System Design Loads and Air Flow Rates[LINK]

Overview[LINK]

The purpose of the system design calculation is to estimate design heating and cooling loads and air flow rates for each air loop in the simulation problem. The calculation sequence for system level design loads and air flow rates resembles the calculation sequence for zone loads and air flow rates. There is an update subroutine UpdateSysSizing called at the beginning, during, and end of a loop in the Sizing Manager over all the design days. The major difference is that this calculation is done at the zone time-step only. There is no idealized component calculation triggered at the system time-step as in the zone calculation. The system design calculation operates at the zone time step using the design environment weather data and the data stored in the zone sizing arrays. The results of the system design calculation are stored in the system sizing arrays described below.

System Design Data Arrays[LINK]

The system design data arrays are:

SysSizInput(i) stores the input data from the Sizing:System objects.

SysSizing(i,j) stores the results of the system design calculations for all systems and all design days. The index i is for air loops, j for design days.

CalcSysSizing(i) stores the results of the system design calculations for the peak heating and cooling cases for each air loop. The index i is for the air loops.

FinalSysSizing(i) corresponds to CalcSysSizing but includes the effect of the user specified sizing factor or user specified system design flow rate.

The data stored in SysSizing, CalcSysSizing and FinalSysSizing includes the following data items.

Table 41. System Sizing Data

Name	Description
All the data from SysSizInput
CoinCoolMassFlow	coincident peak cooling mass flow rate [kg/s]
CoinHeatMassFlow	coincident peak heating mass flow rate [kg/s]
NonCoinCoolMassFlow	noncoincident peak cooling mass flow rate [kg/s]
NonCoinHeatMassFlow	noncoincident peak heating mass flow rate [kg/s]
DesMainVolFlow	design main supply duct volume flow [m3/s]
DesHeatVolFlow	design heat supply duct volume flow [m3/s]
DesCoolVolFlow	design cool supply duct volume flow [m3/s]
SensCoolCap	design sensible cooling capacity [W]
TotCoolCap	design total cooling capacity [W]
HeatCap	design heating capacity [W]
PreheatCap	design preheat capacity [W]
MixTempAtCoolPeak	mixed air temperature at the time of the cooling peak [C]
MixHumRatAtCoolPeak	mixed air humidity ratio at the time of the cooling peak [kg water/kg dry air]
RetTempAtCoolPeak	return air temperature at the time of the cooling peak [C]
RetHumRatAtCoolPeak	return air humidity ratio at the time of the cooling peak [kg water/kg dry air]
OutTempAtCoolPeak	outside air temperature at the time of the cooling peak [C]
OutHumRatAtCoolPeak	outside air humidity ratio at the time of the cooling peak [kg water/kg dry air]
HeatMixTemp	design mixed air temperature for heating [C]
HeatMixHumRat	design mixed air humidity ratio for heating [kg water/kg dry air]
HeatRetTemp	design return air temperature for heating [C]
HeatRetHumRat	design return air humidity ratio for heating [kg water/kg dry air]
HeatOutTemp	design outside air temperature for heating [C]
HeatOutHumRat	design outside air humidity ratio for heating [kg water/kg dry air]
HeatFlowSeq(i)	daily sequence of system heating air mass flow rate (zone time step) [kg/s]
CoolFlowSeq(i)	daily sequence of system cooling air mass flow rate (zone time step) [kg/s]
SumZoneCoolLoadSeq(I)	daily sequence of zones’ summed cooling load (zone time step) [W]
CoolZoneAvgTempSeq(I)	daily sequence of zones flow weighted average temperature (zone time step) [W]
SensCoolCapSeq(I)	daily sequence of system sensible cooling capacity (zone time step) [W]
TotCoolCapSeq(I)	daily sequence of system total cooling capacity (zone time step) [W]
HeatCapSeq(i)	daily sequence of system heating capacity (zone time step) [W]
PreHeatCapSeq(i)	daily sequence of system preheat capacity (zone time step) [W]
SysCoolRetTempSeq(i)	daily sequence of system cooling return temperatures (zone time step) [C]
SysCoolRetHumRatSeq(I)	daily sequence of system cooling return humidity ratios (zone time step) [kg water/kg dry air]
SysHeatRetTempSeq(i)	daily sequence of system heating return temperatures (zone time step) [C]
SysHeatRetHumRatSeq(I)	daily sequence of system heating return humidity ratios (zone time step) [kg water/kg dry air]
SysCoolOutTempSeq	daily sequence of system cooling outside temperatures (zone time step) [C]
SysCoolOutHumRatSeq	daily sequence of system cooling outside humidity ratios (zone time step) [kg water/kg dry air]
SysHeatOutTempSeq	daily sequence of system heating outside temperatures (zone time step) [C]
SysHeatOutHumRatSeq	daily sequence of system heating outside humidity ratios (zone time step) [kg water/kg dry air]

System Design Flow Rate and Load Summation and Adjustment[LINK]

There is no system level subroutine corresponding to SizeZoneEquipment. Instead the system design loads and flow rates are calculated using the zone level results. The zone design flow rates for the zones served by an air loop are summed to obtain the system level design flow rates. These air flows are mixed with the system level design minimum outside air flow rate to obtain system design coil loads. These activities are all performed within the UpdateSysSizing subroutine in the SimAirServingZones module. It is called at the start of each design day (CallIndicator = BeginDay), at the zone time-step (CallIndicator = DuringDay), at the end of the design day (CallIndicator = EndDay) and at the end of the zone design calculation (CallIndicator = EndSysSizingCalc).

There is a logical flag SysSizingCalc corresponding to ZoneSizingCalc. It is used to allow the component routines to distinguish a normal simulation call from a being called during a system sizing calculation.

BeginDay[LINK]

1. The environment (in this case, a design day) name is stored in the system sizing data structures.

2. Loop over the zones cooled by this air loop:

1. NonCoinCoolMassFlow_sys = DesCoolMassFlow_zone

3. Loop over the zones heated by this air loop:

1. NonCoinHeatMassFlow_sys = DesHeatMassFlow_zone

DuringDay[LINK]

1. Loop over the zones cooled by this air loop:

CoolFlowSeq_sys(i) = CoolFlowSeq _zone(i)

SysCoolRetTemp(i) = (CoolZoneRetTempSeq(i) * CoolFlowSeq_zone(i))/ CoolFlowSeq_sys(i)

SysCoolRetHumRat(i) = (CoolZoneHumRatSeq(i) * CoolFlowSeq_zone(i))/ CoolFlowSeq_sys(i)

FracOA = r_air * DesOutAirVolFlow_sys/ CoolFlowSeq_sys(i)

T_mix = T_outside * FracOA + SysCoolRetTemp(i)(1 - FracOA)

W_mix = W_outside * FracOA + SysCoolRetHumRat (i)(1 - FracOA)

SysCoolOutTempSeq(i) = T_outside

SysCoolOutHumRatSeq(i) = W_outside

Get the current (zone time-step) system cooling capacity:

SysSensCoolCap_cur = C_p,air * CoolFlowSeq_sys(i) *( T_mix-T_sup)

SensCoolCapSeq(I) = SysSensCoolCap_cur

If SysSensCoolCap_cur is the maximum for the day so far then save SysSensCoolCap_cur as the design value:

SensCoolCap(i )_sys = SysSensCoolCap_cur

And save the corresponding mixed, return and outside conditions:

CoolMixTemp_sys = T_mix

CoolMixHumRat_sys = W_mix

CoolRetTemp_sys = SysCoolRetTemp(i)

CoolRetHumRat_sys = SysCoolRetHumRat(I)

CoolOutTemp_sys = T_outside

CoolOutHumRat_sys = W_outside

Here r_airis the density of dry air at 20C and standard elevation corrected pressure, [kg/m^3];

*FracOA* is the outside air fraction;

• C_p,air* is the specific heat of dry air at 20C, [J/kg-K];

• T_sup* is the user specified design cooling supply temperature [C];

• T_mix* is the current mixed air temperature [C];

• W_mix* is the current mixed air humidity ratio [kg water / kg dry air];

  *T<sub>outside</sub>* is the current outside air temperature [C];

• W_outside* is the current outside air humidity ratio [kg water / kg dry air].

2. Loop over the zones heated by this air loop.

HeatFlowSeq_sys(i) = HeatFlowSeq _zone(i)

SysHeatRetTemp(i) = (HeatZoneRetTempSeq(i) * HeatFlowSeq_zone(i))/

HeatFlowSeq_sys(i)

SysHeatRetHumRat(i) = (HeatZoneHumRatSeq(i) * HeatFlowSeq_zone(i))/

• HeatFlowSeq_sys(i)*

FracOA = r_air * DesOutAirVolFlow_sys/ HeatFlowSeq_sys(i)

T_mix = T_outside * FracOA + SysHeatRetTemp(i)(1 - FracOA)

W_mix = W_outside * FracOA + SysHeatRetHumRat (i)(1 - FracOA)

SysHeatOutTempSeq(i) = T_outside

SysHeatOutHumRatSeq(i) = W_outside

Get the current (zone time-step) system heating capacity:

SysHeatCap_cur = C_p,air * MinFlowRat_sys *HeatFlowSeq_sys(i) *( T_sup-T_mix)

HeatCapSeq(I) = SysHeatCap_cur

If SysHeatCap_cur is the maximum for the day so far then save SysHeatCap_cur as the design value:

HeatCap(i )_sys = SysHeatCap_cur

And save the corresponding mixed, return and outside conditions:

HeatMixTemp_sys = T_mix

HeatMixHumRat_sys = W_mix

HeatRetTemp_sys = SysHeatRetTemp(i)

HeatRetHumRat_sys = SysHeatRetHumRat(I)

HeatOutTemp_sys = T_outside

HeatOutHumRat_sys = W_outside

Here MinFlowRat_sys is the user specified minimum supply flow ratio.

EndDay[LINK]

If the user has specified coincident system sizing then:

DesCoolVolFlow_sys = r_air *CoinCoolMassFlow_sys

DesHeatVolFlow_sys = r_air *CoinHeatMassFlow_sys

DesMainVolFlow_sys = Max(DesCoolVolFlow_sys, DesHeatVolFlow_sys)

If the user has specified noncoincidentsystem sizing then:

DesCoolVolFlow_sys = r_air *NonCoinCoolMassFlow_sys

DesHeatVolFlow_sys = r_air *NonCoinHeatMassFlow_sys

DesMainVolFlow_sys = Max(DesCoolVolFlow_sys, DesHeatVolFlow_sys)

Based on the outdoor air method selected, the DesCoolVolFlow_sys and DesHeatVolFlow_sys are modified based on the system ventilation effciency calculated based on the maximum outdoor air fraction.

EndSysSizingCalc[LINK]

At this point all the calculations have been done in SysSizing(i,j): we have results for each design day. Now these results need to be processed to find the heating and cooling design quantities for each system over all the design days.

For coincident sizing the task is quite easy.

1. Loop over all of the air loops.

1. Loop over all of the design days.

2. If the value of DesCoolVolFlow in SysSizing for the current design day is greater than the value stored in CalcSysSizing, then move DesCoolVolFlow from SysSizing into CalcSysSizing along with CoolDesDay, CoinCoolMassFlow, SensCoolCap, CoolFlowSeq(i), SensCoolCapSeq(i), CoolMixTemp, CoolRetTemp, CoolMixHumRat, CoolRetHumRat, CoolOutTemp, CoolOutHumRat, SysCoolRetTempSeq(i), SysCoolRetHumRatSeq(i), SysCoolOutTempSeq(i) and SysCoolOutHumRatSeq(i).

2. If the value of DesHeatVolFlow in SysSizing for the current design day is greater than the value stored in CalcSysSizing, then move DesHeatVolFlow from SysSizing into CalcSysSizing along with HeatDesDay, CoinHeatMassFlow, HeatCap, PreHeatCap, HeatFlowSeq(i), HeatCapSeq(i), PreHeatCapSeq(i), HeatMixTemp, HeatRetTemp, HeatMixHumRat, HeatRetHumRat, HeatOutTemp, HeatOutHumRat, SysHeatRetTempSeq(i), SysHeatRetHumRatSeq(i), SysHeatOutTempSeq(i) and SysHeatOutHumRatSeq(i).

At the end of each design day loop the peak cooling and the peak heating data will be stored in CalcSysSizing. At this point we set DesMainVolFlow in CalcSysSizing equal to the maximum of DesCoolVolFlow and DesHeatVolFlow.

For noncoincident sizing the task is harder since we don’t have a single time-step during which all the zone peaks occur. So there is no obvious value for outside air temperature at the peak, return air temperature at the peak and so forth. We must return to the zone sizing data and calculate average values for return and outside conditions.

2. Loop over all of the zones cooled by this air loop

3. In FinalZoneSizing replace the value in DesCoolCoilInTemp with the user specified CoolSupTemp_sys. Do the same for DesCoolCoilInHumRat and CoolSupHumRat. This ensures that zone equipment connected to an air loop will use the system design supply air conditions as coil entering conditions.

2. NonCoinCoolMassFlow_sys = DesCoolMassFlow_zone

SysCoolRetTemp = (ZoneRetTempAtCoolPeak *DesCoolMassFlow_zone)

/NonCoinCoolMassFlow_sys

SysCoolRetHumRat = (ZoneHumRatAtCoolPeak *

DesCoolMassFlow_zone)/NonCoinCoolMassFlow_sys

SysCoolOutTemp = (T_{OA,zone\ peak} *DesCoolMassFlow_zone)/

• NonCoinCoolMassFlow_sys*

SysCoolOutHumRat = (W_{OA,zone\ peak} *DesCoolMassFlow_zone)/

• NonCoinCoolMassFlow_sys*

At the end of the zone loop calculate mixed air conditions and the system sensible cooling capacity.

FracOA = r_air * DesOutAirVolFlow_sys/ NonCoinCoolMassFlow_sys

T_mix = SysCoolOutTemp * FracOA + SysCoolRetTemp * (1 - FracOA)

W_mix = SysCoolOutHumRat * FracOA + SysCoolRetHumRat *

(1 - FracOA)

SysSensCoolCap = C_p,air * NonCoinCoolMassFlow *( T_mix-T_sup)

Then (for noncoincident sizing) the variables calculated in section (ii) are moved into the CalcSysSizing Array.

3. Loop over all of the zones heated by this air loop.

4. In FinalZoneSizing replace the value in DesHeatCoilInTemp with the user specified HeatSupTemp_sys. Do the same for DesHeatCoilInHumRat and HeatSupHumRat. This ensures that zone equipment connected to an air loop will use the system design supply air conditions as coil entering conditions.

2. NonCoinHeatMassFlow_sys = DesHeatMassFlow_zone

SysHeatRetTemp = (ZoneRetTempAtHeatPeak *DesHeatMassFlow_zone)

/NonCoinHeatMassFlow_sys

SysHeatRetHumRat = (ZoneHumRatAtHeatPeak *

DesHeatMassFlow_zone)/NonCoinHeatMassFlow_sys

SysHeatOutTemp = (T_{OA,zone\ peak} *DesHeatMassFlow_zone)/

• NonCoinHeatMassFlow_sys*

SysHeatOutHumRat = (W_{OA,zone\ peak} *DesHeatMassFlow_zone)/

• NonCoinHeatMassFlow_sys*

At the end of the zone loop calculate mixed air conditions and the system sensible cooling capacity.

FracOA = r_air * DesOutAirVolFlow_sys/ NonCoinHeatMassFlow_sys

T_mix = SysHeatOutTemp * FracOA + SysHeatRetTemp * (1 - FracOA)

W_mix = SysHeatOutHumRat * FracOA + SysHeatRetHumRat *

(1 - FracOA)

SysHeatlCap = C_p,air * NonCoinHeatlMassFlow *( T_sup-T_mix)

Then (for noncoincident sizing) the variables calculated in section (ii) are moved into the CalcSysSizing Array.

2. We now have the calculated system sizing data. This data needs to be altered to take into account the user input system design flow rates (if any), or the fact that the user may have requested that the system flow rate be sized on the ventilation requirement. Note that user specified sizing ratios have already been applied to the zone sizing data which have been used in out preceding system sizing calculation. Thus the user specified sizing ratios do not have to be explicitly taken into account at the system level.

First we move the calculated system sizing data from CalcSysSizing array into the FinalSysSizing array. FinalSysSizing will contain the user modified system design data when we are all done.

Loop over the air loops.

1. As in the zone case, the user specified system design flow rates are turned into sizing ratios by dividing the user input value by the calculated value. The same strategy is employed for sizing on the ventilation requirement: the design ventilation flow rate is divided by the calculated design flow rate value. For each air loop this gives us a SizRat_cool and SizRat_heat.

CoinCoolMassFlow = SizRat_cool * CoinCoolMassFlow_calc

NonCoinCoolMassFlow = SizRat_cool * NonCoinCoolMassFlow_calc

DesCoolVolFlow = SizRat_cool * DesCoolVolFlow_calc

Since the flow rates have been altered the outside air fraction will change. This will alter the design mixed air conditions and lead to an altered value for the cooling capacity. This must be done for the time-step sequence and for the peak value.

2. Loop over the zone timesteps (index = i).

CoolFlowSeq_sys(i) = SizRat_cool * CoolFlowSeq_sys,calc(i)

FracOA = r_air * DesOutAirVolFlow_sys/ CoolFlowSeq_sys(i)

T_mix = SysCoolOutTempSeq(i) *FracOA +

SysCoolRetTempSeq(i) *(1-FracOA)

SensCoolCapSeq(i) = C_p,air * CoolFlowSeq_sys(i) *( T_mix-T_sup)

3. Do the same calculation for peak cooling.

FracOA = r_air * DesOutAirVolFlow_sys/ DesCoolVolFlow

T_mix = CoolOutTemp_sys *FracOA + CoolRetTemp_sys *(1-FracOA)

W_mix = CoolOutHumRat_sys *FracOA + CoolRetHumRat_sys *

(1-FracOA)

SensCoolCap_sys = C_p,air * DesCoolVolFlow_sys *( T_mix-T_sup)

T_mix and W_mix are saved in FinalSysSizing .

4. Do the same calculation for the heating case.

CoinHeatMassFlow = SizRat_heat * CoinHeatMassFlow_calc

NonCoinHeatMassFlow = SizRat_heat * NonCoinHeatMassFlow_calc

DesHeatVolFlow = SizRat_heat * DesHeatVolFlow_calc

22. Loop over the zone timesteps (index = i).

HeatFlowSeq_sys(i) = SizRat_Heat * HeatFlowSeq_sys,calc(i)

FracOA = r_air * DesOutAirVolFlow_sys/ HeatFlowSeq_sys(i)

T_mix = SysHeatOutTempSeq(i) * FracOA +

• SysHeatRetTempSeq(i) ** (1-FracOA)

HeatCapSeq(i) = C_p,air * HeatFlowSeq_sys(i) *(T_sup-T_mix)

6. Do the same calculation for peak heating.

FracOA = r_air * DesOutAirVolFlow_sys/ DesHeatVolFlow

T_mix = HeatOutTemp_sys *FracOA + HeatRetTemp_sys * (1-FracOA)

W_mix = HeatOutHumRat_sys *FracOA + HeatRetHumRat_sys *

(1-FracOA)

HeatCap_sys = C_p,air * DesHeatVolFlow_sys *( T_sup-T_mix)

T_mix and W_mix are saved in FinalSysSizing .

(vii)DesMainVolFlow_sys = MAX(DesCoolVolFlow_sys,DesHeatVolFlow_sys)

This concludes the system design calculation.

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Scalable System HVAC Sizing

The scalable system sizing applies to system supply air flow rates and sysyem capacity in coolin and heating modes.

Scalable System Air Flow Sizing

The scalable sizing methods for supply air flow rate allowed are either, FlowPerFloorArea, FractionOfAutosizedCoolingAirflow, or FlowPerCoolingCapacity. The scalable system air flow sizing methods are defined as follows:

FlowPerFloorArea means the program calculates the cooling supply air volume flow rate from zone floor area served by the airloop and user specified Flow Per Floor Area value.

FractionOfAutosizedCoolingAirflow means the program calculates the cooling supply air volume flow rate from user specified fraction and the autosized design cooling supply air volume flow rate value determined by the simulation.

FractionOfAutosizedHeatingAirflow means the program calculates the heating supply air volume flow rate from user specified fraction and the autosized design heating supply air volume flow rate value determined by the simulation.

FlowPerCoolingCapacity means the supply air volume is calculated from user specified flow per cooling capacity and design cooling capacity determined by the simulation.

FlowPerHeatingCapacity means the supply air volume is calculated from user specified flow per heating capacity and design heating capacity determined by the simulation.

Scalable System Capacity Sizing

The scalable sizing methods for system capacity available are: CapacityPerFloorArea, FractionOfAutosizedCoolingCapacity and FractionOfAutosizedHeatingCapacity. The scalable system capacity sizing methods are defined as follows:

CapacityPerFloorArea means the program calculates the design capacity from user specified capacity per floor area and floor area of the zones served by the airloop.

FractionOfAutosizedCoolingCapacity means the program calculates the design cooling capacity from user specified fraction and the auto-sized design cooling capacity.

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FractionOfAutosizedHeatingCapacity means the program calculates the design heating capacity from user specified fraction and the auto-sized design heating capacity.