whereEnergy use for small electric water heaters is calculated as described in the HPWHsim Project Report (Ecotope, 2015 and 2016). The HPWH model uses a detailed, physically based, multi-node model that operates on a one-minute time step implemented using a suitable loop at the time-step level within CSE. Tank heat losses and heat pump source temperatures are linked to the CSE zone heat balance as appropriate. Thus, for example, the modeled air temperature of a garage containing a heat pump water heater will reflect the heat extracted.
HPWH can model three classes of equipment:
•Specific air-source heat pump water heaters identified by manufacturer and model. These units have been tested by Ecotope and measured parameters are built into the HPWH code.
•Generic air-source heat pump water heaters, characterized by EF and tank volume. This approach provides compliance flexibility. The performance characteristics of the generic model are tuned to use somewhat more energy than any specific unit across a realistic range of EF values.
•Electric resistance water heaters, characterized by EF, tank volume, and resistance element power.
Several issues arise from integration of a detailed, short time step model into an hourly framework. HPWH is driven by water draw quantities, not energy requirements. Thus to approximate central system distribution and unfired tank losses, fictitious draws are added to the scheduled water uses, as follows:
|
NLk HRDLk +∑HJLl VSk ,t + 1 60 × 8.345 ×(ts − tinlet ) Vj,t = NWH k |
Equation 39 |
where
Vj,t = Hot water draw (gal) on jth water heater for minute t.
Another issue is that the HPWH hot water output temperature varies based on factors like control hysteresis and tank mixing. For compliance applications, it is required that all system alternatives deliver the same energy. To address this, the HPWH tank setup point is modeled at 125 °F and delivered water is tempered to ts. If the HPWH output temperature is above ts,it is assumed that inlet water is mixed with it (thus reducing Vi,t). If the output temperature is below ts, sufficient electrical resistance heating is supplied to bring the temperature up to ts (preventing under capacity from being exploited as a compliance advantage).