Manual of Method for Calculating Primary Energy Consumptions under 2016 Building Energy Code (Non-residential Buildings)

National Institute for Land and Infrastructure Management (NILIM), Ministry of Land, Infrastructure and Building Research Institute (BRI), Transport and Tourism, National Research and Development Agency

5. Evaluation Method of Hot-water Supply Systems

This chapter shows the logic for calculating primary energy consumptions of hot-water supply systems.

5.1 Introduction

5.1.1 Scope of Application

The hot-water supply systems that should be evaluated for calculation are defined below.

Dual hot-water supply system
- e.g., circulating hot-water supply in hospital, hotel or other facility, multi circulating water heater that connects instantaneous water heaters
Single hot-water supply system
- Central water heater without domestic hot water return pipe
- Local hot-water supply system with a pair of heat source equipment and hot-water tap, such as washhand water heater in toilet

The following hot-water supply systems are not evaluated.

Individual tea dispenser and automatic dispenser that are placed in offices or waiting rooms
Hot-water supply system without hot-water tap (No. 7 water heater etc.)
Hot-water supply system for use of non-potable water (for washing machine)
Hot-water supply system for circulating heating (heating system for public bath or heated pool) However, hot-water supply systems for showers or washbasins are evaluated, even if they are installed in the public bath or heated pool.

5.1.2 Definition of Terms

Accumulated daily hot-water supply load
This is the sum of amounts of heat produced daily by a hot-water supply system. It is equal to the amounts of heat that is required by a room receiving hot water from the supply system. Its unit is kJ/day.
Accumulated daily pipe heat loss
This is the sum of amounts of heat lost by a pipe of a hot-water supply system. Its unit is kJ/day.
Number of hot-water supply systems
This is the number of hot-water supply systems that are installed in a subject building
Hot-water temperature
This is a temperature of hot water from a faucet. Its unit is ℃.
Daily mean feed-water temperature
This is a temperature of water supplied to a hot-water supply system. Its unit is ℃.
Accumulated daily hot-water supply amount
This is the sum of hot-water amounts that are daily supplied by a hot-water supply system. Its unit is L/day.
Circulating water temperature
This is a temperature that is circulated in a pipe of a hot-water supply system. Its unit is ℃.
Pipe’s perimeter temperature
This is an air temperature around a pipe. Its unit is ℃.
Pipe’s linear heat loss coefficient
This is an index that indicates heat conductivity in a pipe. It is expressed as a heat transfer amount per 1 m of a pipe when a difference between temperatures of its outside and inside is 1K. Its unit is W/(m・K).
Room for hot-water supply
This is a room where there is a person that may use a hot-water supply system.

5.1.3 Common Constants

A common constant that is used in this chapter is shown below.

Table 1. Constant
Constant name	Description	Value	Unit
\(c_\{w}\)	Specific heat of water	4.2	kJ/(kg・K)

5.1.4 Input/Output

The inputs and outputs throughout this chapter are shown in the table below.

Table 2. Input
Variable name	Description	Unit	Input sheet
\(BuildingType\)	Building use	-	Form 5-1: ① Building and room uses
\(RoomType_\{i}\)	Room use of room	-	Form 5-1: ① Building and room uses
\(ClimateZone\)	Climate zone of building to be evaluated	-	Form 0: ⑤ Climate zone under the Building Energy Code
\(D_\{Wp}\)	Pipe connection diameter	mm	Form 5-2: ⑥Connection diameter
\(A_{W,solar,i}\)	Effective collecting area of a solar water heater that is included in a hot-water supply system	m²	Form 5-2: ⑦ Effective collecting area
\(\psi_{Wsolar,drct,i}\)	Azimuth angle of the collecting surface of a solar water heater that is included in a hot-water supply system	°	Form 5-2: ⑧ Azimuth angle of collecting surface
\(\psi_{Wsolar,slp,i}\)	Effective collecting area of a solar water heater that is included in a hot-water supply system	°	Form 5-2: ⑨ Tilt angle of collecting surface
\(I_{DNI,d,t}\)	Direct normal irradiance at date d and time	W/m²	2.2.1
\(I_{DHI,d,t}\)	Horizontal sky solar radiation at time t of date	W/m²	2.2.1
\(\psi_\{lati}\)	Latitude	°	2.2.1
\(\psi_\{longi}\)	Longitude	°	2.2.1
\(A_\{r}\)	Area of room r for hot-water supply	m²	Form 5-1: ① Room area
\(Q_{W,i,r}\)	Rated heating capacity of a hot-water supply system that feeds hot water to a room r for hot-water supply	kW	Form 5-2: ③ Rated heating capacity
\(A_{Wsolar,i}\)	Effective collecting area of a solar water heater that is included in a hot-water supply system	m²	Form 5-2: ⑦ Effective collecting area
\(\eta_{W,i}\)	Operating efficiency of hot-water supply system	-	Form 5-2: ④ Heat source efficiency (converted to primary energy)

Table 3. Output
Variable Name	Description	Unit
\(E_\{HW}\)	Design primary energy consumption of hot-water supply system	MJ/year

5.2 Accumulated Daily Hot-water Consumption

Calculate an accumulated daily hot water consumption for each room for hot-water supply.

Table 4. Input
Variable Name	Description	Unit	Reference
\(Q_{W,i,r}\)	Rated heating capacity of a hot-water supply system that feeds hot water to a room r for hot-water supply	kW	Form 5-2: ③ Rated heating capacity
\(V_{WS0,r,d}\)	This is a standard-based accumulated daily hot water consumption per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	D.1
\(V_{WS1,r,d}\)	This is a standard accumulated daily hot water consumption (for washbasins) per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	D.1
\(V_{WS1,r,d}\)	This is a standard accumulated daily hot water consumption (for washbasins) per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	D.1
\(V_{WS2,r,d}\)	This is a standard accumulated daily hot water consumption (for showers) per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	D.1
\(V_{WS3,r,d}\)	This is a standard accumulated daily hot water consumption (for kitchens) per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	D.1
\(V_{WS4,r,d}\)	This is a standard accumulated daily hot water consumption (for other purpose) per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	D.1
\(A_\{r}\)	Area of room r for hot-water supply	m²	Form 5-1: ① Room area
\(\phi_{Wa,i,r}\)	This is a rate of hot-water consumption reduction by a hot-water saving device (automatic hot-water faucet) for a hot-water supply system that feeds hot water to a room r for hot-water supply.	-	D.3
\(\phi_{Wb,i,r}\)	This is a rate of hot-water consumption reduction by a hot-water saving device (hot-water saving B1) for a hot-water supply system that feeds hot water to a room r for hot-water supply.	-	D.3

Table 5. Output
Variable Name	Description	Unit	References
\(V_{W0,i,d}\)	This is a standard-based accumulated daily hot water amount that is fed by a hot-water supply system at a date d.	L/d	5.3
\(V_{W,i,d}\)	This is an accumulated daily hot water amount that are fed by a hot-water supply system at a date d.	L/d	5.4、5.5、5.6

In order to calculate a standard-based accumulated daily hot water consumption of a hot-water supply system i that feeds hot water to a room r for hot-water supply, \(V_{W0,i,r,d}\), and an accumulated daily hot water consumption, \(V_{W,i,r,d}\), multiply a standard-based accumulated daily hot water consumption per unit area by the rate of hot-water consumption reduction, and then, by a room area, and allocate the multiplied result to these consumptions in proportion with the rated capacity of the system. However, the rate of hot-water consumption reduction by a hot-water saving device does not apply to the standard-based accumulated daily hot water consumption.

\[V_{W0,i,r,d} = V_{WS0,r,d} \times A_\{r} \times \frac{Q_{W,i,r}}{\sum_{i=1}Q_{W,i,r}}\]

\[V_{W,i,r,d} = \{ ( V_{WS1,r,d} \times \phi_{Wa,i,r} + V_{WS2,r,d} \times \phi_{Wb,i,r} + V_{WS3,r,d} + V_{WS4,r,d} ) \times A_\{r} \} \times \frac {Q_{W,i,r}} {\sum_{i=1}Q_{W,i,r}}\]

A standard-based accumulated daily hot water supply amount of a hot-water supply system i that feeds hot water to a room r for hot-water supply, \(V_{W0,i,d}\), and a total daily hot water supply, [V_{W,i,d}] are a total of hot-water consumptions for all of rooms r for hot-water supply.

\[V_{W0,i,d} = \sum_{r=1}V_{W0,i,r,d}\]

\[V_{W,i,d} = \sum_{r=1}V_{W,i,r,d}\]

5.3 Pipe Length

Calculate a length of a hot-water supply pipe. In terms of simplification of review and evaluation, the Building Energy Code prescribes that an actual length of a hot-water supply pipe should be estimated from an accumulated daily hot water consumption without detail input of the length.

Table 6. Input
Variable Name	Description	Unit	Reference
\(V_{W0,i,d}\)	This is a standard-based accumulated daily hot water amount that is fed by a hot-water supply system at a date d.	L/d	5.2

Table 7. Output
Variable Name	Description	Unit	References
\(L_{W,i}\)	Pipe length of hot-water supply system	m	5.4

Table 8. Constant
Constant Name	Description	Unit	Value
\(Ix_\{SW}\)	Standard-based Ix value	-	7

　Calculate a pipe length \(L_{W,i}\) from the following formula.

\[L_{W,i} = \frac{V_{SW,i}}{1000} \times Ix_\{SW}\]

An average in a day when \(V_{W0,i,d}\) is maximized is used as an averaged accumulated daily hot water consumption of a hot-water supply system i, \(V_{SW,i}\)［L/day].

The value of Ix is defined as a value obtained after an overall pipe length is divided by an accumulated daily hot water consumption. Under the old Code, a standard value of CEC/HW was specified. Under the 2013 Building Energy Code, a work to read a pipe length from drawings was omitted in order to simplify applications and reviews. However, as this standard-based Ix value, \(Ix_\{SW}\)|, was defined as 7, a visual pipe length was determined based on a hot-water supply load. Accordingly, it was decided to calculate a heat loss of this pipe length. A standard-based equipment efficiency that is used when a standard primary energy consumption is determined has almost the same level as under the old Code due to that the relevant efficiency is specified from a standard value CEC/HW=1.5 of the old Code in the case of an Ix value of 7.

5.4 Annual Pipe Heat Loss

Calculate an accumulated annual heat loss from a pipe.

Table 9. Input
Variable Name	Description	Unit	Reference
\(V_{W,i,d}\)	This is an accumulated daily hot water amount that are fed by a hot-water supply system at a date d.	L/d	5.2
\(L_{W,i}\)	Pipe length of hot-water supply system	m	5.3
\(\theta_{amb,d}\)	Perimeter temperature of pipe at a date	℃	D.4
\(k_{W,i}\)	Linear heat loss coefficient of pipe of hot-water supply system	W/(m・K)	D.5

Table 10. Output
Variable Name	Description	Unit	References
\(Q_{Wp,i}\)	Annual pipe heat loss of hot-water supply system	kJ/year	5.7

Table 11. Constant
Constant Name	Description	Unit	Value
\(\theta_\{Wp}\)	Circulating water temperature	℃	60
\(T_{W,i,d}\)	Operation time of hot-water supply system i at date	h/d	24

Calculate an annual pipe heat loss [kJ/year] of a hot-water supply system i from the following equation. The day when hot water is not fed by the hot-water supply system i is assumed to be a day without pipe heat loss.

\[Q_{Wp,i} = \sum_{d=1}^{365} Q_{Wp,i,d}\]

\[Q_{Wp,i,d} = \begin\{cases} (L_{W,i} \times k_{W,i} \times (\theta_\{Wp} - \theta_{amb,d}) \times 3600 \times T_{W,i,d}) \times 10^{-3} & ,(V_{W,i,d} > 0) \\ 0 & ,(V_{W,i,d} = 0) \end\{cases}\]

5.5 Amount of Usage of Heat from Solar Heating System

Calculate an amount of usage of heat from a solar heating system.

Table 12. Input
Variable Name	Description	Unit	Reference
\(A_{Wsolar,i}\)	Effective collecting area of a solar water heater that is included in a hot-water supply system	m²	Form 5-2: ⑦ Effective collecting area
\(\theta_{Win,d}\)	Daily average hot water temperature at date	℃	D.6
\(I_{Wds,d}\)	Solar irradiance on heat collecting surface in the relevant region at date	MJ/(m²・d)	D.7
\(V_{W,i,d}\)	This is an accumulated daily hot water amount that are fed by a hot-water supply system at a date d.	L/d	5.2
\(\theta_{AC,oa,d}\)	Daily average outside temperature at date	℃	2.2.3

Table 13. Output
Variable Name	Description	Unit	References
\(Q_{Wsolar,i,d}\)	Hot-water supply system i’ s usage of heat from solar heating system at data	kJ/d	5.6

Table 14. Constant
Constant Name	Description	Unit	Value
\(c_\{Weff}\)	Collector efficiency of solar water heater	-	0.40
\(c_\{Wsolar}\)	Collector efficiency including heat loss in a pipe when a solar water heater is connected to an auxiliary heat source	-	0.85
\(\theta_\{Wtap}\)	Hot-water temperature	℃	43

<<<<Calculate a hot-water supply system’s usage of heat from a solar heating system at a data d as follows.

a) In the case of absence of solar heating system

\[Q_{Wsolar,i,d} = 0\]

b) In the case of presence of solar heating system

b-1) Case of daily average outside temperature of 5℃ or less

\[Q_{Wsolar,i,d} = 0\]

b-2) Case of daily average outside temperature of more than 5℃

Deeming it impossible to cover a whole hot-water supply load, \(c_\{w} \times \rho_\{w} \times (\theta_\{Wtap} - \theta_{Win,d}) \times V_{W,i,d}\), with a hot-water supply system’s usage of heat from a solar heating system, tem:[Q_{Wsolar,i,d}], the upper limit of the usage is assumed to be 90% of the hot-water supply load.

\[Q_{Wsolar,i,d} = \min ( A_\{Wsolar} \times I_{Wds,d} \times c_\{Weff} \times c_\{Wsolar} , 0.9 \times c_\{w} \times \rho_\{w} \times (\theta_\{Wtap} - \theta_{Win,d}) \times V_{W,i,d} )\]

Note: This calculation method is the same as that described in “Explanation of Energy Consumption Calculation Method in the
Criteria of Judgment of Housing Business Builder of the ”Institute for Built Environment and Carbon Neutral for SDGs (IBECs).

5.6 Annual Hot-water Supply Load

Table 15. Input
Variable Name	Description	Unit	Reference
\(V_{W,i,d}\)	This is an accumulated daily hot water amount that are fed by a hot-water supply system at a date d.	L/d	5.2
\(Q_{Wsolar,i,d}\)	Hot-water supply system i’ s usage of heat from solar heating system at data	kJ/d	5.5
\(\theta_{Win,d}\)	Daily average hot water temperature at date	℃	D.6

Table 16. Output
Variable Name	Description	Unit	References
\(Q_{Wr,i}\)	Annual hot-water supply load of hot-water supply system	kJ/year	5.7

Table 17. Constant
Constant Name	Description	Unit	Value
\(\theta_\{Wtap}\)	Hot-water temperature	℃	43

An annual hot-water supply load of a hot-water supply system, \(Q_{Wr,i}\)［kJ/year] is calculated from the following formula.

\[Q_{Wr,i} = \sum_{d=1}^{365}( c_\{w} \times \rho_\{w} \times (\theta_\{Wtap} - \theta_{Win,d}) \times V_{W,i,d} - Q_{Wsolar,i,d})\]

5.7 Design Primary Energy Consumption of Hot-water Supply System

Calculate an annual primary energy consumption of a hot-water supply system, \(E_\{HW}\) [MJ/year].

Table 18. Input
Variable Name	Description	Unit	Reference
\(Q_{Wp,i}\)	Annual pipe heat loss of hot-water supply system	kJ/year	5.4
\(Q_{Wr,i}\)	Annual hot-water supply load of hot-water supply system	kJ/year	5.6
\(\eta_{W,i}\)	Operating efficiency of hot-water supply system i (converted to primary energy)	-	Form 5-2: ④ Heat source efficiency (converted to primary energy)

Table 19. Output
Variable Name	Description	Unit	References
\(E_\{HW}\)	Design primary energy consumption of hot-water supply system	MJ/year	-

Table 20. Constant
Constant Name	Description	Unit	Value
\(C_\{W}\)	Correction coefficient	-	2.5

\[E_\{HW} = \sum_{i=1} ( \frac{ Q_{Wr,i} + C_\{W} \times Q_{Wp,i} }{ \eta_{W,i} } ) \times 10^{-3}\]

\(10^{-3}\) in the formula is a coefficient that converts from [kJ] to [MJ]. The above formula does not explicitly represent a power consumption of a hot-water supply pump, but the effect of the power consumption is included in the correction coefficient.

Assuming that the operating efficiency of the system is an efficiency converted to primary energy, calculate it as follows.

a) In the case of combustion hot-water supply system
　Heat source efficiency of combustion hot-water supply system =
　　　　　Rated heating capacity of single hot-water heat source [kW]× 3600[kJ/kWh] / (Fuel consumption of single hot-water heat source [kJ/h] + Power consumption [kJ/h])

Fuel consumption of single hot-water heat source (gas)[kJ/]h] = Gas consumption [m³/h] × Gas heat generation (high-level)[kJ/m³]
Fuel consumption of single hot-water heat source (oil))[kJ/h] = Oil consumption [L/h] × Density [kg /L] × Oil heat generation (high-level)[kJ/kg]

b) In the case of electric hot-water supply system
　Efficiency of electric hot-water heat source = Rated COP × 3600 / 9760 [kJ/kWh]

Rated COP of electric hot-water heat source = Rated heating capacity of hot-water heat source [kW] / Rated power consumption of hot-water heat source [kW]
When using a heat pump electric water heater, input a value of “high-temperature storage heating (during winter).”

In the case where several water heaters are connected to one hot-water supply system and operated jointly, the heat source efficiencies of these heaters are weighted by a rated heating capacity of each piece of heat source equipment, and averaged, in order to determine the operating efficiency of the system.

Annex D (Hot-water Supply)

D.1 Standard accumulated daily hot water consumption (Standard room use conditions)

A standard accumulated daily hot water consumption is specified according to a room use of a room r for hot-water supply. Standard room use conditions are specified in the following four files. Accordingly, extract a value that corresponds to building room uses of the relevant room.

List of building uses and room uses: https://github.com/WEBPRO-NR/BESJP_Webpro_RouteB/blob/dev/database/ROOM_NAME.csv ROOM_NAME.csv
Reference values such as rate of concurrent use of rooms:
Schedule by time: ROOM_COND.csv
Calendar pattern: CALENDAR.csv

Table 21. Input
Variable Name	Description	Unit	Reference
\(BuildingType\)	Building Use	-	Form 5-1: ① Building and room uses
\(RoomType_\{i}\)	Room use of room	-	Form 5-1: ① Building and room uses

Table 22. Output
Variable Name	Description	Unit	References
\(V_{WS0,r,d}\)	This is a standard-based accumulated daily hot water consumption per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	5.2
\(V_{WS1,r,d}\)	This is a standard accumulated daily hot water consumption (for washbasins) per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	5.2
\(V_{WS2,r,d}\)	This is a standard accumulated daily hot water consumption (for showers) per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	5.2
\(V_{WS3,r,d}\)	This is a standard accumulated daily hot water consumption (for kitchens) per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	5.2
\(V_{WS4,r,d}\)	This is a standard accumulated daily hot water consumption (for other purpose) per unit area of a room r for hot-water supply at a date d.	L/(m²・d)	5.2

The unit of a standard accumulated daily hot water consumption depends on use rooms, and is specified based on one of [L/man-day], [L/floor・day] and [L/m²day]. The unit is described in the column of “Standard-based hot water consumption” in ROOM_SPEC_H28.csv. The unit of [L/man-day] or [L/floor・day] is multiplied by a reference value of occupant density [person/m²] that is designated in the column of “Reference value of heat generated by human body” in ROOM_SPEC_H28.csv and converted to a value per floor area.

<<<< Where, an accumulated daily hot water consumption for the use of “Shower” in “Guest room of hotel etc.” was calculated based on the following assumption.
　　10.5 min/person　×　10 L/min × 0.75 (rate of concurrent use) = 79 L/person

In addition, an accumulated daily hot water consumption for the use of “Shower” in “Patient bedroom of hospital etc.” was calculated based on the following assumption.
　　2.1 min/person × 10 L/min　× 0.90 (rate of concurrent use) = 21 L/ person

10.5 min/person and 2.1 min/person in the above formulas are derived from Water-saving Effects in Public Facilities of Japan that was reported by the Team for Promotion of TAKUMI Style.

From the standard room use conditions, extract the room use condition that is applicable to a room use of a room r for hot-water supply, and use it as a use condition for the room r.

Standard room use conditions are defined for each room use, and there are three "basic schedules (room use patterns 1, 2, and 3)" for each room use, and the basic schedule of each day is defined as the "calendar patterns".

The calendar pattern is specified in "CALENDAR.csv", the calendar pattern used for each room use is specified in "ROOM_SPEC.csv", and the search key required when using the above files is specified in "ROOM_NAME.csv".

Obtain a search key for the database.

Retrieve the search key from ROOM_NAME.csv using the building use \(BuildingType\) and the room use \(RoomType_i\).

Example: If the building use is "Office, etc." and the room use is "Office Room", the search key is "O-1".

Obtain a calendar pattern code (A, B, C, D, E or F).

Obtain a calendar pattern from ROOM_SPEC.csv, using the search key.

Example: If the search key is "O-1," the calendar pattern code is "A".

Obtain a daily calendar pattern (1, 2 or 3).

Obtain the calendar pattern from ROOM_CALENDAR.csv ,using the date d and the calendar code.

Example: If the date d is "January 1st" and the calendar code is "A", the calendar pattern on the date is "3".

Obtain a rate of concurrent use of rooms by time.

Obtain a rate of concurrent use of rooms pattern from ROOM_SPEC.csv, using the search key and the calendar pattern.

Example: If the search key is "O-1" and the calendar pattern is "3,” a rate of concurrent use of rooms at the time of 0 is “0.”

Obtain a rate of concurrent use of rooms by day.

Accumulate a rate of daily concurrent use of rooms by time and obtain an accumulated daily concurrent use rate of rooms.

Example: If the search key is "O-1" and the calendar pattern is "3, an accumulated daily rate of concurrent use of rooms (totalization of T0~T23) is “0.”

Obtain a hot water consumption.

Obtain a hot water consumption from ROOM_SPEC.csv, using the search key.
- A standard-based accumulated daily hot water consumption, \(V_{WS0,r}\), is a value in the row that the search key in the column “Standard-based hot water consumption” matches.
- A hot water consumption (for washbasins), \(V_{WS1,r}\), is a value in the row that the search key in the column “Standard-based hot water consumption (for washbasins)” matches.
- A hot water consumption (for showers), \(V_{WS2,r}\), is a value in the row that the search key in the column “Standard-based hot water consumption (for showers)” matches.
- A hot water consumption (for kitchens), \(V_{WS3,r}\), is a value in the row that the search key in the column “Standard-based hot water consumption (for kitchens)” matches.
- A hot water consumption (for other), tem:[V_{WS4,r}], is a value in the row that the search key in the column “Standard-based hot water consumption (for other)” matches.

Example: If the search key is "O-1,"a standard-based accumulated daily hot water consumption is "3.8".

<<<< If an accumulated daily rate of concurrent use of rooms at a date d in a room r for hot-water supply is more than 0, “the room r at the date d” is judged to be used. On the other hand, if this accumulated daily value is 0, “the room r at the date d” is judged not to be used.
If the room r is judged to be used at the date d, the presence or absence of hot water use at the date d, \(\phi_{WS,r,d}\) is 1, but if the room r is judged not to be used, \(\phi_{WS,r,d}\) is 0.

\[V_{WS0,r,d} = V_{WS0,r} \times \phi_{WS,r,d}\]

\[V_{WS1,r,d} = V_{WS1,r} \times \phi_{WS,r,d}\]

\[V_{WS2,r,d} = V_{WS2,r} \times \phi_{WS,r,d}\]

\[V_{WS3,r,d} = V_{WS3,r} \times \phi_{WS,r,d}\]

\[V_{WS4,r,d} = V_{WS4,r} \times \phi_{WS,r,d}\]

====D.2 Pipe heat insulation specifications

Pipe heat insulation specifications, as shown in the following table, are specified from “pipe diameter” and “thickness of heat insulator.”

Table 23. Pipe heat insulation specifications
Option	Definition (Thickness of heat insulator)
Insulation specifications 1	For a pipe with its diameter of less than 40 mm, the thickness of its heat insulator is 30 mm or more. For a pipe with its diameter of 40 mm or more and less than 125 mm, the thickness of its heat insulator is 40 mm or more. For a pipe with its diameter of 125 mm or more, the thickness of its heat insulator is 50 mm or more.
Insulation specifications 2	For a pipe with its diameter of less than 50 mm, the thickness of its heat insulator is 20 mm or more. For a pipe with its diameter of 50 mm or more and less than 125 mm, the thickness of its heat insulator is 25 mm or more. For a pipe with its diameter of 125 mm or more, the thickness of its heat insulator is 30 mm or more.
Insulation specifications 3	For a pipe with its diameter of less than 125 mm, the thickness of its heat insulator is 20 mm or more. For a pipe with its diameter of 125 mm or more, the thickness of its heat insulator is 25 mm or more.
Bare pipe	Uncovered pipe that is not applicable to the above heat insulation specifications 1, 2 and 3

D.3 Rate of hot-water consumption reduction by hot-water saving device

A rate of hot-water consumption reduction is specified for each type of a hot-water saving device.

Table 24. Input
Variable Name	Description	Unit	Reference
\(FaucetType_{i,r}\)	Type of hot-water saving device that is used by connecting to a water heater supplying hot water to a room	-	Form 5-1: ③ Hot-water saving device

Table 25. Output
Variable Name	Description	Unit	References
\(\phi_{Wa,i,r}\)	Rate of hot-water consumption reduction by an automatic hot-water faucet that is used by connecting to a water heater supplying hot water to a room	-	5.2
\(\phi_{Wb,i,r}\)	Rate of hot-water consumption reduction by a hot-water saving B1 that is used by connecting to a water heater supplying hot water to a room	-	5.2

First, the type and definition of a hot-water saving device are defined below.

Table 26. Type of hot-water saving device
Option	Definition
Automatic hot-water faucet	Hot-water faucet that is installed in a washbasin and automatically stops water when water is used Hot-water faucet that electrically opens/closes and stops water if hands are distanced from the faucet However, a self-closing faucet (automatically stops water after discharging water for a certain time) that is used in public baths etc. is widely prevalent, and has been already expected to have its hot-water saving effect has been already expected in the unit of the accumulated daily hot water consumption. Therefore, it shall not be deemed to be an “automatic hot-water faucet.”
Hot-water saving device B1 (Low-flow spouting mechanism)	After spouting power of an automatic hot-water faucet is measured by a test method specified in the standard (http://www.j-valve.or.jp/suisen/setsuyu/f_setsuyu-a1b1c1-kijun_201405.pdf), the value of measured discharge power conforms to the following conditions. Faucet that does not have a structure that entraps air into running water → 0.60 N or more Faucet that has a structure that entraps air into running water → 0.55 N or more
Absence	All other than those with the above mechanisms In the case of adoption of a “two-valve faucet,” the above mechanisms are deemed to be “absent,” regardless of the presence or absence of the mechanisms. Unless all of hot-water faucets in a room r matches “automatic hot-water faucet” or “hot-water saving B1,” they shall not be deemed to adopt a hot-water saving device. Due to that the hot-water saving effect of hot-water saving devices A1(Hand water stopping mechanism) and C1 (Water priority spouting mechanism), installed in a non-residential building, is unclear (the way of using hot water for domestic use is different from that for commercial use), these devices are not deemed to be a hot-water saving device in the method for evaluating non-residential buildings.

The rate of hot-water consumption reduction by a hot-water saving device is shown below.

The rate is \(\phi_{Wa,i,r}\)=0.6 in the case of installation of the automatic hot-water faucet, and \(\phi_{Wa,i,r}\)=1.0 in the case of non-installation of the faucet.
The rate is tem:[\phi_{Wb,i,r}]=0.75 (Total reduction of 25; 15% by water-saving shower nozzle and 10% by thermostat) in the case of installation of the hot-water saving device B1. The rate is \(\phi_{Wb,i,r}\)=1.0 in the case of non-installation of the device.

However, it is assumed that the “automatic hot-water faucet” and the “hot-water saving device B1” are not concurrently installed.

D.4 Perimeter temperature of pipe

A perimeter temperature of a pipe is specified according to a climate zone.

Table 27. Input
Variable Name	Description	Unit	Reference
\(ClimateZone\)	Climate zone of the location of the building subject to evaluation	-	Form 0: ⑤ Climate zone under the Building Energy Code
\(\theta_{oa,d}\)	Daily average outside temperature at date	℃	2.2.3

Table 28. Output
Variable Name	Description	Unit	References
\(\theta_{amb,d}\)	Perimeter temperature of pipe at a date	℃	5.4

The perimeter temperature of the pipe is assumed to be an average of daily average outside and room temperatures.

\[\theta_{amb,d} = \frac{ \theta_{oa,d} + \theta_{room,d}}{ 2 }\]

A daily average outside temperature is calculated based on the outside temperature of meteorological data that is read from a climate zone. In order to determine a room temperature \(\theta_{room,d}\), heating, intermediate and cooling periods are set (in the same way as an operating mode of an air conditioner), thereby assuming that the room temperatures are 22℃, 24℃ and 26℃ during heating, intermediate and cooling periods, respectively.

Table 29. Setting of air conditioner’s operating mode
Climate zone	January	February	March	April	May	June	July	August	September	October	November	December
Climate 1	Heating	Heating	Heating	Heating	Intermediate	Intermediate	Cooling	Cooling	Cooling	Intermediate	Heating	Heating
Climate 2	Heating	Heating	Heating	Heating	Intermediate	Intermediate	Cooling	Cooling	Cooling	Intermediate	Heating	Heating
Climate 3	Heating	Heating	Heating	Intermediate	Intermediate	Cooling	Cooling	Cooling	Cooling	Intermediate	Intermediate	Heating
Climate 4	Heating	Heating	Heating	Intermediate	Intermediate	Cooling	Cooling	Cooling	Cooling	Intermediate	Intermediate	Heating
Climate 5	Heating	Heating	Heating	Intermediate	Intermediate	Cooling	Cooling	Cooling	Cooling	Intermediate	Intermediate	Heating
Climate 6	Heating	Heating	Heating	Intermediate	Intermediate	Cooling	Cooling	Cooling	Cooling	Intermediate	Intermediate	Heating
Climate 7	Heating	Heating	Heating	Intermediate	Intermediate	Cooling	Cooling	Cooling	Cooling	Intermediate	Intermediate	Heating
Climate 8	Heating	Heating	Heating	Intermediate	Cooling	Cooling	Cooling	Cooling	Cooling	Cooling	Intermediate	Intermediate

D.5 Linear heat loss coefficient of hot-water supply pipe

A linear heat loss coefficient of a hot-water supply pipe, \(k_{W,i}\) [W/(m・K)], is determined based on Pipe heat insulation specifications (D.2) and pipe connection diameter \(D_\{Wp}\)［mm ] (Input) from the following table.

Table 30. Input
Variable Name	Description	Unit	Reference
\(Type_{insulation,pipe}\)	Pipe heat insulation specifications	-	D.2
\(D_\{Wp}\)	Pipe connection diameter	mm	Form 5-2: ⑥ Connection diameter

Table 31. Output
Variable Name	Description	Unit	References
\(k_{W,i}\)	Linear heat loss coefficient of hot-water supply pipe	W/(m・K)	5.4

Table 32. Pipe heat conductivity
Pipe connection diameter	Insulation specifications 1	Insulation specifications 2	Insulation specifications 3	Bare pipe
13A or less	0.159	0.191	0.191	0.599
20A or less	0.189	0.213	0.231	0.838
25A or less	0.218	0.270	0.270	1.077
30A or less	0.242	0.303	0.303	1.282
40A or less	0.237	0.354	0.354	1.610
50A or less	0.257	0.388	0.388	1.832
60A or less	0.296	0.457	0.457	2.281
75A or less	0.346	0.472	0.548	2.876
80A or less	0.387	0.532	0.621	3.359
100A or less	0.466	0.651	0.651	4.309
125A or less	0.464	0.770	0.770	5.270
More than 125A	0.528	0.774	0.889	6.228

D.6 Daily average feed-water temperature

A daily average feed-water temperature is specified for each climate zone.

Table 33. Output
Variable Name	Description	Unit	References
\(\theta_{Win,d}\)	Daily average hot water temperature at date	℃	5.5

Calculate a daily average feed-water temperature at a date d from the following formula. Where, \(\theta_{oa,d}\) is a daily average feed-water temperature at a date d and specified for each climate zone.

\[\theta_{Win,d}= a_\{w} \times \theta_{oa,d} + b_\{w}\]

The coefficients in the formula, \(a_\{w}\) and \(b_\{w}\), are specified by climate as shown in the following table. For reference, this calculation method is quoted from the Calculation Method in the Criteria of Judgment of Housing Business Builder.

Table 34. Coefficients of estimation formula for daily average feed-water temperature
Climate zone	Coefficient \(a_\{w}\)	Coefficient \(b_\{w}\)
Climate 1	0.6639	3.466
Climate 2	0.6639	3.466
Climate 3	0.6054	4.515
Climate 4	0.6054	4.515
Climate 5	0.8660	1.665
Climate 6	0.8516	2.473
Climate 7	0.9223	2.097
Climate 8	0.6921	7.167

D.7 Solar irradiance in solar heat utilization of hot-water supply system

Table 35. Input
Variable Name	Description	Unit	Reference
\(\psi_{Wsolar,drct,i}\)	Azimuth angle of the collecting surface of a solar water heater that is included in a hot-water supply system	°	Form 5-2: ⑧ Azimuth angle of collecting surface
\(\psi_{Wsolar,slp,i}\)	Effective collecting area of a solar water heater that is included in a hot-water supply system	°	Form 5-2: ⑨ Tilt angle of collecting surface
\(I_{DNI,d,t}\)	Direct normal irradiance at date \(d\), time	W/m²	2.2.1
\(I_{DHI,d,t}\)	Horizontal sky solar radiation at date \(d\), time	W/m²	2.2.1
\(\psi_\{lati}\)	Latitude	°	2.2.1
\(\psi_\{longi}\)	Longitude	°	2.2.1

Table 36. Output
Variable Name	Description	Unit	Reference
\(I_{Wds,d}\)	Solar irradiance on heat collecting surface in the relevant region at date	MJ/(m²・d)	5.5

A declination of sun at a date d, \(DOS_{ d }\) and an equation of time, \(EOT_{ d }\) are determined from the following formula.

\[\begin{eqnarray*} DOS_{ d } & = & 0.006322 \\ & \quad & - 0.405748 \times \cos(w + 0.153231) \\ & \quad & - 0.005880 \times \cos(2 \times w - 0.207099) \\ & \quad & - 0.003233 \times \cos(3 \times w + 0.620129) \end{eqnarray*}\]

\[\begin{eqnarray*} EOT_{ d } & = & - 0.0002786409 \\ & \quad & + 0.1227715 \times \cos(w + 1.498311) \\ & \quad & - 0.1654575 \times \cos(2 \times w - 1.261546) \\ & \quad & - 0.00535383 \times \cos(3 \times w -1.1571) \end{eqnarray*}\]

Where, \(w\) is an angle with a period of one year [rad], \({\rm daynum}(m, d)\) is a function used to determine the number of days lapsed from January 1 on dd/mm, and \({\rm floor}(x)\) is a function used to determine the largest integer less than or equal to \(x\) for a real number:[x].

\[w = {\rm daynum}( m, d ) \times \frac{ 2 \pi }{ 366 }\]

\[\begin{eqnarray*} {\rm daynum}(m, d) = {\rm floor}\left( 30 \times ( m - 1 ) + {\rm floor}\left( \frac{ m + {\rm floor}(\frac{ m }{ 8 } ) }{ 2 } - {\rm floor}\left( \frac{ m + 7 }{ 10 } \right) + d \right) \right) \end{eqnarray*}\]

Determine a hour angle at a time t of a date d, \(HA_{ d, t }\) [rad]. A time t is assumed to be 1 to 24.

\[HA_{ d, t } = ( 15 \times t + 15 \times EOT_{ d } + \psi_{ longi } - 315 ) \times \frac{ 2 \pi }{ 360 }\]

Determine a sine of a solar altitude, \(\sin SAl_{ d, t }\).

\[\sin SAl_{ d, t }　 = \sin \Psi_{ lati } \times \sin DOS_{ d } + \cos \Psi_{ lati } \times \cos DOS_{ d } \times \cos HA_{ d, t }\]

\[\Psi_{ lati } = \psi_{ lati } \times \frac{ 2 \pi }{ 360 }\]

Determine a cosine of a solar altitude, \(\cos SAl_{ d, t }\).

\[\cos SAl_{ d, t } = \sqrt{ 1 - \sin^2 SAl_{ d, t } }\]

Determine a sine of a solar azimuth, \(\sin SAz_{ d, t }\).

\[\sin SAz_{ d, t } = \frac { \cos ( DOS_{ d } ) \times \sin ( HA_{ d, t } ) } { \cos SAl_{ d, t }}\]

Determine a cosine of a solar azimuth, \(\cos SAz_{ d, t }\).

\[\cos SAz_{ d, t } = \frac { \sin SAl_{ d, t } \times \sin \Psi_{ lati } - \sin DOS_{ d } } { \cos SAl_{ d, t } \times \cos \Psi_{ lati } }\]

\[\Psi_{ lati } = \psi_{ lati } \times \frac{ 2 \pi }{ 360 }\]

Determine a sine of a solar altitude viewed from a heat collecting surface,

\[\sin SAl_{ Wsolar, d, t } = \max \{ 0, \sin SAl_{ d, t } \times \cos \Psi_{ Wsolar, slp, i } + \cos SAl_{ d, t } \times \sin \Psi_{ Wsolar, slp, i } \times ( \cos SAz_{ d, t } \times \cos \Psi_{ Wsolar, drct, i } + \sin SAz_{ d, t } \times \sin \Psi_{ Wsolar, drct, i } ) \}\]

\[\Psi_{ Wsolar, slp, i } = \psi_{ Wsolar, slp, i } \times \frac{ 2 \pi }{ 360 }\]

\[\Psi_{ Wsolar, drct, i } = \psi_{ Wsolar, drct, i } \times \frac{ 2 \pi }{ 360 }\]

Determine a direct normal irradiance on a heat collecting surface, \(I_{ DNI, Wsolar, d, t }\).

\[I_{ DNI, Wsolar, d, t } = I_{ DNI, d, t } \times \sin SAl_{ panel, d, t }\]

Determine a diffuse horizontal irradiance on a heat collecting surface, \(I_{ DHI, Wsolar, d, t }\).

\[I_{ DHI, Wsolar, d, t } = \begin{cases} I_{ DHI, d, t } & , \psi_{ Wsolar, slp, i } = 0 \\ 0.5 \times I_{ DHI, d, t } + 0.1 \times 0.5 \times ( I_{ DHI, d, t } + I_{ DNI, d, t } \times \sin SAl_{ d, t }) & , \psi_{ Wsolar, slp, i } = 90 \\ \frac { 1 + \cos \Psi_{ Wsolar, slp, i } } { 2 } \times I_{ DHI, d, t } + \frac { 1 - \cos \Psi_{ Wsolar, slp, i } } { 2 } \times 0.8 \times ( I_{ DHI, d, t } + I_{ DNI, d, t } \times \sin SAl_{ d, t } ) & , \mbox(other} \end{cases}\]

\[\Psi_{ Wsolar, slp, i } = \psi_{ Wsolar, slp, i } \times \frac{ 2 \pi }{ 360 }\]

Determine a solar irradiance on a heat collecting surface in the relevant region at date d from a direct normal irradiance and diffuse horizontal irradiance on a heat collecting surface, \(I_{Wds,d}\) [MJ/(m²・d)].

\[I_{ Wds, d } = \sum_{t=1}^{24} I_{ Wds, d, t }\]

\[I_{ Wds, d ,t } = ( I_{ DNI, Wsolar, d, t } + I_{ DHI, Wsolar, d, t } ) \times 3600 \times 10^{-6}\]