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2.1 Heating Project Load and Energy Calculation
Three kinds of heating loads are considered by the RETScreen CHP model: space heating, domestic hot water heating, and process heating. The annual total heating energy use of the system, QH, is the sum of the energy use for space heating, QSH, the energy use from domestic hot water heating,QDHW, and the energy use from process heating,QPH. Therefore:
Three kinds of heating loads are considered by the RETScreen CHP model: space heating, domestic hot water heating, and process heating. The annual total heating energy use of the system, QH, is the sum of the energy use for space heating, QSH, the energy use from domestic hot water heating,QDHW, and the energy use from process heating,QPH. Therefore:
Space heating is calculated by using the concept of heating degree-days. This concept is explained in section 2.1.1. The concept can be extended to include domestic hot water heating, as explained in section 2.1.2. Calculation of the peak heating load is covered in section 2.1.3. The peak heating load and the monthly heating degree-days can then be used together to calculate the heating load duration curve, as explained in section 2.1.4. The duration curve is then converted to monthly average loads and a peak load period (section 2.1.5). Process loads can be added as described in section 2.1.6. The calculation of the equivalent full load hours is found in section 2.1.7 and the impact of energy efficiency measures is briefly reviewed in section 2.1.8.
2.1.1 Site climatic conditions
Site conditions for heating are defined through two user-entered parameters:
The heating design temperature corresponds to the temperature of an exceptionally cold day in the area. It is often specified by the local building code. For example ASHRAE (1997) defines it as the minimum temperature that has been measured for a frequency level of at least 1% over a long period of record (usually 20 to 30 years), for the specified location. In Sweden it is defined as the coldest/warmest temperature that is expected once every 20 years. The capacity of the building’s heating equipment typically depends on the design heating temperature since the equipment needs to be sized to keep the building comfortable under the coldest conditions. The heating design temperature is used to determine the peak heating load and to size the heating system (section 2.1.3).
Heating degree-days, on the other hand, help determine the heating energy use. Heating degree-days are defined as the sum of daily differences between a set temperature Tset (usually 18°C) and the average daily temperature below the set temperature. Mathematically:
Site conditions for heating are defined through two user-entered parameters:
- the heating design temperature, and
- the monthly heating degree-days.
The heating design temperature corresponds to the temperature of an exceptionally cold day in the area. It is often specified by the local building code. For example ASHRAE (1997) defines it as the minimum temperature that has been measured for a frequency level of at least 1% over a long period of record (usually 20 to 30 years), for the specified location. In Sweden it is defined as the coldest/warmest temperature that is expected once every 20 years. The capacity of the building’s heating equipment typically depends on the design heating temperature since the equipment needs to be sized to keep the building comfortable under the coldest conditions. The heating design temperature is used to determine the peak heating load and to size the heating system (section 2.1.3).
Heating degree-days, on the other hand, help determine the heating energy use. Heating degree-days are defined as the sum of daily differences between a set temperature Tset (usually 18°C) and the average daily temperature below the set temperature. Mathematically:
where HDDi is the monthly heating degree-days for month i, Ni is the number of days in month i , and Ta,k is the average daily temperature for day k of the month. The annual heating degree-days HDD is calculated by adding the monthly heating degree-days:
The main advantage of using heating degree-days is that in a first approximation for space heating, the heating needs of a building can be assumed to be proportional to the number of heating degree-days (a refinement of this will be shown in section 2.1.5). Degree-days can also be used to describe hot water consumption, as will be seen in the next section.
2.1.2 Equivalent degree-days for hot water heating
The RETScreen CHP model allows the user to include domestic hot water as part of the energy needs met by the heating system. The domestic hot water demand is assumed constant throughout the year and is expressed by the user as a fraction d of the annual heating use (excluding process heat). Thus if QH is the annual heating use excluding process heat, QSH the portion of the energy use corresponding to space heating, and QDHW the portion of the energy use corresponding to domestic hot water heating, one has:
The RETScreen CHP model allows the user to include domestic hot water as part of the energy needs met by the heating system. The domestic hot water demand is assumed constant throughout the year and is expressed by the user as a fraction d of the annual heating use (excluding process heat). Thus if QH is the annual heating use excluding process heat, QSH the portion of the energy use corresponding to space heating, and QDHW the portion of the energy use corresponding to domestic hot water heating, one has:
and therefore:
Since the space heating needs is roughly proportional to the number of heating degree-days, the model defines an equivalent number of heating degree-days corresponding to the domestic hot water demand. If HDD is the number of degree-days for heating from equation (3), the equivalent degree-days for domestic hot water demand HDDDHW follows the same relationship as equation (6):
The equivalent heating degree-days is often expressed as their average daily value by dividing equation (7) by the number of days in a year. This leads to a value hddDHW which is expressed in heating degree-days per day:
The use of hddDHW in establishing a heating load duration curve for the chosen location will be shown in section 2.1.4. It should be noted that the model takes into account domestic hot water demand in a rather coarse way. For example the model assumes that the domestic hot water demand is the same for every day of the year. This may be a reasonable approximation for a large district energy system, but may be inappropriate for, say, a school where there will be no domestic hot water load during the night, weekends and holidays. Similarly, the hot water load varies over the course of the year, both because input water is colder during the winter months and because hot water consumption may be reduced during the summer months. The DHW load can be as much as 30 to 50% more in the winter compared to the summer. This is not modeled in the RETScreen CHP model.
2.1.3 Calculation of peak heating load
The peak load for space heating usually occurs under very cold conditions, although it depends not only on outside weather conditions (temperature, wind, etc) but also on other parameters such as the thermal mass of the building and the infiltration rate.
In the RETScreen CHP Project Model, the peak heating load for a building (or a cluster of buildings with identical thermal properties) is a value pSH,j expressed in Watts per square metre of heated floor area. This value is entered by the user and depends on the heating design temperature for the specific location (see section 2.1.1) and on the building design (insulation, ventilation, etc.). Typical values are given in section 2.6.1. The total peak heat load PSH,j for the jth cluster of buildings is calculated as:
The peak load for space heating usually occurs under very cold conditions, although it depends not only on outside weather conditions (temperature, wind, etc) but also on other parameters such as the thermal mass of the building and the infiltration rate.
In the RETScreen CHP Project Model, the peak heating load for a building (or a cluster of buildings with identical thermal properties) is a value pSH,j expressed in Watts per square metre of heated floor area. This value is entered by the user and depends on the heating design temperature for the specific location (see section 2.1.1) and on the building design (insulation, ventilation, etc.). Typical values are given in section 2.6.1. The total peak heat load PSH,j for the jth cluster of buildings is calculated as:
where Aj is the total heated area of the jth cluster of buildings. The total peak heating load PSH seen by the heating system is:
where the summation is done on all clusters. Up to 14 different building clusters can be specified by the user.
2.1.4 Heating load duration curve
The peak heating load occurs only for a limited time of the year – usually during short and very cold spells. For the majority of the year, depending upon climatic conditions, the heating load of the system is only a fraction of the peak heating load. A heating load duration curve is used to describe how heating loads vary over the year and it is explained in this section. The heating load duration curve will be used to calculate the heating use for the system, as will be seen in section 2.1.5.
The heating load duration curve shows the cumulative duration for different loads in the system over a full year. An example of a heating load duration curve is shown in Figure 4. The load for a district heating system (excluding any process load, which will be treated in section 2.1.6) consists of three main contributions, namely: distribution losses, domestic hot water and building heating load. Distribution losses correspond to loss of heat from the buried pipes to their environment and stay fairly constant over the year (slightly higher in the winter as the supply and return temperatures are higher and the ground temperature is lower). The domestic hot water load is also fairly constant over the year, with a reduction during the night and during summer months (see section 2.1.2). Finally, the building heating load is the dominating load for most of the year and follows the seasonal variations of the climate.
The peak heating load occurs only for a limited time of the year – usually during short and very cold spells. For the majority of the year, depending upon climatic conditions, the heating load of the system is only a fraction of the peak heating load. A heating load duration curve is used to describe how heating loads vary over the year and it is explained in this section. The heating load duration curve will be used to calculate the heating use for the system, as will be seen in section 2.1.5.
The heating load duration curve shows the cumulative duration for different loads in the system over a full year. An example of a heating load duration curve is shown in Figure 4. The load for a district heating system (excluding any process load, which will be treated in section 2.1.6) consists of three main contributions, namely: distribution losses, domestic hot water and building heating load. Distribution losses correspond to loss of heat from the buried pipes to their environment and stay fairly constant over the year (slightly higher in the winter as the supply and return temperatures are higher and the ground temperature is lower). The domestic hot water load is also fairly constant over the year, with a reduction during the night and during summer months (see section 2.1.2). Finally, the building heating load is the dominating load for most of the year and follows the seasonal variations of the climate.
Figure 4: Example of Heating Load Duration Curve for Stockholm, Sweden
In principle the heating load duration curve should be derived from hourly loads to show all possible variations to the system. However, this information is rarely available for a system in the design or feasibility stage. For that reason, a method has been developed to derive the load duration curve from monthly degree-days. The data used to develop the method is taken from very detailed studies of a relatively large system in Uppsala, Sweden (Larsson, 2003). It includes empirical monthly factors that represent the influence of solar gains, wind, and occupants’ habits on the energy requirements of the building.
The algorithm is described below and is illustrated on an example that of a heating system for Stockholm, Sweden. The heating design temperature (see note 7) is –19.4°C; heating degree-days can be obtained from RETScreen’s Climate Database and are given in Table 1. The domestic hot water demand is equal to 19% of the annual heating energy use (excluding process heating). According to Table 1 the annual heating degree-days for space heating only is equal to 4128.8; equation (8) enables to calculate the equivalent number of degree-days per day for domestic hot water heating; the value is 2.65 ºC•d/d.
The algorithm is described below and is illustrated on an example that of a heating system for Stockholm, Sweden. The heating design temperature (see note 7) is –19.4°C; heating degree-days can be obtained from RETScreen’s Climate Database and are given in Table 1. The domestic hot water demand is equal to 19% of the annual heating energy use (excluding process heating). According to Table 1 the annual heating degree-days for space heating only is equal to 4128.8; equation (8) enables to calculate the equivalent number of degree-days per day for domestic hot water heating; the value is 2.65 ºC•d/d.
Table 1: Heating Degree-Days for Stockholm, Sweden
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The fourteen points (Ci, Di) define the heating load duration curve expressed as a percentage of the peak heating load. The calculation of coefficients Di for the example is shown in Table 3 and the resulting load duration curve is shown in Figure 5.
Table 2: Empirical Factors for Fi Heating
Table 3: Example of Coefficient Calculation
Figure 5: Example of Heating Load Duration Curve
2.1.5 Monthly average load and peak load period
Monthly average heating load
The area under the curve in Figure 5, when multiplied by the peak heating load calculated in section 2.1.3, represents the heating energy use of the system over the whole year. Since the points on the curve of Figure 5 represent individual months, sorted by decreasing degree-days per day, it is possible to calculate the monthly heating use from this curve. Continuing with the example from the previous section, a sample calculation is shown in Figure 6 for the point (C8, D8); the shaded area multiplied by the peak load is equal to the energy use for that month. Referring to Table 3 and Table 1, one observes that the month represented by the point (C8, D8) is the month of November.
The same procedure can be applied for all months. A trapezoidal rule could be used to calculate the shaded area in Figure 6. Using this method, the peak heating load is related to the month with the highest number of degree-days. Moreover, the duration of that peak heating load is dependant on that month. This leads to a variable peak load duration and is not reliable. However, rather than calculate the monthly use directly this way, an approximation of the monthly average heating load, which is valid for most months, is to assume that the average heating load for the month is Di multiply by the peak heating load, or:
Monthly average heating load
The area under the curve in Figure 5, when multiplied by the peak heating load calculated in section 2.1.3, represents the heating energy use of the system over the whole year. Since the points on the curve of Figure 5 represent individual months, sorted by decreasing degree-days per day, it is possible to calculate the monthly heating use from this curve. Continuing with the example from the previous section, a sample calculation is shown in Figure 6 for the point (C8, D8); the shaded area multiplied by the peak load is equal to the energy use for that month. Referring to Table 3 and Table 1, one observes that the month represented by the point (C8, D8) is the month of November.
The same procedure can be applied for all months. A trapezoidal rule could be used to calculate the shaded area in Figure 6. Using this method, the peak heating load is related to the month with the highest number of degree-days. Moreover, the duration of that peak heating load is dependant on that month. This leads to a variable peak load duration and is not reliable. However, rather than calculate the monthly use directly this way, an approximation of the monthly average heating load, which is valid for most months, is to assume that the average heating load for the month is Di multiply by the peak heating load, or:
where 
SH,i is the average monthly space heating load (including domestic hot water for month i), Di is the fraction of peak load from section 2.1.4, and PSH is the peak space heating load (including domestic hot water) calculated in section 2.1.3.
The only month for which this approximation is not valid is the month corresponding to (C12, D12), the month in the leftmost part of Figure 6, since the heating load exhibits a very large peak for that month. One could modify equation (15) to include the peak in the calculation of the average load for that month; however due to the limitations listed above, another method is preferred, one which treats the peak separately, as will now be explained.
The only month for which this approximation is not valid is the month corresponding to (C12, D12), the month in the leftmost part of Figure 6, since the heating load exhibits a very large peak for that month. One could modify equation (15) to include the peak in the calculation of the average load for that month; however due to the limitations listed above, another method is preferred, one which treats the peak separately, as will now be explained.
Figure 6: Example of Monthly Heating Energy Use Calculation
Peak heating load period
As mentioned, the method described in section 2.1.4 calculates the duration of the peak period as a function of the number of days in the month with the highest number of heating degree-days per day. However, in CHP systems the occurrence of the peak period can be highly variable. Depending on heating, cooling and power needs, it can happen in any month and have variable duration. For this reason an additional, fictitious ‘peak period’ is added to the calculation (this peak period is hidden from the user and is used for calculations only; it does not appear in the results of the workbook.) Tests have shown that a reasonable duration for the peak period is somewhere between 140 and 150 hours.
Of course, a side effect of this additional peak period is to make the year slightly longer which then needs to be corrected. The simplest method is to reduce the apparent length of each individual month. In RETScreen, the length of each month is reduced by 12 hours, except for February which, being a shorter month, is reduced by only 11 hours. The length of the peak period is thus set to 143 hours (11 months × 12 hours plus one month × 11 hours) so that the total number of hours in the year remains equal to 8,760. The monthly load curve, derived using the method described in section 2.1.5, and the additional peak period, are shown in Figure 5. The corrected number of hours n'i in each month and in the peak period are summarised in Table 4.
As mentioned, the method described in section 2.1.4 calculates the duration of the peak period as a function of the number of days in the month with the highest number of heating degree-days per day. However, in CHP systems the occurrence of the peak period can be highly variable. Depending on heating, cooling and power needs, it can happen in any month and have variable duration. For this reason an additional, fictitious ‘peak period’ is added to the calculation (this peak period is hidden from the user and is used for calculations only; it does not appear in the results of the workbook.) Tests have shown that a reasonable duration for the peak period is somewhere between 140 and 150 hours.
Of course, a side effect of this additional peak period is to make the year slightly longer which then needs to be corrected. The simplest method is to reduce the apparent length of each individual month. In RETScreen, the length of each month is reduced by 12 hours, except for February which, being a shorter month, is reduced by only 11 hours. The length of the peak period is thus set to 143 hours (11 months × 12 hours plus one month × 11 hours) so that the total number of hours in the year remains equal to 8,760. The monthly load curve, derived using the method described in section 2.1.5, and the additional peak period, are shown in Figure 5. The corrected number of hours n'i in each month and in the peak period are summarised in Table 4.
Table 4: Corrected Number of Hours in Each Month and in the Peak Period
Total energy needs
It is now possible to proceed with the calculation of the total space heating needs (including domestic hot water heating) QSH. It is simply the area under the curve in Figure 7, or:
It is now possible to proceed with the calculation of the total space heating needs (including domestic hot water heating) QSH. It is simply the area under the curve in Figure 7, or:
where PSH is the peak space heating load, SH,i is the net monthly average space heating load (including domestic hot water heating) as per equation (15), n'i is the corrected number of hours per month as per Table 4 and n'13 is the number of hours of the peak period (143).
This completes the estimation of space and domestic hot water heating load and use for the system: peak heating load is defined by equation (10), monthly average heating loads are defined by the method exposed in section 2.1.5, equation (15), and yearly heating use is calculated by equation (16). Process heating is weather independent, and is therefore treated separately.
This completes the estimation of space and domestic hot water heating load and use for the system: peak heating load is defined by equation (10), monthly average heating loads are defined by the method exposed in section 2.1.5, equation (15), and yearly heating use is calculated by equation (16). Process heating is weather independent, and is therefore treated separately.
Figure 7: Average Monthly Heating Loads and Additional Peak Period
2.1.6 Process heat
So far the calculations have dealt only with space heating and domestic hot water heating (through the equivalent degree-days). It is now time to consider process loads as well.
Process heating loads are entered by the user through one of two methods, “standard” or “detailed.” In the standard method the user enters the equivalent full load duration hours for the process. In the second method, the user inputs the percentage of time, for each month, that process load is operating. In both cases, the user also specifies the peak process heating load.
The process heating peak load is assumed to occur during the same period of time as the space heating peak load. This may or may not be the case in practice, but this assumption in RETScreen represents a ‘worst case’ scenario for which the system is designed. The process heating peak load is therefore simply added to the space heating peak load calculated through equation (10):
So far the calculations have dealt only with space heating and domestic hot water heating (through the equivalent degree-days). It is now time to consider process loads as well.
Process heating loads are entered by the user through one of two methods, “standard” or “detailed.” In the standard method the user enters the equivalent full load duration hours for the process. In the second method, the user inputs the percentage of time, for each month, that process load is operating. In both cases, the user also specifies the peak process heating load.
The process heating peak load is assumed to occur during the same period of time as the space heating peak load. This may or may not be the case in practice, but this assumption in RETScreen represents a ‘worst case’ scenario for which the system is designed. The process heating peak load is therefore simply added to the space heating peak load calculated through equation (10):
where PH is the total peak heating load, PSH is the peak heating load for space heating and domestic hot water heating from equation (10), and PPH is the peak process heating load entered by the user.
In the “standard” method, the process heating load is equal to the peak load PPH during the peak period defined in section 2.1.5, and is set to a constant valuePH during all months of the year so that the total annual heating use is equal to the peak load times the equivalent full load duration hours specified by the user. When the “detailed” method is used, the user inputs of the equivalent percentage of time per month that process load is operating at full load. The monthly average load PH,i is calculated as:
In the “standard” method, the process heating load is equal to the peak load PPH during the peak period defined in section 2.1.5, and is set to a constant value
where ei is the equivalent percentage of time in month i that the process load is operating at full load.
The peak process heating load PPH and the monthly average process loadsPH or PH,i are then added to their space-heating (and domestic hot water heating) equivalents in equation (16) to calculate the total annual energy use for heating, QH.
The peak process heating load PPH and the monthly average process loads
2.1.7 Equivalent full load hours
Equivalent full load hours E flh can be described as the amount of hours a system designed exactly for the peak heating load would operate at full load during one year. It is simply calculated as:
Equivalent full load hours E flh can be described as the amount of hours a system designed exactly for the peak heating load would operate at full load during one year. It is simply calculated as:
with QH the total annual energy use, given by equation (1), and PH total peak load given by equation (17).
2.1.8 Energy efficiency measures
When energy efficiency measures are considered, they simply reduce both the load and the energy use by the percentage specified by the user.
When energy efficiency measures are considered, they simply reduce both the load and the energy use by the percentage specified by the user.
7. Note that this value is colder than the design temperature in the RETScreen climate database, which is -14.4 °C. The -19.4 °C value corresponds to a more conservative design.
