# Component Sizing[LINK]

In EnergyPlus each HVAC component sizes itself. Each component module contains a sizing subroutine. When a component is called for the first time in a simulation, it reads in its user specified input data and then calls the sizing subroutine. This routine checks the autosizable input fields for missing data and calculates the data when needed.

A number of high-level variables are used in the sizing subroutines.

*CurDuctType* (in *DataSizing*) contains the information about the current duct type. The types can be *main*, *cooling*, *heating* or *other*.

*CurZoneEqNum* (in *DataSizing*) is the current zone equipment set index and indicates that the component is a piece of zone equipment and should size itself using the zone sizing data arrays.

*CurSysNum* (in *DataSizing*) is the current air loop index and indicates that the component is part of the primary air system and should size itself using the system sizing data arrays.

Fan sizing is done in subroutine *SizeFan*.

### Max Flow Rate[LINK]

If the fan is part of the central air system then check the duct type.

For duct type = *main, other* or default

˙Vfan,max=DesMainVolFlowsys

*F*or duct type=*cooling*

˙Vfan,max=DesCoolVolFlowsys

*F*or duct type=*heating*

˙Vfan,max=DesHeatVolFlowsys

If the fan is zone equipment then check whether it is part of a component that only does heating.

For heating only ˙Vfan,max=DesHeatVolFlowzone;

Otherwise ˙Vfan,max=Max(DesHeatVolFlowzone,DesCoolVolFlowzone)

If the max fan flow rate is less than *SmallAirVolFlow* the max flow rate is set to zero.

## Coil:Cooling:Water[LINK]

The sizing is done in function *SizeWaterCoil* of module *WaterCoils*

### Initial Calculations[LINK]

For central cooling coils, the first step is to determine the design air flow rate, load, and design air entering and exit conditions. The coil design air flow rate is not generally the same as the maximum system air flow rate (used to size the central fans). The cooling coil peak load (either sensible or total) can occur at a different time than the system peak flow rate. Hence the coil air entering conditions can be different than those at the peak system flow rate. Also, the method of controlling the coil’s cooling output may also affect coil design flow rate as well as the coil design exit temperature and humidity.

By choosing *Type of Load to Size On* = *Sensible* or *Total* in *Sizing:System* the user indicates to the program to save the cooling coil air flow rate and system air conditions (mixed, return, outside) at the time of either the system cooling sensible or total load peak. Note that the choice *VentilationRequirement* uses the time of the sensible peak.

Choosing *Central Cooling Capacity Control Method* = *VAV*, *Bypass*, *VT*, or *OnOff* indicates which type of cooling output control the program should assume when calculating the design air flow rate. The function *GetCoilDesFlowT* in module *ReportSizingManager* calculates the air flow rate and exit air temperature for each capacity control method.

VAV: Tcc,exit=Tcool,supply and ˙Vcc,air=˙mcc,air,peak/ρair

Bypass: Tcc,exit=Tcool,supply and ˙Vcc,air=˙Vcc,air,max(max[0,min[1,(Tmix,atpeak−Tsup,avg)/(Tmix,atpeak−Tcc,exit)]]) where Tsup,avg=Tzones,avg−∑zones˙Qsens,atpeak/(ρaircp,air˙Vcool,air,max)

VT: Tcc,exit=max[Tcool,supply,(Tzones,avg−∑zones˙Qsens,atpeak/(ρaircp,air˙Vcool,air,max))] and ˙Vcc,air=˙Vcc,air,max

OnOff: Tcc,exit=Tcool,supply and ˙Vcc,air=˙Vsys,air,max

cp,air: the specific heat of air [J/kg°C]
˙mcc,air,peak: the air mass flow rate through the cooling coil at the sensible or total system peak cooling load [m^{3}/s]
∑zones˙Qsens,atpeak: sum of the zone sensible cooling loads at the time of the peak system cooling load.
ρair: the density of air [kg/m3]
Tcc,exit: the design cooling coil exit temperature [°C]
Tcool,supply: the supply air temperature for cooling specified in Sizing:System [°C]
Tmix,atpeak: the mixed air temperature at the time of the system peak cooling load [°C]
Tzones,avg: the average zone temperature at the time of the system peak cooling load [°C]
˙Vcc,air: the design volumetric air flow rate through the cooling coil [m3/s]. This is the flow rate at either the sensible or total cooling load peak from the design period calculations.
˙Vcool,air,max: the maximum cooling volumetric air flow rate from the design calculations [m3/s]. This flow rate occurs at the maximum zone cooling demand.
˙Vsys,air,max: the maximum volumetric air flow rate from the design calculations [m3/s]. This flow rate occurs at either the maximum zone cooling or heating demand.

### Design Coil Load (W)[LINK]

Design coil load (cooling capacity) is not an input for *Coil:Cooling:Water*. It is used for calculating the design water flow rate.

The design load ˙Qcoil,des is calculated using:

˙Qcoil,des=˙ma,coil,des(ha,coil,des,in−ha,coil,des,out)

where

ha,coil,des,in is the coil design inlet air enthalpy [J/kg];

ha,coil,des,out is the coil design outlet air enthalpy [J/kg]; and

˙ma,coil,des is the coil design air mass flow rate [kg/s].

The design air mass flow rate depends on the location of the coil. If the coil is in the outside air stream the flow rate is set to ρair˙Va,coil,oa,des, where ˙Va,coil,oa,des is the design outside air volumetric flow rate for the system. Otherwise ˙ma,coil,des is set to ρair˙Vcc,air where ˙Vcc,air is calculated above in the Initial Calculations section.

To obtain the inlet and outlet enthalpies, we need the inlet and outlet temperatures and humidity ratios. The inlet and outlet conditions depend on whether the coil is in the outside air stream and if it is not, whether or not there is outside air preconditioning.

- Coil in outside air stream
Tair,in,des=Tout,cool,atpeak (the outside air temperature at the design cooling peak)

Tair,out,des=Tsys,precool (the specified Precool Design Temperature from the *Sizing:System* object).

Wair,in,des=Wout,cool,atpeak (the outside humidity ratio at the design cooling peak)

Wair,out,des=Wsys,precool (the specified Precool Design Humidity Ratio from the *Sizing:System* object)

- Coil in main air stream, no preconditioning of outside air
Tair,in,des=Tmix,cool,atpeak (the mixed air temperature at the design cooling peak)

Wair,in,des=Wmix,cool,atpeak (the mixed air humidity ratio at the design cooling peak)

*T*_{air,out,des} is set to *T_{cc,exit} calculated above in the Initial Calculation section

Wair,out,des=Wsup,cool (the specified *Central Cooling Design Supply Air Humidity Ratio* from the *Sizing:System* object)

- Coil in main air stream, outside air preconditioned. The outside air fraction is calculated as foa=˙Vair,out,des/˙Vcc,air where ˙Vcc,air is calculated above
Tair,in,des=foaTprecool+(1−foa)Tret,cool,atpeak where Tprecool is the specified *Precool Design Temperature* from *System:Sizing*. Tret,cool,atpeak is the return temperature at the system cooling peak load.

Wair,in,des=foaWprecool+(1−foa)Wret,cool,atpeak where Wprecool is the specified *Precool Design Humidity Ratio* from *Sizing:System* and Wret,cool,atpeak is the return humidity ratio at the system cooling peak load.

*T*_{air,out,des} and *W*_{air,out,des} are defined as in 2).

With the inlet and outlet conditions established, we can obtain the inlet and outlet enthalpies:

*h*_{air,coil,des,in} = *PsyHFnTdbW*(*T*_{air,in,des}, *W*_{air,in,des})

*h*_{air,coil,des,out} = *PsyHFnTdbW*(*T*_{air,out,des}, *W*_{air,out,des})

where *PsyHFnTdbW* is the EnergyPlus function for calculating air specific enthalpy given the air temperature and humidity ratio. We now have all we need to calculate ˙Qcoil,des.

If the coil is part of an *AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* unit or an *ZoneHVAC:FourPipeFanCoil*, the cooling load (cooling capacity) is passed down from the terminal unit or fan coil sizing calculations. Otherwise the load is defined as:

˙Qcoil,des=˙ma,coil,des(ha,coil,des,in−ha,coil,des,out)

where

ha,coil,des,in is the coil design inlet air enthalpy [J/kg];
ha,coil,des,out is the coil design outlet air enthalpy [J/kg]; and
˙ma,coil,des is the coil design air mass flow rate [kg/s].

The enthalpies are given by:

hair,coil,des,in=PsyHFnTdbW(Tair,in,des,Wair,in,des)

hair,coil,des,out=PsyHFnTdbW(Tair,out,des,Wair,out,des)

where *T*_{air,in,des} and *W*_{air,in,des} are the coil inlet design conditions. For coils in terminal units these are set at the system level to the system design supply air temperature. For zonal usits they are set to design return air, mixed air, or outside air as appropriate to the unit. *T*_{air,out,des} is set to the zone cooling design supply air temperature as specified in the *Zone:Sizing* inputs. *W*_{air,out,des} is set to the zone cooling design supply air humidity ratio as specified in the *Zone:Sizing* inputs.

### Design Water Flow Rate (m^{3}/s)[LINK]

The design water volumetric flow rate is calculated using:

˙Vw,coil,des=˙Qcoil,des/(ρwcp,wΔTw,des)

where ΔTw,des is just the *Loop Design Temperature Difference* user input from *Sizing:Plant* (if the coil is in the outside air stream, ½ the *Loop Design Temperature Difference* is used).

If the coil is part of an *AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* unit or a *ZoneHVAC:FourPipeFanCoil*, the chilled water flow rate is passed down from the terminal unit or fan coil sizing calculations. Otherwise the flow is set to:

˙Vw,coil,des=˙Qcoil,des/(ρwcp,wΔTw,des)

where ΔTw,des is just the *Loop Design Temperature Difference* user input from *Sizing:Plant*. ˙Qcoil,des is calculated as described above.

### Design Air Flow Rate[LINK]

The design air volumetric flow rate for the system cooling coil is set to:

- the design outside air flow rate if the coil is in the outside air stream;
- the coil design flow rate from function
*GetCoilDesFlowT* described in section “Initial Calculations”;
- the design flow rate set by the parent component (such as a unitary system) containing the cooling coil.

Zone chilled water coils are always part of a zone HVAC component. In almost all cases the design flow rate is passed down from the design flow rate of the parent component. Otherwise if the parent component does cooling only the flow rate for the coil is set to the zone design cooling flow rate. And if the parent component does both cooling and heating, the coil flow rate is set to the maximum of the zone design cooling and heating flow rates.

### Design Inlet Air Temperature[LINK]

The inlet air temperature depends on whether the coil is in the outside air stream and if it is not, whether or not there is outside air preconditioning.

Coil in outside air stream: Tair,in,des=Tout,cool,atpeak (the outside air temperature at the design cooling peak). Coil in main air stream, no preconditioning of outside air: Tair,in,des=Tmix,cool,atpeak (the mixed air temperature at the design cooling peak). Coil in main air stream, outside air preconditioned. The outside air fraction is calculated as foa=˙Vair,out,des/˙Vcc,air, where ˙Vcc,air is calculated above. Then Tair,in,des=foaTprecool+(1−foa)Tret,cool,atpeak where Tprecool is the specified *Precool Design Temperature* from *System:Sizing*. Tret,cool,atpeak is the return temperature at the system cooling peak load.

The design inlet temperature depends on whether the coil is in a terminal unit or a zonal unit, and where the coil is positioned within the unit.

- For the
*AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* terminal unit the design inlet temperature is set to the zone temperature at the time of the zone cooling peak, since the coil is located in the induced air stream.
- For fan coil units the design inlet temperature is set to the mixed air temperature: Tair,in,des=foaToa,coolpeak+(1−foa)Tz,coolpeak where foa=ρa˙Vz,oa,des/˙mz,cool,des.
- In all other cases the design inlet temperature is set to the zone design cooling coil inlet temperature which is calculated in the zone sizing simulation and is basically the same calculation as the fan coil unit.

### Design Outlet Air Temperature[LINK]

The outlet air temperature depends on whether the coil is in the outside air stream.

- Coil in outside air stream:
*T*_{air,out,des} = *T*_{sys,des,precool} (the specified *Precool Design Temperature* from the *Sizing:System* object).
- Coil in main air stream: the design outlet air temperature is set to the temperature calculated in the Initial Calculation section above

If the coil is part of an *AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* unit, then:

˙Qcoil,des=cp,airρair˙Vw,coil,desΔTw,des

T1=Tair,in,des−˙Qcoil,des/(ρaircp,air˙Vair,coil,des)

T2=Tw,out,des+2

Tair,out,des=max(T1,T2)

For all other cases *T*_{air,out,des} is set to *T*_{z,sup,des} (the zone design supply air temperature as specified in *Sizing:Zone*).

### Design Inlet Air Humidity Ratio[LINK]

The design inlet humidity ratio depends on whether the coil is in the outside air stream and if it is not, whether or not there is outside air preconditioning.

- Coil in outside air stream: Wair,in,des=Wout,cool,atpeak (the outside air humidity ratio at the design cooling peak).
- Coil in main air stream, no preconditioning of outside air: Wair,in,des=Wmix,cool,atpeak (the mixed air humidity ratio at the design cooling peak).
- Coil in main air stream, outside air preconditioned. The outside air fraction is calculated as foa=˙Vair,out,des/˙Vcc,air, where ˙Vcc,air is calculated above. Then Wair,in,des=foaWprecool+(1−foa)Wret,cool,atpeak where Wprecool is the specified
*Precool Design Humidity Ratio* from *System:Sizing*. Wret,cool,atpeak is the return air humidity ratio at the system cooling peak load.

The design inlet humidity depends on whether the coil is in a terminal unit or a zonal unit, and where the coil is positioned within the unit.

- For the
*AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* terminal unit the design inlet humidity ratio is set to the zone humidity ratio at the time of the zone cooling peak, since the coil is located in the induced air stream.
- For fan coil units the design inlet humidity ratio is set to the mixed air humidity ratio: Wair,in,des=foaWoa,coolpeak+(1−foa)Wz,coolpeak where foa=ρa˙Vz,oa,des/˙mz,cool,des.
- In all other cases the design inlet temperature is set to the zone design cooling coil inlet humidity ratio which is calculated in the zone sizing simulation and is basically the same calculation as the fan coil unit.

### Design Outlet Air Humidity Ratio[LINK]

The outlet air humidity ratio depends on whether the coil is in the outside air stream.

- Coil in outside air stream:
*W*_{air,out,des} = *W*_{sys,des,precool} (the specified *Precool Design Humidity Ratio* from the *Sizing:System* object)
- Coil in main air stream: Wair,out,des=PsyWFnTdbRhPb(Tair,out,des,0.9,Pair,std) where
*PsyWFnTdbRhPb* is the EnergyPlus psychrometric function to calculate humidity ratio from drybulb temperature, relative humidity, and atmospheric pressure. The design outlet humidity ratio is being set to the humidity ratio at 90% relative humidity and design outlet temperature.

If the coil is part of an *AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* unit, then: get the dewpoint temperature at *W*_{air,in,des}:

Tdp,in=PsyTdpFnWPb(Wair,in,des,Pair,std).
If *T*_{dp,in} ≤ *T*_{w,in,des} set *W*_{air,out,des} = *W*_{air,in,des}. Otherwise set
Wair,out,des=min(PsyWFnTdbRhPb(Tair,out,des,0.9,Pair,std),Wair,in,des)

If the coil is not part of an *AirTerminal:SingleDuct:ConstantVolume:FourPipeInduction* unit, set *W*_{air,out,des} to *W*_{z,sup,des} (the zone design supply air humidity ratio as specified in *Sizing:Zone*).

### Design Inlet Water Temperature[LINK]

The Design Inlet Water Temperature is set to the *Design Loop Exit Temperature* specified in the *Sizing:Plant* object for the water loop serving this coil.

The Design Inlet Water Temperature is set to the *Design Loop Exit Temperature* specified in the *Sizing:Plant* object for the water loop serving this coil.

## Coil:Cooling:Water:DetailedGeometry Sizing[LINK]

The sizing is done in subroutine *SizeWaterCoil*

### Max Water Flow Rate of Coil[LINK]

The calculation is identical to that done for *Coil:Cooling:Water*.

### Number of Tubes per Row[LINK]

Ntube/row=Int(13750˙Vcoil,water,max)

*N*_{tube/row}=**Max**(*N*_{tube/row},3)

Depending on the duct type, get the coil design air flow rate.

For duct type = *main, other* or default

˙mair,des=ρairDesMainVolFlowsys

*for duct type=cooling*

˙mair,des=ρairDesCoolVolFlowsys

*for duct type=heating*

˙mair,des=ρairDesHeatVolFlowsys

Dfin=0.335˙mair,des

### Minimum Air Flow Area[LINK]

Depending on the duct type, get the coil design air flow rate.

For duct type = *main, other* or default

˙mair,des=ρairDesMainVolFlowsys

*for duct type=cooling*

˙mair,des=ρairDesCoolVolFlowsys

*for duct type=heating*

˙mair,des=ρairDesHeatVolFlowsys

AMinAirFlow=0.44˙mair,des

### Fin Surface Area[LINK]

Depending on the duct type, get the coil design air flow rate.

For duct type = *main, other* or default

˙mair,des=ρairDesMainVolFlowsys

*for duct type=cooling*

˙mair,des=ρairDesCoolVolFlowsys

*for duct type=heating*

˙mair,des=ρairDesHeatVolFlowsys

AFinSurf=78.5˙mair,des

### Total Tube Inside Area[LINK]

*A~tube,total inside*_{=4.4D}tube,inside_{N}tube rows_{N}tubes/row~

Where *D*_{tube,inside} is the tube inside diameter.

### Tube Outside Surf Area[LINK]

*A*_{tube,outside}=4.1*D*_{tube,outside}N~tube rows_{N}tubes/row~

Where *D*_{tube,outside} is the tube outside diameter.

*Depth*_{coil}=*Depth~tube spacing~ N~tube rows~*

## Coil:Cooling:WaterToAirHeatPump:EquationFit Sizing[LINK]

The sizing is done in subroutine *SizeHVACWaterToAir*

### Rated Air Flow Rate[LINK]

The calculation is identical to that done for *Coil:Cooling:Water*.

### Rated Water Flow Rate[LINK]

The calculation is identical to that done for *Coil:Cooling:Water*, which is the coil design load divided by the *Loop Design Temperature Difference* user input from *Sizing:Plant.* If there is a companion heating coil, the heating coil design load is used so that both modes will have the same rated water flow rate. For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.

### Rated Total Cooling Capacity[LINK]

The calculation for coil operating temperatures (inlet and outlet) are identical to that done for *Coil:Cooling:Water*. The following calculations are then performed to determine the rated total cooling capacity.

TWB,ratio=(TWB,air,in,des+273.15C)283.15C

TS,ratio=29.44C+273.15C283.15C

where:

TWB,ratio = ratio of load-side inlet air wet-bulb temperature in Kelvin to a reference temperature

TS,ratio = ratio of source-side inlet water temperature in Kelvin to a reference temperature

TCC1 = user input for Total Cooling Capacity Coefficient 1

TCC2 = user input for Total Cooling Capacity Coefficient 2

TCC3 = user input for Total Cooling Capacity Coefficient 3

TCC4 = user input for Total Cooling Capacity Coefficient 4

TCC5 = user input for Total Cooling Capacity Coefficient 5

TotCapTempModFac=TCC1+TCC2(TWB,ratio)+TCC3(TS,ratio)+TCC4+TCC5

The 4^{th} and 5^{th} coefficient (TCC4 and TCC5) used in the above equation are multipliers for the load-side and source-side flow ratios, respectively. For sizing, these ratios are assumed to be 1.

The enthalpy of the entering air is then compared with the enthalpy of the exiting air. The calculations for air enthalpy are identical to that done for *Coil:Cooling:Water*. If the entering air enthalpy is less than the exiting air enthalpy, a reference value of 48,000 J/kg is used as the entering air enthalpy. If the TotCapTempModFac calculation above yields 0 as the result, a value of 1 is used in the following calculation. If the design air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil total cooling capacity is set equal to 0.

### Rated Sensible Cooling Capacity[LINK]

The calculation for coil operating temperatures (inlet and outlet) are identical to that done for *Coil:Cooling:Water*. The following calculations are then performed to determine the rated sensible cooling capacity.

TDB,ratio=(TDB,air,in,des+273.15C283.15C

TS,ratio=(29.44C+273.15C283.15C

where:

TDB,ratio = ratio of load-side inlet air dry-bulb temperature in Kelvin to a reference temperature

SCC1 = user input for Sensible Cooling Capacity Coefficient 1

SCC2 = user input for Sensible Cooling Capacity Coefficient 2

SCC3 = user input for Sensible Cooling Capacity Coefficient 3

SCC4 = user input for Sensible Cooling Capacity Coefficient 4

SCC5 = user input for Sensible Cooling Capacity Coefficient 5

SCC6 = user input for Sensible Cooling Capacity Coefficient 6

SensCapTempModFac=SCC1+SCC2(TDB,ratio)+SCC3(TWB,ratio)+SCC4(TS,ratio)+SCC5+SCC6

The 5^{th} and 6^{th} coefficient (SCC5 and SCC6) used in the above equation are multipliers for the load-side and source-side flow ratios, respectively. For sizing, these ratios are assumed to be 1.

The dry-bulb temperature of the entering air is then compared with the dry-bulb temperature of the exiting air. The calculations for air dry-bulb temperature are identical to that done for *Coil:Cooling:Water*. If the entering air dry-bulb temperature is less than the exiting air dry-bulb temperature, a reference value of 24 C is used as the entering air dry-bulb temperature. If the SensCapTempModFac calculation above yields 0 as the result, a value of 1 is used in the following calculation. If the design air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil sensible cooling capacity is set equal to 0.

## Coil:Cooling:WaterToAirHeatPump:VariableSpeedEquationFit Sizing[LINK]

For the cooling coil of VS WSHP, we specify a nominal speed level. During the sizing calculation, the Rated Air Volume Flow Rate, the Rated Water Volume Flow Rate and the Rated Total Cooling Capacity at the Selected Nominal Speed Level are determined in the same way as the *Coil:Cooling:WaterToAirHeatPump:EquationFit* object. The sensible heat transfer rate is not allowed for auto-sizing, instead, it is a function of the rated air and water flow rates, rated total cooling capacity and the Reference Unit SHR at the nominal speed level. The default nominal speed level is the highest speed. However, the model allows the user to select a nominal speed level rather than the highest.

### Rated Air Flow Rate[LINK]

The calculation is identical to that done for *Coil:Cooling:WaterToAirHeatPump:EquationFit*.

### Rated Water Flow Rate[LINK]

The calculation is identical to that done for *Coil:Cooling:WaterToAirHeatPump:EquationFit* , which is the coil design load divided by the *Loop Design Temperature Difference* user input from *Sizing:Plant.* If there is a companion heating coil, the heating coil design load is used so that both modes will have the same rated water flow rate. For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.

### Rated Total Cooling Capacity[LINK]

The calculation for coil operating temperatures (inlet and outlet) are identical to that done for *Coil:Cooling:WaterToAirHeatPump:EquationFit*. The calculations for air enthalpy are similar to that done for *Coil:Cooling:WaterToAirHeatPump:EquationFit.* The difference is in calculating the total cooling capacity temperature modifier function at the selected nominal speed level, as below:

TotCapTempModFracNominalSpeed=a+b∗WBi+c∗WB2i+d∗EWT+e∗EWT2+f∗WBi∗EWT

where

WB_{i} = wet-bulb temperature of the air entering the heating coil, °C

EWT = entering water temperature, °C

a-f = regression curve-fit coefficients.

If the entering air enthalpy is less than the exiting air enthalpy, a reference value of 48,000 J/kg is used as the entering air enthalpy. If the *TotCapTempModFac* calculation above yields 0 as the result, a value of 1 is used in the following calculation. If the rated air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil total cooling capacity is set equal to 0.

*If H*_{in} > H_{out} Then

˙Qcoil,rated,total=mair,rated(Hin−Hout)/TotCapTempModFracNominalSpeed

*Else*

˙Qcoil,rated,total=mair,rated(48000−Hout)/TotCapTempModFracNominalSpeed

*End If*

## Coil:Heating:WaterToAirHeatPump:EquationFit Sizing[LINK]

The sizing is done in subroutine *SizeHVACWaterToAir.*

### Rated Air Flow Rate[LINK]

The calculation is identical to that done for *Coil:Cooling:Water*.

### Rated Water Flow Rate[LINK]

The calculation is identical to that done for *Coil:Cooling:Water* , which is the coil design load divided by the *Loop Design Temperature Difference* user input from *Sizing:Plant.* For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.

### Rated Total Heating Capacity[LINK]

The rated total heating capacity is set equal to the rated total cooling capacity.

## Coil:Heating:WaterToAirHeatPump:VariableSpeedEquationFit Sizing[LINK]

For the heating coil of VS WSHP, we specify a nominal speed level. During the sizing calculation, the Rated Air Volume Flow Rate and the Rated Water Volume Flow Rate are determined in the same way as the *Coil:Heating:WaterToAirHeatPump:EquationFit* object. On the other hand, the Rated Heating Capacity at the Selected Nominal Speed Level should be the same as the total cooling capacity of its corresponding cooling coil, which has to be sized first. The default nominal speed level will be the highest speed. However, the model allows the user to select a nominal speed level rather than the highest.

### Rated Air Flow Rate[LINK]

The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit.

### Rated Water Flow Rate[LINK]

The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit, which is the coil design load divided by the *Loop Design Temperature Difference* user input from *Sizing:Plant.* For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.

### Rated Total Heating Capacity[LINK]

The rated total heating capacity is set equal to the rated total cooling capacity.

## Coil:Heating:Water Sizing[LINK]

The sizing is done in subroutine *SizeWaterCoil*.

### Max Water Flow Rate of Coil[LINK]

With the coil load from the system design data array and the user specified (in a Sizing:Plant object) design hot water temperature fall, calculate the max water flow rate:

˙Vcoil,water,max=HeatCapsys/(Cp,waterρwaterΔTplt,hw,des)

Using the zone design coil inlet and supply air conditions calculate the design coil load.

If the coil is not part of an induction unit then obtain the coil inlet temperature from the zone design data array;

*T*_{in,air}= DesHeatCoilInTemp_{zone}

If the coil is part of an induction unit take into account the induced air:

*Frac*_{minflow} = *MinFlowFrac*_{zone}

*T*_{in,air} = *DesHeatCoilInTemp*_{zone} Frac_{minflow} + *ZoneTempAtHeatPeak*_{zone}(1 *Frac*_{minflow})

*T*_{out,air} = HeatDesTemp_{zone}

*W*_{out,air} = HeatDesHumRat_{zone}

If the coil is part of a terminal unit the mass flow rate is determined by the volumetric flow rate of the terminal unit:

˙mair,des=ρair˙mair,des,tu

Otherwise the design flow is obtained from the zone design data array:

˙mair,des=DesHeatMassFlowzone

Qcoil,des=cp,air˙mair,des(Tout,air−Tin,air)

Here *c*_{p,air} is calculated at the outlet humidity and the average of the inlet and outlet temperatures.

With the coil load and the user specified (in a Sizing:Plant object) design hot water temperature decrease, calculate the max water flow rate:

˙Vcoil,water,max=Qcoil,des/(Cp,waterρwaterΔTplt,hw,des)

### UA of the Coil[LINK]

To obtain the UA of the coil, we specify the model inputs (other than the UA) at design conditions and the design coil load that the coil must meet. Then we numerically invert the coil model to solve for the UA that will enable the coil to meet the design coil load given the specified inputs.

The design coil load is the system design sensible cooling capacity;

*Q*_{coil,des}= *HeatCap*_{sys}

The required inputs for the simple coil model are:

*T*_{in,air}= *HeatMixTemp*_{sys}

*W*_{in,air}= *HeatMixHumRat*_{sys}

*T*_{in,water}= *ExitTemp*_{plt,hw,des}

˙min,water=ρwater˙Vcoil,water,max

Depending on the duct type, get the coil design air flow rate.

For duct type = *main, other* or default

˙min,air=ρairDesMainVolFlowsys

*for duct type=cooling*

˙min,air=ρairDesCoolVolFlowsys

*for duct type=heating*

˙min,air=ρairDesHeatVolFlowsys

We now have all the data needed to obtain UA. The numerical inversion is carried out by calling subroutine *SolveRegulaFalsi*. This is a general utility routine for finding the zero of a function. In this case it finds the UA that will zero the residual function - the difference between the design coil load and the coil output divided by the design coil load. The residual is calculated in the function *SimpleHeatingCoilUAResidual*.

If the coil is not part of an induction unit then obtain the coil inlet temperature from the zone design data array;

*T*_{in,air} = DesHeatCoilInTemp_{zone}

If the coil is part of an induction unit take into account the induced air:

*Frac*_{minflow} = *MinFlowFrac*_{zone}

*T*_{in,air} = *DesHeatCoilInTemp*_{zone} Frac_{minflow} +

*ZoneTempAtHeatPeak*_{zone}(1 *Frac*_{minflow})

*W*_{in,air}= *DesHeatCoilInHumRat*_{zone}

*T*_{in,water}= *ExitTemp*_{plt,hw,des}

˙min,water=ρwater˙Vcoil,water,max

*T*_{out,air} = HeatDesTemp_{zone}

*W*_{out,air} = HeatDesHumRat_{zone}

If the coil is part of a terminal unit the mass flow rate is determined by the volumetric flow rate of the terminal unit:

˙mair,des=ρair˙mair,des,tu

Otherwise the design flow is obtained from the zone design data array:

˙mair,des=DesHeatMassFlowzone

˙Qcoil,des=cp,air˙mair,des(Tout,air−Tin,air)

Here *c*_{p,air} is calculated at the outlet humidity and the average of the inlet and outlet temperatures.

We now have all the data needed to obtain UA. The numerical inversion is carried out by calling subroutine *SolveRegulaFalsi*. This is a general utility routine for finding the zero of a function. In this case it finds the UA that will zero the residual function - the difference between the design coil load and the coil output divided by the design coil load. The residual is calculated in the function *SimpleHeatingCoilUAResidual*.

## Coil:Heating:Steam Sizing[LINK]

The sizing is done in subroutine *SizeSteamCoil*.

### Maximum Steam Flow Rate[LINK]

The maximum steam volumetric flow rate is calculated using:

The steam density (ρsteam) is for saturated steam at 100°C (101325.0 Pa) and *h*_{fg} is the latent heat of vaporization of water at 100°C (101325.0 Pa). *C*_{p,w} is the heat capacity of saturated water (condensate) at 100°C (101325.0 Pa) and ΔTsc is the Degree of Subcooling defined in the Coil:Heating:Steam object input. The design coil load *Load*_{coil,des} is calculated from:

Loadcoil,des=˙mair,des(cp,air)(Tair,coil,des,out−Tair,coil,des,in)

The design air mass flow rate depends on the location of the coil (duct type). For duct type = *main,* the flow rate is set to _{air}DesMainVolFlow_{sys}MinSysAirFlowRatio. If the coil is in a cooling duct the flow rate is set to _{air}DesCoolVolFlow_{sys}MinSysAirFlowRatio. If the coil is in a heating duct the flow rate is set to _{air}DesHeatVolFlow_{sys}. If the coil is in any other kind of duct, the flow rate is set to _{air}DesMainVolFlow_{sys}.

For sizing, the design outlet air temperature (*T*_{air,coil,des,out}) is the Central Heating Design Supply Air Temperature specified in the Sizing:System object.

The design inlet air temperature depends on whether the coil is being sized for 100% outdoor air or minimum outdoor air flow (per 100% Outdoor Air in Heating input field in the Sizing:System object).

- Sizing based on 100% Outdoor Air in Heating

*T*_{air,coil,des,in} = *HeatOutTemp*_{sys} (the outdoor air temperature at the design heating peak)

- Sizing based on minimum outdoor air flow. The outdoor air fraction is calculated as
*Frac*_{oa} **= *DesOutAirVolFlow*_{sys} / *DesVolFlow*. *DesVolFlow* is ˙mair,desρair.

*T*_{air,coil,des,in} = *Frac*_{oa} *HeatOutTemp*_{sys} + (1. - *Frac*_{oa}) *HeatRetTemp*_{sys} (see Table 41. System Sizing Data)

If the coil is part of an *AirTerminal:SingleDuct:** unit (e.g., *AirTerminal:SingleDuct:ConstantVolume:Reheat, AirTerminal:SingleDuct:VAV:Reheat, AirTerminal:SingleDuct:SeriesPIU:Reheat, etc.)*, the maximum steam flow rate is set equal to the terminal unit’s maximum steam flow rate. Otherwise (e.g., the zone-level coil is part of *ZoneHVAC:PackagedTerminalAirConditioner, ZoneHVAC:UnitVentilator, ZoneHVAC:UnitHeater or ZoneHVAC:VentilatedSlab*) the calculation is similar to that at the system level. A design load is calculated:

Loadcoil,des=˙mair,des(cp,air)(Tair,coil,des,out−Tair,coil,des,in)

where:

˙mair,des= *DesHeatMassFlow*_{zone} (see Table 40. Zone Sizing Data)

*T*_{air,coil,des,in} = *DesHeatCoilInTemp*_{zone} (see Table 40)

*T*_{air,coil,des,out} = *HeatDesTemp*_{zone} (user input from Sizing:Zone object)

cp,air = Specific heat of air (evaluated at the average of inlet and outlet air temperatures, and at the zone heating design supply air humidity ratio *HeatDesHumRat*_{zone} [user input from Sizing:Zone object])

The terms in the denominator of this equation (*ρ*_{steam}, *h*_{fg}, etc.) are evaluated in the same way as described above for steam System Coils.

## Sizing of Gas and Electric Heating Coils[LINK]

The sizing calculation is done in subroutine *SizeHeatingCoil* in module *HeatingCoils*.

### Nominal Capacity of the Coil[LINK]

The value is obtained from the system design array.

*Cap*_{nom}= *HeatCap*_{sys}

The capacity is calculated from the design coil inlet and outlet conditions.

If the coil is not part of an induction unit then obtain the coil inlet temperature from the zone design data array;

*T*_{in,air} = DesHeatCoilInTemp_{zone}

If the coil is part of an induction unit take into account the induced air:

*Frac*_{minflow} = *MinFlowFrac*_{zone}

*T*_{in,air} = *DesHeatCoilInTemp*_{zone} Frac_{minflow} +

*ZoneTempAtHeatPeak*_{zone}(1 *Frac*_{minflow})

*T*_{out,air} = HeatDesTemp_{zone}

*W*_{out,air} = HeatDesHumRat_{zone}

*Q*_{coil,des} = *C*_{p,air} DesHeatMassFlow_{zone}(*T*_{out,air}T_{in,air})

Here *c*_{p,air} is calculated at the outlet humidity and the average of the inlet and outlet temperatures.

## DX Coil Sizing[LINK]

The sizing calculations are done in subroutine *SizeDXCoil* in module *DXCoils*. This section covers the sizing of the objects

Coil:Cooling:DX:SingleSpeed

Coil:Heating:DX:SingleSpeed

Coil:Cooling:DX:TwoSpeed

### Rated Air Volume Flow Rate[LINK]

The rated air flow rate is obtained from the system design array.

˙Vair,rated=DesMainVolFlowsys

The rated air flow rate is the maximum of the heating and cooling design flow rates from the zone design array.

˙Vair,rated=Max(DesCoolVolFlowzone,DesHeatVolFlowzone)

### Rated Total Cooling Capacity[LINK]

The rated cooling capacity is obtained by dividing the peak cooling capacity by the *Cooling Capacity Modifier Curve* evaluated at peak mixed wetbulb and outdoor drybulb temperatures.

*T*_{mix}= *CoolMixTemp*_{sys}

*W*_{mix}=*CoolMixHumRat*_{sys}

*T*_{sup}=*CoolSupTemp*_{sys}

*W*_{sup}=*CoolSupHumRat*_{sys}

*T*_{outside}=*CoolOutTemp*_{sys}

_{air}=*PsyRhoAirFnPbTdbW*(*p*_{air,std}, *T*_{mix},*W*_{mix})

*h*_{mix}= *PsyHFnTdbW*(*T*_{mix},*W*_{mix})

*h*_{sup}= *PsyHFnTdbW*(*T*_{sup},*W*_{sup})

*T*_{mix,wb}= *PsyTwbFnTdbWPb*(*T*_{mix},*W*_{mix}, *p*_{air,std})

*CapModFac*=*CurveValue*(CCapFTemp,*T*_{mix,wb},*T*_{outside})

CCappeak=ρair˙Vair,rated(hmix−hsup)

*CCap*_{rated}=*CCap*_{peak} CapModFac

We check that the design volume flow per total capacity is within the prescribed range:

FlowCapRatio=˙Vair,rated/CCaprated

If *FlowCapRatio* < *FlowCapRatio*_{min} then

CCaprated=˙Vair,rated/FlowCapRatiomin

If *FlowCapRatio* > *FlowCapRatio*_{max} then

CCaprated=˙Vair,rated/FlowCapRatiomax

where

*FlowCapRatio*_{min} = 0.00004027 m^{3}/s per watt (300 cfm/ton)

And

*FlowCapRatio*_{max}= 0.00006041 m^{3}/s per watt (450 cfm/ton)

The sizing calculation for DX cooling coils for 100% dedicated outdor air system (DOAS) are identical to regular DX cooling coils. However, they operate operate at different flow to capacity ratio ranges and are within the prescribed range below:

*FlowCapRatio*_{min} = 0.00001677 m^{3}/s per Watt (125 cfm/ton)

And

*FlowCapRatio*_{max}= 0.00003355 m^{3}/s per Watt (250 cfm/ton)

The rated cooling capacity for zone coils is calculated in the same manner as for system coils.

*T*_{mix}= *DesCoolCoilInTemp*_{zone}

*W*_{mix}= *DesCoolCoilInHumRat*_{zone}

*T*_{sup}= *CoolDesTemp*_{zone}

*W*_{sup}= *CoolDesHumRat*_{zone}

*T*_{outside}=*T*_{outside},_{desday,peak}

_{air}=*PsyRhoAirFnPbTdbW*(*p*_{air,std}, *T*_{mix},*W*_{mix})

*h*_{mix}= *PsyHFnTdbW*(*T*_{mix},*W*_{mix})

*h*_{sup}= *PsyHFnTdbW*(*T*_{sup},*W*_{sup})

*T*_{mix,wb}= *PsyTwbFnTdbWPb*(*T*_{mix},*W*_{mix}, *p*_{air,std})

*CapModFac*=*CurveValue*(CCapFTemp,*T*_{mix,wb},*T*_{outside})

CCappeak=ρair˙Vair,rated(hmix−hsup)

*CCap*_{rated}=*CCap*_{peak} CapModFac

We check that the design volume flow per total capacity is within the prescribed range:

FlowCapRatio=˙Vair,rated/CCaprated

If *FlowCapRatio* < *FlowCapRatio*_{min} then

CCaprated=˙Vair,rated/FlowCapRatiomin

If *FlowCapRatio* > *FlowCapRatio*_{max} then

CCaprated=˙Vair,rated/FlowCapRatiomax

where

*FlowCapRatio*_{min} = 0.00004027 m^{3}/s per watt (300 cfm/ton)

And

*FlowCapRatio*_{max}= 0.00006041 m^{3}/s per watt (450 cfm/ton)

We check the design flow to the total cooling capacity rato for dedicated zone outdoor unit DX cooling coils to be within the limits prescribed below:

*FlowCapRatio*_{min} = 0.00001677 m^{3}/s per Watt (125 cfm/ton)

And

*FlowCapRatio*_{max}= 0.00003355 m^{3}/s per Watt (250 cfm/ton)

### Rated Total Heating Capacity[LINK]

For Coil:Heating:DX:SingleSpeed the rated heating capacity is set equal to the cooling capacity.

The rated sensible heat ratio is calculated to be the sensible cooling (from rated inlet conditions to user specified supply conditions) divided by the total cooling (from rated inlet to specified supply).

*T*_{in,rated}= 26.6667 ^{o}C (80 ^{o}F)

*W*_{in,rated}= 0.01125 (corresponds to 80 ^{o}F drybulb, 67 ^{o}F wetbulb)

*C*_{p,air}= *PsyCpAirFnWTdb*(*W*_{in,rated}, *T*_{in,rated})

For system coils

*T*_{sup}=*CoolSupTemp*_{sys}

*W*_{sup}=*CoolSupHumRat*_{sys}

For zone coils

*T*_{sup}= *CoolDesTemp*_{zone}

*W*_{sup}= *CoolDesHumRat*_{zone}

Then

*h*_{rated}= *PsyHFnTdbW*(*T*_{in,rated}, *W*_{in,rated})

*h*_{sup}= *PsyHFnTdbW*(*T*_{sup}, *W*_{sup})

*h*_{rated,sup}=*h*_{rated}h_{sup}

*Qs*_{rated,sup}=*C*_{p,air}(*T*_{in,rated}T_{sup})

*SHR*_{rated}=*Qs*_{rated,sup}h_{rated,sup}

### Evaporative Condenser Air Volume Flow Rate[LINK]

The evaporative condenser air volume flow rate (m^{3}/s) is set to 0.000114 m^{3}/s per watt (850 cfm/ton) times the total rated cooling capacity.

### Evaporative Condenser Air Volume Flow Rate, Low Speed[LINK]

The evaporative condenser air volume flow rate, low speed (m^{3}/s) is set to 1/3 times 0.000114 m^{3}/s per watt (850 cfm/ton) times the total rated cooling capacity.

### Evaporative Condenser Pump Rated Power Consumption[LINK]

The evaporative condenser pump rated power consumption is set equal to the total cooling capacity times 0.004266 watts pump power per watt capacity (15 W/ton).

### Evaporative Condenser Pump Rated Power Consumption, Low Speed[LINK]

The evaporative condenser pump rated power consumption, low speed, is set equal to 1/3 times the total cooling capacity times 0.004266 watts pump power per watt capacity (15 W/ton).

### Rated Air Volume Flow Rate, low speed[LINK]

The rated air volume flow rate, low speed, is set equal to 1/3 times the full rated air volume flow rate.

### Rated Total Cooling Capacity, Low Speed[LINK]

The rated total cooling capacity, low speed, is set equal to 1/3 times the full rated total cooling capacity.

### Rated SHR, low speed[LINK]

The rated sensible heat ratio, low speed, is set equal to the full speed SHR.

### Resistive Defrost Heater Capacity[LINK]

For the heat pump the resistive defrost heat capacity is set equal to the cooling capacity.

## DX MultiSpeed Coil Sizing[LINK]

The sizing calculations are done in subroutine *SizeDXCoil* in module *DXCoils*. This section covers the sizing of the objects

The rated air volume flow rate, rated total cooling capacity, rated heating capacity, rated SHR, evaporative condenser air volume flow rate, evaporative condenser pump rated power consumption at the highest speed are sized in the same ways as DX Coil Sizing.

After the sizes are determined at the highest speed, the sizes in the rest of speeds are assumed to

Valuen=nNumberOfSpeed∗ValueNumberOfSpeed

where

Value_{n}= Any autosizable variable at Speed n, except SHR

SHR_{n} = SHR_{NumberOfSpeed}

n= Speed Index number from 1 to NumberOfSpeed-1

NumberOfSpeed= The highest speed number

## Coil:Cooling:DX:VariableSpeed Sizing[LINK]

For the variable-speed DX cooling coil, we specify a nominal speed level. During the sizing calculation, the Rated Total Cooling Capacity at the Selected Nominal Speed Level is determined in the same way as the Coil:Cooling:DX:SingleSpeed object. If the user chooses to autosize the Rated Air Volume Flow Rate, the flow rate, as compared to the Rated Total Cooling Capacity, is sized to have the same ratio as the air volume flow rate to the total cooling capacity at the nominal speed, of the Reference Unit. The sensible heat transfer rate is not allowed for auto-sizing, instead, it is a function of the rated air flow, rated total cooling capacity and the Reference Unit SHR at the nominal speed level. The default nominal speed level is the highest speed. However, the model allows the user to select a nominal speed level rather than the highest.

**Rated Total Cooling Capacity**

The calculation for coil operating temperatures (inlet and outlet) are identical to that done for Coil:Cooling:DX:SingleSpeed. The calculations for air enthalpy are similar to that done for Coil:Cooling:DX:SingleSpeed*.* The difference is in calculating the total cooling capacity temperature modifier function at the selected nominal speed level, as below:

TotCapTempModFracNominalSpeed=a+b∗WBi+c∗WB2i+d∗DBo+e∗DBoT2+f∗WBi∗DBo

where

WB_{i} = wet-bulb temperature of the air entering the cooling coil, °C

DB_{o} = condenser entering air temperature, °C

a-f = regression curve-fit coefficients.

If the entering air enthalpy is less than the exiting air enthalpy, a reference value of 48,000 J/kg is used as the entering air enthalpy. If the *TotCapTempModFac* calculation above yields 0 as the result, a value of 1 is used in the following calculation. If the rated air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil total cooling capacity is set equal to 0.

*If H*_{in} > H_{out} Then

˙Qcoil,rated,total=mair,rated(Hin−Hout)/TotCapTempModFracNominalSpeed

*Else*

˙Qcoil,rated,total=mair,rated(48000−Hout)/TotCapTempModFracNominalSpeed

*End If*

The other sizing procedures, e.g. evaporative condenser pump, etc., are the same as Coil:Cooling:DX:SingleSpeed.

## Coil:Heating:DX:VariableSpeed Sizing[LINK]

For the variable-speed DX heating coil, we specify a nominal speed level. During the sizing calculation, the Rated Heating Capacity at the Selected Nominal Speed Level should be the same as the total cooling capacity of its corresponding cooling coil, which has to be sized first. The default nominal speed level will be the highest speed. However, the model allows the user to select a nominal speed level rather than the highest. If the user chooses to autosize the Rated Air Volume Flow Rate, the flow rate, as compared to the Rated Heating Capacity, is sized to have the same ratio as the air volume flow rate to the heating capacity at the nominal speed, of the Reference Unit. The other sizing procedures are the same as Coil:Heating:DX:SingleSpeed.

The loop pumps’ autosizable inputs are nominal volumetric flow rate and nominal power consumption. We have

*Eff*_{tot}=*Eff*_{mot}Eff_{impeller}

The motor efficiency is an input. Since we need the total efficiency to calculate the nominal power consumption we assume an impeller efficiency of 0,78 for purposes of sizing.

### Rated Volumetric Flow Rate[LINK]

This is just set equal to the design loop demand obtained from summing the needs of the components on the demand side of the loop.

### Rated Power Consumption[LINK]

˙Qnom=Hnom˙Vnom/Efftot

*H*_{nom}, the nominal head, is an input.

## Electric Chiller Sizing[LINK]

Generally chillers will need nominal cooling capacity, evaporator flow rate and condenser flow rate. All 3 quantities can be straightforwardly obtained using the user specified loop sizing data and the loop design flow rates.

All chillers on a loop are sized to meet the full loop load. If there are multiple chillers on a loop that call for autosizing, they will all be assigned the same cooling capacity and evaporator flow rate.

### Nominal Cooling Capacity[LINK]

˙Qchiller,nom=Cp,wρwΔTloop,des˙Vloop,des

where

*C*_{p,w} is the specific heat of water at 5 ^{o}C;

_{w} is the density of water at standard conditions (5.05 ^{o}C);

*T*_{loop,des} is the chilled water loop design temperature rise;

˙Vloop,des is the loop design volumetric flow rate.

### Design Evaporator Volumetric Water Flow Rate[LINK]

˙Vevap,des=˙Vloop,des

### Design Condenser Volumetric Water Flow Rate[LINK]

˙Vcond,des=˙Qchiller,nom(1+1/COPchiller,nom)/(ΔTloop,desCp,wρw)

where

*C*_{p,w} is the specific heat of water at design condenser inlet temperature;

_{w} is the density of water at standard conditions (5.05 ^{o}C);

*T*_{loop,des} is the chilled water loop design temperature rise;

*COP*_{chiller,nom} is the chiller nominal COP.

Boiler Sizing

Generally boilers will need nominal heating capacity and rate. Both quantities can be straightforwardly obtained using the user specified loop sizing data and the loop design flow rates.

All boilers on a loop are sized to meet the full loop load. If there are multiple boilers on a loop that call for autosizing, they will all be assigned the same heating capacity and flow rate.

### Nominal Capacity[LINK]

˙Qboiler,nom=Cp,wρwΔTloop,des˙Vloop,des

where

*C*_{p,w} is the specific heat of water at the boiler design outlet temperature;

_{w} is the density of water at standard conditions (5.05 ^{o}C);

*T*_{loop,des} is the hot water loop design temperature decrease;

˙Vloop,des is the loop design volumetric flow rate.

### Design Evaporator Volumetric Water Flow Rate[LINK]

˙Vdes=˙Vloop,des

## Plant Heat Exchanger Sizing[LINK]

The sizing of plant heat exchanger component (object: HeatExchanger:FluidToFluid) involves determining design flow rates for both sides, a UA value, and a nominal capacity for reporting. The component has a sizing factor for fine control and uses the design temperatures defined in the Sizing:Plant object.

The Loop Supply Side design flow rate, ˙VSup,des, is set equal to the design flow rate for that loop, multiplied by the component sizing factor, fcomp.

˙VSup,des=˙Vloop,des∗fcomp

The Loop Demand Side design flow rate,˙VDmd,des , is set equal to the Loop Supply Side design flow rate.

˙VDmd,des=˙VSup,des

The design heat transfer capacity and UA for the heat exchanger are calculated using the design temperatures for the two plant loops. The loop design temperature difference for the Loop Supply Side, ΔTSupLoop,Des, is used to determine a nominal capacity.

˙Q=.VSup,desρcpΔTSupLoop,Des

A loop-to-loop design temperature difference, ΔTLoopToLoop,De

## Component Sizing[LINK]

## Introduction[LINK]

In EnergyPlus each HVAC component sizes itself. Each component module contains a sizing subroutine. When a component is called for the first time in a simulation, it reads in its user specified input data and then calls the sizing subroutine. This routine checks the autosizable input fields for missing data and calculates the data when needed.

A number of high-level variables are used in the sizing subroutines.

CurDuctType(inDataSizing) contains the information about the current duct type. The types can bemain,cooling,heatingorother.CurZoneEqNum(inDataSizing) is the current zone equipment set index and indicates that the component is a piece of zone equipment and should size itself using the zone sizing data arrays.CurSysNum(inDataSizing) is the current air loop index and indicates that the component is part of the primary air system and should size itself using the system sizing data arrays.## Fan Sizing[LINK]

Fan sizing is done in subroutine

SizeFan.## Max Flow Rate[LINK]

If the fan is part of the central air system then check the duct type.

For duct type =

main, otheror default˙Vfan,max=DesMainVolFlowsys

For duct type=cooling˙Vfan,max=DesCoolVolFlowsys

For duct type=heating˙Vfan,max=DesHeatVolFlowsys

If the fan is zone equipment then check whether it is part of a component that only does heating.

For heating only ˙Vfan,max=DesHeatVolFlowzone;

Otherwise ˙Vfan,max=Max(DesHeatVolFlowzone,DesCoolVolFlowzone)

If the max fan flow rate is less than

SmallAirVolFlowthe max flow rate is set to zero.## Coil:Cooling:Water[LINK]

The sizing is done in function

SizeWaterCoilof moduleWaterCoils## Initial Calculations[LINK]

## System Coils[LINK]

For central cooling coils, the first step is to determine the design air flow rate, load, and design air entering and exit conditions. The coil design air flow rate is not generally the same as the maximum system air flow rate (used to size the central fans). The cooling coil peak load (either sensible or total) can occur at a different time than the system peak flow rate. Hence the coil air entering conditions can be different than those at the peak system flow rate. Also, the method of controlling the coil’s cooling output may also affect coil design flow rate as well as the coil design exit temperature and humidity.

By choosing

Type of Load to Size On=SensibleorTotalinSizing:Systemthe user indicates to the program to save the cooling coil air flow rate and system air conditions (mixed, return, outside) at the time of either the system cooling sensible or total load peak. Note that the choiceVentilationRequirementuses the time of the sensible peak.Choosing

Central Cooling Capacity Control Method=VAV,Bypass,VT, orOnOffindicates which type of cooling output control the program should assume when calculating the design air flow rate. The functionGetCoilDesFlowTin moduleReportSizingManagercalculates the air flow rate and exit air temperature for each capacity control method.VAV: Tcc,exit=Tcool,supply and ˙Vcc,air=˙mcc,air,peak/ρair

Bypass: Tcc,exit=Tcool,supply and ˙Vcc,air=˙Vcc,air,max(max[0,min[1,(Tmix,atpeak−Tsup,avg)/(Tmix,atpeak−Tcc,exit)]]) where Tsup,avg=Tzones,avg−∑zones˙Qsens,atpeak/(ρaircp,air˙Vcool,air,max)

VT: Tcc,exit=max[Tcool,supply,(Tzones,avg−∑zones˙Qsens,atpeak/(ρaircp,air˙Vcool,air,max))] and ˙Vcc,air=˙Vcc,air,max

OnOff: Tcc,exit=Tcool,supply and ˙Vcc,air=˙Vsys,air,max

^{3}/s] ∑zones˙Qsens,atpeak: sum of the zone sensible cooling loads at the time of the peak system cooling load. ρair: the density of air [kg/m3] Tcc,exit: the design cooling coil exit temperature [°C] Tcool,supply: the supply air temperature for cooling specified in Sizing:System [°C] Tmix,atpeak: the mixed air temperature at the time of the system peak cooling load [°C] Tzones,avg: the average zone temperature at the time of the system peak cooling load [°C] ˙Vcc,air: the design volumetric air flow rate through the cooling coil [m3/s]. This is the flow rate at either the sensible or total cooling load peak from the design period calculations. ˙Vcool,air,max: the maximum cooling volumetric air flow rate from the design calculations [m3/s]. This flow rate occurs at the maximum zone cooling demand. ˙Vsys,air,max: the maximum volumetric air flow rate from the design calculations [m3/s]. This flow rate occurs at either the maximum zone cooling or heating demand.## Design Coil Load (W)[LINK]

Design coil load (cooling capacity) is not an input for

Coil:Cooling:Water. It is used for calculating the design water flow rate.## System Coils[LINK]

The design load ˙Qcoil,des is calculated using:

˙Qcoil,des=˙ma,coil,des(ha,coil,des,in−ha,coil,des,out)

where

ha,coil,des,in is the coil design inlet air enthalpy [J/kg];

ha,coil,des,out is the coil design outlet air enthalpy [J/kg]; and

˙ma,coil,des is the coil design air mass flow rate [kg/s].

The design air mass flow rate depends on the location of the coil. If the coil is in the outside air stream the flow rate is set to ρair˙Va,coil,oa,des, where ˙Va,coil,oa,des is the design outside air volumetric flow rate for the system. Otherwise ˙ma,coil,des is set to ρair˙Vcc,air where ˙Vcc,air is calculated above in the Initial Calculations section.

To obtain the inlet and outlet enthalpies, we need the inlet and outlet temperatures and humidity ratios. The inlet and outlet conditions depend on whether the coil is in the outside air stream and if it is not, whether or not there is outside air preconditioning.

Tair,in,des=Tout,cool,atpeak (the outside air temperature at the design cooling peak)

Tair,out,des=Tsys,precool (the specified Precool Design Temperature from the

Sizing:Systemobject).Wair,in,des=Wout,cool,atpeak (the outside humidity ratio at the design cooling peak)

Wair,out,des=Wsys,precool (the specified Precool Design Humidity Ratio from the

Sizing:Systemobject)Tair,in,des=Tmix,cool,atpeak (the mixed air temperature at the design cooling peak)

Wair,in,des=Wmix,cool,atpeak (the mixed air humidity ratio at the design cooling peak)

Tis set to *T_{air,out,des}_{cc,exit}calculated above in the Initial Calculation sectionWair,out,des=Wsup,cool (the specified

Central Cooling Design Supply Air Humidity Ratiofrom theSizing:Systemobject)Tair,in,des=foaTprecool+(1−foa)Tret,cool,atpeak where Tprecool is the specified

Precool Design TemperaturefromSystem:Sizing. Tret,cool,atpeak is the return temperature at the system cooling peak load.Wair,in,des=foaWprecool+(1−foa)Wret,cool,atpeak where Wprecool is the specified

Precool Design Humidity RatiofromSizing:Systemand Wret,cool,atpeak is the return humidity ratio at the system cooling peak load.Tand_{air,out,des}Ware defined as in 2)._{air,out,des}With the inlet and outlet conditions established, we can obtain the inlet and outlet enthalpies:

h=_{air,coil,des,in}PsyHFnTdbW(T,_{air,in,des}W)_{air,in,des}h=_{air,coil,des,out}PsyHFnTdbW(T,_{air,out,des}W)_{air,out,des}where

PsyHFnTdbWis the EnergyPlus function for calculating air specific enthalpy given the air temperature and humidity ratio. We now have all we need to calculate ˙Qcoil,des.## Zone Coils[LINK]

If the coil is part of an

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionunit or anZoneHVAC:FourPipeFanCoil, the cooling load (cooling capacity) is passed down from the terminal unit or fan coil sizing calculations. Otherwise the load is defined as:˙Qcoil,des=˙ma,coil,des(ha,coil,des,in−ha,coil,des,out)

where

The enthalpies are given by:

hair,coil,des,in=PsyHFnTdbW(Tair,in,des,Wair,in,des)

hair,coil,des,out=PsyHFnTdbW(Tair,out,des,Wair,out,des)

where

Tand_{air,in,des}Ware the coil inlet design conditions. For coils in terminal units these are set at the system level to the system design supply air temperature. For zonal usits they are set to design return air, mixed air, or outside air as appropriate to the unit._{air,in,des}Tis set to the zone cooling design supply air temperature as specified in the_{air,out,des}Zone:Sizinginputs.Wis set to the zone cooling design supply air humidity ratio as specified in the_{air,out,des}Zone:Sizinginputs.## Design Water Flow Rate (m

^{3}/s)[LINK]## System Coils[LINK]

The design water volumetric flow rate is calculated using:

˙Vw,coil,des=˙Qcoil,des/(ρwcp,wΔTw,des)

where ΔTw,des is just the

Loop Design Temperature Differenceuser input fromSizing:Plant(if the coil is in the outside air stream, ½ theLoop Design Temperature Differenceis used).## Zone Coils[LINK]

If the coil is part of an

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionunit or aZoneHVAC:FourPipeFanCoil, the chilled water flow rate is passed down from the terminal unit or fan coil sizing calculations. Otherwise the flow is set to:˙Vw,coil,des=˙Qcoil,des/(ρwcp,wΔTw,des)

where ΔTw,des is just the

Loop Design Temperature Differenceuser input fromSizing:Plant. ˙Qcoil,des is calculated as described above.## Design Air Flow Rate[LINK]

## System Coils[LINK]

The design air volumetric flow rate for the system cooling coil is set to:

GetCoilDesFlowTdescribed in section “Initial Calculations”;## Zone Coils[LINK]

Zone chilled water coils are always part of a zone HVAC component. In almost all cases the design flow rate is passed down from the design flow rate of the parent component. Otherwise if the parent component does cooling only the flow rate for the coil is set to the zone design cooling flow rate. And if the parent component does both cooling and heating, the coil flow rate is set to the maximum of the zone design cooling and heating flow rates.

## Design Inlet Air Temperature[LINK]

## System Coils[LINK]

The inlet air temperature depends on whether the coil is in the outside air stream and if it is not, whether or not there is outside air preconditioning.

Coil in outside air stream: Tair,in,des=Tout,cool,atpeak (the outside air temperature at the design cooling peak). Coil in main air stream, no preconditioning of outside air: Tair,in,des=Tmix,cool,atpeak (the mixed air temperature at the design cooling peak). Coil in main air stream, outside air preconditioned. The outside air fraction is calculated as foa=˙Vair,out,des/˙Vcc,air, where ˙Vcc,air is calculated above. Then Tair,in,des=foaTprecool+(1−foa)Tret,cool,atpeak where Tprecool is the specified

Precool Design TemperaturefromSystem:Sizing. Tret,cool,atpeak is the return temperature at the system cooling peak load.## Zone Coils[LINK]

The design inlet temperature depends on whether the coil is in a terminal unit or a zonal unit, and where the coil is positioned within the unit.

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionterminal unit the design inlet temperature is set to the zone temperature at the time of the zone cooling peak, since the coil is located in the induced air stream.## Design Outlet Air Temperature[LINK]

## System Coils[LINK]

The outlet air temperature depends on whether the coil is in the outside air stream.

T=_{air,out,des}T(the specified_{sys,des,precool}Precool Design Temperaturefrom theSizing:Systemobject).## Zone Coils[LINK]

If the coil is part of an

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionunit, then:˙Qcoil,des=cp,airρair˙Vw,coil,desΔTw,des

T1=Tair,in,des−˙Qcoil,des/(ρaircp,air˙Vair,coil,des)

T2=Tw,out,des+2

Tair,out,des=max(T1,T2)

For all other cases

Tis set to_{air,out,des}T(the zone design supply air temperature as specified in_{z,sup,des}Sizing:Zone).## Design Inlet Air Humidity Ratio[LINK]

## System Coils[LINK]

The design inlet humidity ratio depends on whether the coil is in the outside air stream and if it is not, whether or not there is outside air preconditioning.

Precool Design Humidity RatiofromSystem:Sizing. Wret,cool,atpeak is the return air humidity ratio at the system cooling peak load.## Zone Coils[LINK]

The design inlet humidity depends on whether the coil is in a terminal unit or a zonal unit, and where the coil is positioned within the unit.

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionterminal unit the design inlet humidity ratio is set to the zone humidity ratio at the time of the zone cooling peak, since the coil is located in the induced air stream.## Design Outlet Air Humidity Ratio[LINK]

## System Coils[LINK]

The outlet air humidity ratio depends on whether the coil is in the outside air stream.

W=_{air,out,des}W(the specified_{sys,des,precool}Precool Design Humidity Ratiofrom theSizing:Systemobject)PsyWFnTdbRhPbis the EnergyPlus psychrometric function to calculate humidity ratio from drybulb temperature, relative humidity, and atmospheric pressure. The design outlet humidity ratio is being set to the humidity ratio at 90% relative humidity and design outlet temperature.## Zone Coils[LINK]

If the coil is part of an

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionunit, then: get the dewpoint temperature atW:_{air,in,des}T≤_{dp,in}Tset_{w,in,des}W=_{air,out,des}W. Otherwise set Wair,out,des=min(PsyWFnTdbRhPb(Tair,out,des,0.9,Pair,std),Wair,in,des)_{air,in,des}If the coil is not part of an

AirTerminal:SingleDuct:ConstantVolume:FourPipeInductionunit, setWto_{air,out,des}W(the zone design supply air humidity ratio as specified in_{z,sup,des}Sizing:Zone).## Design Inlet Water Temperature[LINK]

## System Coils[LINK]

The Design Inlet Water Temperature is set to the

Design Loop Exit Temperaturespecified in theSizing:Plantobject for the water loop serving this coil.## Zone Coils[LINK]

The Design Inlet Water Temperature is set to the

Design Loop Exit Temperaturespecified in theSizing:Plantobject for the water loop serving this coil.## Coil:Cooling:Water:DetailedGeometry Sizing[LINK]

The sizing is done in subroutine

SizeWaterCoil## Max Water Flow Rate of Coil[LINK]

The calculation is identical to that done for

Coil:Cooling:Water.## Number of Tubes per Row[LINK]

Ntube/row=Int(13750˙Vcoil,water,max)

N=_{tube/row}Max(N,3)_{tube/row}## Fin Diameter[LINK]

Depending on the duct type, get the coil design air flow rate.

For duct type =

main, otheror default˙mair,des=ρairDesMainVolFlowsys

for duct type=cooling˙mair,des=ρairDesCoolVolFlowsys

for duct type=heating˙mair,des=ρairDesHeatVolFlowsys

Dfin=0.335˙mair,des

## Minimum Air Flow Area[LINK]

Depending on the duct type, get the coil design air flow rate.

For duct type =

main, otheror default˙mair,des=ρairDesMainVolFlowsys

for duct type=cooling˙mair,des=ρairDesCoolVolFlowsys

for duct type=heating˙mair,des=ρairDesHeatVolFlowsys

AMinAirFlow=0.44˙mair,des

## Fin Surface Area[LINK]

Depending on the duct type, get the coil design air flow rate.

For duct type =

main, otheror default˙mair,des=ρairDesMainVolFlowsys

for duct type=cooling˙mair,des=ρairDesCoolVolFlowsys

for duct type=heating˙mair,des=ρairDesHeatVolFlowsys

AFinSurf=78.5˙mair,des

## Total Tube Inside Area[LINK]

A~tube,total inside_{=4.4D}tube,inside_{N}tube rows_{N}tubes/row~Where

Dis the tube inside diameter._{tube,inside}## Tube Outside Surf Area[LINK]

A=4.1_{tube,outside}D_{tube,outside}N~tube rows_{N}tubes/row~Where

Dis the tube outside diameter._{tube,outside}## Coil Depth[LINK]

Depth=_{coil}Depth~tube spacing~ N~tube rows~## Coil:Cooling:WaterToAirHeatPump:EquationFit Sizing[LINK]

The sizing is done in subroutine

SizeHVACWaterToAir## Rated Air Flow Rate[LINK]

The calculation is identical to that done for

Coil:Cooling:Water.## Rated Water Flow Rate[LINK]

The calculation is identical to that done for

Coil:Cooling:Water, which is the coil design load divided by theLoop Design Temperature Differenceuser input fromSizing:Plant.If there is a companion heating coil, the heating coil design load is used so that both modes will have the same rated water flow rate. For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.## Rated Total Cooling Capacity[LINK]

The calculation for coil operating temperatures (inlet and outlet) are identical to that done for

Coil:Cooling:Water. The following calculations are then performed to determine the rated total cooling capacity.TWB,ratio=(TWB,air,in,des+273.15C)283.15C

TS,ratio=29.44C+273.15C283.15C

where:

TWB,ratio = ratio of load-side inlet air wet-bulb temperature in Kelvin to a reference temperature

TS,ratio = ratio of source-side inlet water temperature in Kelvin to a reference temperature

TCC1 = user input for Total Cooling Capacity Coefficient 1

TCC2 = user input for Total Cooling Capacity Coefficient 2

TCC3 = user input for Total Cooling Capacity Coefficient 3

TCC4 = user input for Total Cooling Capacity Coefficient 4

TCC5 = user input for Total Cooling Capacity Coefficient 5

TotCapTempModFac=TCC1+TCC2(TWB,ratio)+TCC3(TS,ratio)+TCC4+TCC5

The 4

^{th}and 5^{th}coefficient (TCC4 and TCC5) used in the above equation are multipliers for the load-side and source-side flow ratios, respectively. For sizing, these ratios are assumed to be 1.The enthalpy of the entering air is then compared with the enthalpy of the exiting air. The calculations for air enthalpy are identical to that done for

Coil:Cooling:Water. If the entering air enthalpy is less than the exiting air enthalpy, a reference value of 48,000 J/kg is used as the entering air enthalpy. If the TotCapTempModFac calculation above yields 0 as the result, a value of 1 is used in the following calculation. If the design air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil total cooling capacity is set equal to 0.## Rated Sensible Cooling Capacity[LINK]

The calculation for coil operating temperatures (inlet and outlet) are identical to that done for

Coil:Cooling:Water. The following calculations are then performed to determine the rated sensible cooling capacity.TDB,ratio=(TDB,air,in,des+273.15C283.15C

TS,ratio=(29.44C+273.15C283.15C

where:

TDB,ratio = ratio of load-side inlet air dry-bulb temperature in Kelvin to a reference temperature

SCC1 = user input for Sensible Cooling Capacity Coefficient 1

SCC2 = user input for Sensible Cooling Capacity Coefficient 2

SCC3 = user input for Sensible Cooling Capacity Coefficient 3

SCC4 = user input for Sensible Cooling Capacity Coefficient 4

SCC5 = user input for Sensible Cooling Capacity Coefficient 5

SCC6 = user input for Sensible Cooling Capacity Coefficient 6

SensCapTempModFac=SCC1+SCC2(TDB,ratio)+SCC3(TWB,ratio)+SCC4(TS,ratio)+SCC5+SCC6

The 5

^{th}and 6^{th}coefficient (SCC5 and SCC6) used in the above equation are multipliers for the load-side and source-side flow ratios, respectively. For sizing, these ratios are assumed to be 1.The dry-bulb temperature of the entering air is then compared with the dry-bulb temperature of the exiting air. The calculations for air dry-bulb temperature are identical to that done for

Coil:Cooling:Water. If the entering air dry-bulb temperature is less than the exiting air dry-bulb temperature, a reference value of 24 C is used as the entering air dry-bulb temperature. If the SensCapTempModFac calculation above yields 0 as the result, a value of 1 is used in the following calculation. If the design air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil sensible cooling capacity is set equal to 0.## Coil:Cooling:WaterToAirHeatPump:VariableSpeedEquationFit Sizing[LINK]

For the cooling coil of VS WSHP, we specify a nominal speed level. During the sizing calculation, the Rated Air Volume Flow Rate, the Rated Water Volume Flow Rate and the Rated Total Cooling Capacity at the Selected Nominal Speed Level are determined in the same way as the

Coil:Cooling:WaterToAirHeatPump:EquationFitobject. The sensible heat transfer rate is not allowed for auto-sizing, instead, it is a function of the rated air and water flow rates, rated total cooling capacity and the Reference Unit SHR at the nominal speed level. The default nominal speed level is the highest speed. However, the model allows the user to select a nominal speed level rather than the highest.## Rated Air Flow Rate[LINK]

The calculation is identical to that done for

Coil:Cooling:WaterToAirHeatPump:EquationFit.## Rated Water Flow Rate[LINK]

The calculation is identical to that done for

Coil:Cooling:WaterToAirHeatPump:EquationFit, which is the coil design load divided by theLoop Design Temperature Differenceuser input fromSizing:Plant.If there is a companion heating coil, the heating coil design load is used so that both modes will have the same rated water flow rate. For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.## Rated Total Cooling Capacity[LINK]

The calculation for coil operating temperatures (inlet and outlet) are identical to that done for

Coil:Cooling:WaterToAirHeatPump:EquationFit. The calculations for air enthalpy are similar to that done forCoil:Cooling:WaterToAirHeatPump:EquationFit.The difference is in calculating the total cooling capacity temperature modifier function at the selected nominal speed level, as below:TotCapTempModFracNominalSpeed=a+b∗WBi+c∗WB2i+d∗EWT+e∗EWT2+f∗WBi∗EWT

where

WB

_{i}= wet-bulb temperature of the air entering the heating coil, °CEWT = entering water temperature, °C

a-f = regression curve-fit coefficients.

If the entering air enthalpy is less than the exiting air enthalpy, a reference value of 48,000 J/kg is used as the entering air enthalpy. If the

TotCapTempModFaccalculation above yields 0 as the result, a value of 1 is used in the following calculation. If the rated air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil total cooling capacity is set equal to 0.If H_{in}> H_{out}Then˙Qcoil,rated,total=mair,rated(Hin−Hout)/TotCapTempModFracNominalSpeed

Else˙Qcoil,rated,total=mair,rated(48000−Hout)/TotCapTempModFracNominalSpeed

End If## Coil:Heating:WaterToAirHeatPump:EquationFit Sizing[LINK]

The sizing is done in subroutine

SizeHVACWaterToAir.## Rated Air Flow Rate[LINK]

The calculation is identical to that done for

Coil:Cooling:Water.## Rated Water Flow Rate[LINK]

The calculation is identical to that done for

Coil:Cooling:Water, which is the coil design load divided by theLoop Design Temperature Differenceuser input fromSizing:Plant.For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.## Rated Total Heating Capacity[LINK]

The rated total heating capacity is set equal to the rated total cooling capacity.

## Coil:Heating:WaterToAirHeatPump:VariableSpeedEquationFit Sizing[LINK]

For the heating coil of VS WSHP, we specify a nominal speed level. During the sizing calculation, the Rated Air Volume Flow Rate and the Rated Water Volume Flow Rate are determined in the same way as the

Coil:Heating:WaterToAirHeatPump:EquationFitobject. On the other hand, the Rated Heating Capacity at the Selected Nominal Speed Level should be the same as the total cooling capacity of its corresponding cooling coil, which has to be sized first. The default nominal speed level will be the highest speed. However, the model allows the user to select a nominal speed level rather than the highest.## Rated Air Flow Rate[LINK]

The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit.

## Rated Water Flow Rate[LINK]

The calculation is identical to that done for Coil:Cooling:WaterToAirHeatPump:EquationFit, which is the coil design load divided by the

Loop Design Temperature Differenceuser input fromSizing:Plant.For sizing the plant loop serving this coil, only one half of this flow rate is used since both the cooling and heating coil will save a flow rate but only one of these coils will operate at a time.## Rated Total Heating Capacity[LINK]

The rated total heating capacity is set equal to the rated total cooling capacity.

## Coil:Heating:Water Sizing[LINK]

The sizing is done in subroutine

SizeWaterCoil.## Max Water Flow Rate of Coil[LINK]

## System Coils[LINK]

With the coil load from the system design data array and the user specified (in a Sizing:Plant object) design hot water temperature fall, calculate the max water flow rate:

˙Vcoil,water,max=HeatCapsys/(Cp,waterρwaterΔTplt,hw,des)

## Zone Coils[LINK]

Using the zone design coil inlet and supply air conditions calculate the design coil load.

If the coil is not part of an induction unit then obtain the coil inlet temperature from the zone design data array;

T_{in,air}= DesHeatCoilInTemp_{zone}If the coil is part of an induction unit take into account the induced air:

Frac=_{minflow}MinFlowFrac_{zone}T=_{in,air}DesHeatCoilInTemp+_{zone}Frac_{minflow}ZoneTempAtHeatPeak(1_{zone}Frac)_{minflow}T_{out,air}= HeatDesTemp_{zone}W_{out,air}= HeatDesHumRat_{zone}If the coil is part of a terminal unit the mass flow rate is determined by the volumetric flow rate of the terminal unit:

˙mair,des=ρair˙mair,des,tu

Otherwise the design flow is obtained from the zone design data array:

˙mair,des=DesHeatMassFlowzone

Qcoil,des=cp,air˙mair,des(Tout,air−Tin,air)

Here

cis calculated at the outlet humidity and the average of the inlet and outlet temperatures._{p,air}With the coil load and the user specified (in a Sizing:Plant object) design hot water temperature decrease, calculate the max water flow rate:

˙Vcoil,water,max=Qcoil,des/(Cp,waterρwaterΔTplt,hw,des)

## UA of the Coil[LINK]

To obtain the UA of the coil, we specify the model inputs (other than the UA) at design conditions and the design coil load that the coil must meet. Then we numerically invert the coil model to solve for the UA that will enable the coil to meet the design coil load given the specified inputs.

## System Coils[LINK]

The design coil load is the system design sensible cooling capacity;

Q=_{coil,des}HeatCap_{sys}The required inputs for the simple coil model are:

T=_{in,air}HeatMixTemp_{sys}W=_{in,air}HeatMixHumRat_{sys}T=_{in,water}ExitTemp_{plt,hw,des}˙min,water=ρwater˙Vcoil,water,max

Depending on the duct type, get the coil design air flow rate.

For duct type =

main, otheror default˙min,air=ρairDesMainVolFlowsys

for duct type=cooling˙min,air=ρairDesCoolVolFlowsys

for duct type=heating˙min,air=ρairDesHeatVolFlowsys

We now have all the data needed to obtain UA. The numerical inversion is carried out by calling subroutine

SolveRegulaFalsi. This is a general utility routine for finding the zero of a function. In this case it finds the UA that will zero the residual function - the difference between the design coil load and the coil output divided by the design coil load. The residual is calculated in the functionSimpleHeatingCoilUAResidual.## Zone Coils[LINK]

If the coil is not part of an induction unit then obtain the coil inlet temperature from the zone design data array;

T_{in,air}= DesHeatCoilInTemp_{zone}If the coil is part of an induction unit take into account the induced air:

Frac=_{minflow}MinFlowFrac_{zone}T=_{in,air}DesHeatCoilInTemp+_{zone}Frac_{minflow}ZoneTempAtHeatPeak(1_{zone}Frac)_{minflow}W=_{in,air}DesHeatCoilInHumRat_{zone}T=_{in,water}ExitTemp_{plt,hw,des}˙min,water=ρwater˙Vcoil,water,max

T_{out,air}= HeatDesTemp_{zone}W_{out,air}= HeatDesHumRat_{zone}If the coil is part of a terminal unit the mass flow rate is determined by the volumetric flow rate of the terminal unit:

˙mair,des=ρair˙mair,des,tu

Otherwise the design flow is obtained from the zone design data array:

˙mair,des=DesHeatMassFlowzone

˙Qcoil,des=cp,air˙mair,des(Tout,air−Tin,air)

Here

cis calculated at the outlet humidity and the average of the inlet and outlet temperatures._{p,air}We now have all the data needed to obtain UA. The numerical inversion is carried out by calling subroutine

SolveRegulaFalsi. This is a general utility routine for finding the zero of a function. In this case it finds the UA that will zero the residual function - the difference between the design coil load and the coil output divided by the design coil load. The residual is calculated in the functionSimpleHeatingCoilUAResidual.## Coil:Heating:Steam Sizing[LINK]

The sizing is done in subroutine

SizeSteamCoil.## Maximum Steam Flow Rate[LINK]

## System Coils[LINK]

The maximum steam volumetric flow rate is calculated using:

The steam density (ρsteam) is for saturated steam at 100°C (101325.0 Pa) and

his the latent heat of vaporization of water at 100°C (101325.0 Pa)._{fg}Cis the heat capacity of saturated water (condensate) at 100°C (101325.0 Pa) and ΔTsc is the Degree of Subcooling defined in the Coil:Heating:Steam object input. The design coil load_{p,w}Loadis calculated from:_{coil,des}Loadcoil,des=˙mair,des(cp,air)(Tair,coil,des,out−Tair,coil,des,in)

The design air mass flow rate depends on the location of the coil (duct type). For duct type =

main,the flow rate is set to. If the coil is in a cooling duct the flow rate is set to_{air}DesMainVolFlow_{sys}MinSysAirFlowRatio. If the coil is in a heating duct the flow rate is set to_{air}DesCoolVolFlow_{sys}MinSysAirFlowRatio. If the coil is in any other kind of duct, the flow rate is set to_{air}DesHeatVolFlow_{sys}._{air}DesMainVolFlow_{sys}For sizing, the design outlet air temperature (

T) is the Central Heating Design Supply Air Temperature specified in the Sizing:System object._{air,coil,des,out}The design inlet air temperature depends on whether the coil is being sized for 100% outdoor air or minimum outdoor air flow (per 100% Outdoor Air in Heating input field in the Sizing:System object).

T=_{air,coil,des,in}HeatOutTemp(the outdoor air temperature at the design heating peak)_{sys}Frac_{oa}**=DesOutAirVolFlow/_{sys}DesVolFlow.DesVolFlowis ˙mair,desρair.T=_{air,coil,des,in}Frac_{oa}HeatOutTemp+ (1. -_{sys}Frac)_{oa}HeatRetTemp(see Table 41. System Sizing Data)_{sys}## Zone Coils[LINK]

If the coil is part of an

AirTerminal:SingleDuct:*unit (e.g.,AirTerminal:SingleDuct:ConstantVolume:Reheat, AirTerminal:SingleDuct:VAV:Reheat, AirTerminal:SingleDuct:SeriesPIU:Reheat, etc.), the maximum steam flow rate is set equal to the terminal unit’s maximum steam flow rate. Otherwise (e.g., the zone-level coil is part ofZoneHVAC:PackagedTerminalAirConditioner, ZoneHVAC:UnitVentilator, ZoneHVAC:UnitHeater or ZoneHVAC:VentilatedSlab) the calculation is similar to that at the system level. A design load is calculated:Loadcoil,des=˙mair,des(cp,air)(Tair,coil,des,out−Tair,coil,des,in)

where:

˙mair,des=

DesHeatMassFlow(see Table 40. Zone Sizing Data)_{zone}T=_{air,coil,des,in}DesHeatCoilInTemp(see Table 40)_{zone}T=_{air,coil,des,out}HeatDesTemp(user input from Sizing:Zone object)_{zone}cp,air = Specific heat of air (evaluated at the average of inlet and outlet air temperatures, and at the zone heating design supply air humidity ratio

HeatDesHumRat[user input from Sizing:Zone object])_{zone}The terms in the denominator of this equation (

ρ,_{steam}h, etc.) are evaluated in the same way as described above for steam System Coils._{fg}## Sizing of Gas and Electric Heating Coils[LINK]

The sizing calculation is done in subroutine

SizeHeatingCoilin moduleHeatingCoils.## Nominal Capacity of the Coil[LINK]

## System Coils[LINK]

The value is obtained from the system design array.

Cap=_{nom}HeatCap_{sys}## Zone Coils[LINK]

The capacity is calculated from the design coil inlet and outlet conditions.

If the coil is not part of an induction unit then obtain the coil inlet temperature from the zone design data array;

T_{in,air}= DesHeatCoilInTemp_{zone}If the coil is part of an induction unit take into account the induced air:

Frac=_{minflow}MinFlowFrac_{zone}T=_{in,air}DesHeatCoilInTemp+_{zone}Frac_{minflow}ZoneTempAtHeatPeak(1_{zone}Frac)_{minflow}T_{out,air}= HeatDesTemp_{zone}W_{out,air}= HeatDesHumRat_{zone}Q=_{coil,des}C(_{p,air}DesHeatMassFlow_{zone}T)_{out,air}T_{in,air}Here

cis calculated at the outlet humidity and the average of the inlet and outlet temperatures._{p,air}## DX Coil Sizing[LINK]

The sizing calculations are done in subroutine

SizeDXCoilin moduleDXCoils. This section covers the sizing of the objectsCoil:Cooling:DX:SingleSpeed

Coil:Heating:DX:SingleSpeed

Coil:Cooling:DX:TwoSpeed

## Rated Air Volume Flow Rate[LINK]

## System Coils[LINK]

The rated air flow rate is obtained from the system design array.

˙Vair,rated=DesMainVolFlowsys

## Zone Coils[LINK]

The rated air flow rate is the maximum of the heating and cooling design flow rates from the zone design array.

˙Vair,rated=Max(DesCoolVolFlowzone,DesHeatVolFlowzone)

## Rated Total Cooling Capacity[LINK]

## System Coils[LINK]

The rated cooling capacity is obtained by dividing the peak cooling capacity by the

Cooling Capacity Modifier Curveevaluated at peak mixed wetbulb and outdoor drybulb temperatures.T=_{mix}CoolMixTemp_{sys}W=_{mix}CoolMixHumRat_{sys}T=_{sup}CoolSupTemp_{sys}W=_{sup}CoolSupHumRat_{sys}T=_{outside}CoolOutTemp_{sys}=_{air}PsyRhoAirFnPbTdbW(p,_{air,std}T,_{mix}W)_{mix}h=_{mix}PsyHFnTdbW(T,_{mix}W)_{mix}h=_{sup}PsyHFnTdbW(T,_{sup}W)_{sup}T=_{mix,wb}PsyTwbFnTdbWPb(T,_{mix}W,_{mix}p)_{air,std}CapModFac=CurveValue(CCapFTemp,T,_{mix,wb}T)_{outside}CCappeak=ρair˙Vair,rated(hmix−hsup)

CCap=_{rated}CCap_{peak}CapModFacWe check that the design volume flow per total capacity is within the prescribed range:

FlowCapRatio=˙Vair,rated/CCaprated

If

FlowCapRatio<FlowCapRatiothen_{min}CCaprated=˙Vair,rated/FlowCapRatiomin

If

FlowCapRatio>FlowCapRatiothen_{max}CCaprated=˙Vair,rated/FlowCapRatiomax

where

FlowCapRatio= 0.00004027 m_{min}^{3}/s per watt (300 cfm/ton)And

FlowCapRatio= 0.00006041 m_{max}^{3}/s per watt (450 cfm/ton)The sizing calculation for DX cooling coils for 100% dedicated outdor air system (DOAS) are identical to regular DX cooling coils. However, they operate operate at different flow to capacity ratio ranges and are within the prescribed range below:

FlowCapRatio= 0.00001677 m_{min}^{3}/s per Watt (125 cfm/ton)And

FlowCapRatio= 0.00003355 m_{max}^{3}/s per Watt (250 cfm/ton)## Zone Coils[LINK]

The rated cooling capacity for zone coils is calculated in the same manner as for system coils.

T=_{mix}DesCoolCoilInTemp_{zone}W=_{mix}DesCoolCoilInHumRat_{zone}T=_{sup}CoolDesTemp_{zone}W=_{sup}CoolDesHumRat_{zone}T=_{outside}T_{outside},_{desday,peak}=_{air}PsyRhoAirFnPbTdbW(p,_{air,std}T,_{mix}W)_{mix}h=_{mix}PsyHFnTdbW(T,_{mix}W)_{mix}h=_{sup}PsyHFnTdbW(T,_{sup}W)_{sup}T=_{mix,wb}PsyTwbFnTdbWPb(T,_{mix}W,_{mix}p)_{air,std}CapModFac=CurveValue(CCapFTemp,T,_{mix,wb}T)_{outside}CCappeak=ρair˙Vair,rated(hmix−hsup)

CCap=_{rated}CCap_{peak}CapModFacWe check that the design volume flow per total capacity is within the prescribed range:

FlowCapRatio=˙Vair,rated/CCaprated

If

FlowCapRatio<FlowCapRatiothen_{min}CCaprated=˙Vair,rated/FlowCapRatiomin

If

FlowCapRatio>FlowCapRatiothen_{max}CCaprated=˙Vair,rated/FlowCapRatiomax

where

FlowCapRatio= 0.00004027 m_{min}^{3}/s per watt (300 cfm/ton)And

FlowCapRatio= 0.00006041 m_{max}^{3}/s per watt (450 cfm/ton)We check the design flow to the total cooling capacity rato for dedicated zone outdoor unit DX cooling coils to be within the limits prescribed below:

FlowCapRatio= 0.00001677 m_{min}^{3}/s per Watt (125 cfm/ton)And

FlowCapRatio= 0.00003355 m_{max}^{3}/s per Watt (250 cfm/ton)## Rated Total Heating Capacity[LINK]

For Coil:Heating:DX:SingleSpeed the rated heating capacity is set equal to the cooling capacity.

## Rated SHR[LINK]

The rated sensible heat ratio is calculated to be the sensible cooling (from rated inlet conditions to user specified supply conditions) divided by the total cooling (from rated inlet to specified supply).

T= 26.6667_{in,rated}^{o}C (80^{o}F)W= 0.01125 (corresponds to 80_{in,rated}^{o}F drybulb, 67^{o}F wetbulb)C=_{p,air}PsyCpAirFnWTdb(W,_{in,rated}T)_{in,rated}For system coils

T=_{sup}CoolSupTemp_{sys}W=_{sup}CoolSupHumRat_{sys}For zone coils

T=_{sup}CoolDesTemp_{zone}W=_{sup}CoolDesHumRat_{zone}Then

h=_{rated}PsyHFnTdbW(T,_{in,rated}W)_{in,rated}h=_{sup}PsyHFnTdbW(T,_{sup}W)_{sup}h_{rated,sup}=h_{rated}h_{sup}Qs=_{rated,sup}C(_{p,air}T)_{in,rated}T_{sup}SHR=_{rated}Qs_{rated,sup}h_{rated,sup}## Evaporative Condenser Air Volume Flow Rate[LINK]

The evaporative condenser air volume flow rate (m

^{3}/s) is set to 0.000114 m^{3}/s per watt (850 cfm/ton) times the total rated cooling capacity.## Evaporative Condenser Air Volume Flow Rate, Low Speed[LINK]

The evaporative condenser air volume flow rate, low speed (m

^{3}/s) is set to 1/3 times 0.000114 m^{3}/s per watt (850 cfm/ton) times the total rated cooling capacity.## Evaporative Condenser Pump Rated Power Consumption[LINK]

The evaporative condenser pump rated power consumption is set equal to the total cooling capacity times 0.004266 watts pump power per watt capacity (15 W/ton).

## Evaporative Condenser Pump Rated Power Consumption, Low Speed[LINK]

The evaporative condenser pump rated power consumption, low speed, is set equal to 1/3 times the total cooling capacity times 0.004266 watts pump power per watt capacity (15 W/ton).

## Rated Air Volume Flow Rate, low speed[LINK]

The rated air volume flow rate, low speed, is set equal to 1/3 times the full rated air volume flow rate.

## Rated Total Cooling Capacity, Low Speed[LINK]

The rated total cooling capacity, low speed, is set equal to 1/3 times the full rated total cooling capacity.

## Rated SHR, low speed[LINK]

The rated sensible heat ratio, low speed, is set equal to the full speed SHR.

## Resistive Defrost Heater Capacity[LINK]

For the heat pump the resistive defrost heat capacity is set equal to the cooling capacity.

## DX MultiSpeed Coil Sizing[LINK]

The sizing calculations are done in subroutine

SizeDXCoilin moduleDXCoils. This section covers the sizing of the objectsCoil:Heating:DX:MultiSpeed

Coil:Cooling:DX: MultiSpeed

The rated air volume flow rate, rated total cooling capacity, rated heating capacity, rated SHR, evaporative condenser air volume flow rate, evaporative condenser pump rated power consumption at the highest speed are sized in the same ways as DX Coil Sizing.

After the sizes are determined at the highest speed, the sizes in the rest of speeds are assumed to

Valuen=nNumberOfSpeed∗ValueNumberOfSpeed

where

Value

_{n}= Any autosizable variable at Speed n, except SHRSHR

_{n}= SHR_{NumberOfSpeed}n= Speed Index number from 1 to NumberOfSpeed-1

NumberOfSpeed= The highest speed number

## Coil:Cooling:DX:VariableSpeed Sizing[LINK]

For the variable-speed DX cooling coil, we specify a nominal speed level. During the sizing calculation, the Rated Total Cooling Capacity at the Selected Nominal Speed Level is determined in the same way as the Coil:Cooling:DX:SingleSpeed object. If the user chooses to autosize the Rated Air Volume Flow Rate, the flow rate, as compared to the Rated Total Cooling Capacity, is sized to have the same ratio as the air volume flow rate to the total cooling capacity at the nominal speed, of the Reference Unit. The sensible heat transfer rate is not allowed for auto-sizing, instead, it is a function of the rated air flow, rated total cooling capacity and the Reference Unit SHR at the nominal speed level. The default nominal speed level is the highest speed. However, the model allows the user to select a nominal speed level rather than the highest.

Rated Total Cooling CapacityThe calculation for coil operating temperatures (inlet and outlet) are identical to that done for Coil:Cooling:DX:SingleSpeed. The calculations for air enthalpy are similar to that done for Coil:Cooling:DX:SingleSpeed

.The difference is in calculating the total cooling capacity temperature modifier function at the selected nominal speed level, as below:TotCapTempModFracNominalSpeed=a+b∗WBi+c∗WB2i+d∗DBo+e∗DBoT2+f∗WBi∗DBo

where

WB

_{i}= wet-bulb temperature of the air entering the cooling coil, °CDB

_{o}= condenser entering air temperature, °Ca-f = regression curve-fit coefficients.

If the entering air enthalpy is less than the exiting air enthalpy, a reference value of 48,000 J/kg is used as the entering air enthalpy. If the

TotCapTempModFaccalculation above yields 0 as the result, a value of 1 is used in the following calculation. If the rated air mass flow rate is determined to be less than a very small flow value (0.001 kg/s) or the capacity calculated here is less than 0, the coil total cooling capacity is set equal to 0.If H_{in}> H_{out}Then˙Qcoil,rated,total=mair,rated(Hin−Hout)/TotCapTempModFracNominalSpeed

Else˙Qcoil,rated,total=mair,rated(48000−Hout)/TotCapTempModFracNominalSpeed

End IfThe other sizing procedures, e.g. evaporative condenser pump, etc., are the same as Coil:Cooling:DX:SingleSpeed.

## Coil:Heating:DX:VariableSpeed Sizing[LINK]

For the variable-speed DX heating coil, we specify a nominal speed level. During the sizing calculation, the Rated Heating Capacity at the Selected Nominal Speed Level should be the same as the total cooling capacity of its corresponding cooling coil, which has to be sized first. The default nominal speed level will be the highest speed. However, the model allows the user to select a nominal speed level rather than the highest. If the user chooses to autosize the Rated Air Volume Flow Rate, the flow rate, as compared to the Rated Heating Capacity, is sized to have the same ratio as the air volume flow rate to the heating capacity at the nominal speed, of the Reference Unit. The other sizing procedures are the same as Coil:Heating:DX:SingleSpeed.

## Pump Sizing[LINK]

The loop pumps’ autosizable inputs are nominal volumetric flow rate and nominal power consumption. We have

Eff=_{tot}Eff_{mot}Eff_{impeller}The motor efficiency is an input. Since we need the total efficiency to calculate the nominal power consumption we assume an impeller efficiency of 0,78 for purposes of sizing.

## Rated Volumetric Flow Rate[LINK]

This is just set equal to the design loop demand obtained from summing the needs of the components on the demand side of the loop.

## Rated Power Consumption[LINK]

˙Qnom=Hnom˙Vnom/Efftot

H, the nominal head, is an input._{nom}## Electric Chiller Sizing[LINK]

Generally chillers will need nominal cooling capacity, evaporator flow rate and condenser flow rate. All 3 quantities can be straightforwardly obtained using the user specified loop sizing data and the loop design flow rates.

All chillers on a loop are sized to meet the full loop load. If there are multiple chillers on a loop that call for autosizing, they will all be assigned the same cooling capacity and evaporator flow rate.

## Nominal Cooling Capacity[LINK]

˙Qchiller,nom=Cp,wρwΔTloop,des˙Vloop,des

where

Cis the specific heat of water at 5_{p,w}^{o}C;is the density of water at standard conditions (5.05_{w}^{o}C);Tis the chilled water loop design temperature rise;_{loop,des}˙Vloop,des is the loop design volumetric flow rate.

## Design Evaporator Volumetric Water Flow Rate[LINK]

˙Vevap,des=˙Vloop,des

## Design Condenser Volumetric Water Flow Rate[LINK]

˙Vcond,des=˙Qchiller,nom(1+1/COPchiller,nom)/(ΔTloop,desCp,wρw)

where

Cis the specific heat of water at design condenser inlet temperature;_{p,w}is the density of water at standard conditions (5.05_{w}^{o}C);Tis the chilled water loop design temperature rise;_{loop,des}COPis the chiller nominal COP._{chiller,nom}Boiler Sizing

Generally boilers will need nominal heating capacity and rate. Both quantities can be straightforwardly obtained using the user specified loop sizing data and the loop design flow rates.

All boilers on a loop are sized to meet the full loop load. If there are multiple boilers on a loop that call for autosizing, they will all be assigned the same heating capacity and flow rate.

## Nominal Capacity[LINK]

˙Qboiler,nom=Cp,wρwΔTloop,des˙Vloop,des

where

Cis the specific heat of water at the boiler design outlet temperature;_{p,w}is the density of water at standard conditions (5.05_{w}^{o}C);Tis the hot water loop design temperature decrease;_{loop,des}˙Vloop,des is the loop design volumetric flow rate.

## Design Evaporator Volumetric Water Flow Rate[LINK]

˙Vdes=˙Vloop,des

## Plant Heat Exchanger Sizing[LINK]

The sizing of plant heat exchanger component (object: HeatExchanger:FluidToFluid) involves determining design flow rates for both sides, a UA value, and a nominal capacity for reporting. The component has a sizing factor for fine control and uses the design temperatures defined in the Sizing:Plant object.

The Loop Supply Side design flow rate, ˙VSup,des, is set equal to the design flow rate for that loop, multiplied by the component sizing factor, fcomp.

˙VSup,des=˙Vloop,des∗fcomp

The Loop Demand Side design flow rate,˙VDmd,des , is set equal to the Loop Supply Side design flow rate.

˙VDmd,des=˙VSup,des

The design heat transfer capacity and UA for the heat exchanger are calculated using the design temperatures for the two plant loops. The loop design temperature difference for the Loop Supply Side, ΔTSupLoop,Des, is used to determine a nominal capacity.

˙Q=.VSup,desρcpΔTSupLoop,Des

A loop-to-loop design temperature difference, ΔTLoopToLoop,De