerate heat and power, which results in reducing the amount of electricity imported from the grid. Therefore, the investing bodies – local authority, building owner, people living in the flats – receive the economic returns from the investment they’ve made on cogeneration systems due to the price difference between importing natural gas and electricity.
To determine the impact of cogeneration systems, it is required to calculate the savings such systems incur. The terms 𝑆𝐶𝑂2(𝑟) and 𝑆𝑐𝑜𝑠𝑡(𝑟) refer to the CO2 and cost savings of a
cogeneration system during the rth year of its operation, respectively. These values are calculated in equation 3.35 and 3.36. Additionally, the relative CO2 savings of a
cogeneration system is calculated in 3.37. 𝑆𝐶𝑂2(𝑟) = 𝑚𝐶𝑂2 𝑐𝑜𝑛𝑣(𝑟) − 𝑚 𝐶𝑂2 𝑐𝑜𝑔 (𝑟) 𝑘𝑔𝐶𝑂2 3.35 𝑆𝑐𝑜𝑠𝑡(𝑟) = 𝐶𝑐𝑜𝑠𝑡𝑐𝑜𝑛𝑣(𝑟) − 𝐶 𝑐𝑜𝑠𝑡 𝑐𝑜𝑔 (𝑟) £ 3.36 𝑆𝐶𝑂%2(𝑟) = (𝑚𝐶𝑂2 𝑐𝑜𝑛𝑣(𝑟) − 𝑚 𝐶𝑂2 𝑐𝑜𝑔 (𝑟) 𝑚𝐶𝑂𝑐𝑜𝑛𝑣2 (𝑟) ) × 100 % 3.37
This study assesses the lifetime economic performances of the cogeneration systems with two metrics: payback analysis and the tolerable capital cost [77]. The author was unable to find a mathematical formula which calculates the payback period for cases with uneven annual savings which is the case in this study. Therefore, the payback period of a cogeneration system is calculated by the following for loop:
2#For 𝑟 = 1 to 𝑁𝑦𝑐ℎ𝑝 3# AS = AS + 𝑆𝑐𝑜𝑠𝑡(𝑟) × (1 − 𝐷𝑅)𝑟 4#If AS ≥ 𝐶𝐶𝑐𝑜𝑔 5#PP =(𝑟 − 1) + AS−𝐶𝐶𝑐𝑜𝑔 𝑆𝑐𝑜𝑠𝑡(𝑟)×(1−𝐷𝑅)𝑟 Else
6#PP = Not feasible yet! End if
Next 𝑟
The description of the code shown above is as following:
1# Set the Accumulated Savings (AS) to zero as the cogeneration system has not operated yet.
2# Loop through each year of the number of years in which the cogeneration system stays operational.
3# The index r stands for a year and 𝑁𝑦𝑐ℎ𝑝stand for the number of operational years.
𝑁𝑦𝑐ℎ𝑝 is calculated in equation 3.41. Add the current year’s discounted savings to the AS, where 𝑆𝑐𝑜𝑠𝑡(𝑟)stands for the savings in the rth year, and DR stands for the
discount rate.
4# Check whether AS is greater than or equal to the capital cost of the cogeneration system(𝐶𝐶𝑐𝑜𝑔). 𝐶𝐶𝑐𝑜𝑔 is calculated in equation 3.39.
5# The code executes this line for cases in which the cogeneration system has became economically feasible. The Payback Period (PP) is then calculated as the summation of full operating calendar years(𝑟 − 1), and the rest ( AS−𝐶𝐶𝑐𝑜𝑔
𝑆𝑐𝑜𝑠𝑡(𝑟)×(1−𝐷𝑅)𝑟).
6# At this point the cogeneration system has not yet became economically feasible. This study uses equation 3.39 to calculate the capital cost of the cogeneration systems.
The capital cost of the cogeneration system consists of the capital cost of the CHP unit imported from [78], the TES unit imported from [79], and the heat distributor unit. The price of the heat distributor is added to equation 3.39, by personally communicating with the CHP manufacturers. Additionally, this study neglects the difference in the capital cost of boiler units which exists between a cogeneration system and its conventional counterpart.
Besides the payback analysis, this study uses the concept of tolerable capital cost, used by [77, 80], to evaluate the cost savings of the cogeneration systems. The key feature of this metric is that the capital cost of a cogeneration system is the output of the analysis, rather than being its input. The tolerable capital cost analysis is a useful metric due to the possible uncertainties in the capital cost values which have been assumed for the cogeneration system. This study calculates the tolerable capital cost of a cogeneration as follows: 𝑇𝐶𝐶 =∑ 𝑆𝑐𝑜𝑠𝑡 𝑁𝑦 𝑐𝑜𝑔 𝑟=1 (𝑟) × (1 − 𝐷𝑅)𝑟 𝑃𝑒𝑙,𝑚𝑎𝑥𝑐ℎ𝑝 £/kW e 3.40
Here, the term 𝑁𝑦𝑐𝑜𝑔stands for the number of operational years of a cogeneration
system; 𝑆𝑐𝑜𝑠𝑡(𝑟)stands for the cost savings of the cogeneration system during the rth year
of its operation; DR stands for the discount rate and 𝑃𝑒𝑙,𝑚𝑎𝑥𝑐ℎ𝑝 represents the electrical rating
of the CHP unit in the cogeneration system.
One of the key inputs to either payback or tolerable cost analyses is the number of operational years of the cogeneration systems. About the lifetime of the cogeneration system, the author consulted the design engineers who were working for a CHP manufacturing company at the time. They estimated that lifetimes of the engines used in small-scale CHP units typically range between 40000 and 50000 hours. Based on this value, this study assumes that all the CHP units operated for 45000 hours. Additionally, this study limits the lifetimes of the other components (e.g. generator) of the cogeneration system to 15 years. Based on these assumptions, the number of years in which a cogeneration system operates is calculated as follows:
𝑁𝑦𝑐𝑜𝑔 = { 15 𝑡𝑜𝑝𝑐ℎ𝑝 ≤ 3000 45000 𝑡𝑜𝑝𝑐ℎ𝑝 𝑡𝑜𝑝 𝑐ℎ𝑝 > 3000 years 3.41
Here, the term 𝑡𝑜𝑝𝑐ℎ𝑝
stands for the annual operating period of the cogeneration system. If this value is more than 3000 hours/year, the lifetime of the cogeneration system is limited to its engine’s lifetime. Otherwise, if the CHP unit operates for less than 3000 hours/year then the lifetime of the cogeneration system equal 15 years.
There is one aspect of the equation 3.41 which needs further clarification. If the value of the 𝑁𝑦𝑐𝑜𝑔, for a cogeneration system, is not a whole number then this study accounts for a
fraction of its cost and CO2 savings in its final year of operation. For instance, if 𝑁𝑦𝑐𝑜𝑔 =
8.2, this study only accounts for 20% of the savings of the cogeneration systems which is achieved between the 8th and 9th year of its operation.