# Air System Compound Component Groups[LINK]

## Unitary Systems[LINK]

The input object AirLoopHVAC:UnitarySystem provides a “virtual” component that collects and controls a set of components: fan, heating coil, cooling coil, and/or reheat coil. Reheat coil is modeled for controlling high zone humidity levels or supplementing a heat pump heating coil. The unit may be configured to have either a blow through or draw through fan. In a blow through configuration, fan is generally the fist component upstream of heating or cooling coil. In a draw through fan configuration, fan is placed directly after the heating coil and before reheat coil.

### Model Description[LINK]

As described previously, the unitary system is a “virtual” component consisting of a fan, heating coil, cooling coil and reheat coil. The sole purpose of the unitary system model is to properly coordinate the operation of the various system components. The following sections describe the flow of information within the model, as well as the differences between cycling and continuous supply air fan operation.

There are three types of control types allowed to be specified in the unitary system which are setpoint based, load based or a load based control method according to ASHRAE Standard 90.1. Each control type is described in detail below.

### Setpoint based control:[LINK]

The unitary system calculates the current sensible load using the temperature of the inlet node and the System Node Setpoint Temp on the control node. If the control node is not the outlet node, the desired outlet node temperature is adjusted for the current temperature difference between the outlet node and the control node. Likewise, the current latent load is calculated using the humidity ratio of the inlet node and the System Node Humidity Ratio Max on the control node. The controls determine the required coil run-time fraction and dehumidification mode (if applicable) using the steps outlined below.

#### Step 1 – Meet Sensible Load Requirement[LINK]

The controls first attempt to meet the sensible requirement. The specified coil model is called with a part-load ratio (PLR) of 1.0 to determine the full-load output of the coil. This is compared with the desired outlet node temperature and a sensible PLR is calculated. If the PLR is <1.0, a root solver iteration routine is called to determine the coil run-time fraction which results in the desired outlet node temperature. For a variable-speed DX cooling coil, if the load is smaller than the sensible capacity at the lowest speed, the coil run-time fraction is determined in the same way as a single-speed DX cooling coil. Otherwise, its speed number and speed ratio between two neighboring speeds are selected to match the load.

#### Step 2 – Meet Latent Load Requirement (if activated)[LINK]

If dehumidification controls are active, the leaving humidity ratio resulting from operation to meet the sensible load (Step 1 above) is compared with the desired outlet node humidity ratio. If the humidity requirement is already met, then no further control action is taken. If the humidity requirement has not been met, then the coil is re-simulated depending on the type of humidity control.

#### Step 2a – Humidity Control = MultiMode[LINK]

If the humidity control type is MultiMode, then the coil’s enhanced dehumidification mode is activated when the coil type is Coil:Cooling:DX:TwoStageWithHumidityControlMode and Step 1 above is repeated to meet the sensible load using the coil performance resulting from the enhanced dehumidificaiton mode. This is a semi-passive approach to dehumidification which may fall short or may exceed the dehumidification requirement.

#### Step 2b – Humidity Control = CoolReheat[LINK]

If the humidity control type is CoolReheat, the coil is re-simulated to achieve the desired outlet node humidity ratio. This option is valid for all cooling coil types. When the coil type is Coil:Cooling:DX:TwoStageWithHumidityControlMode, only the cooling performance mode is used for this step and enhanced dehumidification mode is not activated.

### Load based control:[LINK]

While the unitary system may be configured to serve multiple zones, system operation is controlled by a thermostat located in a single “control” zone. One of the key parameters for the unitary system component is the fraction of the total system air flow that goes through the control zone. This fraction is calculated as the ratio of the maximum air mass flow rate for the air loop’s supply inlet node for the control zone (e.g., AirTerminal:SingleDuct:ConstantVolume:NoReheat, field = Maximum Air Flow Rate, converted to mass flow) to the sum of the maximum air mass flow rates for the air loop’s supply inlet nodes for all zones served by this air loop. The unitary system module scales the calculated load for the control zone upward based on this fraction to determine the total load to be met by the unitary system. The module then proceeds to calculate the required part-load ratio for the system coil and the supply air fan to meet this total load. The heating or cooling capacity delivered by the unitary system is distributed to all of the zones served by this system via the terminal units that supply air to each zone. The supply air fraction that goes though the control zone is calculated as follows:

ControlZoneAirFlowFraction=˙mTUMaxControlZoneNumOfZones∑j=1˙mTUMaxZonej

where:

˙mTUMaxControlledZone is the maximum air mass flow rate for the air loop’s supply inlet node (terminal unit) for the control zone (kg/s)

˙mTUMaxZonej is the maximum air mass flow rate for the air loop’s supply inlet node for the jth zone (kg/s)

NumOfZones is the number of zones, or number of air loop supply air inlet nodes for all zones served by the air loop.

The unitary system component is able to model supply air fan operation in two modes: cycling fan – cycling coil (i.e., AUTO fan) and continuous fan – cycling coil (i.e., fan ON). Fan:OnOff must be used to model AUTO fan, while Fan:OnOff or Fan:ConstantVolume can be used to model fan ON. The fan operation mode is specified using a supply air fan operating mode schedule where schedule values of 0 denote cycling fan operation and schedule values other than 0 (a 1 is usually used) denote continuous fan operation. Using this schedule, the unitary system fan may be cycled with cooling or heating coil operation or operated continuously based on time of day (e.g., cycling fan operation at night and continuous fan operation during the daytime). If the fan operating mode schedule name field is left blank in the unitary system object, the unitary system assumes cycling or AUTO fan mode operation throughout the simulation.

The unitary system operates based on the user-specified (or autosized) design supply air flow rate(s). The ‘design’ supply air mass flow rate may be different for cooling, heating, and when no cooling or heating is required and the fan operates continuously based on user-specified inputs.

**Cooling Operation**

If EnergyPlus determines that the unitary system must supply cooling to the control zone to meet the zone air temperature setpoint, then the model computes the total sensible cooling load to be met by the unitary system based on the control zone sensible cooling load and the fraction of the unitary system air flow that goes through the control zone.

UnitarySystemCoolingLoad=ControlZoneCoolingLoadControlZoneAirFlowFraction

If the supply air fan operating mode schedule requests cycling fan operation, the model first checks for the presence of an ecomomizer in the outside air system serving the unitary system’s air loop (Ref. AirLoopHVAC:OutdoorAirSystem). If an outside air system is not present or if an air-side economizer is not used, the unitary system’s compressor is used to meet the unitary system cooling load. If an air-side economizer is used and is active (i.e., economizer controls indicate that conditions are favorable to increase the outside air flow rate), the unitary system will try to meet the cooling load by operating only the supply air fan. If the fan is able to satisfy the unitary system cooling load, the compressor remains off for the entire simulation time step. If the operation of the fan alone is unable to meet the entire cooling load, then the compressor is enabled and additional calculations are performed to determine the compressor’s part-load ratio.

The model then calculates the unitary system’s sensible cooling energy rate delivered to the zones being served when the system runs at full-load conditions and when the cooling coil is OFF. If the supply air fan cycles with the compressor, then the sensible cooling energy rate is zero when the cooling coil is OFF. However if the fan is configured to run continuously regardless of coil operation, then the sensible cooling energy rate will probably not be zero when the cooling coil is OFF. Calculating the sensible cooling energy rate involves modeling the supply air fan (and associated fan heat), the cooling coil, and the heating and reheat coil (simply to pass the air properties and mass flow rate from its inlet node to its outlet node). For each of these cases (full load and cooling coil OFF), the sensible cooling energy rate delivered by the unitary system is calculated as follows:

Full Cool Output=(Mass Flow Ratefullload)(hout,full load−hcontrol zone)HRmin−Δsen,full load

No Cool Output=(Mass Flow Ratecoil off)(hout,coil off−hcontrol zone)HRmin−Δsen,coil off

where:

*Mass Flow Ratefull load* is the air mass flow rate through unitary system at full-load conditions (kg/s)

*hcoil,full load* is the enthalpy of air exiting the unitary system at full-load conditions (J/kg)

hcontrol zone is the enthalpy of air in the control zone where the thermostat is located (J/kg)

*HRmin* is the enthalpies evaluated at a constant humidity ratio, the minimum humidity ratio of the unitary system exiting air or the air in the control zone

*Mass Flow Ratecoil off* is the air mass flow rate through the unitary system with the cooling coil OFF (kg/s)

*hout,coil off* is the enthalpy of air exiting the unitary system with the cooling coil OFF (J/kg)

Δsen,full load is the sensible load difference between the system output node and the zone inlet node at full-load conditions.

Δsen,full load=MassFlowRateZone InletFrac(hOut,full load−hZone Inlet)HRmin+(MassFlowRatefull load−MassFlowRateZone InletFrac)(hOut,full load−hControl Zone)HRmin

where:

Frac is the control zone air fraction with respect to the system mass flow rate

Δsen,coiloff is the sensible load difference between the system output node and the zone inlet node with the heating coil OFF conditions.

Δsen,coil off=MassFlowRateZone InletFrac(hOut,coil off−hZone Inlet)HRmin+(MassFlowRatecoil off−MassFlowRateZone InletFrac)(hOut,coil off−hControl Zone)HRmin

With the calculated sensible cooling energy rates and the total sensible cooling load to be met by the system, the part-load ratio for the unitary system is estimated.

PartLoadRatio=MAX(0.0,(UnitarySystemCoolingLoad−NoCoolOutput)(FullCoolOutput−NoCoolOutput))

Since the part-load performance of the cooling coil is frequently non-linear, and the supply air fan heat varies based on cooling coil operation for the case of cycling fan/cycling coil (AUTO fan), the final part-load ratio for the cooling coil compressor and fan are determined through iterative calculations (successive modeling of the cooling coil and fan) until the unitary system’s cooling output matches the cooling load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s cooling output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemCoolingLoad−QUnitarySystem)UnitarySystemCoolingLoad

where QUnitarySystem is the unitary system delivered sensible capacity (W).

If the unitary system has been specified with cycling fan/cycling coil (AUTO fan), then the unitary system’s operating supply air mass flow rate is multiplied by PartLoadRatio to determine the average air mass flow rate for the system simulation time step. In this case, the air conditions at nodes downstream of the cooling coil represent the full-load (steady-state) values when the coil is operating.

If the fan operates continuously (i.e., when the supply air fan operating mode schedule values are NOT equal to 0), the operating air mass flow rate through the unitary system is calculated as the average of the user-specified air flow rate when the cooling coil is ON and the user-specified air flow rate when the cooling coil is OFF (user-specified supply air volumetric flow rates converted to dry air mass flow rates).

˙mUnitarySystem=PartLoadRatio(˙mCoolCoilON)+(1−PartLoadRatio)(˙mCoilOFF)

where:

˙mHeatCoilON is the air mass flow rate through unitary system when the cooling coil is ON (kg/s)

˙mCoilOFF is the air mass flow rate through unitary system when no cooling or heating is needed (kg/s).

In this case, the air conditions at nodes downstream of the cooling coil are calculated as the average conditions over the simulation time step (i.e., the weighted average of full-load conditions when the coil is operating and inlet air conditions when the coil is OFF).

**Cooling Operation (multi or variable speed coils)**

After the unitary system cooling load is determined as described in Equation [eq:UnitarySystemCoolingLoad] above, the multi or variable speed cooling coil models calculations are described in this section.

The model calculates the unitary system’s sensible cooling energy rate delivered to the zones being served when the system runs at full-load conditions at the highest speed and when the DX cooling coil is OFF. If the supply air fan cycles with the compressor, then the sensible cooling energy rate is zero when the cooling coil is OFF. However if the fan is scheduled to run continuously regardless of coil operation, then the sensible cooling energy rate will not be zero when the cooling coil is OFF. Calculating the sensible cooling energy rate involves modeling the supply air fan (and associated fan heat) and the multi/variable speed DX cooling coil. The multi/variable speed DX heating coil and the supplemental heating coil are also modeled, but only to pass the air properties and mass flow rate from their inlet nodes to their outlet nodes. For each of these cases (full load at highest cooling speed and DX cooling coil OFF), the sensible cooling energy rate delivered by the unitary system is calculated as follows:

FullCoolOutputHighestSpeed=(˙mHighestSpeed)(hout,full load−hcontrol zone)HRmin−Δsen,HighestSpeed

NoCoolOutput=(˙mCoilOff)(hout,coil off−hcontrol zone)HRmin−Δsen,coil off

where:

˙mHighestSpeed is the air mass flow rate through unitary system at the highest cooling speed (kg/s)

hout,full load is the enthalpy of air exiting the unitary system at full-load conditions [J/kg]

hcontrol zone is the enthalpy of air leaving the control zone (where thermostat is located) (J/kg)

HRmin is the minimum humidity ratio of the unitary system exiting air or the air leaving the control zone (kg/kg)

˙mCoilOff is the air mass flow rate through the unitary system with the cooling coil OFF (kg/s)

hout,coil off is the enthalpy of air exiting the unitary system with the cooling coil OFF (J/kg)

Δsen,HighestSpeed is the sensible load difference between the system output node and the zone inlet node at full-load conditions

Δsen,coil off is the sensible load difference between the system output node and the zone inlet node with the cooling coil OFF conditions.

Δsen,HighestSpeed=˙mZone InletFrac(hOut,full load−hZone Inlet)HRmin+(˙mHighestSpeed−˙mZone InletFrac)(hOut,full load−hControl Zone)HRmin

Δsen,coil off=˙mZone InletFrac(hOut,coil off−hZone Inlet)HRmin+(˙mcoil off−˙mZone InletFrac)(hOut,coil off−hControl Zone)HRmin

where Frac is the control zone air fraction with respect to the system mass flow rate.

If the unitary system’s sensible cooling rate at the highest speed (full load, no cycling) is insufficient to meet the entire cooling load, the controlled zone conditions will not be met. The reported cycling rate and speed ratio are 1, and the speed number is set to the highest index number. If the total sensible cooling load to be met by the system is less than the sensible cooling rate at the highest speed, then the following steps are performed.

First, calculate the sensible cooling energy rate at Speed 1:

FullCoolOutputSpeed1=(˙mSpeed1)(hout,fullload−hcontrol zone)HRmin−Δsen,Speed1

where:

*˙mSpeed1* is the air mass flow rate through unitary system at Speed 1 (kg/s)

Δsen,Speed1 is th sensible load difference between the system output node and the zone inlet node at full-load conditions at Speed 1.

Δsen,Speed1=˙mZone InletFrac(hOut,full load−hZone Inlet)HRmin+(˙mSpeed1−˙mZone InletFrac)(hOut,full load−hControl Zone)HRmin

If the sensible cooling energy rate delivered by the unitary system at Speed 1 is greater or equal to the sensible load, the cycling ratio (part-load ratio) for the unitary system is estimated.

CyclingRatio=|(CoolingCoilSensibleLoad)|FullCoolingCoilCapacity=max(0.0,UnitarySystemCoolingLoad−AddedFanHeatFullCoolOutputSpeed1−AddedFanHeatSpeed1)

where:

*AddedFanHeat* is the generated supply air fan heat, which is a function of part load ratio and as internal component cooling load (W)

*AddedFanHeatSpeed1* is the generated supply air fan heat at Speed 1 for a part load ratio = 1 (W).

Since the part-load performance of the DX cooling coil is frequently non-linear,and the supply air fan heat varies based on cooling coil operation for the case of cycling fan/cycling coil (AUTO fan), the final part-load ratio for the cooling coil compressor and fan are determined through iterative calculations (successive modeling of the cooling coil and fan) until the unitary system’s cooling output matches the cooling load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s cooling output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemOutputcycling−QUnitarySystem)UnitarySystemCoolingLoad

where the UnitarySystemOutputCycling is the unitary system delivered sensible capacity for Speed 1 operating at a specific cycling ratio (W).

UnitarySystemOutputcycling=˙mUnitarySystem(hout−hControlZone)HRmin−Δcycling

where:

˙mUnitarySystem is the average air mass flow rate defined in the next section (kg/s)

*hout* is the enthalpy of air exiting the unitary system at part load conditions (J/kg)

Δcycling is the average sensible load difference between the system output node and the zone inlet node.

Δcycling=˙mZoneInletfrac(hZoneInlet−hControlZone)+(˙mUnitarySystem−˙mZoneInletfrac)(hOut−hControlZone)

where ˙mZoneInlet is the air mass flow rate in the supply inlet node in the controlled zone (kg/s).

For this case where speed 1 operation was able to meet the required cooling load, the speed ratio is set to zero and speed number is equal to 1.

If the unitary system’s cooling output at full load for Speed 1 is insufficient to meet the entire cooling load, the Cycling ratio is set equal to 1.0 (compressor and fan are not cycling). Then the cooling speed is increased and the delivered sensible capacity is calculated. If the full load sensible capacity at Speed n is greater than or equal to the sensible load, the speed ratio for the unitary system is estimated:

SpeedRatio=ABS(UnitarySystemCoolingLoad−AddedFanHeat−FullCoolOutputSpeedn−1)ABS(FullCoolOutputSpeedn−FullCoolOutputSpeedn−1)

Although a linear relationship is assumed by applying the speed ratio to obtain the effective capacity and mass flow rate between speed n and n-1, the outlet air node conditions are dependent on the combined outputs and may not be linear. In addition, the supply air fan heat varies with the speed ratio due to different supply mass flow rates between speed n and n-1 . Therefore, the final speed ratio for the cooling coil compressor and fan are determined through iterative calculations (successive modeling of the cooling coil and fan) until the unitary system’s cooling output matches the cooling load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s cooling output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemCoolingLoad−UnitarySystemOutputSpeedRatio)UnitarySystemCoolingLoad

where *UnitarySystemOutputSpeedn* is the unitary system delivered sensible capacity between two consecutive speeds at a specific speed ratio (W).

UnitarySystemOutputSpeedRatio=(SpeedRatio)FullCoolOutputSpeedn+(1−SpeedRatio)FullCoolOutputSpeedn−1−AddedFanHeatSpeedRatio

where *AddedFanHeatSpeedRatio* is the generated supply air fan heat at a specific speed ratio (W).

In this case, the reported cycling ratio is 1 and speed number is equal to n.

#### Air Mass Flow Rate Calculation[LINK]

*Speed 1 operation*

If the unitary system has been specified with cycling fan/cycling coil (AUTO fan), then the unitary system’s operating supply air mass flow rate is determined by the cycling ratio (PartLoadRatio) for Speed 1. The supply air mass flow rate is multiplied by the cycling ratio to determine the average air mass flow rate for the system simulation time step. The air conditions at nodes downstream of the cooling coils represent the full-load (steady-state) values when the coil is operating.

˙mUnitarySystem=(CyclingRatio)˙mSpeed1

If the fan operates continuously (i.e., when the supply air fan operating mode schedule values are NOT equal to 0), the operating air mass flow rate through the unitary system is calculated as the average of the user-specified air flow rate when the unitary system cooling coil is ON at Speed 1 and the user-specified air flow rate when the unitary system cooling coil is OFF (user-specified supply air volumetric flow rates converted to dry air mass flow rates).

˙mUnitarySystem=(CyclingRatio)˙mSpeed1+(1−CyclingRatio)˙mCoilOff

where:

˙mUnitarySystem is the average air mass flow rate through unitary system (kg/s)

˙mSpeed1 is the air mass flow rate through unitary system when cooling coil is ON at Speed 1 (kg/s)

˙mCoilOff is the air mass flow rate through unitary system when no heating or cooling is needed (kg/s).

In this case, the air conditions at nodes downstream of the cooling coils are calculated as the average conditions over the simulation time step (i.e., the weighted average of full-load conditions when the coil is operating and inlet air conditions when the coil is OFF).

#### Higher Speed Operation[LINK]

When the unitary system operates at higher speeds to meet the required cooling load, the supply air mass flow rate is linearly interpolated between two consecutive speeds:

˙mUnitarySystem=(SpeedRatio)˙mSpeedn+(1−SpeedRatio)˙mSpeedn−1

where:

˙mUnitarySystem is the average air mass flow rate through the unitary system for the time step (kg/s)

˙mSpeedn is the air mass flow rate through unitary system when cooling coil is ON at Speed n (kg/s)

˙mSpeedn−1 is the air mass flow rate through unitary system when cooling coil is ON at Speed n-1 (kg/s).

For this case of higher speed operation, the air conditions at nodes downstream of the cooling coils are determined by the delivered cooling capacity and supply air mass flow rates between two consecutive speeds.

Although the above sections present the capacity and air mass flow rate calculation separately, they are dependent and change every iteration until convergence is reached for the time step being simulated.

**Heating Operation**

Calculations for heating operation are similar to those for cooling operation in most respects. However, due to the inclusion of a supplemental heating coil, additional calculations are necessary to properly meet the total heating load for the zones being served.

If EnergyPlus determines that the unitary system must supply heating to the control zone to meet the zone air temperature setpoint, then the unitary system model computes the total sensible heating load to be delivered to the zones being served based on the control zone sensible heating load and the control zone airflow fraction.

UnitarySystemHeatingLoad=ControlZoneHeatingLoadControlZoneAirFlowFraction

The model then calculates the unitary system’s sensible heating energy rate delivered to the zones being served when the system runs at full-load conditions and when the heating coil is OFF (without supplemental heater operation in either case). If the supply air fan cycles with the compressor, then the sensible heating energy rate is zero when the compressor is OFF. However if the fan is scheduled to run continuously regardless of coil operation, then the sensible heating energy rate will not be zero when the compressor is OFF. Calculating the sensible heating energy rate involves modeling the supply air fan (and associated fan heat), the cooling coil (simply to pass the air properties and mass flow rate from its inlet node to its outlet node), the heating coil, and the supplemental heating coil (simply to pass the air properties and mass flow rate from its inlet node to its outlet node). For each of these cases (full load and heating coil OFF, without supplemental heater operation in either case), the sensible heating energy rate delivered by the unitary system is calculated as follows:

Full Heat Output=(Mass Flow Ratefull load)(hout,full load−hcontrol zone)HRmin−Δsen,full load

No Heat Output=(Mass Flow Ratecoil off)(hout,coil off−hcontrol zone)HRmin−Δsen,coil off

where:

*Mass Flow Ratefull load* is the air mass flow rate through unitary system at full-load conditions (kg/s)

*hout,full load* is the enthalpy of air exiting the unitary system at full-load conditions (J/kg)

*hcontrol zone* is the enthalpy of air leaving the control zone (where thermostat is located) (J/kg)

*HRmin* are the enthalpies evaluated at a constant humidity ratio, the minimum humidity ratio of the unitary system exiting air or the air leaving the control zone

*Mass Flow Ratecoil off* is the air mass flow rate through the unitary system with the heating coil OFF (kg/s)

*hout,coil off* is the enthalpy of air exiting the unitary system with the heating coil OFF (J/kg)

Δsen,full load is the sensible load difference between the system output node and the zone inlet node at full-load conditions.

Δsen,full load=˙mZone InletFrac(hOut,full load−hZone Inlet)HRmin+(˙mfull load−˙mZone InletFrac)(hOut,full load−hControl Zone)HRmin

where:

Frac is the control zone air fraction with respect to the system mass flow rate

Δsen,coil off is the sensible load difference between the system output node and the zone inlet node with the heating coil OFF conditions.

Δsen,coil off=˙mZone InletFrac(hOut,coil off−hZone Inlet)HRmin+(˙mcoil off−˙mZone InletFrac)(hOut,coil off−hControl Zone)HRmin

With the calculated sensible heating energy rates and the total sensible heating load to be met by the system, the part-load ratio for the unitary system is estimated.

PartLoadRatio=MAX(0.0,(UnitarySystemHeatingLoad−NoHeatOutput)(FullHeatOutput−NoHeatOutput))

Since the part-load performance of the heating coil is frequently non-linear, and the supply air fan heat varies based on heating coil operation for the case of cycling fan/cycling coil (AUTO fan), the final part-load ratio for the heating coil compressor and fan are determined through iterative calculations (successive modeling of the heating coil and fan) until the unitary system’s heating output matches the heating load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s heating output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemHeatingLoad−QUnitarySystem)UnitarySystemHeatingLoad

where QUnitarySystem is the unitary system delivered sensible capacity (W).

If the unitary system’s heating coil output at full load is insufficient to meet the entire heating load, PartLoadRatio is set equal to 1.0 (compressor and fan are not cycling) and the remaining heating load is passed to the supplemental heating coil. If the unitary system model determines that the outdoor air temperature is below the minimum outdoor air temperature for compressor operation, the compressor is turned off and the entire heating load is passed to the supplemental gas or electric heating coil. The unitary system exiting air conditions and energy consumption are calculated and reported by the individual component models (fan, heating coil, and supplemental gas or electric heating coil).

If the unitary system has been specified with cycling fan/cycling coil (AUTO fan), then the unitary system’s operating supply air mass flow rate is multiplied by PartLoadRatio to determine the average air mass flow rate for the system simulation time step. The air conditions at nodes downstream of the heating coils represent the full-load (steady-state) values when the coils are operating. If the fan operates continuously (i.e., when the supply air fan operating mode schedule values are NOT equal to 0), the operating air mass flow rate through the unitary system is calculated as the average of the user-specified air flow rate when the unitary system heating coil is ON and the user-specified air flow rate when the unitary system heating coil is OFF (user-specified supply air volumetric flow rates converted to dry air mass flow rates).

˙mUnitarySystem=PartLoadRatio(˙mHeatCoilON)+(1−PartLoadRatio)(˙mCoilOFF)

where:

˙mHeatCoilON is the air mass flow rate through unitary system when the heating coil is ON (kg/s)

˙mCoilOFF is the air mass flow rate through unitary system when no heating or cooling is needed (kg/s).

In this case, the air conditions at nodes downstream of the heating coils are calculated as the average conditions over the simulation time step (i.e., the weighted average of full-load conditions when the coils are operating and inlet air conditions when the coils are OFF).

### Heating Operation (multi or variable speed coils )[LINK]

After the unitary system heating load is determined as described in Equation [eq:UnitarySystemHeatingLoad] above, the multi or variable speed heating coil models calculation are described in this section.

The model calculates the unitary system’s sensible heating energy rate delivered to the zones being served when the system runs at full-load conditions at the highest speed and when the DX heating coil is OFF (without supplemental heater operation in either case). If the supply air fan cycles with the compressor, then the sensible heating energy rate is zero when the compressor is OFF. However if the fan is scheduled to run continuously regardless of coil operation, then the sensible heating energy rate will not be zero when the compressor is OFF. Calculating the sensible heating energy rate involves modeling the supply air fan (and associated fan heat), the DX cooling coil (simply to pass the air properties and mass flow rate from its inlet node to its outlet node), the DX heating coil, and the supplemental heating coil (simply to pass the air properties and mass flow rate from its inlet node to its outlet node). For each of these cases (full load and DX heating coil OFF, without supplemental heater operation in either case), the sensible heating energy rate delivered by the unitary system is calculated as follows:

FullHeatOutputHighestSpeed=(˙mHighestSpeed)(hout,full load−hcontrol zone)HRmin−Δsen,HighestSpeed

NoHeatOutput=(˙mCoilOff)(hout,coil off−hcontrol zone)HRmin−Δsen,coil off

where:

*˙mHighestSpeed* is the air mass flow rate through unitary system at the highest heating speed (kg/s)

*hout,full load* is the enthalpy of air exiting the unitary system at full-load conditions (J/kg)

*hcontrol zone* is the enthalpy of air leaving the control zone (where thermostat is located) (J/kg)

*HRmin* are the enthalpies evaluated at a constant humidity ratio, the minimum humidity ratio of the unitary system exiting air or the air leaving the control zone

˙mCoilOff is the air mass flow rate through the unitary system with the heating coil OFF (kg/s)

*hout,coil off* is the enthalpy of air exiting the unitary system with the heating coil OFF (J/kg)

Δsen,full load is the sensible load difference between the system output node and the zone inlet node at full-load conditions.

Δsen,HighestSpeed=˙mZone InletFrac(hOut,full load−hZone Inlet)HRmin+(˙mHighestSpeed−˙mZone InletFrac)(hOut,coil off−hControl Zone)HRmin

where:

Frac is the control zone air fraction with respect to the system mass flow rate

Δsen,coiloff is the sensible load difference between the system output node and the zone inlet node with the heating coil OFF conditions.

Δsen,coil off=˙mZone InletFrac(hOut,coil off−hZone Inlet)HRmin+(˙mcoil off−˙mZone InletFrac)(hOut,coil off−hControl Zone)HRmin

If the unitary system’s DX heating coil output full load at the highest speed is insufficient to meet the entire heating load, the remaining heating load is passed to the supplemental heating coil. If the unitary system model determines that the outdoor air temperature is below the minimum outdoor air temperature for compressor operation (specified by the user), the compressor is turned off and the entire heating load is passed to the supplemental gas or electric heating coil. The unitary system exiting air conditions and energy consumption are calculated and reported by the individual component models (fan, DX heating coil, and supplemental gas or electric heating coil).

If the total heating load to be met by the system is less than the sensible heating rate at the highest speed, then the following steps are performed.

First, calculate the sensible heating energy rate at Speed 1:

FullHeatOutputSpeed1=(˙mSpeed1)(hout,full load−hcontrol zone)HRmin−Δsen,Speed1

where:

˙mSpeed1 is the air mass flow rate through unitary system at Speed 1 (kg/s)

Δsen,Speed1 is the sensible load difference between the system output node and the zone inlet node at full-load conditions at Speed 1.

Δsen,Speed1=˙mZone InletFrac(hOut,full load−hZoneInlet)HRmin+(˙mSpeed1−˙mZone InletFrac)(hOut,coil off−hControl Zone)HRmin

Second, if the sensible heating energy rate delivered by the unitary system at Speed 1 is greater or equal to the sensible load, the cycling ratio (part-load ratio) for the unitary system is estimated.

CyclingRatio=|(HeatingCoilSensibleLoad)|FullHeatingCoilCapacity=max(0.0,UnitarySystemHeatingLoad−AddedFanHeatFullHeatOutputSpeed1−AddedFanHeatSpeed1)

where:

*AddedFanHeat* is the generated supply air fan heat, which is a function of part load ratio and as internal component heating load (W)

*AddedFanHeatSpeed1* is the generated supply air fan heat at Speed 1 (part load ratio = 1) (W).

Since the part-load performance of the DX heating coil is frequently non-linear, and the supply air fan heat varies based on heating coil operation for the case of cycling fan/cycling coil (AUTO fan), the final part-load ratio for the heating coil compressor and fan are determined through iterative calculations (successive modeling of the heating coil and fan) until the unitary system’s heating output matches the heating load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s heating output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemHeatingLoad−UnitarySystemOutputcycling)UnitarySystemHeatingLoad

where *UnitarySystemOutputcycling* is the unitary system delivered sensible capacity for Speed 1 operating at a specific cycling ratio (W).

UnitarySystemOutputcycling=˙mUnitarySystem(hout−hControl Zone)HRmin−Δcycling

where

˙mUnitarySystem is the average air mass flow rate defined in the next section (kg/s)

hout is the enthalpy of air exiting the unitary system at part load conditions (J/kg)

Δcycling is the average sensible load difference between the system output node and the zone inlet node.

Δcycling=˙mZoneInletfrac(hZoneInlet−hControlZone)+(˙mUnitarySystem−˙mZoneInletfrac)(hOut−hControlZone)

where ˙mZone Inlet is the air mass flow rate in the supply inlet node in the controlled zone (kg/s).

For this case where Speed 1 operation was able to meet the required heating load, the speed ratio is set to zero and speed number is equal to 1.

Third, if the unitary system’s heating output at full load for Speed 1 is insufficient to meet the entire heating load, the Cycling ratio (PartLoadRatio) is set equal to 1.0 (compressor and fan are not cycling). Then the heating speed is increased and the delivered sensible capacity is calculated. If the full load sensible capacity at Speed n is greater than or equal to the sensible load, the speed ratio for the unitary system is estimated:

SpeedRatio=ABS(UnitarySystemHeatingLoad−AddedFanHeat−FullHeatOutputSpeedn−1)ABS(FullHeatOutputSpeedn−FullHeatOutputSpeedn−1)

Although a linear relationship is assumed by applying the speed ratio to obtain the effective capacity and air mass flow rate between speed n and n-1, the outlet node conditions are dependent on the combined outputs and may not be linear. In addition, the supply air fan heat varies based on heating coil operation for the case of cycling fan/cycling coil (AUTO fan). Therefore, the final speed ratio for the heating coil compressor and fan are determined through iterative calculations (successive modeling of the heating coil and fan) until the unitary system’s heating output matches the heating load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s heating output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemHeatingLoad−UnitarySystemOutputSpeedRatio)UnitarySyste

## Air System Compound Component Groups[LINK]

## Unitary Systems[LINK]

## Overview[LINK]

The input object AirLoopHVAC:UnitarySystem provides a “virtual” component that collects and controls a set of components: fan, heating coil, cooling coil, and/or reheat coil. Reheat coil is modeled for controlling high zone humidity levels or supplementing a heat pump heating coil. The unit may be configured to have either a blow through or draw through fan. In a blow through configuration, fan is generally the fist component upstream of heating or cooling coil. In a draw through fan configuration, fan is placed directly after the heating coil and before reheat coil.

Schematic of the EnergyPlus Unitary System (Blow Through Configuration) [fig:schematic-of-the-energyplus-unitary-system]

## Model Description[LINK]

As described previously, the unitary system is a “virtual” component consisting of a fan, heating coil, cooling coil and reheat coil. The sole purpose of the unitary system model is to properly coordinate the operation of the various system components. The following sections describe the flow of information within the model, as well as the differences between cycling and continuous supply air fan operation.

## Controls[LINK]

There are three types of control types allowed to be specified in the unitary system which are setpoint based, load based or a load based control method according to ASHRAE Standard 90.1. Each control type is described in detail below.

## Setpoint based control:[LINK]

The unitary system calculates the current sensible load using the temperature of the inlet node and the System Node Setpoint Temp on the control node. If the control node is not the outlet node, the desired outlet node temperature is adjusted for the current temperature difference between the outlet node and the control node. Likewise, the current latent load is calculated using the humidity ratio of the inlet node and the System Node Humidity Ratio Max on the control node. The controls determine the required coil run-time fraction and dehumidification mode (if applicable) using the steps outlined below.

## Step 1 – Meet Sensible Load Requirement[LINK]

The controls first attempt to meet the sensible requirement. The specified coil model is called with a part-load ratio (PLR) of 1.0 to determine the full-load output of the coil. This is compared with the desired outlet node temperature and a sensible PLR is calculated. If the PLR is <1.0, a root solver iteration routine is called to determine the coil run-time fraction which results in the desired outlet node temperature. For a variable-speed DX cooling coil, if the load is smaller than the sensible capacity at the lowest speed, the coil run-time fraction is determined in the same way as a single-speed DX cooling coil. Otherwise, its speed number and speed ratio between two neighboring speeds are selected to match the load.

## Step 2 – Meet Latent Load Requirement (if activated)[LINK]

If dehumidification controls are active, the leaving humidity ratio resulting from operation to meet the sensible load (Step 1 above) is compared with the desired outlet node humidity ratio. If the humidity requirement is already met, then no further control action is taken. If the humidity requirement has not been met, then the coil is re-simulated depending on the type of humidity control.

## Step 2a – Humidity Control = MultiMode[LINK]

If the humidity control type is MultiMode, then the coil’s enhanced dehumidification mode is activated when the coil type is Coil:Cooling:DX:TwoStageWithHumidityControlMode and Step 1 above is repeated to meet the sensible load using the coil performance resulting from the enhanced dehumidificaiton mode. This is a semi-passive approach to dehumidification which may fall short or may exceed the dehumidification requirement.

## Step 2b – Humidity Control = CoolReheat[LINK]

If the humidity control type is CoolReheat, the coil is re-simulated to achieve the desired outlet node humidity ratio. This option is valid for all cooling coil types. When the coil type is Coil:Cooling:DX:TwoStageWithHumidityControlMode, only the cooling performance mode is used for this step and enhanced dehumidification mode is not activated.

## Load based control:[LINK]

While the unitary system may be configured to serve multiple zones, system operation is controlled by a thermostat located in a single “control” zone. One of the key parameters for the unitary system component is the fraction of the total system air flow that goes through the control zone. This fraction is calculated as the ratio of the maximum air mass flow rate for the air loop’s supply inlet node for the control zone (e.g., AirTerminal:SingleDuct:ConstantVolume:NoReheat, field = Maximum Air Flow Rate, converted to mass flow) to the sum of the maximum air mass flow rates for the air loop’s supply inlet nodes for all zones served by this air loop. The unitary system module scales the calculated load for the control zone upward based on this fraction to determine the total load to be met by the unitary system. The module then proceeds to calculate the required part-load ratio for the system coil and the supply air fan to meet this total load. The heating or cooling capacity delivered by the unitary system is distributed to all of the zones served by this system via the terminal units that supply air to each zone. The supply air fraction that goes though the control zone is calculated as follows:

ControlZoneAirFlowFraction=˙mTUMaxControlZoneNumOfZones∑j=1˙mTUMaxZonej

where:

˙mTUMaxControlledZone is the maximum air mass flow rate for the air loop’s supply inlet node (terminal unit) for the control zone (kg/s)

˙mTUMaxZonej is the maximum air mass flow rate for the air loop’s supply inlet node for the jth zone (kg/s)

NumOfZones is the number of zones, or number of air loop supply air inlet nodes for all zones served by the air loop.

The unitary system component is able to model supply air fan operation in two modes: cycling fan – cycling coil (i.e., AUTO fan) and continuous fan – cycling coil (i.e., fan ON). Fan:OnOff must be used to model AUTO fan, while Fan:OnOff or Fan:ConstantVolume can be used to model fan ON. The fan operation mode is specified using a supply air fan operating mode schedule where schedule values of 0 denote cycling fan operation and schedule values other than 0 (a 1 is usually used) denote continuous fan operation. Using this schedule, the unitary system fan may be cycled with cooling or heating coil operation or operated continuously based on time of day (e.g., cycling fan operation at night and continuous fan operation during the daytime). If the fan operating mode schedule name field is left blank in the unitary system object, the unitary system assumes cycling or AUTO fan mode operation throughout the simulation.

The unitary system operates based on the user-specified (or autosized) design supply air flow rate(s). The ‘design’ supply air mass flow rate may be different for cooling, heating, and when no cooling or heating is required and the fan operates continuously based on user-specified inputs.

Cooling OperationIf EnergyPlus determines that the unitary system must supply cooling to the control zone to meet the zone air temperature setpoint, then the model computes the total sensible cooling load to be met by the unitary system based on the control zone sensible cooling load and the fraction of the unitary system air flow that goes through the control zone.

UnitarySystemCoolingLoad=ControlZoneCoolingLoadControlZoneAirFlowFraction

If the supply air fan operating mode schedule requests cycling fan operation, the model first checks for the presence of an ecomomizer in the outside air system serving the unitary system’s air loop (Ref. AirLoopHVAC:OutdoorAirSystem). If an outside air system is not present or if an air-side economizer is not used, the unitary system’s compressor is used to meet the unitary system cooling load. If an air-side economizer is used and is active (i.e., economizer controls indicate that conditions are favorable to increase the outside air flow rate), the unitary system will try to meet the cooling load by operating only the supply air fan. If the fan is able to satisfy the unitary system cooling load, the compressor remains off for the entire simulation time step. If the operation of the fan alone is unable to meet the entire cooling load, then the compressor is enabled and additional calculations are performed to determine the compressor’s part-load ratio.

The model then calculates the unitary system’s sensible cooling energy rate delivered to the zones being served when the system runs at full-load conditions and when the cooling coil is OFF. If the supply air fan cycles with the compressor, then the sensible cooling energy rate is zero when the cooling coil is OFF. However if the fan is configured to run continuously regardless of coil operation, then the sensible cooling energy rate will probably not be zero when the cooling coil is OFF. Calculating the sensible cooling energy rate involves modeling the supply air fan (and associated fan heat), the cooling coil, and the heating and reheat coil (simply to pass the air properties and mass flow rate from its inlet node to its outlet node). For each of these cases (full load and cooling coil OFF), the sensible cooling energy rate delivered by the unitary system is calculated as follows:

Full Cool Output=(Mass Flow Ratefullload)(hout,full load−hcontrol zone)HRmin−Δsen,full load

No Cool Output=(Mass Flow Ratecoil off)(hout,coil off−hcontrol zone)HRmin−Δsen,coil off

where:

Mass Flow Ratefull loadis the air mass flow rate through unitary system at full-load conditions (kg/s)hcoil,full loadis the enthalpy of air exiting the unitary system at full-load conditions (J/kg)hcontrol zone is the enthalpy of air in the control zone where the thermostat is located (J/kg)

HRminis the enthalpies evaluated at a constant humidity ratio, the minimum humidity ratio of the unitary system exiting air or the air in the control zoneMass Flow Ratecoil offis the air mass flow rate through the unitary system with the cooling coil OFF (kg/s)hout,coil offis the enthalpy of air exiting the unitary system with the cooling coil OFF (J/kg)Δsen,full load is the sensible load difference between the system output node and the zone inlet node at full-load conditions.

Δsen,full load=MassFlowRateZone InletFrac(hOut,full load−hZone Inlet)HRmin+(MassFlowRatefull load−MassFlowRateZone InletFrac)(hOut,full load−hControl Zone)HRmin

where:

Frac is the control zone air fraction with respect to the system mass flow rate

Δsen,coiloff is the sensible load difference between the system output node and the zone inlet node with the heating coil OFF conditions.

Δsen,coil off=MassFlowRateZone InletFrac(hOut,coil off−hZone Inlet)HRmin+(MassFlowRatecoil off−MassFlowRateZone InletFrac)(hOut,coil off−hControl Zone)HRmin

With the calculated sensible cooling energy rates and the total sensible cooling load to be met by the system, the part-load ratio for the unitary system is estimated.

PartLoadRatio=MAX(0.0,(UnitarySystemCoolingLoad−NoCoolOutput)(FullCoolOutput−NoCoolOutput))

Since the part-load performance of the cooling coil is frequently non-linear, and the supply air fan heat varies based on cooling coil operation for the case of cycling fan/cycling coil (AUTO fan), the final part-load ratio for the cooling coil compressor and fan are determined through iterative calculations (successive modeling of the cooling coil and fan) until the unitary system’s cooling output matches the cooling load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s cooling output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemCoolingLoad−QUnitarySystem)UnitarySystemCoolingLoad

where QUnitarySystem is the unitary system delivered sensible capacity (W).

If the unitary system has been specified with cycling fan/cycling coil (AUTO fan), then the unitary system’s operating supply air mass flow rate is multiplied by PartLoadRatio to determine the average air mass flow rate for the system simulation time step. In this case, the air conditions at nodes downstream of the cooling coil represent the full-load (steady-state) values when the coil is operating.

If the fan operates continuously (i.e., when the supply air fan operating mode schedule values are NOT equal to 0), the operating air mass flow rate through the unitary system is calculated as the average of the user-specified air flow rate when the cooling coil is ON and the user-specified air flow rate when the cooling coil is OFF (user-specified supply air volumetric flow rates converted to dry air mass flow rates).

˙mUnitarySystem=PartLoadRatio(˙mCoolCoilON)+(1−PartLoadRatio)(˙mCoilOFF)

where:

˙mHeatCoilON is the air mass flow rate through unitary system when the cooling coil is ON (kg/s)

˙mCoilOFF is the air mass flow rate through unitary system when no cooling or heating is needed (kg/s).

In this case, the air conditions at nodes downstream of the cooling coil are calculated as the average conditions over the simulation time step (i.e., the weighted average of full-load conditions when the coil is operating and inlet air conditions when the coil is OFF).

Cooling Operation (multi or variable speed coils)After the unitary system cooling load is determined as described in Equation [eq:UnitarySystemCoolingLoad] above, the multi or variable speed cooling coil models calculations are described in this section.

The model calculates the unitary system’s sensible cooling energy rate delivered to the zones being served when the system runs at full-load conditions at the highest speed and when the DX cooling coil is OFF. If the supply air fan cycles with the compressor, then the sensible cooling energy rate is zero when the cooling coil is OFF. However if the fan is scheduled to run continuously regardless of coil operation, then the sensible cooling energy rate will not be zero when the cooling coil is OFF. Calculating the sensible cooling energy rate involves modeling the supply air fan (and associated fan heat) and the multi/variable speed DX cooling coil. The multi/variable speed DX heating coil and the supplemental heating coil are also modeled, but only to pass the air properties and mass flow rate from their inlet nodes to their outlet nodes. For each of these cases (full load at highest cooling speed and DX cooling coil OFF), the sensible cooling energy rate delivered by the unitary system is calculated as follows:

FullCoolOutputHighestSpeed=(˙mHighestSpeed)(hout,full load−hcontrol zone)HRmin−Δsen,HighestSpeed

NoCoolOutput=(˙mCoilOff)(hout,coil off−hcontrol zone)HRmin−Δsen,coil off

where:

˙mHighestSpeed is the air mass flow rate through unitary system at the highest cooling speed (kg/s)

hout,full load is the enthalpy of air exiting the unitary system at full-load conditions [J/kg]

hcontrol zone is the enthalpy of air leaving the control zone (where thermostat is located) (J/kg)

HRmin is the minimum humidity ratio of the unitary system exiting air or the air leaving the control zone (kg/kg)

˙mCoilOff is the air mass flow rate through the unitary system with the cooling coil OFF (kg/s)

hout,coil off is the enthalpy of air exiting the unitary system with the cooling coil OFF (J/kg)

Δsen,HighestSpeed is the sensible load difference between the system output node and the zone inlet node at full-load conditions

Δsen,coil off is the sensible load difference between the system output node and the zone inlet node with the cooling coil OFF conditions.

Δsen,HighestSpeed=˙mZone InletFrac(hOut,full load−hZone Inlet)HRmin+(˙mHighestSpeed−˙mZone InletFrac)(hOut,full load−hControl Zone)HRmin

Δsen,coil off=˙mZone InletFrac(hOut,coil off−hZone Inlet)HRmin+(˙mcoil off−˙mZone InletFrac)(hOut,coil off−hControl Zone)HRmin

where Frac is the control zone air fraction with respect to the system mass flow rate.

If the unitary system’s sensible cooling rate at the highest speed (full load, no cycling) is insufficient to meet the entire cooling load, the controlled zone conditions will not be met. The reported cycling rate and speed ratio are 1, and the speed number is set to the highest index number. If the total sensible cooling load to be met by the system is less than the sensible cooling rate at the highest speed, then the following steps are performed.

First, calculate the sensible cooling energy rate at Speed 1:

FullCoolOutputSpeed1=(˙mSpeed1)(hout,fullload−hcontrol zone)HRmin−Δsen,Speed1

where:

˙mSpeed1is the air mass flow rate through unitary system at Speed 1 (kg/s)Δsen,Speed1 is th sensible load difference between the system output node and the zone inlet node at full-load conditions at Speed 1.

Δsen,Speed1=˙mZone InletFrac(hOut,full load−hZone Inlet)HRmin+(˙mSpeed1−˙mZone InletFrac)(hOut,full load−hControl Zone)HRmin

If the sensible cooling energy rate delivered by the unitary system at Speed 1 is greater or equal to the sensible load, the cycling ratio (part-load ratio) for the unitary system is estimated.

CyclingRatio=|(CoolingCoilSensibleLoad)|FullCoolingCoilCapacity=max(0.0,UnitarySystemCoolingLoad−AddedFanHeatFullCoolOutputSpeed1−AddedFanHeatSpeed1)

where:

AddedFanHeatis the generated supply air fan heat, which is a function of part load ratio and as internal component cooling load (W)AddedFanHeatSpeed1is the generated supply air fan heat at Speed 1 for a part load ratio = 1 (W).Since the part-load performance of the DX cooling coil is frequently non-linear,and the supply air fan heat varies based on cooling coil operation for the case of cycling fan/cycling coil (AUTO fan), the final part-load ratio for the cooling coil compressor and fan are determined through iterative calculations (successive modeling of the cooling coil and fan) until the unitary system’s cooling output matches the cooling load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s cooling output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemOutputcycling−QUnitarySystem)UnitarySystemCoolingLoad

where the UnitarySystemOutputCycling is the unitary system delivered sensible capacity for Speed 1 operating at a specific cycling ratio (W).

UnitarySystemOutputcycling=˙mUnitarySystem(hout−hControlZone)HRmin−Δcycling

where:

˙mUnitarySystem is the average air mass flow rate defined in the next section (kg/s)

houtis the enthalpy of air exiting the unitary system at part load conditions (J/kg)Δcycling is the average sensible load difference between the system output node and the zone inlet node.

Δcycling=˙mZoneInletfrac(hZoneInlet−hControlZone)+(˙mUnitarySystem−˙mZoneInletfrac)(hOut−hControlZone)

where ˙mZoneInlet is the air mass flow rate in the supply inlet node in the controlled zone (kg/s).

For this case where speed 1 operation was able to meet the required cooling load, the speed ratio is set to zero and speed number is equal to 1.

If the unitary system’s cooling output at full load for Speed 1 is insufficient to meet the entire cooling load, the Cycling ratio is set equal to 1.0 (compressor and fan are not cycling). Then the cooling speed is increased and the delivered sensible capacity is calculated. If the full load sensible capacity at Speed n is greater than or equal to the sensible load, the speed ratio for the unitary system is estimated:

SpeedRatio=ABS(UnitarySystemCoolingLoad−AddedFanHeat−FullCoolOutputSpeedn−1)ABS(FullCoolOutputSpeedn−FullCoolOutputSpeedn−1)

Although a linear relationship is assumed by applying the speed ratio to obtain the effective capacity and mass flow rate between speed n and n-1, the outlet air node conditions are dependent on the combined outputs and may not be linear. In addition, the supply air fan heat varies with the speed ratio due to different supply mass flow rates between speed n and n-1 . Therefore, the final speed ratio for the cooling coil compressor and fan are determined through iterative calculations (successive modeling of the cooling coil and fan) until the unitary system’s cooling output matches the cooling load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s cooling output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemCoolingLoad−UnitarySystemOutputSpeedRatio)UnitarySystemCoolingLoad

where

UnitarySystemOutputSpeednis the unitary system delivered sensible capacity between two consecutive speeds at a specific speed ratio (W).UnitarySystemOutputSpeedRatio=(SpeedRatio)FullCoolOutputSpeedn+(1−SpeedRatio)FullCoolOutputSpeedn−1−AddedFanHeatSpeedRatio

where

AddedFanHeatSpeedRatiois the generated supply air fan heat at a specific speed ratio (W).In this case, the reported cycling ratio is 1 and speed number is equal to n.

## Air Mass Flow Rate Calculation[LINK]

Speed 1 operationIf the unitary system has been specified with cycling fan/cycling coil (AUTO fan), then the unitary system’s operating supply air mass flow rate is determined by the cycling ratio (PartLoadRatio) for Speed 1. The supply air mass flow rate is multiplied by the cycling ratio to determine the average air mass flow rate for the system simulation time step. The air conditions at nodes downstream of the cooling coils represent the full-load (steady-state) values when the coil is operating.

˙mUnitarySystem=(CyclingRatio)˙mSpeed1

If the fan operates continuously (i.e., when the supply air fan operating mode schedule values are NOT equal to 0), the operating air mass flow rate through the unitary system is calculated as the average of the user-specified air flow rate when the unitary system cooling coil is ON at Speed 1 and the user-specified air flow rate when the unitary system cooling coil is OFF (user-specified supply air volumetric flow rates converted to dry air mass flow rates).

˙mUnitarySystem=(CyclingRatio)˙mSpeed1+(1−CyclingRatio)˙mCoilOff

where:

˙mUnitarySystem is the average air mass flow rate through unitary system (kg/s)

˙mSpeed1 is the air mass flow rate through unitary system when cooling coil is ON at Speed 1 (kg/s)

˙mCoilOff is the air mass flow rate through unitary system when no heating or cooling is needed (kg/s).

In this case, the air conditions at nodes downstream of the cooling coils are calculated as the average conditions over the simulation time step (i.e., the weighted average of full-load conditions when the coil is operating and inlet air conditions when the coil is OFF).

## Higher Speed Operation[LINK]

When the unitary system operates at higher speeds to meet the required cooling load, the supply air mass flow rate is linearly interpolated between two consecutive speeds:

˙mUnitarySystem=(SpeedRatio)˙mSpeedn+(1−SpeedRatio)˙mSpeedn−1

where:

˙mUnitarySystem is the average air mass flow rate through the unitary system for the time step (kg/s)

˙mSpeedn is the air mass flow rate through unitary system when cooling coil is ON at Speed n (kg/s)

˙mSpeedn−1 is the air mass flow rate through unitary system when cooling coil is ON at Speed n-1 (kg/s).

For this case of higher speed operation, the air conditions at nodes downstream of the cooling coils are determined by the delivered cooling capacity and supply air mass flow rates between two consecutive speeds.

Although the above sections present the capacity and air mass flow rate calculation separately, they are dependent and change every iteration until convergence is reached for the time step being simulated.

Heating OperationCalculations for heating operation are similar to those for cooling operation in most respects. However, due to the inclusion of a supplemental heating coil, additional calculations are necessary to properly meet the total heating load for the zones being served.

If EnergyPlus determines that the unitary system must supply heating to the control zone to meet the zone air temperature setpoint, then the unitary system model computes the total sensible heating load to be delivered to the zones being served based on the control zone sensible heating load and the control zone airflow fraction.

UnitarySystemHeatingLoad=ControlZoneHeatingLoadControlZoneAirFlowFraction

The model then calculates the unitary system’s sensible heating energy rate delivered to the zones being served when the system runs at full-load conditions and when the heating coil is OFF (without supplemental heater operation in either case). If the supply air fan cycles with the compressor, then the sensible heating energy rate is zero when the compressor is OFF. However if the fan is scheduled to run continuously regardless of coil operation, then the sensible heating energy rate will not be zero when the compressor is OFF. Calculating the sensible heating energy rate involves modeling the supply air fan (and associated fan heat), the cooling coil (simply to pass the air properties and mass flow rate from its inlet node to its outlet node), the heating coil, and the supplemental heating coil (simply to pass the air properties and mass flow rate from its inlet node to its outlet node). For each of these cases (full load and heating coil OFF, without supplemental heater operation in either case), the sensible heating energy rate delivered by the unitary system is calculated as follows:

Full Heat Output=(Mass Flow Ratefull load)(hout,full load−hcontrol zone)HRmin−Δsen,full load

No Heat Output=(Mass Flow Ratecoil off)(hout,coil off−hcontrol zone)HRmin−Δsen,coil off

where:

Mass Flow Ratefull loadis the air mass flow rate through unitary system at full-load conditions (kg/s)hout,full loadis the enthalpy of air exiting the unitary system at full-load conditions (J/kg)hcontrol zoneis the enthalpy of air leaving the control zone (where thermostat is located) (J/kg)HRminare the enthalpies evaluated at a constant humidity ratio, the minimum humidity ratio of the unitary system exiting air or the air leaving the control zoneMass Flow Ratecoil offis the air mass flow rate through the unitary system with the heating coil OFF (kg/s)hout,coil offis the enthalpy of air exiting the unitary system with the heating coil OFF (J/kg)Δsen,full load is the sensible load difference between the system output node and the zone inlet node at full-load conditions.

Δsen,full load=˙mZone InletFrac(hOut,full load−hZone Inlet)HRmin+(˙mfull load−˙mZone InletFrac)(hOut,full load−hControl Zone)HRmin

where:

Frac is the control zone air fraction with respect to the system mass flow rate

Δsen,coil off is the sensible load difference between the system output node and the zone inlet node with the heating coil OFF conditions.

Δsen,coil off=˙mZone InletFrac(hOut,coil off−hZone Inlet)HRmin+(˙mcoil off−˙mZone InletFrac)(hOut,coil off−hControl Zone)HRmin

With the calculated sensible heating energy rates and the total sensible heating load to be met by the system, the part-load ratio for the unitary system is estimated.

PartLoadRatio=MAX(0.0,(UnitarySystemHeatingLoad−NoHeatOutput)(FullHeatOutput−NoHeatOutput))

Since the part-load performance of the heating coil is frequently non-linear, and the supply air fan heat varies based on heating coil operation for the case of cycling fan/cycling coil (AUTO fan), the final part-load ratio for the heating coil compressor and fan are determined through iterative calculations (successive modeling of the heating coil and fan) until the unitary system’s heating output matches the heating load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s heating output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemHeatingLoad−QUnitarySystem)UnitarySystemHeatingLoad

where QUnitarySystem is the unitary system delivered sensible capacity (W).

If the unitary system’s heating coil output at full load is insufficient to meet the entire heating load, PartLoadRatio is set equal to 1.0 (compressor and fan are not cycling) and the remaining heating load is passed to the supplemental heating coil. If the unitary system model determines that the outdoor air temperature is below the minimum outdoor air temperature for compressor operation, the compressor is turned off and the entire heating load is passed to the supplemental gas or electric heating coil. The unitary system exiting air conditions and energy consumption are calculated and reported by the individual component models (fan, heating coil, and supplemental gas or electric heating coil).

If the unitary system has been specified with cycling fan/cycling coil (AUTO fan), then the unitary system’s operating supply air mass flow rate is multiplied by PartLoadRatio to determine the average air mass flow rate for the system simulation time step. The air conditions at nodes downstream of the heating coils represent the full-load (steady-state) values when the coils are operating. If the fan operates continuously (i.e., when the supply air fan operating mode schedule values are NOT equal to 0), the operating air mass flow rate through the unitary system is calculated as the average of the user-specified air flow rate when the unitary system heating coil is ON and the user-specified air flow rate when the unitary system heating coil is OFF (user-specified supply air volumetric flow rates converted to dry air mass flow rates).

˙mUnitarySystem=PartLoadRatio(˙mHeatCoilON)+(1−PartLoadRatio)(˙mCoilOFF)

where:

˙mHeatCoilON is the air mass flow rate through unitary system when the heating coil is ON (kg/s)

˙mCoilOFF is the air mass flow rate through unitary system when no heating or cooling is needed (kg/s).

In this case, the air conditions at nodes downstream of the heating coils are calculated as the average conditions over the simulation time step (i.e., the weighted average of full-load conditions when the coils are operating and inlet air conditions when the coils are OFF).

## Heating Operation (multi or variable speed coils )[LINK]

After the unitary system heating load is determined as described in Equation [eq:UnitarySystemHeatingLoad] above, the multi or variable speed heating coil models calculation are described in this section.

The model calculates the unitary system’s sensible heating energy rate delivered to the zones being served when the system runs at full-load conditions at the highest speed and when the DX heating coil is OFF (without supplemental heater operation in either case). If the supply air fan cycles with the compressor, then the sensible heating energy rate is zero when the compressor is OFF. However if the fan is scheduled to run continuously regardless of coil operation, then the sensible heating energy rate will not be zero when the compressor is OFF. Calculating the sensible heating energy rate involves modeling the supply air fan (and associated fan heat), the DX cooling coil (simply to pass the air properties and mass flow rate from its inlet node to its outlet node), the DX heating coil, and the supplemental heating coil (simply to pass the air properties and mass flow rate from its inlet node to its outlet node). For each of these cases (full load and DX heating coil OFF, without supplemental heater operation in either case), the sensible heating energy rate delivered by the unitary system is calculated as follows:

FullHeatOutputHighestSpeed=(˙mHighestSpeed)(hout,full load−hcontrol zone)HRmin−Δsen,HighestSpeed

NoHeatOutput=(˙mCoilOff)(hout,coil off−hcontrol zone)HRmin−Δsen,coil off

where:

˙mHighestSpeedis the air mass flow rate through unitary system at the highest heating speed (kg/s)hout,full loadis the enthalpy of air exiting the unitary system at full-load conditions (J/kg)hcontrol zoneis the enthalpy of air leaving the control zone (where thermostat is located) (J/kg)HRminare the enthalpies evaluated at a constant humidity ratio, the minimum humidity ratio of the unitary system exiting air or the air leaving the control zone˙mCoilOff is the air mass flow rate through the unitary system with the heating coil OFF (kg/s)

hout,coil offis the enthalpy of air exiting the unitary system with the heating coil OFF (J/kg)Δsen,full load is the sensible load difference between the system output node and the zone inlet node at full-load conditions.

Δsen,HighestSpeed=˙mZone InletFrac(hOut,full load−hZone Inlet)HRmin+(˙mHighestSpeed−˙mZone InletFrac)(hOut,coil off−hControl Zone)HRmin

where:

Frac is the control zone air fraction with respect to the system mass flow rate

Δsen,coiloff is the sensible load difference between the system output node and the zone inlet node with the heating coil OFF conditions.

Δsen,coil off=˙mZone InletFrac(hOut,coil off−hZone Inlet)HRmin+(˙mcoil off−˙mZone InletFrac)(hOut,coil off−hControl Zone)HRmin

If the unitary system’s DX heating coil output full load at the highest speed is insufficient to meet the entire heating load, the remaining heating load is passed to the supplemental heating coil. If the unitary system model determines that the outdoor air temperature is below the minimum outdoor air temperature for compressor operation (specified by the user), the compressor is turned off and the entire heating load is passed to the supplemental gas or electric heating coil. The unitary system exiting air conditions and energy consumption are calculated and reported by the individual component models (fan, DX heating coil, and supplemental gas or electric heating coil).

If the total heating load to be met by the system is less than the sensible heating rate at the highest speed, then the following steps are performed.

First, calculate the sensible heating energy rate at Speed 1:

FullHeatOutputSpeed1=(˙mSpeed1)(hout,full load−hcontrol zone)HRmin−Δsen,Speed1

where:

˙mSpeed1 is the air mass flow rate through unitary system at Speed 1 (kg/s)

Δsen,Speed1 is the sensible load difference between the system output node and the zone inlet node at full-load conditions at Speed 1.

Δsen,Speed1=˙mZone InletFrac(hOut,full load−hZoneInlet)HRmin+(˙mSpeed1−˙mZone InletFrac)(hOut,coil off−hControl Zone)HRmin

Second, if the sensible heating energy rate delivered by the unitary system at Speed 1 is greater or equal to the sensible load, the cycling ratio (part-load ratio) for the unitary system is estimated.

CyclingRatio=|(HeatingCoilSensibleLoad)|FullHeatingCoilCapacity=max(0.0,UnitarySystemHeatingLoad−AddedFanHeatFullHeatOutputSpeed1−AddedFanHeatSpeed1)

where:

AddedFanHeatis the generated supply air fan heat, which is a function of part load ratio and as internal component heating load (W)AddedFanHeatSpeed1is the generated supply air fan heat at Speed 1 (part load ratio = 1) (W).Since the part-load performance of the DX heating coil is frequently non-linear, and the supply air fan heat varies based on heating coil operation for the case of cycling fan/cycling coil (AUTO fan), the final part-load ratio for the heating coil compressor and fan are determined through iterative calculations (successive modeling of the heating coil and fan) until the unitary system’s heating output matches the heating load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s heating output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemHeatingLoad−UnitarySystemOutputcycling)UnitarySystemHeatingLoad

where

UnitarySystemOutputcyclingis the unitary system delivered sensible capacity for Speed 1 operating at a specific cycling ratio (W).UnitarySystemOutputcycling=˙mUnitarySystem(hout−hControl Zone)HRmin−Δcycling

where

˙mUnitarySystem is the average air mass flow rate defined in the next section (kg/s)

hout is the enthalpy of air exiting the unitary system at part load conditions (J/kg)

Δcycling is the average sensible load difference between the system output node and the zone inlet node.

Δcycling=˙mZoneInletfrac(hZoneInlet−hControlZone)+(˙mUnitarySystem−˙mZoneInletfrac)(hOut−hControlZone)

where ˙mZone Inlet is the air mass flow rate in the supply inlet node in the controlled zone (kg/s).

For this case where Speed 1 operation was able to meet the required heating load, the speed ratio is set to zero and speed number is equal to 1.

Third, if the unitary system’s heating output at full load for Speed 1 is insufficient to meet the entire heating load, the Cycling ratio (PartLoadRatio) is set equal to 1.0 (compressor and fan are not cycling). Then the heating speed is increased and the delivered sensible capacity is calculated. If the full load sensible capacity at Speed n is greater than or equal to the sensible load, the speed ratio for the unitary system is estimated:

SpeedRatio=ABS(UnitarySystemHeatingLoad−AddedFanHeat−FullHeatOutputSpeedn−1)ABS(FullHeatOutputSpeedn−FullHeatOutputSpeedn−1)

Although a linear relationship is assumed by applying the speed ratio to obtain the effective capacity and air mass flow rate between speed n and n-1, the outlet node conditions are dependent on the combined outputs and may not be linear. In addition, the supply air fan heat varies based on heating coil operation for the case of cycling fan/cycling coil (AUTO fan). Therefore, the final speed ratio for the heating coil compressor and fan are determined through iterative calculations (successive modeling of the heating coil and fan) until the unitary system’s heating output matches the heating load to be met within the convergence tolerance. The convergence tolerance is fixed at 0.001 and is calculated based on the difference between the load to be met and the unitary system’s heating output divided by the load to be met.

Tolerance=0.001≥(UnitarySystemHeatingLoad−UnitarySystemOutputSpeedRatio)UnitarySyste