La época colonial: la ciudad articulada en torno a la plaza mayor

Average temperature measurement is the simplest metric for comparing delivered service demand. Within domestic building energy research, average indoor temperature has been used as a proxy for thermal comfort (Shrubsole et al. 2015).

Although average temperature is most easily calculated when including an entire modelled period, the time in which average temperature is calculated can significantly affect results. Beizaee (2015) made comparisons of heating control strategies over an extended time period (a 56 day trial), using a temperature metric for the whole house which comprised a floor area weighted average daily air temperature. A conventional heating control strategy was found to deliver a higher average temperature than a zonal heating control approach; average temperature measurement for conventional control was consistently approximately 0.5 °C higher than for zonal control. However, further comparison was undertaken using an eight week average of indoor temperature for each room of the house based only on time when the heating is on, and when the rooms are ‘occupied’; for this metric, average temperature was found not to have been affected by the heating control approach. This study demonstrates the importance of measuring thermal comfort delivery when it is required and not throughout the whole day.

In this work, average temperature will be calculated for both an overall average temperature (for a full 24 hour period, 𝑇_24ℎ𝑟) and an average temperature during occupied periods only, 𝑇_𝑜𝑐𝑐 for comparison. The overall average temperature of room j, 𝑇_{24ℎ𝑟,𝑗}, will be calculated using a simple mean calculation as in (6-1) where 𝑇_{𝑖𝑛𝑡,𝑗} is the internal

temperature of room j, 𝑡_𝑠𝑖𝑚 is the total length of the simulation, and 𝛿𝑡 is the length of each time step (such that 𝑛𝛿𝑡 is the total number of time steps in the simulation).

𝑇_{24ℎ𝑟,𝑗} = 1 𝑛_𝛿𝑡 ∑ 𝑇𝑖𝑛𝑡,𝑗,𝑡 24 ℎ𝑟 𝑡=0 where 𝑛_𝛿𝑡=𝑡𝑠𝑖𝑚 𝛿𝑡 (6-1)

Average temperature of room j when occupied, 𝑇_{𝑜𝑐𝑐,𝑗}, is calculated using the demand temperature profile as in (6-2)4

𝑇_{𝑜𝑐𝑐,𝑗}=∑ { 𝑇𝑖𝑛𝑡,𝑗 | 𝑇𝑑𝑒𝑚,𝑗 ≥ 𝑇𝑠𝑒𝑡,𝑚𝑖𝑛,𝑗 } {𝑛𝛿𝑡 | 𝑇𝑑𝑒𝑚,𝑗 ≥ 𝑇𝑠𝑒𝑡,𝑚𝑖𝑛,𝑗 }

(6-2)

Where 𝑇_{𝑠𝑒𝑡,𝑚𝑖𝑛,𝑗} is 20 °C for the living room and 18 °C for the bedroom.

6.2.2

Averaged daily temperature profile

Temperature profile is a line graph of modelled temperature as compared to the demanded temperature profile. The profile gives a clear visual comparison of how technologies are delivering HTC compared to the demanded level of service. The benefit of a temperature profile was demonstrated by Beizaee et al. (2015) in their comparison of conventional heating control and zonal heating control strategies. Interpretation of results from a temperature profile of a single day showed that although conventional control delivered higher temperatures throughout most of the day, the delivered temperatures were similar for each control strategy during occupied periods, and therefore the delivery of thermal comfort was found not to have been compromised. A temperature profile clearly shows how well the house heating system can respond to changes in demand; where time lags exists (additional time taken to reach the set-point temperature) and where overshoots exist (heating beyond demand either in temperature (higher temperature than required) or time (heating on longer than required)).

The daily temperature profile is produced from the calculated internal temperature in each zone or air node of the model for each time step in the model. The internal temperature profile will vary throughout the day and the daily pattern will vary over the whole modelled period due to the changing external temperature. For the choice of a type of temperature profile with which to compare EEMs, two options are shown in Figure 6-1; (a) shows an extended modelled period, (here 10 days of the full 30 day period are displayed) and (b) shows a single day period made up of a temperature average over every time step

within the day. The former option presents lack of clarity when differentiating between different plot lines, especially if it is desired to display a whole modelled period (for example 30 days instead of 10). By averaging temperatures over an extended time period at each time step, an aggregate averaged daily profile can be used to represent the variation of delivered internal temperature between EEMs and allows for greater resolution for the comparison of many EEM scenarios. However, this is achieved at the expense of some loss of detail of thermal comfort satisfaction variation for different days within the modelled period.

Figure 6-1 Comparison temperature profile plots showing (a) extended time period, (b) time averaged day

6.2.3

Temperature shortfall stack

A development upon the temperature profile is named in this work as the ‘temperature shortfall stack’ which is a quantification of the extent to which delivered indoor temperature does not meet the temperature demand. Within the temperature shortfall stack, the time for which a room is below the demand temperature is summed for each integer degree of temperature ‘shortfall’. The stack displays the total hours that the temperature has a shortfall of 1 °C, 2 °C, 3 °C etc., plotted as bars of increasing darkness of colour and showing visually the scale of temperature dissatisfaction for each energy efficiency scenario. A temperature shortfall stack allows technologies to be compared visually based on how well they satisfy the temperature demand and the level of temperature shortfall over an extended period of time.

The calculation of each data bar of hours per average day, ℎ_{𝑠𝑓,𝑖𝑗} for a shortfall of 𝑖 °𝐶 in room 𝑗 is given in (6-3) 5_{, where the bracket notation dictates the occurrence or not of the} internal temperature being below the demand temperature, 𝑛_𝑑 are the number of days in the modelled period, 𝑇𝑑𝑒𝑚,𝑗,𝑘 is the temperature demand in room 𝑗 at time-step 𝑘, 𝑇𝑖𝑛𝑡,𝑗,𝑘 is the modelled internal temperature in room 𝑗 at time-step 𝑘, and 𝛿𝑡 is the length of time-step used in the simulation.

ℎ_{𝑠𝑓,𝑖𝑗} = 1

𝑛_𝑑( ∑ [ 𝑖 ≤ (𝑇𝑑𝑒𝑚,𝑗,𝑘− 𝑇𝑖𝑛𝑡,𝑗,𝑘 ) < (𝑖 + 1) ] 𝑘=𝒕𝒆𝒏𝒅

𝑘=𝒕𝒔𝒕𝒂𝒓𝒕

) × 𝛿𝑡 _(6-3)5

6.2.4

Heating comfort gap

Further developing upon the temperature profile and temperature shortfall stack, the heating comfort gap (HCG) is a single metric with which the temperature shortfall can be measured. The HCG is a relatively novel measurement for the extent to which a desired temperature profile has been delivered and is similar to the Weighted Discomfort Time described in Annex F of EN 15251 (European Standard 2006) which, at the time of writing this chapter, has only been found to have been previously used in literature three times (Penna et al. 2014; Atzeri et al. 2014; Carlucci et al. 2014). The HCG is based on the modelled temperature profile compared to the desired temperature profile and is derived

from the method for the calculation of degree-days (as described in Box 2-3, representing both the scale of the shortfall and the length of time for which temperature demand is not met. The HCG metric is an integration of the area between the calculated temperature profile and temperature demand profile, for the time when the temperature is below the demand temperature, over an extended period, as illustrated in Figure 6-2, and calculated by equation (6-4). 𝐻𝐶𝐺𝑗= ∑ ∫ ( 𝑇𝑑𝑒𝑚,𝑗𝑘− 𝑇𝑖𝑛𝑡,𝑗 | 𝑇𝑑𝑒𝑚,𝑗𝑘> 𝑇𝑖𝑛𝑡,𝑗 ) 𝑑𝑡 𝑡𝑒𝑛𝑑,𝑘 𝑡𝑠𝑡𝑎𝑟𝑡,𝑘 𝑛 𝑘=1 (6-4)

where 𝑡_{𝑠𝑡𝑎𝑟𝑡,𝑘} and 𝑡_{𝑒𝑛𝑑,𝑘} mark the start and end of the occupied period 𝑘 out of 𝑛 occupied periods in total, 𝑇_{𝑑𝑒𝑚,𝑗} is the demanded temperature of room 𝑗 during occupied period 𝑘 and 𝑇_{𝑖𝑛𝑡,𝑗} is the internal temperature calculated by the model for each time step. The result is a single value for each investigated technology for the period of consideration. The accuracy of the HCG metric depends on the accuracy with which the internal temperature profile is modelled and is sensitive to the value of demand temperature which is used.

Energy efficiency technologies and measures