# 5 APPENDIX B – WATER HEATING CALCULATION METHOD

B1. Purpose and Scope

This appendix documents the methods and assumptions used for calculating the hourly energy use for residential water heating systems for both the proposed design and the standard design. The hourly fuel and electricity energy use for water heating will be combined with hourly space heating and cooling energy use to come up with the hourly total fuel and electricity energy use to be factored by the hourly TDV energy multiplier. The calculation procedure applies to low-rise single family, low-rise multi-family, and high-rise residential.

When buildings have multiple water heaters, the hourly total water heating energy use is the hourly water heating energy use summed over all water heating systems, all water heaters, and all dwelling units being modeled.

The following diagrams illustrate the domestic hot water (DHW) system types recognized by the compliance software.

1 | One distribution system with one or multiple water heaters serving a single dwelling unit. The system might include recirculation loops within the dwelling unit. |
2 | Two water heaters with independent distribution systems serving a single dwelling unit. One or more of the distribution systems may include a recirculation loop within the dwelling unit. |
3 | One distribution system without recirculation loop and with one or multiple water heaters serving multiple dwelling units. |
4 | One distribution system with one or multiple recirculation loops and with one or multiple water heaters serving multiple dwelling units. |

B2. Water Heating Systems

Water heating distribution systems may serve more than one dwelling unit and may have more than one water heating appliance. The energy used by a water heating system is calculated as the sum of the energy used by each individual water heater in the system. Energy used for the whole building is calculated as the sum of the energy used by each of the water heating systems. To delineate different water heating elements several indices are used.

i Used to describe an individual dwelling unit. For instance, CFAi would be the conditioned floor area of the ith dwelling unit. Nunit is the total number of dwelling units.

j Used to refer to the number of water heaters in a system. NWH is the total number of water heaters.

k Used to refer to a water heating system or distribution system. A building can have more than one system and each system can have more than one water heater.

l Used to refer to the lth unfired- or indirectly-fired storage tank in the kth system. NLk is the total number of unfired- or indirectly-fired storage tanks in the kth system. Temperature buffering tanks with electric heating (e.g., minitanks) shall not to be treated as unfired or indirectly-fired storage tanks.

Symbol | Definition | Notes
CFA | Conditioned floor area, ft2 |
NFloor | Number of floors in building |
Nunit | Number of units in building |
NK | Number of water heating systems |
NWHk | Number of water heaters in kth system |
NLoopk | Number of recirculation loops in kth system (multi- unit dwellings only) |
CFAi | Conditioned floor area of ith dwelling unit |
CFAUk | Average unit conditioned floor area served by kth system, ft2 |

B3. Hot Water Consumption

The schedule of hot water use that drives energy calculations is derived from measured data as described in (Kruis, 2016). That analysis produced 365 day sets of fixture water draw events for dwelling units having a range of number of bedrooms. The draws are defined in the files DHWDUSF.TXT (for single family) and DHWDUMF.TXT (for multifamily) that ship with CBECC- Res. Each draw is characterized by a start time, duration, flow rate, and end use. The flow rates given are the total flow at the point of use (fixture or appliance). This detailed representation allows derivation of draw patterns at 1 minute intervals as is required for realistic simulation of heat pump water heaters.

The fixture flow events are converted to water heater (hot water) draws by 1) accounting for mixing at the point of use and 2) accounting for waste, distribution heat losses, and solar savings --

VS k = VF k × f hot × f wh

Equation 1

Where

VS k = Hot water draw at the kth water heating system’s delivery point (gal)

VF k = Mixed water draw at an appliance or fixture (gal) served by the kth water heating system, as specified by input schedule

f hot, f wh = End-use-specific factors from the following –

End use | fhot | fwh
Shower | 105 − Tinlet Ts − T inlet | WF k × max(0, DLM k − SSF k )
Bath
Faucet | 0.50 | 1 − SSF k
Clothes washer | 0.22
Dish washer | 1

Ts = Hot water supply temperature (ºF). Assumed to be 115 °F. Tinlet = Cold water inlet temperature (ºF) as defined in Section B3.3. WFk = Hot water waste factor.

• WFk = 0.9 for within-dwelling-unit pumped circulation systems (see Table B-1).

• WFk = 1.0 otherwise

DLMk = Distribution loss multiplier (unitless), see Equation 5.

SSFk = Hourly solar savings fraction (unitless) for the kth water heating system, which is the fraction of the total water heating load that is provided by solar hot water heating.

The annual average value for SSF is provided from the results generated by the CEC approved calculations approaches for the OG-100 and OG-300 test procedure. A CEC approved method shall be used to convert the annual average value for SSF to hourly SSFk values for use in compliance calculations.

The individual water heater draws are combined to derive the overall demand for hot water.

For each hour of the simulation, all water heater draws are allocated to 1 minute bins using each draw’s starting time and duration. This yields a set of 60 VSk,t values for each hour that are used as input to the detailed heat pump water heating model (HPWH) as discussed in section B7.7. For

hourly efficiency-based models used for some water heater types, the minute-by-minute values are summed to give an hourly hot water requirement --

60

GPH k = ∑VS k ,t

t =1

Equation 2

In cases where multiple dwelling units are served by a common water heating system, the dwelling unit draws are summed.

In cases where there are multiple water heating systems within a dwelling unit, the draws are divided equally among the systems. For minute-by-minute draws (for HPWH models), this allocation is accomplished by assigning draws to systems in rotation within each end use. This ensures that some peak draw events get assigned to each system. Since heat pump water heater performance is non-linear with load (due to activation of resistance backup), allocation of entire events to systems is essential. Note that realistic assignment of draws to specific systems requires information about the plumbing layout of the residence and capturing that is deemed to impose an unacceptable user input burden.

B4. Hourly Adjusted Recovery Load

The hourly adjusted recovery load for the kth water heating system is calculated as follows:

NL k

HARL k = HSEU k + HRDL k +∑HJ L l

1

Equation 3

where

HSEUk = Hourly standard end use at all use points (Btu), see Equation 4.

HRDLk = Hourly recirculation distribution loss (Btu), see Equation 11. HDRLk is non-zero only for multi-family central water heating systems.

NLk = Number of unfired or indirectly-fired storage tanks in the kth system

HJLl = Tank surface losses of the lth unfired tank of the kth system (Btu), see Equation 40.

quation 4 calculates the hourly standard end use (HSEU). The heat content of the water delivered at the fixture is the draw volume in gallons (GPH) times the temperature rise ∆T (difference between the cold water inlet temperature and the hot water supply temperature) times the heat required to elevate a gallon of water 1 ºF (the 8.345 constant).

HSEU k = 8.345 × GPH k × (T s − T inlet )

Equation 4

where

HSEUk = Hourly standard end use (Btu).

GPHk = Hourly hot water consumption (gallons) from Equation 2

Equation 5 calculates the distribution loss multiplier (DLM) which combines two terms: the standard distribution loss multiplier (SDLM), which depends on the floor area of the dwelling unit and the distribution system multiplier (DSM) listed in Table B-1.

DLM k = 1 + (SDLM k − 1)× DSM k | Equation 5

where

DLMk = Distribution loss multiplier (unitless)

SDLMk = Standard distribution loss multiplier (unitless), see Equation 6. DSMk = Distribution system multiplier (unitless), see Section 3.2.

Several relationships below depend on CFAk, the floor area served

Equation 6 calculates the standard distribution loss multiplier (SDLM) based on dwelling unit floor area. Note that in Equation 6, that floor area is capped at 2500 ft2 -- without that limit, Equation 6 produces unrealistic SDLMk values for large floor areas.

SDLM k = 1.004 − 0.0000000231× min (2500, CFAU k ) × min (2500, CFAU k ) | Equation 6

where

SDLMk= Standard distribution loss multiplier (unitless).

CFAUk= Dwelling unit conditioned floor area (ft2) served by the kth system, calculated using methods specified in Equation 7.

Single dwelling unit, CFAU k = CFA / NK For multiple dwelling units served by a central system: ∑all units s erved by s y st em k C FA i CFAU k = Nunit k Alternatively, if the system-to-unit relationships not known: ∑all units s erved by any central s y st em C FA i CFAU k = Number of units served by any central system | Equation 7 Method WH-CFAU

Note: “Method” designations are invariant tags that facilitate cross-references from comments in implementation code.

When a water heating system has more than one water heater, the total system load is assumed to be shared equally by each water heater, as shown in Equation 8.

HARL = HARL k j NWH k | Equation 8

where

HARLj = Hourly adjusted recovery load for the jth water heater of the kth system (Btu). HARLk Hourly adjusted total recovery load for the kth system (Btu)

NWHk = The number of water heaters in the kth system.

Additional Topics:

5.1 B4.1. Distribution Losses within the Dwelling Unit

5.2 B4.2. Cold Water Inlet Temperature

5.3 B5.1. Hourly Recirculation Loop Pipe Heat Loss Calculation

5.4 B5.2. Hourly Recirculation Branch Pipe Heat Loss Calculation

5.5 B5.3. Recirculation System Plumbing Designs

5.6 B7.1. Small Consumer Gas or Oil Storage Water Heaters

5.7 B7.2. Small consumer Gas or Oil Instantaneous Water Heater

5.8 B7.3. Small consumer Electric Instantaneous Water Heater

5.9 B7.6. Large COMMERCIAL Instantaneous, Indirect Gas, and Hot Water Supply Boilers

5.10 B7.7. Small consumer Storage Electric or Heat Pump Water Heaters

5.11 B7.8. Jacket Loss

5.12 B7.9. Electricity Use for Circulation Pumping

5.13 B7.10. Conversion between Energy Factor and Uniform Energy Factor