# Zone Equipment and Zone Forced Air Units[LINK]

## Air Distribution Terminal Unit[LINK]

The ZoneHVAC:AirDistributionUnit is a special piece of zone equipment – it connects centrally conditioned air with a zone. It encompasses the various types of air terminal units in EnergyPlus: *AirTerminal:DualDuct:ConstantVolume*, *AirTerminal:SingleDuct:VAV:Reheat*, etc. It is a generalized component that accesses the calculations for the different types of air terminal unit.

The air distribution function is encapsulated in the module *ZoneAirEquipmentManager*. The object and module function only to invoke the individual air terminal unit simulations.

The data for this unit consists of the unit name, the air outlet node name (which should be the same as one of the zone inlet nodes), the type of air terminal unit (air distribution equipment), and the name of the air terminal unit.

All input data for air distribution units is stored in the array *AirDistUnit* in data module *DataDefineEquip*.

There is no calculation associated with ZoneHVAC:AirDistributionUnit.

### Simulation and Control[LINK]

*SimZoneAirLoopEquipment* in module *ZoneAirEquipmentManager* calls the individual air terminal unit simulations.

No specific references.

## Air Terminal Single Duct Mixer[LINK]

The mixer object AirTerminal:SingleDuct:Mixer provides a means for using a ZoneHVAC equipment as a terminal unit by mixing central system conditioned air with the inlet or supply side air stream of the ZoneHVAC equipment. Usually the central system would be a Direct Outside Air System (DOAS) providing centrally conditioned ventilation air to the controlled zones. The inlet or supply side connection type is specified by user.

The mixer uses the equations for adiabatic mixing of two moist air streams. Namely, dry air mass balance, water mass balance, and enthalpy balance. For inlet side mixer connection, the primary air and outlet air flow rates are known, and the condition of the primary and secondary air streams are also known. The mass balance yields the secondary air mass flow rate, and the outlet conditions are determined from enthalpy and water mass balance. For the supply side mixer connection, the primary and secondary air stream conditions and flow rates are known so the outlet condition and flow rate is calculated.

The only input data are the name and type of the ZoneHVAC equipment unit plus the node names of the primary and the secondary air nodes and the outlet air node. No flow rate data is needed.

All input data for the inlet and supply side mixer units is stored in the data structure *SysATMixer*.

The following equations for the mixing of two moist air streams are used:

˙mda1h1+˙mda2h2=˙mda3h3

˙mda1+˙mda2=˙mda3

˙mda1W1+˙mda2W2=˙mda3W3

The mixed air temperature is determined using the following psychometric function: T3=PsyHFnTdbW(h3,w3)

where ˙mda is dry air mass flow rate in kg/s, *h* is specific enthalpy in J/kg, *T* is temperature in C, and W is humidity ratio in (kg of water)/(kg of dry air).

For a mixer unit connected to the inlet side of a ZoneHVAC equipment, the outlet air mass flow rate has been set by the zone HVAC equipment. The air mass flow rate of one of the inlets - the primary air from the central system - is also known. So the air mass balance equation is used to obtain the secondary air mass flow rate.

The inlet conditions - specific enthalpy and humidity ratio - for both inlet air streams are known. Now that both inlet air streams’ mass flow rate is known, the enthalpy and water mass balance equations are used to get the outlet conditions.

For a mixer unit connected to the supply side of a ZoneHVAC equipment, the conditions and flow rates of the primary air and secondary air streams are known, are taken from the inlet nodes’ data. The balance equations are then used to calculate the outlet flow rate and conditions.

### Simulation and Control[LINK]

The mixer model is invoked from within the zone HVAC model. Basically the mixer becomes a subcomponent of the zone HVAC equipment model. This allows the zone unit to allow for the mixing of central supply air with its inlet or supply air stream of the ZoneHVAC equipment in calculating how much cooling or heating it needs to do in order to meet the zone load.

See Chapter 1, page 1.17 of the 2013 ASHRAE Handbook of Fundamentals

## Simple Duct Leakage Model[LINK]

The input object ZoneHVAC:AirDistributionUnit also provides access to a model for duct leakage that can be a significant source of energy inefficiency in forced-air HVAC systems. Evaluating duct leakage energy losses can involve considerable user effort and computer resources if an airflow network is defined through a detailed description of the system components and airflow paths (including leakage paths). A nonlinear pressure-based solver is used to solve for pressures and flow rates in the network. By making certain assumptions and approximations for certain well defined configurations, however, it is possible to obtain accurate results with a simple mass and energy balance calculation and thus avoid the input and calculation costs of doing a full pressure-based airflow network simulation.

The Simple Duct Leakage Model (SDLM) assumes a central VAV air conditioning system with a constant static pressure setpoint. The model assumes that the leaks are in the supply ducts and that the system returns air through a ceiling plenum that contains the ducts. Thus, the ducts leak into the return plenum, and this part of the supply does not reach the conditioned zones. With the additional assumptions described below, it is possible to model this configuration with heat and mass balance equations and avoid the use of a nonlinear pressure-based solver. In the EnergyPlus context, this means that use of AirflowNetwork is avoided and the leakage calculations are obtained in the course of the normal thermal simulation.

### Principles and Description[LINK]

Constant Flow Rate

The airflow rate through a duct leak is a function of the pressure difference between the duct and the surrounding space:

˙Vleak=C1⋅Δpnduct−space

The exponent *n* is 0.5 for leaks that look like orifices (holes that are large relative to the thickness of the duct wall); for leaks that resemble cracks (e.g., lap joints), *n* is approximately 0.6 to 0.65.

For a duct with constant flow rate and a linear pressure drop through the duct, the average static pressure in the duct will equal half of the duct static pressure drop. Assuming turbulent flow in the duct, the duct pressure drop is proportional to the square of the airflow through the duct. This can be expressed as:

Δpduct−space=Δpduct2=C2⎛⎝˙V2duct2⎞⎠

Combining equations and and assuming the leaks are large holes (*n* equals 0.5). gives:

˙Vleak=C1⋅Δp0.5duct−space=C3⋅˙Vduct

where

C3=C1⋅(C2/2)0.5

Thus the leakage fraction *C*3 remains constant regardless of the duct flow rate or static pressure. This result depends on the following assumptions:

· the duct airflow is turbulent;

· the duct pressure varies linearly along the duct;

· the average duct pressure approximates the pressure drop across the duct;

· the leaks are large and have pressure exponent 0.5.

Effects of Constant Pressure Upstream and Variable Flow and Pressure Downstrean

Commonly VAV systems maintain a constant static pressure at some point in the duct system upstream of the VAV terminal units. That is, airflow rate will vary depending on the cooling requirement, but a constant pressure will be maintained at the static pressure sensor. Consequently, the leakage flow for a leak upstream of the VAV boxes will be approximately constant. Or to put it another way, the leakage fraction will vary in proportion to the flow rate.

For leaks downstream of the VAV terminal units, the airflow through the duct and the pressure in the downstream duct will vary as the box damper modulates in response to the differential between the room temperature and the thermostat setpoint. In this case, the situation is similar to the constant flow case: for an orifice-like leak, the pressure difference across the leak will vary linearly with the air speed (or flow rate); i.e., the leakage fraction will be approximately constant.

SDLM

For SDLM, our leakage model is then:

· for leaks upstream of the terminal units, the leakage flow rate will be constant;

· for leaks downstream of the terminal units, the leakage fraction will be constant.

This model assumes, in addition to the assumptions given above, that the VAV system is controlled to a constant static pressure setpoint. In EnergyPlus SDLM is not currently applicable to systems using static pressure reset. Using SDLM would require knowledge of static pressure as a function of system air flow rate.

User data for the SDLM is entered through The ZoneHVAC:AirDistributionUnit (ADU) object. There are 2 data items per ADU:

1. the upstream nominal leakage fraction;

2. the downstream fixed leakage fraction.

Both inputs are leakage fractions. Input (1) is the leakage fraction at design flow rate, which together can be used to determine the constant leakage flow rate upstream of the VAV boxes; this leakage fraction varies with the flow rate. Input (2) is a fixed leakage fraction and is constant as the flow rate varies.

### Implementation[LINK]

The various zone mass flow rates are related in the following manner.

˙ms,us=˙mtu+˙mlk,us

˙mtu=˙mlk,ds+˙ms,z

˙mlk,us=Fracus⋅˙ms,us,max

˙mlk,ds=Fracds⋅˙mtu $$

Here

˙ms,us is the constant zone supply air mass flow rate upstream of the leaks [kg/s];

˙mtu is the air mass flow rate through the terminal unit [kg/s];

˙mlk,us is the upstream leakage air mass flow rate [kg/s];

˙mlk,ds is the downstream leakage air mass flow rate [kg/s];

˙ms,us,max is the maximum upstream supply air mass flow rate (program input) [kg/s];

˙ms,z is the supply air mass flow rate delivered to the zone [kg/s];

Fracus is the design upstream leakage fraction (program input);

Fracds is the constant downstream leakage fraction (program input);

˙mtu is calculated in the VAV terminal unit model in the usual manner: the mass flow rate is varied to meet the zone load. The limits on the mass flow rate variation are set by the ˙mMaxAvail and ˙mMinAvail values stored at the terminal unit’s air inlet node. To account for upstream leakage the maximum air mass flow rate available is reset to:

˙m′MaxAvail=˙mMaxAvail−˙mlk,us

Downstream leakage must also be accounted for because not all of ˙mtu will reach the zone. This is done by having ˙mtu meet an adjusted zone load:

˙Qz,adjusted=11−Fracds˙Qz

Here ˙Qz [watts] is the actual zone load (met by ˙ms,z ) and ˙Qz,adjusted is the load used in the VAV terminal unit model to obtain ˙mtu .

Once ˙mtu is known, all the other flow rates can be calculated. ˙ms,us is assigned to the air distribution unit’s air inlet node and ˙ms,z is assigned to the unit’s air outlet node. Thus, air mass flow is not conserved through the unit: the two air leakage flow rates disappear. These two vanished flow rates are stored in the air distribution unit data structure. When the downstream return air plenum mass and energy balances are calculated, the leakage flow rate data is accessed and added back in as inlets to the return air plenum. Thus, the overall air system preserves a mass balance.

Wray, C.P. 2003. “Duct Thermal Performance Models for Large Commercial Buildings”, Lawrence Berkeley National Laboratory Report to the California Energy Commission. LBNL-53410.

Wray, C.P. and N.E. Matson. 2003. “Duct Leakage Impacts on VAV System Performance in California Large Commercial Buildings”, Lawrence Berkeley National Laboratory Report to the California Energy Commission. LBNL-53605.

Wray, C.P., R.C. Diamond, and M.H. Sherman. 2005. “Rationale for Measuring Duct Leakage Flows in Large Commercial Buildings”. Proceedings – 26th AIVC Conference, Brussels, Belgium, September. LBNL-58252.

## Fan Coil Unit[LINK]

The input object ZoneHVAC:FourPipeFanCoil provides a model for a 4 pipe fan coil zonal hydronic unit that can supply heating and cooling to a zone. It contains a hot water or electric heating coil, a chilled water coil, and a fan. It can supply a fixed amount of outdoor air, but cannot operate in an economizer mode. The fan runs at constant speed – control is achieved by throttling the hot or cold water flow. The fan coil configuration and control is rather limited. The fan position is always *blow-through*, control is always by varying the water flow, never by holding the water flow constant and cycling the fan.

The 4 pipe fan coil unit is modeled as a compound component consisting of 4 sub-components: an outdoor air mixer, a fan, a cooling coil, and a heating coil. In terms of EnergyPlus objects these are:

*OutdoorAir:Mixer*

*Fan:ConstantVolume*

*Coil:Cooling:Water, Coil:Cooling:Water:DetailedGeometry,* or

*CoilSystem:Cooling:Water:HeatExchangerAssisted*

*Coil:Heating:Water or Coil:Heating:Electric*

The unit is a forward model: its inputs are defined by the state of its inlets: namely its 2 air streams – recirculated and outdoor air. The outputs of the model are the conditions of the outlet air stream: flow rate, temperature and humidity ratio. The unit data and simulation are encapsulated in the module *FanCoilUnits.*

The user describes the 4 pipe fan coil unit by inputting the names of the outdoor air mixer, the fan, the heating coil, and the cooling coil. The heating and cooling coil types must also be specified.

The unit is connected to the overall HVAC system by specifying node names for the unit air inlet (for recirculated air) node, air outlet node, outdoor air node, relief node, inlet hot water node, and inlet chilled water node. The individual components comprising the fan coil must also be input and connected together properly. Specifically the outdoor air mixer mixed air node must be the same as the fan inlet node; the fan outlet node must be the same as the cooling coil air inlet node; the cooling coil air outlet node must be the same as the heating coil air inlet node; and the heating coil air outlet node must be the same as the unit air outlet node; the outdoor air mixer inlet nodes must match the unit inlet nodes; and the outdoor air mixer relief node must match the unit relief node.

The user needs to also specify (unless the unit is autosized) various maximum flow rates: the supply air flow rate, the outdoor air inlet flow rate, the maximum (and minimum) chilled water flow rate, and the maximum (and minimum) hot water flow rate. Heating and cooling convergence tolerances need to be specified or defaulted. And there is an on/off availability schedule for the unit.

All the input data for the fan coil unit is stored in the array *FanCoil*.

Given the needed inputs, the output is calculated in subroutine *Calc4PipeFanCoil*. The temperature, humidity ratio and flow rate of the recirculated and outdoor air streams are taken from the inlet air nodes The inlet hot and chilled water flow rates have been set by local controllers – temperatures are taken from the inlet water nodes. Then

1. The outdoor air mixer is simulated (Call *SimOAMixer*);

2. the fan is simulated (Call *SimulateFanComponents*);

3. the cooling coil is simulated (Call *SimulateWaterCoilComponents* or *SimHXAssistedCoolingCoil*);

4. the heating coil is simulated (Call *SimulateWaterCoilComponents or SimulateHeatingCoilComponents*).

The load met (sensible cooling or heating) is calculated and passed back to the calling routine:

˙Qsens,out=˙mtot(PsyHFnTdbW(Tout,Win)−PsyHFnTdbW(Tin,Win))

where *PsyHFnTdbW* is the EnergyPlus function for calculating the specific enthalpy of air given the drybulb temperature and the humidity ratio. The subscript *in* indicates the conditions at the inlet recirculated air node.

### Simulation and Control[LINK]

From the result of the zone simulation we have the current heating/cooling demand on the unit ˙Qz,req . The first step is to decide whether the unit is on for the current time step. If the load is less than 1 watt or the flow rate is less than .001 kg/s, the unit is off. If the availability schedule is off, the mass flow rate is set to zero, so the second condition holds. When the unit is off there will be no air flow through the unit and outlet conditions will be equal to inlet conditions.

˙Qz,req is not the demand on the heating or cooling coil. To obtain the actual coil load, we need to calculate the unit output with no heating or cooling by the coils (˙Qunit,nohc ). We obtain this by calling *Calc4PipeFanCoil* with the water flow rates set to zero. Then the coil loads are calculated:

˙Qhc=˙Qz,hsp−˙Qunit,nohc

˙Qcc=˙Qz,csp−˙Qunit,nohc

where ˙Qhc is the heating coil load, ˙Qz,hsp is the current zone load to the heating setpoint, ˙Qcc is the cooling coil load, and ˙Qz,csp is the current zone load to the cooling setpoint.

If the unit is on and ˙Qcc < 0 and the thermostat type is not “single heating setpoint”, *ControlCompOutput* is called with the control node set to the cold water inlet node. *ControlCompOutput* is a general component control routine. In this case calls *Calc4PipeFanCoil* repeatedly while varying the cold water flow rate and minimizing (˙Qsens,out−˙Qz,csp)/˙Qz,csp to within the cooling convergence tolerance. Similarly if the unit is on and ˙Qhc >0 and the thermostat type is not “single cooling setpoint”, *ControlCompOutput* is called with the control node set to the hot water inlet node (for hydronic heating coil only). *ControlCompOutput* varies the hot water flow rate or the electric heating coil part-load ratio is varied to minimize (˙Qsens,out−˙Qz,hsp)/˙Qz,hsp to within the heating tolerance. *ControlCompOutput* executes a slow but safe interval halving algorithm to do its minimization. Once control is achieved, the total cooling/heating output is calculated:

˙Qtot,out=˙m⋅(PsyHFnTdbW(Tout,Wout)−PsyHFnTdbW(Tin,Win)

#### Multi-Speed Fan In FanCoil[LINK]

When modeling multi-speed fan in FanCoil unit, capacity is modulated using speed ratio or part load ratio. The supply air fan speed is varied while operating the coils at maximum water flow. When there is no system load to meet, the water control valve is fully closed. When the FanCoil fan is cycling between two consecutive fan speed levels a speed ratio is calculated, but when the FanCoil unit cycles between the minimum fan speed and off-position, then part load ratio is calculated. The fan may be off or run continuously at lowest speed to provide ventilation air depending the fan operating schedule specified. When the FanCoil is operating at the lowest fan speed (Speed = 1), the water flow rate is reported as the average for the time step by multiplying the maximum water flow by part load ratio. The speed ratio and part-load ratio are calculated such that the FanCoil unit satisfies the required system zone cooling or heating load.The set of equations used for the multi-speed fan capacity control methods in FanCoil unit are summarized next.

##### Cycling Between Speeds

When the supply fan is cycling between consecutive speeds, then the speed ratio (SR) and the average mass flow rate are calculated as follows:

SRn=Abs(SystemLoad−FullLoadOutputn−1)/Abs(FullLoadOutputn−FullLoadOutputn−1)

˙m=˙mon,nSRn+˙mon,n−1(1−SRn)

˙mw=˙mw,max

##### Cycling OnOff at Lowest Speed

The average supply air flow rate calculation when the fan is running at the lowest fan speed level depends on the fan operating schedule and load. The fan coil unit part load ratio is given by:

PLR=Abs(SystemLoad−NoLoadOutput)/Abs(FullLoadOutput1−NoLoadOutput)

Continuous Fan

˙m=˙mon,1PLR+˙moff(1−PLR)

Cycling Fan:

˙m=˙mon,1PLR˙mw=˙mw,maxPLR

where:

SRn = speed ratio of the fan coil unit at speed n, (-)

PLR = part load ratio of the fan coil uni at speed 1, (-)

˙m = average mass flow rate of supply air, (kg/s

˙mon,n−1 = mass flow rate of supply air at fan speed level n-1, (kg/s)

˙mon,n = mass flow rate of supply air at fan speed level n, (kg/s)

˙moff = mass flow rate of supply air when the coils are off, (kg/s)

˙mw = average mass flow rate of chilled or hot water, (kg/s)

˙mw,max = maximum or full mass flow rate of chilled or hot water, (kg/s)

SystemLoad = system load to be met by the fan coil unit, (W)

FullLoadOutputn−1 = fully load fan coil unit output at fan speed level n-1, (W)

FullLoadOutputn = fully load fan coil unit output at fan speed level n, (W)

The ASHRAE90.1 control method uses a simple technique to adjust fan speed based on zone design sensible load. The specific section of the Standard is described as:

```
Section 6.4.3.10 (“Single Zone Variable-Air-Volume Controls”) of ASHRAE Standard 90.1-2010.
HVAC systems shall have variable airflow controls as follows:
(a) Air-handling and fan-coil units with chilled-water cooling coils and supply fans with motors
greater than or equal to 5 hp shall have their supply fans controlled by two-speed motors or
variable-speed drives. At cooling demands less than or equal to 50%, the supply fan controls
shall be able to reduce the airflow to no greater than the larger of the following:
• One-half of the full fan speed, or
• The volume of outdoor air required to meet the ventilation requirements of Standard 62.1.
(b) Effective January 1, 2012, all air-conditioning equipment and air-handling units with direct
expansion cooling and a cooling capacity at AHRI conditions greater than or equal to 110,000
Btu/h that serve single zones shall have their supply fans controlled by two-speed motors or
variable-speed drives. At cooling demands less than or equal to 50%, the supply fan controls
shall be able to reduce the airflow to no greater than the larger of the following:
• Two-thirds of the full fan speed, or
• The volume of outdoor air required to meet the ventilation requirements of Standard 62.1.
```

This control method assumes that a simulation sizing run is performed to determine the zone design sensible cooling and heating load ˙Qz,design .

For fan coil units, the limit used to determine if reduced zone loads are met with reduced fan speed is the fan coil’s Low Speed Supply Air Flow Ratio input.

˙Qreduced=˙Qz,design∗Ratiofan,lowspeed

If the zone load, ˙Qz,req , is less than Qreduced then the fan is maintained at the reduced speed while the water coils (or electric heating coil) are modulated to meet the zone load.

If the zone load is greater than the design zone sensible load, ˙Qz,design , the fan will operate at the maximum supply air flow rate and the water or electric heating coils will modulate to meet the zone load.

If the zone load is between these two extremes, the fan and coil will modulate to meet the zone load.

An example of the ASHRAE 90.1 control method is provided in the following figure. In this figure, the X-axis represents the zone cooling (-) or heating (+) load.

No specific references.

## Window Air Conditioner[LINK]

The input object ZoneHVAC:WindowAirConditioner provides a model for a window air conditioner unit that is a packaged unit that supplies cooling to a zone (it is part of zone equipment, not part of the air loop equipment). It contains a fan, a DX cooling coil, and an outdoor air inlet. The coil meets the cooling load by cycling on/off. The fan can operate continuously or cycle on/off in conjunction with the coil.

The window air conditioner is modeled as a compound component consisting of 3 sub-components: an outdoor air mixer, a fan, and a DX coil. In terms of EnergyPlus objects these are OutdoorAir:Mixer, Fan:ConstantVolume or Fan:OnOff, and Coil:Coolilng:DX:SingleSpeed or CoilSystem:Cooling:DX:HeatExchangerAssisted. The unit is a forward model: its inputs are defined by the state of its inlets: namely its 2 air streams – recirculated and outdoor air. The outputs of the model are the conditions of the outlet air stream: flow rate, temperature and humidity ratio. The model is also an averaged model: the performance of the unit is averaged over the time step. That is, the unit is assumed to cycle on/off during the time step and this on/off cycling is averaged over the simulation time step. The unit data and simulation are encapsulated in the module WindowAC.

The user describes the window air conditioner by inputting the names of the outdoor air mixer, the fan, and the cooling coil. The user can also choose fan placement – blow through or draw through; fan operation – cycling or continuous; and cooling coil type – normal DX or DX with heat exchanger assistance.

The connectivity of the unit needs to be specified: a recirculated (inlet) air node (same as a zone exhaust node); an air outlet node (same as a zone inlet node); an outdoor air inlet node; and a relief air node. The individual components comprising the window air conditioner must of course also be input and connected together properly. For instance, for a blow through fan configuration the outdoor air mixer mixed air node must be the same as the fan inlet node; the fan outlet node must be the same as the coil inlet node; the coil outlet node must be the same as the unit outlet node; the outdoor air mixer inlet nodes must match the unit inlet nodes; and the outdoor air mixer relief node must match the unit relief node.

The user also specifies the air conditioner flow rate delivered to the zone (when cycled on) and the outdoor air flow rate. The user also needs to specify an availability schedule for the unit (this is an on/off schedule).

Note that there is no input specifying the unit’s design cooling capacity. This is an input in the DX coil object and is not repeated here.

All the input data for the window air conditioner is stored in the array *WindAC*.

Given the needed inputs, the output is calculated in subroutine CalcCyclingWindowAC. The temperature, humidity ratio and flow rate of the recirculated and outdoor air streams are taken from the inlet air nodes. The part load ratio is specified by the calling routine. Then

· The outdoor air mixer is simulated (Call SimOAMixer);

· For blow-through fan position:

· the fan is simulated (Call SimulateFanComponents);

· the coil is simulated (Call SimDXCoil or SimHXAssistedCoolingCoil).

For draw-through fan position, the simulation order of the fan and coil is reversed. Note that data is never explicitly passed between the sub-components. This is all handled automatically by the node connections and the data stored on the nodes.

### Simulation and Control[LINK]

From the result of the zone simulation we have the heating/cooling demand on the unit ˙Qz,req . The first step is to decide whether the unit is on for the current time step. For a unit with a cycling fan, the entire unit is assumed to be off if there is no cooling load, the cooling load is very small (less than 1 watt), the unit is scheduled off, or the zone temperature is in the deadband. For a unit with a continuous flow the fan operates if the unit is scheduled on, whether or not there is a cooling demand. The coil however only operates if there is a cooling demand and the zone temperature is not in the deadband.

If the unit is determined to be on, the next step is to find the unit part load fraction that will satisfy the cooling load. This is done in *ControlCycWindACOutput*. In this routine *CalcCyclingWindowAC* is first called with part load fraction equal to 0, then with part load fraction equal to 1. These calls establish the minimum and maximum cooling output possible by the unit given the current conditions. An initial estimate of the part load fraction is then made:

PLF=(˙Qz,req−˙Qout,min)/|˙Qout,max−˙Qout,min|

Since the unit’s cooling output is a nonlinear function of the part load fraction, this *PLF* will not give exactly the desired ˙Qz,req . To obtain the exact *PLF* that will give ˙Qz,req , it is necessary to iteratively call *CalcCyclingWindowAC*, varying *PLF* until the desired cooling output is obtained, within the error tolerance specified by the user in the input.

Once *PLF* is determined, *ControlCycWindACOutput* is exited. One last call to *CalcCyclingWindowAC* is made to establish the final outlet conditions at the unit’s air outlet node. Finally, the inlet and outlet node conditions are used to calculate the reporting variables: sensible and total cooling output.

∙Qcooling,max=(∙mSA,fullload)(hout,fullload−hzoneair)HRmin

∙Qcooling,min=(∙mSA,coiloff)(hout,coiloff−hzoneair)HRmin

where *PsyHFnTdb* is the EnergyPlus function giving enthalpy as a function of temperature and humidity ratio.

No specific references.

## Packaged Terminal Air Conditioner[LINK]

The input object ZoneHVAC:PackagedTerminalAirConditioner provides a model for a packaged terminal air conditioner (PTAC) that is a compound object made up of other components. Each PTAC consists of an outdoor air mixer, direct expansion (DX) cooling coil, heating coil (gas, electric, hot water, or steam) and a supply air fan. While the figure below shows the PTAC with draw through fan placement, blow through fan placement can also be modeled by positioning the supply air fan between the outdoor air mixer and DX cooling coil. The packaged terminal air conditioner coordinates the operation of these components and is modeled as a type of zone equipment (Ref. ZoneHVAC:EquipmentList and ZoneHVAC:EquipmentConnections).

The PTAC conditions a single zone and is controlled by a thermostat located in that zone. The PTAC operates to meet the zone sensible cooling or sensible heating requirements as dictated by the thermostat schedule. The model calculates the required part-load ratio for the air conditioner’s coils and the supply air fan to meet the cooling/heating requirements. The heating or cooling energy provided by the PTAC is delivered to the zone via the zone air inlet node.

The PTAC 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). Supply air fan operation is coordinated with the use of a supply air fan operating mode schedule. Schedule values of 0 denote cycling fan operation (AUTO fan). Schedule values other than 0 denote continuous fan operation (fan ON). Fan:OnOff must be used to model AUTO fan (i.e. if schedule values of 0 occur in the supply air fan operating mode schedule), while Fan:OnOff or Fan:ConstantVolume can be used to model fan ON (i.e. if schedule values of 0 do not occur in the supply air fan operating mode schedule). The supply air fan operating mode schedule specified for the PTAC overrides the operating mode specified in the DX cooling coil object.

Output variables reported by the PTAC object include the supply air fan part-load ratio, the air conditioner’s part-load ratio (cooling or heating), and the electric consumption of the PTAC. Additional output variables report the total zone heating rate and the total zone cooling rate provided by the air conditioner. The sensible and latent components of zone cooling are also available as output variables. Reporting of other variables of interest for the PTAC (DX coil cooling rate, coil heating rate, crankcase heater power, fan power, etc.) is done by the individual system components (fan, DX cooling coil and heating coil).

### Model Description[LINK]

As described previously, the PTAC conditions a single zone and is controlled by a zone thermostat (ZoneControl:Thermostatic). Each simulation time step, EnergyPlus performs a zone air heat balance to determine if cooling or heating is required to meet the thermostat setpoints, excluding any impacts from PTAC operation. PTAC performance is then modeled with all heating/cooling coils off but the supply air fan operates as specified by the user. If the zone air heat balance plus the impact of PTAC operation with coils off results in no requirement for heating or cooling by the PTAC coils, or if the PTAC is scheduled off (via its availability schedule), then the PTAC coils do not operate and the air conditioner’s part-load ratio output variable is set to 0. If the model determines that cooling or heating is required and the PTAC is scheduled to operate, the model calculates the average air flow rate through the unit and the part-load ratio of the cooling and heating coils in order to meet the thermostat setpoint temperature.

The remainder of this section describes the calculations performed during the latter situation, when cooling or heating coil operation is required. For any HVAC simulation time step, the PTAC can only be cooling or heating, not both. Because the PTAC cycles its coil(s) on and off to meet the required load, the coil(s) operate for a portion of the time step and are off for the rest of the time step. If the user specifies continuous fan operation (i.e. supply air fan operating mode schedule value is greater than 0), then the supply air fan continues to operate at a user-specified flow rate even during periods when the coils cycle off. If the user specifies AUTO fan operation (i.e. supply air fan operating mode schedule value is equal to 0), then the supply air fan cycles on and off with the coils. The model accounts for these variations in air flow through the PTAC within a simulation time step when it determines the total cooling or heating energy delivered to the zone, the average supply air conditions and air flow rate, and the energy consumed by the air conditioner.

### Cooling Operation[LINK]

If EnergyPlus determines that the air conditioner must supply cooling to the zone in order to meet the zone air temperature setpoint, then the model first calculates the PTAC’s sensible cooling rate to the zone under two conditions: when the unit runs at full-load (steady-state) conditions and when the DX cooling coil is OFF. If the supply air fan cycles on/off with the compressor, then the sensible cooling 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 rate will not be zero when the cooling coil is OFF. Calculating the sensible cooling rate involves modeling the supply air fan (and associated fan heat), the outdoor air mixer, and the DX cooling coil. The heating coil is also modeled, but only to pass the air properties and mass flow rate from it’s inlet node to it’s outlet node. For each of these cases (full load and DX cooling coil OFF), the sensible cooling rate delivered to the zone by the PTAC is calculated as follows:

˙Qcooling,max=(˙mSA,fullload)(hout,fullload−hzoneair)HRmin

˙Qcooling,min=(˙mSA,coiloff)(hout,coiloff−hzoneair)HRmin

where:

˙Qcooling,max = maximum PTAC sensible cooling rate with cooling coil ON, W

˙mSA,fullload = supply air mass flow rate at full-load (steady-state) conditions, kg/s

*hout,fullload* = enthalpy of air exiting the PTAC at full-load conditions, J/kg

*hzoneair* = enthalpy of zone (exhaust) air, J/kg

*HRmin* = enthalpies evaluated at a constant humidity ratio, the minimum humidity ratio of the PTAC exiting air or the zone (exhaust) air

˙Qcooling,min = minimum PTAC sensible cooling rate with cooling coil OFF, W

˙mSA,coiloff = supply air mass flow rate with the cooling coil OFF, kg/s

*hout,coiloff* = enthalpy of air exiting the PTAC with the cooling coil OFF, J/kg

With the calculated PTAC sensible cooling rates and the zone sensible cooling load to be met, the compressor part-load ratio for the PTAC is approximately equal to:

PartLoadRatio=MAX⎛⎜
⎜⎝0.0,ABS(˙Qzone,cooling−˙Qcooling,min)ABS(˙Qcooling,max−˙Qcooling,min)⎞⎟
⎟⎠

where:

PartLoadRatio = compressor part-load ratio required to meet the zone load

˙Qzone,cooling = required zone sensible cooling rate to meet setpoint, W

Since the part-load performance of the DX cooling coil is frequently non-linear (Ref: DX Cooling Coil Model), and the supply air fan heat varies based on cooling coil operation for the case of cycling fan/cycling coil (AUTO fan), the actual part-load ratio for the cooling coil compressor and fan are determined through iterative calculations (successive modeling of the individual PTAC component models) until the PTAC’s cooling output (including on/off cycling effects) matches the zone cooling load requirement.

If the PTAC has been specified with cycling fan/cycling coil (AUTO fan), then the user-defined supply air flow rate during cooling operation (volumetric flow rate converted to mass flow rate) is multiplied by the final PartLoadRatio value to determine the average supply air mass flow rate for the HVAC system simulation time step. For this case, the air conditions (temperature, humidity ratio and enthalpy) at nodes downstream of the cooling coil represent the full-load (steady-state) values when the coil is operating. If the supply air fan is specified to run continuously (fan ON), then the supply air mass flow rate is calculated as the average of the air mass flow rate when the compressor is on and the air mass flow rate when the compressor is off. 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 mixed inlet air conditions when the coil is OFF). Additional discussion regarding the calculation of the average supply air flow and supply air conditions is provided later in this section.

### Heating Operation[LINK]

Calculations of the PTAC’s sensible heating rate delivered to the zone at full load and with the heating coil OFF are identical to the calculations described above for cooling operation.

˙Qheating,max=(˙mSA,fullload)(hout,fullload−hzoneair)HRmin

˙Qheating,min=(˙mSA,coiloff)(hout,coiloff−hzoneair)HRmin

where:

˙Qheating,max = maximum PTAC sensible heating rate with heating coil ON, W

˙Qheating,min = minimum PTAC sensible heating rate with heating coil OFF, W

With the calculated PTAC sensible heating rates and the zone sensible heating load to be met, the heating coil part-load ratio for the PTAC is approximately equal to:

PartLoadRatio=MAX⎛⎜
⎜⎝0.0,ABS(˙Qzone,heating−˙Qheating,min)ABS(˙Qheating,max−˙Qheating,min)⎞⎟
⎟⎠

where:

PartLoadRatio = heating coil part-load ratio required to meet the zone load

˙Qzone,heating = required zone sensible heating rate to meet setpoint, W

Iterative calculations (successive modeling of the individual PTAC component models) are used to determine the final heating part-load ratio to account for the non-linear performance of the heating coil at part-load conditions and the variation in supply air fan heat for the case of cycling fan/cycling coil (AUTO fan). If heating coil operation at full load is unable to meet the entire zone heating load (e.g., the heating coil capacity is insufficient or the coil is scheduled OFF), the air conditioner’s part-load ratio is set to 1 to meet the zone heating load to the extent possible.

### Average Air Flow Calculations[LINK]

The packaged terminal air conditioner operates based on user-specified (or autosized) air flow rates. The PTAC’s supply air flow rate during cooling operation may be different than the supply air flow rate during heating operation. In addition, the supply air flow rate when no cooling or heating is required but the supply air fan remains ON can be different than the air flow rates when cooling or heating is required. The outdoor air flow rates can likewise be different in these various operating modes. The model takes these different flow rates into account when modeling the air conditioner, and the average air flow rate for each simulation time step is reported on the inlet/outlet air nodes of the various PTAC components in proportion to the calculated part-load ratio of the coil.

The average supply air and outdoor air mass flow rates through the air conditioner for the HVAC simulation time step are calculated based on the part-load ratio of the DX cooling coil or heating coil (whichever coil is operating) as follows:

˙mSA,avg=˙mSA,coilon(PartLoadRatio)+˙mSA,coiloff(1−PartLoadRatio)

˙mOA,avg=˙mOA,coilon(PartLoadRatio)+˙mOA,coiloff(1−PartLoadRatio)

where:

˙mSA,avg = average supply air mass flow rate during the time step, kg/s

˙mSA,coilon = supply air mass flow rate when the coil is ON, kg/s

*PartLoadRatio* = part-load ratio of the coil (heating or cooling)

˙mSA,coiloff = supply air mass flow rate when the coil is OFF, kg/s

˙mOA,avg = average outdoor air mass flow rate during the time step, kg/s

˙mOA,coilon = average outdoor air mass flow rate when the coil is ON, kg/s

˙mOA,coiloff = average outdoor air mass flow rate when the coil is OFF, kg/s

The supply air and outdoor air flow rates when the DX cooling coil or the heating coil is ON are specified by the user (i.e., supply air volumetric flow rate during cooling operation, supply air volumetric flow rate during heating operation, outdoor air volumetric air flow rate during cooling operation, and outdoor air volumetric air flow rate during heating operation) and are converted from volumetric to mass flow rate. If the user has specified cycling fan operation (i.e. supply air fan operating mode schedule value is equal to 0), then the supply air and outdoor air mass flow rates when the coil is OFF are zero. If the user has specified constant fan operation (i.e. supply air fan operating mode schedule value is greater than 0), then the user-defined air flow rates when no cooling or heating is needed are used when the coil is OFF.

There is one special case. If the supply air fan operating mode schedule value specifies constant fan operation and the user also specifies that the supply air volumetric flow rate when no cooling or heating is needed is zero (or field is left blank), then the model assumes that the supply air and outdoor air mass flow rates when the coil is OFF are equal to the corresponding air mass flow rates when the cooling or heating coil was last operating (ON).

### Calculation of Outlet Air Conditions[LINK]

When the supply air fan cycles on and off with the PTAC coils (AUTO fan), the calculated outlet air conditions (temperature, humidity ratio, and enthalpy) from the heating coil or the DX cooling coil at full-load (steady-state) operation are reported on the appropriate coil outlet air node. The air mass flow rate reported on the air nodes is the average air mass flow rate proportional to the part-load ratio of the coil (see Average Air Flow Calculations above).

When the supply air fan operates continuously while the PTAC coils cycle on and off (fan ON), the air mass flow rate reported on the air nodes is the average air mass flow rate proportional to the part-load ratio of the coil (see Average Air Flow Calculations above). Since the air flow rate can be different when the coil is ON compared to when the coil is OFF, then the average outlet air conditions from the heating coil or the DX cooling coil are reported on the appropriate coil outlet air node.

For hot water or steam coils, the water or steam mass flow rate is also proportional to the part-load ratio of the coil regardless of the supply air fan operating mode. Refer to the sections in the document that describe the heating and DX cooling coils for further explanation on how they report their outlet air (and water or steam) conditions.

### Calculation of Zone Heating and Cooling Rates[LINK]

At the end of each HVAC simulation time step, this compound object reports the heating or cooling rate and energy delivered to the zone, as well as the electric power and consumption by the air conditioner. In terms of thermal energy delivered to the zone, the sensible, latent and total energy transfer rate to the zone is calculated as follows:

˙QTotal=(˙mSA,avg)(hout,avg−hzoneair)

˙QSensible=(˙mSA,avg)(hout,avg−hzoneair)HRmin

˙QLatent=˙QTotal−˙QSensible

where:

˙QTotal = total energy transfer rate to the zone, W

˙QSensible = sensible energy transfer rate to the zone, W

˙QLatent = latent energy transfer rate to the zone, W

˙mSA,avg = average mass flow rate of the supply air stream, kg/s

*hout,avg* = enthalpy of the air being supplied to the zone, J/kg

Since each of these energy transfer rates can be calculated as positive or negative values, individual reporting variables are established for cooling and heating and only positive values are reported. The following calculations are representative of what is done for each of the energy transfer rates:

IF (˙QTotal<0.0) THEN

˙QTotalCooling=ABS(˙QTotal)

˙QTotalHeating=0.0

ELSE

˙QTotalCooling=0.0

˙QTotalHeating=˙QTotal

where:

˙QTotalCooling = output variable ‘Packaged Terminal Air Conditioner Total Zone Cooling Rate, W’

˙QTotalHeating = output variable ‘Packaged Terminal Air Conditioner Total Zone Heating Rate, W’

In addition to heating and cooling rates, the heating and cooling energy supplied to the zone is also calculated for the time step being reported. The following example for total zone cooling energy is representative of what is done for the sensible and latent energy as well as the heating counterparts.

QTotalCooling=˙QTotalCooling⋅TimeStepSys⋅3600

where:

QTotalCooling = output variable ‘Packaged Terminal Air Conditioner Total Zone Cooling Energy, J’

*TimeStepSys* = HVAC system simulation time step, hr

## Packaged Terminal Heat Pump[LINK]

The input object ZoneHVAC:PackagedTerminalHeatPump provides a model for a packaged terminal heat pump (PTHP) that is a compound object made up of other components. Each PTHP consists of an outdoor air mixer, direct expansion (DX) cooling coil, DX heating coil, supply air fan, and a supplemental heating coil. While the figure below shows the PTHP with draw through fan placement, blow through fan placement can also be modeled by moving the supply air fan before the DX cooling coil. The packaged terminal heat pump coordinates the operation of these components and is modeled as a type of zone equipment (Ref. ZoneHVAC:EquipmentList and ZoneHVAC:EquipmentConnections).

The PTHP conditions a single zone and is controlled by a thermostat located in that zone. The PTHP operates to meet the zone sensible cooling or sensible heating requirements as dictated by the thermostat schedule. The model calculates the required part-load ratio for the heat pump’s coils and the supply air fan to meet the cooling/heating requirements. The heating or cooling energy provided by the PTHP is delivered to the zone via the zone air inlet node.

The PTHP 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.

Output variables reported by the PTHP object include the supply air fan part-load ratio, the compressor part-load ratio, and the electric consumption of the PTHP. Additional output variables report the total zone heating rate and the total zone cooling rate provided by the heat pump. The sensible and latent components of zone cooling are also available as output variables. Reporting of other variables of interest for the PTHP (DX coil cooling rate, DX coil heating rate, crankcase heater power, fan power, etc.) is done by the individual system components (fan, DX cooling coil, DX heating coil, and supplemental heating coil).

### Model Description[LINK]

As described previously, the PTHP conditions a single zone and is controlled by a zone thermostat (ZoneControl:Thermostat). Each simulation time step, EnergyPlus performs a zone air heat balance to determine if cooling or heating is required to meet the thermostat setpoints, excluding any impacts from PTHP operation. PTHP performance is then modeled with all heating/cooling coils off but the supply air fan operates as specified by the user. If the zone air heat balance plus the impact of PTHP operation with coils off results in no requirement for heating or cooling by the PTHP coils, or if the PTHP is scheduled off (via its availability schedule), then the PTHP coils do not operate and the compressor part-load ratio output variable is set to 0. If the model determines that cooling or heating is required and the PTHP is scheduled to operate, the model calculates the average air flow rate through the unit and the part-load ratio of the cooling and heating coils in order to meet the thermostat setpoint temperature.

The remainder of this section describes the calculations performed during the latter situation, when cooling or heating coil operation is required. For any HVAC simulation time step, the PTHP can only be cooling or heating, not both. Because the PTHP cycles its coil(s) on and off to meet the required load, the coil(s) operate for a portion of the time step and are off for the rest of the time step. If the user specifies continuous fan operation (supply air fan operating mode schedule value > 0), then the supply air fan continues to operate at a user-specified flow rate even during periods when the coils cycle off. If the user specifies AUTO fan operation (supply air fan operating mode schedule value = 0), then the supply air fan cycles on and off with the coils. The model accounts for these variations in air flow through the PTHP within a simulation time step when it determines the total cooling or heating energy delivered to the zone, the average supply air conditions and air flow rate, and the energy consumed by the heat pump.

### Cooling Operation[LINK]

If EnergyPlus determines that the heat pump must supply cooling to the zone in order to meet the zone air temperature setpoint, then the model first calculates the PTHP’s sensible cooling rate to the zone under two conditions: when the unit runs at full-load (steady-state) conditions and when the DX cooling coil is OFF. If the supply air fan cycles on/off with the compressor, then the sensible cooling 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 rate will not be zero when the cooling coil is OFF. Calculating the sensible cooling rate involves modeling the supply air fan (and associated fan heat), the outdoor air mixer, and the DX cooling coil. The DX heating coil and the gas or electric 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 and DX cooling coil OFF), the sensible cooling rate delivered to the zone by the PTHP is calculated as follows:

˙Qcooling,max=(˙mSA,fullload)(hout,fullload−hzoneair)HRmin

˙Qcooling,min=(˙mSA,coiloff)(hout,coiloff−hzoneair)HRmin

where:

˙Qcooling,max = maximum PTHP sensible cooling rate with cooling coil ON, W

˙QSA,fullload = supply air mass flow rate at full-load (steady-state) conditions, kg/s

*hout,fullload* = enthalpy of air exiting the PTHP at full-load conditions, J/kg

*hzoneair* = enthalpy of zone (exhaust) air, J/kg

*HRmin =* enthalpies evaluated at a constant humidity ratio, the minimum humidity ratio of the PTHP exiting air or the zone (exhaust) air

˙Qcooling,min = minimum PTHP sensible cooling rate with cooling coil OFF, W

˙QSA,coiloff = supply air mass flow rate with the cooling coil OFF, kg/s

*hout,coiloff* = enthalpy of air exiting the PTHP with the cooling coil OFF, J/kg

With the calculated PTHP sensible cooling rates and the zone sensible cooling load to be met, the compressor part-load ratio for the PTHP is approximately equal to:

PartLoadRatio=MAX⎛⎜
⎜⎝0.0,ABS(˙Qzone,cooling−˙Qcooling,min)ABS(˙Qcooling,max−˙Qcooling,min)⎞⎟
⎟⎠

where:

PartLoadRatio = compressor part-load ratio required to meet the zone load

˙Qzone,cooling = required zone sensible cooling rate to meet setpoint, W

Since the part-load performance of the DX cooling coil is frequently non-linear (Ref: DX Cooling Coil Model), and the supply air fan heat varies based on cooling coil operation for the case of cycling fan/cycling coil (AUTO fan), the actual part-load ratio for the cooling coil compressor and fan are determined through iterative calculations (successive modeling of the individual PTHP component models) until the PTHP’s cooling output (including on/off cycling effects) matches the zone cooling load requirement within the cooling convergence tolerance that is specified.

If the PTHP is specified to operate with cycling fan/cycling coil (AUTO fan), then the user-defined supply air flow rate during cooling operation (volumetric flow rate converted to mass flow rate) is multiplied by the final PartLoadRatio value to determine the average supply air mass flow rate for the HVAC system simulation time step. For this case, the air conditions (temperature, humidity ratio and enthalpy) at nodes downstream of the cooling coil represent the full-load (steady-state) values when the coil is operating. If the supply air fan is specified to operate continuously (fan ON), then the supply air mass flow rate is calculated as the average of the air mass flow rate when the compressor is on and the air mass flow rate when the compressor is off. 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 mixed inlet air conditions when the coil is OFF). Additional discussion regarding the calculation of the average supply air flow and supply air conditions is provided later in this section.

### Heating Operation[LINK]

Calculations of the PTHP’s sensible heating rate delivered to the zone at full load and with the DX heating coil OFF are identical to the calculations described above for cooling operation.

˙Qheating,max=(˙mSA,fullload)(hout,fullload−hzoneair)HRmin

˙Qheating,min=(˙mSA,coiloff)(hout,coiloff−hzoneair)HRmin

where:

˙Qheating,max = maximum PTHP sensible heating rate with DX heating coil ON, W

˙Qheating,min = minimum PTHP sensible heating rate with DX heating coil OFF, W

With the calculated PTHP sensible heating rates and the zone sensible heating load to be met, the compressor part-load ratio for the PTHP is approximately equal to:

PartLoadRatio=MAX⎛⎜
⎜⎝0.0,ABS(˙Qzone,heating−˙Qheating,min)ABS(˙Qheating,max−˙Qheating,min)⎞⎟
⎟⎠

where:

PartLoadRatio = compressor part-load ratio required to meet the zone load

˙Qzone,heating = required zone sensible heating rate to meet setpoint, W

Iterative calculations (successive modeling of the individual PTHP component models) are used to determine the final heating part-load ratio to account for the non-linear performance of the DX heating coil at part-load conditions and the variation in supply air fan heat for the case of cycling fan/cycling coil (AUTO fan). If DX heating coil operating at full load is unable to meet the entire zone heating load (e.g., the DX heating coil capacity is insufficient or the coil is scheduled OFF, or the outdoor temperature is below the PTHP’s minimum outdoor dry-bulb temperature for compressor operation), the supplemental heating coil is activated to meet the remaining zone heating load to the extent possible.

### Average Air Flow Calculations[LINK]

The packaged terminal heat pump operates based on user-specified (or autosized) air flow rates. The PTHP’s supply air flow rate during cooling operation may be different than the supply air flow rate during heating operation. In addition, the supply air flow rate when no cooling or heating is required but the supply air fan remains ON can be different than the air flow rates when cooling or heating is required. The outdoor air flow rates can likewise be different in these various operating modes. The model takes these different flow rates into account when modeling the heat pump, and the average air flow rate for each simulation time step is reported on the inlet/outlet air nodes of the various PTHP components in proportion to the calculated part-load ratio of the DX coil compressor.

The average supply air and outdoor air mass flow rates through the heat pump for the HVAC simulation time step are calculated based on the part-load ratio of the DX cooling coil or DX heating coil (whichever coil is operating) as follows:

˙mSA,avg=˙mSA,compon(PartLoadRatio)+˙mSA,compoff(1−PartLoadRatio)

˙mOA,avg=˙mOA,compon(PartLoadRatio)+˙mOA,compoff(1−PartLoadRatio)

where:

˙mSA,avg = average supply air mass flow rate during the time step, kg/s

˙mSA,compon = supply air mass flow rate when the DX coil compressor is ON, kg/s

*PartLoadRatio* = part-load ratio of the DX coil compressor (heating or cooling)

˙mSA,compoff = supply air mass flow rate when the DX coil compressor is OFF, kg/s

˙mOA,avg = average outdoor air mass flow rate during the time step, kg/s

˙mOA,compon = average outdoor air mass flow rate when the DX coil compressor is ON, kg/s

˙mOA,compoff = average outdoor air mass flow rate when the DX coil compressor is OFF, kg/s

The supply air and outdoor air flow rates when the DX cooling or DX heating coil compressor is ON are specified by the user (e.g., supply air volumetric flow rate during cooling operation, supply air volumetric flow rate during heating operation, outdoor air volumetric air flow rate during cooling operation, and outdoor air volumetric air flow rate during heating operation) and are converted from volumetric to mass flow rate. If the user has specified cycling fan operation (supply air fan operating mode schedule value = 0), then the supply air and outdoor air mass flow rates when the DX compressor is OFF are zero. If the user has specified constant fan operation (supply air fan operating mode schedule value > 0), then the user-defined air flow rates when no cooling or heating is needed are used when the DX compressor is OFF.

There is one special case. If the user has specified constant fan operation (supply air fan operating mode schedule value > 0) and they specify that the supply air volumetric flow rate when no cooling or heating is needed is zero (or field is left blank), then the model assumes that the supply air and outdoor air mass flow rates when the DX coil compressor is OFF are equal to the corresponding air mass flow rates when the compressor was last operating (ON).

### Calculation of Outlet Air Conditions[LINK]

When the supply air fan cycles on and off with the PTHP coils (AUTO fan), the calculated outlet air conditions (temperature, humidity ratio, and enthalpy) from the DX heating or DX cooling coil at full-load (steady-state) operation are reported on the appropriate coil outlet air node. The air mass flow rate reported on the air nodes is the average air mass flow rate proportional to the part-load ratio of the DX coil compressor (see Average Air Flow Calculations above).

When the supply air fan operates continuously while the PTHP coils cycle on and off (fan ON), the air mass flow rate reported on the air nodes is the average air mass flow rate proportional to the part-load ratio of the DX coil compressor (see Average Air Flow Calculations above). Since the air flow rate can be different when the coil is ON compared to when the coil is OFF, then the average outlet air conditions from the DX heating or DX cooling coil are reported on the appropriate coil outlet air node.

Refer to the sections in the document that describe the DX heating and DX cooling coils for further explanation on how they report their outlet air conditions.

### Calculation of Zone Heating and Cooling Rates[LINK]

At the end of each HVAC simulation time step, this compound object reports the heating or cooling rate and energy delivered to the zone, as well as the electric power and consumption by the heat pump. In terms of thermal energy delivered to the zone, the sensible, latent and total energy transfer rate to the zone is calculated as follows:

˙QTotal=(˙mSA,avg)(hout,avg−hzoneair)

˙QSensible=(˙mSA,avg)(hout,avg−hzoneair)HRmin

˙QLatent=˙QTotal−˙QSensible

where:

˙QTotal = total energy transfer rate to the zone, W

˙QSensible = sensible energy transfer rate to the zone, W

˙QLatent = latent energy transfer rate to the zone, W

˙mSA,avg = average mass flow rate of the supply air stream, kg/s

*hout,avg* = enthalpy of the air being supplied to the zone, J/kg

Since each of these energy transfer rates can be calculated as positive or negative values, individual reporting variables are established for cooling and heating and only positive values are reported. The following calculations are representative of what is done for each of the energy transfer rates:

IF (˙QTotal *< 0.0 )*THEN

˙QTotalCooling = ABS (˙QTotal )

˙QTotalHeating = *0.0*

ELSE

˙QTotalCooling = *0.0*

˙QTotalHeating = ˙QTotal

where:

˙QTotalCooling = output variable ‘Packaged Terminal Heat Pump Total Zone Cooling Rate, W’

˙QTotalHeating = output variable ‘Packaged Terminal Heat Pump Total Zone Heating Rate, W’

In addition to heating and cooling rates, the heating and cooling energy supplied to the zone is also calculated for the time step being reported. The following example for total zone cooling energy is representative of what is done for the sensible and latent energy as well as the heating counterparts.

QTotalCooling=˙QTotalCooling∗TimeStepSys∗3600.

where:

QTotalCooling = output variable ‘Packaged Terminal Heat Pump Total Zone Cooling Energy, J’

*TimeStepSys* = HVAC system simulation time step, hr

## Zone Single Speed Water-To-Air Heat Pump[LINK]

The input object ZoneHVAC:WaterToAirHeatPump provides a zone equipment model for a water-to-air heat pump that is a “virtual” component consisting of an on/off fan component, a water-to-air heat pump cooling coil, a water-to-air heat pump heating coil, and a gas or electric supplemental heating coil. The specific configuration of the blowthru heat pump is shown in the following figure. For a drawthru heat pump, the fan is located between the water-to-air heat pump heating coil and the supplemental heating coil. In addition, a water-to-air heat pump has a water loop connection on its source side. The water loop can be served by a condenser loop (like GHE for Ground source systems), or by a cooling tower/ boiler plant loop (for water loop systems).

There are two models for zone water-to-air heat pump cooling and heating coils, i.e. Single-Speed and Variable-Speed Equation Fit models. Cooling and heating coils are modeled using the Equation Fit model described here.

### Single Speed Equation-Fit Model:[LINK]

This section describes the equation-fit model for Water-to-Air heat pump (Object names: Coil:Cooling:WaterToAirHeatPump:EquationFit and Coil:Heating:WaterToAirHeatPump:EquationFit). This documentation is derived from the M.S. dissertation of Tang (2005) which is available on the Oklahoma State University web site . The model uses five non-dimensional equations or curves to predict the heat pump performance in cooling and heating mode. The methodology involves using the generalized least square method to generate a set of performance coefficients from the catalog data at indicated reference conditions. Then the respective coefficients and indicated reference conditions are used in the model to simulate the heat pump performance. The variables or inlet conditions that influenced the water-to-air heat pump performance are load side inlet water temperature, source side inlet temperature, source side water flow rate and load side water flow rate. The governing equations for the cooling and heating mode are as following:

Cooling Mode:

PowercPowerc,ref=C1+C2[TwbTref]+C3[Tw,inTref]+C4[˙Vair˙Vair,ref]+C5[˙Vw˙Vw,ref]

QhQh,ref=E1+E2[TdbTref]+E3[Tw,inTref]+E4[˙Vair˙Vair,ref]+E5[˙Vw˙Vw,ref]

PowerhPowerh,ref=F1+F2[TdbTref]+F3[Tw,inTref]+F4[˙Vair˙Vair,ref]+F5[˙Vw˙Vw,ref]

Heating Mode:

˙mwater,ss=ρwater(˙Vwater,rated)(WaterRemovalModFac)(24hr/dy)(3600sec/hr)(1000L/m3)

Pdehumid,ss=˙Vwater,rated(WaterRemovalModFac)(1000W/kW)EFrated(EFModFac)(24hr/day)Pdehumid,avg=Pdehumid,ss(RTF)+(Poff−cycle∗(1−RTF))

Assuming no losses, the source side heat transfer rate for cooling and heating mode is calculated as following;

Qsource,c=Qtotal+Powerc

Qsource,h=Qh−Powerh

where:

A1−F5 = Equation fit coefficients for the cooling and heating mode

Tref = 283K

Tw,in = Entering water temperature, K

Tdb = Entering air dry-bulb temperature, K

Twb = Entering air wet-bulb temperature, K

˙Vair = Load side air volumetric flow rate, m3/s

˙Vw = Source side water volumetric flow rate, m3/s

Qtotal = Total cooling capacity, W

Qsens = Sensible cooling capacity, W

Powerc = Power consumption (cooling mode), W

Qsource,c = Source side heat transfer rate (cooling mode), W

Qh = Total heating capacity, W

Powerh = Power consumption (heating mode), W

Qsource,h = Source side heat transfer rate (heating mode), W

The inlet conditions or variables are divided by the reference conditions. This formulation allows the coefficients to fall into smaller range of values. Moreover, the value of the coefficient indirectly represents the sensitivity of the output to that particular inlet variable. The reference conditions used when generating the performance coefficients must be the same as the reference conditions used later in the model. The reference temperature Tref is fixed at 283K. Temperature unit of Kelvin is used instead of Celsius to keep the ratio of the water inlet temperature and reference temperature positive should the water inlet temperature drop below the freezing point.

For cooling mode, the reference conditions; reference load side air volumetric flow rate (˙Vair,ref) ,reference source side water volumetric flow rate(˙Vw,ref) ,reference sensible capacity (Qsens,ref) and reference power input (Powerc,ref) are the conditions when the heat pump is operating at the highest cooling capacity or reference cooling capacity(Qtotal,ref) indicated in the manufacturer’s catalog. Note that the reference conditions for heating mode might differ from the reference conditions specified for the cooling mode.

### Coefficient estimation procedure:[LINK]

The generalized least square method is used to generate the coefficients. This method utilizes an optimization method which calculates the coefficients that will give the least amount of differences between the model outputs and the catalog data. A set of coefficients for the cooling mode is generated which includes A1-A5 for total cooling capacity, B1-B6 for sensible cooling capacity, and C1-C5 for power consumption. The same procedure is repeated for the heating mode to generate the coefficients E1-E5 (total heating capacity) and F1-F5 (power consumption). An information flow chart showing the inputs, reference conditions, performance coefficients and outputs are shown in the figure below:

## Zone Air DX Dehumidifier[LINK]

This model, object name ZoneHVAC:Dehumidifier:DX, simulates the thermal performance and electric power consumption of conventional mechanical dehumidifiers. These systems use a direct expansion (DX) cooling coil to cool and dehumidify an airstream. Heat from the DX system’s condenser section is rejected into the cooled/dehumidified airstream, resulting in warm dry air being supplied from the unit. In EnergyPlus, this object is modeled as a type of zone equipment (ref. ZoneHVAC:EquipmentList and ZoneHVAC:EquipmentConnections).

The model assumes that this equipment dehumidifies and heats the air. If used in tandem with another system that cools and dehumidifies the zone air, then the zone dehumidifier should be specified as the lowest cooling priority in the ZoneHVAC:EquipmentList object for best control of zone temperature and humidity levels. With this zone equipment prioritization, the other cooling and dehumidification system would operate first to meet the temperature setpoint (and possibly meet the high humidity setpoint as well). If additional dehumidification is needed, then the zone dehumidifier would operate. The sensible heat generated by the dehumidifier is carried over to the zone air heat balance for the next HVAC time step.

### Model Description[LINK]

The user must input water removal, energy factor and air flow rate at rated conditions (26.7°C, 60% RH). Three performance curves must also be specified to characterize the change in water removal and energy consumption at part-load conditions:

1) Water removal curve (function of inlet air temperature and relative humidity)

2) Energy factor curve (function of inlet air temperature and relative humidity)

3) Part load fraction correlation (function of part load ratio)

· The water removal modifier curve is a biquadratic curve with two independent variables: dry-bulb temperature and relative humidity of the air entering the dehumidifier. The output of this curve is multiplied by the Rated Water Removal to give the water removal rate at the specific entering air conditions at which the dehumidifier is operating (i.e., at temperature/relative humidity different from the rating point conditions). If the output of this curve is negative, then a warning message is issued and it is reset to 0.0.

WaterRemovalModFac=a+b(Tin)+c(Tin)2+d(RHin)+e(RHin)2+f(Tin)(RHin)

where

*Tin* = dry-bulb temperature of the air entering the dehumidifier, °C

*RHin* = relative of the air entering the dehumidifier, % (0-100)

· The energy factor modifier curve is a biquadratic curve with two independent variables: dry-bulb temperature and relative humidity of the air entering the dehumidifier. The output of this curve is multiplied by the Rated Energy Factor to give the energy factor at the specific entering air conditions at which the dehumidifier is operating (i.e., at temperature/relative humidity different from the rating point conditions). If the output of this curve is negative, then a warning message is issued and it is reset to 0.0.

EFModFac=a+b(Tin)+c(Tin)2+d(RHin)+e(RHin)2+f(Tin)(RHin)

· The part load fraction (PLF) correlation curve is a quadratic or a cubic curve with the independent variable being part load ratio (PLR = water removal load to be met / dehumidifier steady-state water removal rate). The part load ratio is divided by the output of this curve to determine the dehumidifier runtime fraction. The part load fraction correlation accounts for efficiency losses due to compressor cycling.

∙Qheating=∙Qheating,rated(HCapFTemp)(HCapFAirFlow)(HCapFWaterFlow)

or

IF(CondenserPumpHeatIncludedInRatedHeatingCapacityandRatedCOP)∙Qheating,total=∙QheatingELSE∙Qheating,total=∙Qheating+Ppump(Fracpumptowater)ENDIF

where

PLR=part−loadratio=(waterremovalloadtobemetdehumidifiersteady−statewaterremovalrate)

The part load fraction correlation should be normalized to a value of 1.0 when the part load ratio equals 1.0 (i.e., no efficiency losses when the dehumidifier runs continuously for the simulation timestep). For PLR values between 0 and 1 (0 < = PLR < 1), the following rules apply:

0.7 < = PLF < = 1.0 and PLF > = PLR

If PLF < 0.7 a warning message is issued, the program resets the PLF value to 0.7, and the simulation proceeds. The runtime fraction of the dehumidifier is defined as PLR/PLF. If PLF < PLR, then a warning message is issued and the runtime fraction of the dehumidifier is set to 1.0.

Mechanical dehumidifier typically have long runtimes with minimal compressor cycling. So, a typical part load fraction correlation might be:

PLF = 0.95 + 0.05(PLR)

If the user wishes to model no efficiency degradation due to compressor cycling, the part load fraction correlation should be defined as follows:

PLF = 1.0 + 0.0(PLR)

All three part-load curves are accessed through EnergyPlus’ built-in performance curve equation manager (Curve:Quadratic, Curve:Cubic and Curve:Biquadratic). It is not imperative that the user utilize all coefficients shown in curve equations above if their performance equation has fewer terms (e.g., if the user’s PartLoadFrac performance curve is linear instead of quadratic, simply enter the values for a and b, and set coefficient c equal to zero).

For any simulation time step when there is a water removal load to be met, the dehumidifier is available to operate (via availability schedule), and the inlet air dry-bulb temperature is within the minimum and maximum dry-bulb temperature limits specified in the input file for this object, the water removal rate for the dehumidifier is calculated as follows:

˙mair,avg=ρair(˙Vair,rated)(PLR)

where

˙mwater,ss = dehumidifier steady-state water removal rate, kg/s

ρwater = density of water, kg/m3

˙Vwater,rated = rated water removal rate (user input), L/day

The Zone Dehumidifier Part-Load Ratio (output variable) is then calculated, with the result constrained to be from 0.0 to 1.0:

PLR=waterremovalloadtobemet˙mwater,ss,0.0≤PLR≤1.0

The steady-state and average electrical power consumed by the dehumidifier are calculated next using the following equations:

Pdehumid,ss=˙Vwater,rated(WaterRemovalModFac)(1000)EFrated(EFModFac)(24)

Pdehumid,avg=Pdehumid,ss(RTF)+(Poff−cycle(1−RTF))

where the 1000 and 24 are for conversion between kW and W, and days and hours, and:

Pdehumid,ss = dehumidifier steady-state electric power, W

Pdehumid,avg = Zone Dehumidifier Electric Power, W (output variable)

RTF=PLRPLF=ZoneDehumidifierRuntimeFraction(outputvariable)

E

## Zone Equipment and Zone Forced Air Units[LINK]

## Air Distribution Terminal Unit[LINK]

## Overview[LINK]

The ZoneHVAC:AirDistributionUnit is a special piece of zone equipment – it connects centrally conditioned air with a zone. It encompasses the various types of air terminal units in EnergyPlus:

AirTerminal:DualDuct:ConstantVolume,AirTerminal:SingleDuct:VAV:Reheat, etc. It is a generalized component that accesses the calculations for the different types of air terminal unit.## Model[LINK]

The air distribution function is encapsulated in the module

ZoneAirEquipmentManager. The object and module function only to invoke the individual air terminal unit simulations.## Inputs and Data[LINK]

The data for this unit consists of the unit name, the air outlet node name (which should be the same as one of the zone inlet nodes), the type of air terminal unit (air distribution equipment), and the name of the air terminal unit.

All input data for air distribution units is stored in the array

AirDistUnitin data moduleDataDefineEquip.## Calculation[LINK]

There is no calculation associated with ZoneHVAC:AirDistributionUnit.

## Simulation and Control[LINK]

SimZoneAirLoopEquipmentin moduleZoneAirEquipmentManagercalls the individual air terminal unit simulations.## References[LINK]

No specific references.

## Air Terminal Single Duct Mixer[LINK]

## Overview[LINK]

The mixer object AirTerminal:SingleDuct:Mixer provides a means for using a ZoneHVAC equipment as a terminal unit by mixing central system conditioned air with the inlet or supply side air stream of the ZoneHVAC equipment. Usually the central system would be a Direct Outside Air System (DOAS) providing centrally conditioned ventilation air to the controlled zones. The inlet or supply side connection type is specified by user.

## Model[LINK]

The mixer uses the equations for adiabatic mixing of two moist air streams. Namely, dry air mass balance, water mass balance, and enthalpy balance. For inlet side mixer connection, the primary air and outlet air flow rates are known, and the condition of the primary and secondary air streams are also known. The mass balance yields the secondary air mass flow rate, and the outlet conditions are determined from enthalpy and water mass balance. For the supply side mixer connection, the primary and secondary air stream conditions and flow rates are known so the outlet condition and flow rate is calculated.

## Inputs and Data[LINK]

The only input data are the name and type of the ZoneHVAC equipment unit plus the node names of the primary and the secondary air nodes and the outlet air node. No flow rate data is needed.

All input data for the inlet and supply side mixer units is stored in the data structure

SysATMixer.## Calculation[LINK]

The following equations for the mixing of two moist air streams are used:

˙mda1h1+˙mda2h2=˙mda3h3

˙mda1+˙mda2=˙mda3

˙mda1W1+˙mda2W2=˙mda3W3

The mixed air temperature is determined using the following psychometric function: T3=PsyHFnTdbW(h3,w3)

where ˙mda is dry air mass flow rate in kg/s,

his specific enthalpy in J/kg,Tis temperature in C, and W is humidity ratio in (kg of water)/(kg of dry air).For a mixer unit connected to the inlet side of a ZoneHVAC equipment, the outlet air mass flow rate has been set by the zone HVAC equipment. The air mass flow rate of one of the inlets - the primary air from the central system - is also known. So the air mass balance equation is used to obtain the secondary air mass flow rate.

The inlet conditions - specific enthalpy and humidity ratio - for both inlet air streams are known. Now that both inlet air streams’ mass flow rate is known, the enthalpy and water mass balance equations are used to get the outlet conditions.

For a mixer unit connected to the supply side of a ZoneHVAC equipment, the conditions and flow rates of the primary air and secondary air streams are known, are taken from the inlet nodes’ data. The balance equations are then used to calculate the outlet flow rate and conditions.

## Simulation and Control[LINK]

The mixer model is invoked from within the zone HVAC model. Basically the mixer becomes a subcomponent of the zone HVAC equipment model. This allows the zone unit to allow for the mixing of central supply air with its inlet or supply air stream of the ZoneHVAC equipment in calculating how much cooling or heating it needs to do in order to meet the zone load.

## References[LINK]

See Chapter 1, page 1.17 of the 2013 ASHRAE Handbook of Fundamentals

## Simple Duct Leakage Model[LINK]

## Overview[LINK]

The input object ZoneHVAC:AirDistributionUnit also provides access to a model for duct leakage that can be a significant source of energy inefficiency in forced-air HVAC systems. Evaluating duct leakage energy losses can involve considerable user effort and computer resources if an airflow network is defined through a detailed description of the system components and airflow paths (including leakage paths). A nonlinear pressure-based solver is used to solve for pressures and flow rates in the network. By making certain assumptions and approximations for certain well defined configurations, however, it is possible to obtain accurate results with a simple mass and energy balance calculation and thus avoid the input and calculation costs of doing a full pressure-based airflow network simulation.

The Simple Duct Leakage Model (SDLM) assumes a central VAV air conditioning system with a constant static pressure setpoint. The model assumes that the leaks are in the supply ducts and that the system returns air through a ceiling plenum that contains the ducts. Thus, the ducts leak into the return plenum, and this part of the supply does not reach the conditioned zones. With the additional assumptions described below, it is possible to model this configuration with heat and mass balance equations and avoid the use of a nonlinear pressure-based solver. In the EnergyPlus context, this means that use of AirflowNetwork is avoided and the leakage calculations are obtained in the course of the normal thermal simulation.

## Principles and Description[LINK]

Constant Flow Rate

The airflow rate through a duct leak is a function of the pressure difference between the duct and the surrounding space:

˙Vleak=C1⋅Δpnduct−space

The exponent

nis 0.5 for leaks that look like orifices (holes that are large relative to the thickness of the duct wall); for leaks that resemble cracks (e.g., lap joints),nis approximately 0.6 to 0.65.For a duct with constant flow rate and a linear pressure drop through the duct, the average static pressure in the duct will equal half of the duct static pressure drop. Assuming turbulent flow in the duct, the duct pressure drop is proportional to the square of the airflow through the duct. This can be expressed as:

Δpduct−space=Δpduct2=C2⎛⎝˙V2duct2⎞⎠

Combining equations and and assuming the leaks are large holes (

nequals 0.5). gives:˙Vleak=C1⋅Δp0.5duct−space=C3⋅˙Vduct

where

C3=C1⋅(C2/2)0.5

Thus the leakage fraction

C3 remains constant regardless of the duct flow rate or static pressure. This result depends on the following assumptions:· the duct airflow is turbulent;

· the duct pressure varies linearly along the duct;

· the average duct pressure approximates the pressure drop across the duct;

· the leaks are large and have pressure exponent 0.5.

Effects of Constant Pressure Upstream and Variable Flow and Pressure Downstrean

Commonly VAV systems maintain a constant static pressure at some point in the duct system upstream of the VAV terminal units. That is, airflow rate will vary depending on the cooling requirement, but a constant pressure will be maintained at the static pressure sensor. Consequently, the leakage flow for a leak upstream of the VAV boxes will be approximately constant. Or to put it another way, the leakage fraction will vary in proportion to the flow rate.

For leaks downstream of the VAV terminal units, the airflow through the duct and the pressure in the downstream duct will vary as the box damper modulates in response to the differential between the room temperature and the thermostat setpoint. In this case, the situation is similar to the constant flow case: for an orifice-like leak, the pressure difference across the leak will vary linearly with the air speed (or flow rate); i.e., the leakage fraction will be approximately constant.

SDLM

For SDLM, our leakage model is then:

· for leaks upstream of the terminal units, the leakage flow rate will be constant;

· for leaks downstream of the terminal units, the leakage fraction will be constant.

This model assumes, in addition to the assumptions given above, that the VAV system is controlled to a constant static pressure setpoint. In EnergyPlus SDLM is not currently applicable to systems using static pressure reset. Using SDLM would require knowledge of static pressure as a function of system air flow rate.

## Inputs and Data[LINK]

User data for the SDLM is entered through The ZoneHVAC:AirDistributionUnit (ADU) object. There are 2 data items per ADU:

1. the upstream nominal leakage fraction;

2. the downstream fixed leakage fraction.

Both inputs are leakage fractions. Input (1) is the leakage fraction at design flow rate, which together can be used to determine the constant leakage flow rate upstream of the VAV boxes; this leakage fraction varies with the flow rate. Input (2) is a fixed leakage fraction and is constant as the flow rate varies.

## Implementation[LINK]

The various zone mass flow rates are related in the following manner.

˙ms,us=˙mtu+˙mlk,us

˙mtu=˙mlk,ds+˙ms,z

˙mlk,us=Fracus⋅˙ms,us,max

˙mlk,ds=Fracds⋅˙mtu $$

Here

˙ms,us is the constant zone supply air mass flow rate upstream of the leaks [kg/s];

˙mtu is the air mass flow rate through the terminal unit [kg/s];

˙mlk,us is the upstream leakage air mass flow rate [kg/s];

˙mlk,ds is the downstream leakage air mass flow rate [kg/s];

˙ms,us,max is the maximum upstream supply air mass flow rate (program input) [kg/s];

˙ms,z is the supply air mass flow rate delivered to the zone [kg/s];

Fracus is the design upstream leakage fraction (program input);

Fracds is the constant downstream leakage fraction (program input);

˙mtu is calculated in the VAV terminal unit model in the usual manner: the mass flow rate is varied to meet the zone load. The limits on the mass flow rate variation are set by the ˙mMaxAvail and ˙mMinAvail values stored at the terminal unit’s air inlet node. To account for upstream leakage the maximum air mass flow rate available is reset to:

˙m′MaxAvail=˙mMaxAvail−˙mlk,us

Downstream leakage must also be accounted for because not all of ˙mtu will reach the zone. This is done by having ˙mtu meet an adjusted zone load:

˙Qz,adjusted=11−Fracds˙Qz

Here ˙Qz [watts] is the actual zone load (met by ˙ms,z ) and ˙Qz,adjusted is the load used in the VAV terminal unit model to obtain ˙mtu .

Once ˙mtu is known, all the other flow rates can be calculated. ˙ms,us is assigned to the air distribution unit’s air inlet node and ˙ms,z is assigned to the unit’s air outlet node. Thus, air mass flow is not conserved through the unit: the two air leakage flow rates disappear. These two vanished flow rates are stored in the air distribution unit data structure. When the downstream return air plenum mass and energy balances are calculated, the leakage flow rate data is accessed and added back in as inlets to the return air plenum. Thus, the overall air system preserves a mass balance.

## References[LINK]

Wray, C.P. 2003. “Duct Thermal Performance Models for Large Commercial Buildings”, Lawrence Berkeley National Laboratory Report to the California Energy Commission. LBNL-53410.

Wray, C.P. and N.E. Matson. 2003. “Duct Leakage Impacts on VAV System Performance in California Large Commercial Buildings”, Lawrence Berkeley National Laboratory Report to the California Energy Commission. LBNL-53605.

Wray, C.P., R.C. Diamond, and M.H. Sherman. 2005. “Rationale for Measuring Duct Leakage Flows in Large Commercial Buildings”. Proceedings – 26th AIVC Conference, Brussels, Belgium, September. LBNL-58252.

## Fan Coil Unit[LINK]

## Overview[LINK]

The input object ZoneHVAC:FourPipeFanCoil provides a model for a 4 pipe fan coil zonal hydronic unit that can supply heating and cooling to a zone. It contains a hot water or electric heating coil, a chilled water coil, and a fan. It can supply a fixed amount of outdoor air, but cannot operate in an economizer mode. The fan runs at constant speed – control is achieved by throttling the hot or cold water flow. The fan coil configuration and control is rather limited. The fan position is always

blow-through, control is always by varying the water flow, never by holding the water flow constant and cycling the fan.## Model[LINK]

The 4 pipe fan coil unit is modeled as a compound component consisting of 4 sub-components: an outdoor air mixer, a fan, a cooling coil, and a heating coil. In terms of EnergyPlus objects these are:

OutdoorAir:MixerFan:ConstantVolumeCoil:Cooling:Water, Coil:Cooling:Water:DetailedGeometry,orCoilSystem:Cooling:Water:HeatExchangerAssistedCoil:Heating:Water or Coil:Heating:ElectricThe unit is a forward model: its inputs are defined by the state of its inlets: namely its 2 air streams – recirculated and outdoor air. The outputs of the model are the conditions of the outlet air stream: flow rate, temperature and humidity ratio. The unit data and simulation are encapsulated in the module

FanCoilUnits.## Inputs and Data[LINK]

The user describes the 4 pipe fan coil unit by inputting the names of the outdoor air mixer, the fan, the heating coil, and the cooling coil. The heating and cooling coil types must also be specified.

The unit is connected to the overall HVAC system by specifying node names for the unit air inlet (for recirculated air) node, air outlet node, outdoor air node, relief node, inlet hot water node, and inlet chilled water node. The individual components comprising the fan coil must also be input and connected together properly. Specifically the outdoor air mixer mixed air node must be the same as the fan inlet node; the fan outlet node must be the same as the cooling coil air inlet node; the cooling coil air outlet node must be the same as the heating coil air inlet node; and the heating coil air outlet node must be the same as the unit air outlet node; the outdoor air mixer inlet nodes must match the unit inlet nodes; and the outdoor air mixer relief node must match the unit relief node.

The user needs to also specify (unless the unit is autosized) various maximum flow rates: the supply air flow rate, the outdoor air inlet flow rate, the maximum (and minimum) chilled water flow rate, and the maximum (and minimum) hot water flow rate. Heating and cooling convergence tolerances need to be specified or defaulted. And there is an on/off availability schedule for the unit.

All the input data for the fan coil unit is stored in the array

FanCoil.## Calculation[LINK]

Given the needed inputs, the output is calculated in subroutine

Calc4PipeFanCoil. The temperature, humidity ratio and flow rate of the recirculated and outdoor air streams are taken from the inlet air nodes The inlet hot and chilled water flow rates have been set by local controllers – temperatures are taken from the inlet water nodes. Then1. The outdoor air mixer is simulated (Call

SimOAMixer);2. the fan is simulated (Call

SimulateFanComponents);3. the cooling coil is simulated (Call

SimulateWaterCoilComponentsorSimHXAssistedCoolingCoil);4. the heating coil is simulated (Call

SimulateWaterCoilComponents or SimulateHeatingCoilComponents).The load met (sensible cooling or heating) is calculated and passed back to the calling routine:

˙Qsens,out=˙mtot(PsyHFnTdbW(Tout,Win)−PsyHFnTdbW(Tin,Win))

where

PsyHFnTdbWis the EnergyPlus function for calculating the specific enthalpy of air given the drybulb temperature and the humidity ratio. The subscriptinindicates the conditions at the inlet recirculated air node.## Simulation and Control[LINK]

From the result of the zone simulation we have the current heating/cooling demand on the unit ˙Qz,req . The first step is to decide whether the unit is on for the current time step. If the load is less than 1 watt or the flow rate is less than .001 kg/s, the unit is off. If the availability schedule is off, the mass flow rate is set to zero, so the second condition holds. When the unit is off there will be no air flow through the unit and outlet conditions will be equal to inlet conditions.

˙Qz,req is not the demand on the heating or cooling coil. To obtain the actual coil load, we need to calculate the unit output with no heating or cooling by the coils (˙Qunit,nohc ). We obtain this by calling

Calc4PipeFanCoilwith the water flow rates set to zero. Then the coil loads are calculated:˙Qhc=˙Qz,hsp−˙Qunit,nohc

˙Qcc=˙Qz,csp−˙Qunit,nohc

where ˙Qhc is the heating coil load, ˙Qz,hsp is the current zone load to the heating setpoint, ˙Qcc is the cooling coil load, and ˙Qz,csp is the current zone load to the cooling setpoint.

If the unit is on and ˙Qcc < 0 and the thermostat type is not “single heating setpoint”,

ControlCompOutputis called with the control node set to the cold water inlet node.ControlCompOutputis a general component control routine. In this case callsCalc4PipeFanCoilrepeatedly while varying the cold water flow rate and minimizing (˙Qsens,out−˙Qz,csp)/˙Qz,csp to within the cooling convergence tolerance. Similarly if the unit is on and ˙Qhc >0 and the thermostat type is not “single cooling setpoint”,ControlCompOutputis called with the control node set to the hot water inlet node (for hydronic heating coil only).ControlCompOutputvaries the hot water flow rate or the electric heating coil part-load ratio is varied to minimize (˙Qsens,out−˙Qz,hsp)/˙Qz,hsp to within the heating tolerance.ControlCompOutputexecutes a slow but safe interval halving algorithm to do its minimization. Once control is achieved, the total cooling/heating output is calculated:˙Qtot,out=˙m⋅(PsyHFnTdbW(Tout,Wout)−PsyHFnTdbW(Tin,Win)

## Multi-Speed Fan In FanCoil[LINK]

When modeling multi-speed fan in FanCoil unit, capacity is modulated using speed ratio or part load ratio. The supply air fan speed is varied while operating the coils at maximum water flow. When there is no system load to meet, the water control valve is fully closed. When the FanCoil fan is cycling between two consecutive fan speed levels a speed ratio is calculated, but when the FanCoil unit cycles between the minimum fan speed and off-position, then part load ratio is calculated. The fan may be off or run continuously at lowest speed to provide ventilation air depending the fan operating schedule specified. When the FanCoil is operating at the lowest fan speed (Speed = 1), the water flow rate is reported as the average for the time step by multiplying the maximum water flow by part load ratio. The speed ratio and part-load ratio are calculated such that the FanCoil unit satisfies the required system zone cooling or heating load.The set of equations used for the multi-speed fan capacity control methods in FanCoil unit are summarized next.

## Cycling Between Speeds

When the supply fan is cycling between consecutive speeds, then the speed ratio (SR) and the average mass flow rate are calculated as follows:

SRn=Abs(SystemLoad−FullLoadOutputn−1)/Abs(FullLoadOutputn−FullLoadOutputn−1)

˙m=˙mon,nSRn+˙mon,n−1(1−SRn)

˙mw=˙mw,max

## Cycling OnOff at Lowest Speed

The average supply air flow rate calculation when the fan is running at the lowest fan speed level depends on the fan operating schedule and load. The fan coil unit part load ratio is given by:

PLR=Abs(SystemLoad−NoLoadOutput)/Abs(FullLoadOutput1−NoLoadOutput)

Continuous Fan

˙m=˙mon,1PLR+˙moff(1−PLR)

Cycling Fan:

˙m=˙mon,1PLR˙mw=˙mw,maxPLR

where:

SRn = speed ratio of the fan coil unit at speed n, (-)

PLR = part load ratio of the fan coil uni at speed 1, (-)

˙m = average mass flow rate of supply air, (kg/s

˙mon,n−1 = mass flow rate of supply air at fan speed level n-1, (kg/s)

˙mon,n = mass flow rate of supply air at fan speed level n, (kg/s)

˙moff = mass flow rate of supply air when the coils are off, (kg/s)

˙mw = average mass flow rate of chilled or hot water, (kg/s)

˙mw,max = maximum or full mass flow rate of chilled or hot water, (kg/s)

SystemLoad = system load to be met by the fan coil unit, (W)

FullLoadOutputn−1 = fully load fan coil unit output at fan speed level n-1, (W)

FullLoadOutputn = fully load fan coil unit output at fan speed level n, (W)

## ASHRAE 90.1[LINK]

The ASHRAE90.1 control method uses a simple technique to adjust fan speed based on zone design sensible load. The specific section of the Standard is described as:

This control method assumes that a simulation sizing run is performed to determine the zone design sensible cooling and heating load ˙Qz,design .

For fan coil units, the limit used to determine if reduced zone loads are met with reduced fan speed is the fan coil’s Low Speed Supply Air Flow Ratio input.

˙Qreduced=˙Qz,design∗Ratiofan,lowspeed

If the zone load, ˙Qz,req , is less than Qreduced then the fan is maintained at the reduced speed while the water coils (or electric heating coil) are modulated to meet the zone load.

If the zone load is greater than the design zone sensible load, ˙Qz,design , the fan will operate at the maximum supply air flow rate and the water or electric heating coils will modulate to meet the zone load.

If the zone load is between these two extremes, the fan and coil will modulate to meet the zone load.

An example of the ASHRAE 90.1 control method is provided in the following figure. In this figure, the X-axis represents the zone cooling (-) or heating (+) load.

Single-Zone VAV Fan Control for Fan Coil Units

## References[LINK]

No specific references.

## Window Air Conditioner[LINK]

## Overview[LINK]

The input object ZoneHVAC:WindowAirConditioner provides a model for a window air conditioner unit that is a packaged unit that supplies cooling to a zone (it is part of zone equipment, not part of the air loop equipment). It contains a fan, a DX cooling coil, and an outdoor air inlet. The coil meets the cooling load by cycling on/off. The fan can operate continuously or cycle on/off in conjunction with the coil.

## Model[LINK]

The window air conditioner is modeled as a compound component consisting of 3 sub-components: an outdoor air mixer, a fan, and a DX coil. In terms of EnergyPlus objects these are OutdoorAir:Mixer, Fan:ConstantVolume or Fan:OnOff, and Coil:Coolilng:DX:SingleSpeed or CoilSystem:Cooling:DX:HeatExchangerAssisted. The unit is a forward model: its inputs are defined by the state of its inlets: namely its 2 air streams – recirculated and outdoor air. The outputs of the model are the conditions of the outlet air stream: flow rate, temperature and humidity ratio. The model is also an averaged model: the performance of the unit is averaged over the time step. That is, the unit is assumed to cycle on/off during the time step and this on/off cycling is averaged over the simulation time step. The unit data and simulation are encapsulated in the module WindowAC.

## Inputs and Data[LINK]

The user describes the window air conditioner by inputting the names of the outdoor air mixer, the fan, and the cooling coil. The user can also choose fan placement – blow through or draw through; fan operation – cycling or continuous; and cooling coil type – normal DX or DX with heat exchanger assistance.

The connectivity of the unit needs to be specified: a recirculated (inlet) air node (same as a zone exhaust node); an air outlet node (same as a zone inlet node); an outdoor air inlet node; and a relief air node. The individual components comprising the window air conditioner must of course also be input and connected together properly. For instance, for a blow through fan configuration the outdoor air mixer mixed air node must be the same as the fan inlet node; the fan outlet node must be the same as the coil inlet node; the coil outlet node must be the same as the unit outlet node; the outdoor air mixer inlet nodes must match the unit inlet nodes; and the outdoor air mixer relief node must match the unit relief node.

The user also specifies the air conditioner flow rate delivered to the zone (when cycled on) and the outdoor air flow rate. The user also needs to specify an availability schedule for the unit (this is an on/off schedule).

Note that there is no input specifying the unit’s design cooling capacity. This is an input in the DX coil object and is not repeated here.

All the input data for the window air conditioner is stored in the array

WindAC.## Calculation[LINK]

Given the needed inputs, the output is calculated in subroutine CalcCyclingWindowAC. The temperature, humidity ratio and flow rate of the recirculated and outdoor air streams are taken from the inlet air nodes. The part load ratio is specified by the calling routine. Then

· The outdoor air mixer is simulated (Call SimOAMixer);

· For blow-through fan position:

· the fan is simulated (Call SimulateFanComponents);

· the coil is simulated (Call SimDXCoil or SimHXAssistedCoolingCoil).

For draw-through fan position, the simulation order of the fan and coil is reversed. Note that data is never explicitly passed between the sub-components. This is all handled automatically by the node connections and the data stored on the nodes.

## Simulation and Control[LINK]

From the result of the zone simulation we have the heating/cooling demand on the unit ˙Qz,req . The first step is to decide whether the unit is on for the current time step. For a unit with a cycling fan, the entire unit is assumed to be off if there is no cooling load, the cooling load is very small (less than 1 watt), the unit is scheduled off, or the zone temperature is in the deadband. For a unit with a continuous flow the fan operates if the unit is scheduled on, whether or not there is a cooling demand. The coil however only operates if there is a cooling demand and the zone temperature is not in the deadband.

If the unit is determined to be on, the next step is to find the unit part load fraction that will satisfy the cooling load. This is done in

ControlCycWindACOutput. In this routineCalcCyclingWindowACis first called with part load fraction equal to 0, then with part load fraction equal to 1. These calls establish the minimum and maximum cooling output possible by the unit given the current conditions. An initial estimate of the part load fraction is then made:PLF=(˙Qz,req−˙Qout,min)/|˙Qout,max−˙Qout,min|

Since the unit’s cooling output is a nonlinear function of the part load fraction, this

PLFwill not give exactly the desired ˙Qz,req . To obtain the exactPLFthat will give ˙Qz,req , it is necessary to iteratively callCalcCyclingWindowAC, varyingPLFuntil the desired cooling output is obtained, within the error tolerance specified by the user in the input.Once

PLFis determined,ControlCycWindACOutputis exited. One last call toCalcCyclingWindowACis made to establish the final outlet conditions at the unit’s air outlet node. Finally, the inlet and outlet node conditions are used to calculate the reporting variables: sensible and total cooling output.∙Qcooling,max=(∙mSA,fullload)(hout,fullload−hzoneair)HRmin

∙Qcooling,min=(∙mSA,coiloff)(hout,coiloff−hzoneair)HRmin

where

PsyHFnTdbis the EnergyPlus function giving enthalpy as a function of temperature and humidity ratio.## References[LINK]

No specific references.

## Packaged Terminal Air Conditioner[LINK]

## Overview[LINK]

The input object ZoneHVAC:PackagedTerminalAirConditioner provides a model for a packaged terminal air conditioner (PTAC) that is a compound object made up of other components. Each PTAC consists of an outdoor air mixer, direct expansion (DX) cooling coil, heating coil (gas, electric, hot water, or steam) and a supply air fan. While the figure below shows the PTAC with draw through fan placement, blow through fan placement can also be modeled by positioning the supply air fan between the outdoor air mixer and DX cooling coil. The packaged terminal air conditioner coordinates the operation of these components and is modeled as a type of zone equipment (Ref. ZoneHVAC:EquipmentList and ZoneHVAC:EquipmentConnections).

Schematic of a Packaged Terminal Air Conditioner with Draw Through Fan Placement

The PTAC conditions a single zone and is controlled by a thermostat located in that zone. The PTAC operates to meet the zone sensible cooling or sensible heating requirements as dictated by the thermostat schedule. The model calculates the required part-load ratio for the air conditioner’s coils and the supply air fan to meet the cooling/heating requirements. The heating or cooling energy provided by the PTAC is delivered to the zone via the zone air inlet node.

The PTAC 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). Supply air fan operation is coordinated with the use of a supply air fan operating mode schedule. Schedule values of 0 denote cycling fan operation (AUTO fan). Schedule values other than 0 denote continuous fan operation (fan ON). Fan:OnOff must be used to model AUTO fan (i.e. if schedule values of 0 occur in the supply air fan operating mode schedule), while Fan:OnOff or Fan:ConstantVolume can be used to model fan ON (i.e. if schedule values of 0 do not occur in the supply air fan operating mode schedule). The supply air fan operating mode schedule specified for the PTAC overrides the operating mode specified in the DX cooling coil object.

Output variables reported by the PTAC object include the supply air fan part-load ratio, the air conditioner’s part-load ratio (cooling or heating), and the electric consumption of the PTAC. Additional output variables report the total zone heating rate and the total zone cooling rate provided by the air conditioner. The sensible and latent components of zone cooling are also available as output variables. Reporting of other variables of interest for the PTAC (DX coil cooling rate, coil heating rate, crankcase heater power, fan power, etc.) is done by the individual system components (fan, DX cooling coil and heating coil).

## Model Description[LINK]

As described previously, the PTAC conditions a single zone and is controlled by a zone thermostat (ZoneControl:Thermostatic). Each simulation time step, EnergyPlus performs a zone air heat balance to determine if cooling or heating is required to meet the thermostat setpoints, excluding any impacts from PTAC operation. PTAC performance is then modeled with all heating/cooling coils off but the supply air fan operates as specified by the user. If the zone air heat balance plus the impact of PTAC operation with coils off results in no requirement for heating or cooling by the PTAC coils, or if the PTAC is scheduled off (via its availability schedule), then the PTAC coils do not operate and the air conditioner’s part-load ratio output variable is set to 0. If the model determines that cooling or heating is required and the PTAC is scheduled to operate, the model calculates the average air flow rate through the unit and the part-load ratio of the cooling and heating coils in order to meet the thermostat setpoint temperature.

The remainder of this section describes the calculations performed during the latter situation, when cooling or heating coil operation is required. For any HVAC simulation time step, the PTAC can only be cooling or heating, not both. Because the PTAC cycles its coil(s) on and off to meet the required load, the coil(s) operate for a portion of the time step and are off for the rest of the time step. If the user specifies continuous fan operation (i.e. supply air fan operating mode schedule value is greater than 0), then the supply air fan continues to operate at a user-specified flow rate even during periods when the coils cycle off. If the user specifies AUTO fan operation (i.e. supply air fan operating mode schedule value is equal to 0), then the supply air fan cycles on and off with the coils. The model accounts for these variations in air flow through the PTAC within a simulation time step when it determines the total cooling or heating energy delivered to the zone, the average supply air conditions and air flow rate, and the energy consumed by the air conditioner.

## Cooling Operation[LINK]

If EnergyPlus determines that the air conditioner must supply cooling to the zone in order to meet the zone air temperature setpoint, then the model first calculates the PTAC’s sensible cooling rate to the zone under two conditions: when the unit runs at full-load (steady-state) conditions and when the DX cooling coil is OFF. If the supply air fan cycles on/off with the compressor, then the sensible cooling 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 rate will not be zero when the cooling coil is OFF. Calculating the sensible cooling rate involves modeling the supply air fan (and associated fan heat), the outdoor air mixer, and the DX cooling coil. The heating coil is also modeled, but only to pass the air properties and mass flow rate from it’s inlet node to it’s outlet node. For each of these cases (full load and DX cooling coil OFF), the sensible cooling rate delivered to the zone by the PTAC is calculated as follows:

˙Qcooling,max=(˙mSA,fullload)(hout,fullload−hzoneair)HRmin

˙Qcooling,min=(˙mSA,coiloff)(hout,coiloff−hzoneair)HRmin

where:

˙Qcooling,max = maximum PTAC sensible cooling rate with cooling coil ON, W

˙mSA,fullload = supply air mass flow rate at full-load (steady-state) conditions, kg/s

hout,fullload= enthalpy of air exiting the PTAC at full-load conditions, J/kghzoneair= enthalpy of zone (exhaust) air, J/kgHRmin= enthalpies evaluated at a constant humidity ratio, the minimum humidity ratio of the PTAC exiting air or the zone (exhaust) air˙Qcooling,min = minimum PTAC sensible cooling rate with cooling coil OFF, W

˙mSA,coiloff = supply air mass flow rate with the cooling coil OFF, kg/s

hout,coiloff= enthalpy of air exiting the PTAC with the cooling coil OFF, J/kgWith the calculated PTAC sensible cooling rates and the zone sensible cooling load to be met, the compressor part-load ratio for the PTAC is approximately equal to:

PartLoadRatio=MAX⎛⎜ ⎜⎝0.0,ABS(˙Qzone,cooling−˙Qcooling,min)ABS(˙Qcooling,max−˙Qcooling,min)⎞⎟ ⎟⎠

where:

PartLoadRatio = compressor part-load ratio required to meet the zone load

˙Qzone,cooling = required zone sensible cooling rate to meet setpoint, W

Since the part-load performance of the DX cooling coil is frequently non-linear (Ref: DX Cooling Coil Model), and the supply air fan heat varies based on cooling coil operation for the case of cycling fan/cycling coil (AUTO fan), the actual part-load ratio for the cooling coil compressor and fan are determined through iterative calculations (successive modeling of the individual PTAC component models) until the PTAC’s cooling output (including on/off cycling effects) matches the zone cooling load requirement.

If the PTAC has been specified with cycling fan/cycling coil (AUTO fan), then the user-defined supply air flow rate during cooling operation (volumetric flow rate converted to mass flow rate) is multiplied by the final PartLoadRatio value to determine the average supply air mass flow rate for the HVAC system simulation time step. For this case, the air conditions (temperature, humidity ratio and enthalpy) at nodes downstream of the cooling coil represent the full-load (steady-state) values when the coil is operating. If the supply air fan is specified to run continuously (fan ON), then the supply air mass flow rate is calculated as the average of the air mass flow rate when the compressor is on and the air mass flow rate when the compressor is off. 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 mixed inlet air conditions when the coil is OFF). Additional discussion regarding the calculation of the average supply air flow and supply air conditions is provided later in this section.

## Heating Operation[LINK]

Calculations of the PTAC’s sensible heating rate delivered to the zone at full load and with the heating coil OFF are identical to the calculations described above for cooling operation.

˙Qheating,max=(˙mSA,fullload)(hout,fullload−hzoneair)HRmin

˙Qheating,min=(˙mSA,coiloff)(hout,coiloff−hzoneair)HRmin

where:

˙Qheating,max = maximum PTAC sensible heating rate with heating coil ON, W

˙Qheating,min = minimum PTAC sensible heating rate with heating coil OFF, W

With the calculated PTAC sensible heating rates and the zone sensible heating load to be met, the heating coil part-load ratio for the PTAC is approximately equal to:

PartLoadRatio=MAX⎛⎜ ⎜⎝0.0,ABS(˙Qzone,heating−˙Qheating,min)ABS(˙Qheating,max−˙Qheating,min)⎞⎟ ⎟⎠

where:

PartLoadRatio = heating coil part-load ratio required to meet the zone load

˙Qzone,heating = required zone sensible heating rate to meet setpoint, W

Iterative calculations (successive modeling of the individual PTAC component models) are used to determine the final heating part-load ratio to account for the non-linear performance of the heating coil at part-load conditions and the variation in supply air fan heat for the case of cycling fan/cycling coil (AUTO fan). If heating coil operation at full load is unable to meet the entire zone heating load (e.g., the heating coil capacity is insufficient or the coil is scheduled OFF), the air conditioner’s part-load ratio is set to 1 to meet the zone heating load to the extent possible.

## Average Air Flow Calculations[LINK]

The packaged terminal air conditioner operates based on user-specified (or autosized) air flow rates. The PTAC’s supply air flow rate during cooling operation may be different than the supply air flow rate during heating operation. In addition, the supply air flow rate when no cooling or heating is required but the supply air fan remains ON can be different than the air flow rates when cooling or heating is required. The outdoor air flow rates can likewise be different in these various operating modes. The model takes these different flow rates into account when modeling the air conditioner, and the average air flow rate for each simulation time step is reported on the inlet/outlet air nodes of the various PTAC components in proportion to the calculated part-load ratio of the coil.

The average supply air and outdoor air mass flow rates through the air conditioner for the HVAC simulation time step are calculated based on the part-load ratio of the DX cooling coil or heating coil (whichever coil is operating) as follows:

˙mSA,avg=˙mSA,coilon(PartLoadRatio)+˙mSA,coiloff(1−PartLoadRatio)

˙mOA,avg=˙mOA,coilon(PartLoadRatio)+˙mOA,coiloff(1−PartLoadRatio)

where:

˙mSA,avg = average supply air mass flow rate during the time step, kg/s

˙mSA,coilon = supply air mass flow rate when the coil is ON, kg/s

PartLoadRatio= part-load ratio of the coil (heating or cooling)˙mSA,coiloff = supply air mass flow rate when the coil is OFF, kg/s

˙mOA,avg = average outdoor air mass flow rate during the time step, kg/s

˙mOA,coilon = average outdoor air mass flow rate when the coil is ON, kg/s

˙mOA,coiloff = average outdoor air mass flow rate when the coil is OFF, kg/s

The supply air and outdoor air flow rates when the DX cooling coil or the heating coil is ON are specified by the user (i.e., supply air volumetric flow rate during cooling operation, supply air volumetric flow rate during heating operation, outdoor air volumetric air flow rate during cooling operation, and outdoor air volumetric air flow rate during heating operation) and are converted from volumetric to mass flow rate. If the user has specified cycling fan operation (i.e. supply air fan operating mode schedule value is equal to 0), then the supply air and outdoor air mass flow rates when the coil is OFF are zero. If the user has specified constant fan operation (i.e. supply air fan operating mode schedule value is greater than 0), then the user-defined air flow rates when no cooling or heating is needed are used when the coil is OFF.

There is one special case. If the supply air fan operating mode schedule value specifies constant fan operation and the user also specifies that the supply air volumetric flow rate when no cooling or heating is needed is zero (or field is left blank), then the model assumes that the supply air and outdoor air mass flow rates when the coil is OFF are equal to the corresponding air mass flow rates when the cooling or heating coil was last operating (ON).

## Calculation of Outlet Air Conditions[LINK]

When the supply air fan cycles on and off with the PTAC coils (AUTO fan), the calculated outlet air conditions (temperature, humidity ratio, and enthalpy) from the heating coil or the DX cooling coil at full-load (steady-state) operation are reported on the appropriate coil outlet air node. The air mass flow rate reported on the air nodes is the average air mass flow rate proportional to the part-load ratio of the coil (see Average Air Flow Calculations above).

When the supply air fan operates continuously while the PTAC coils cycle on and off (fan ON), the air mass flow rate reported on the air nodes is the average air mass flow rate proportional to the part-load ratio of the coil (see Average Air Flow Calculations above). Since the air flow rate can be different when the coil is ON compared to when the coil is OFF, then the average outlet air conditions from the heating coil or the DX cooling coil are reported on the appropriate coil outlet air node.

For hot water or steam coils, the water or steam mass flow rate is also proportional to the part-load ratio of the coil regardless of the supply air fan operating mode. Refer to the sections in the document that describe the heating and DX cooling coils for further explanation on how they report their outlet air (and water or steam) conditions.

## Calculation of Zone Heating and Cooling Rates[LINK]

At the end of each HVAC simulation time step, this compound object reports the heating or cooling rate and energy delivered to the zone, as well as the electric power and consumption by the air conditioner. In terms of thermal energy delivered to the zone, the sensible, latent and total energy transfer rate to the zone is calculated as follows:

˙QTotal=(˙mSA,avg)(hout,avg−hzoneair)

˙QSensible=(˙mSA,avg)(hout,avg−hzoneair)HRmin

˙QLatent=˙QTotal−˙QSensible

where:

˙QTotal = total energy transfer rate to the zone, W

˙QSensible = sensible energy transfer rate to the zone, W

˙QLatent = latent energy transfer rate to the zone, W

˙mSA,avg = average mass flow rate of the supply air stream, kg/s

hout,avg= enthalpy of the air being supplied to the zone, J/kgSince each of these energy transfer rates can be calculated as positive or negative values, individual reporting variables are established for cooling and heating and only positive values are reported. The following calculations are representative of what is done for each of the energy transfer rates:

IF (˙QTotal<0.0) THEN

˙QTotalCooling=ABS(˙QTotal)

˙QTotalHeating=0.0

ELSE

˙QTotalCooling=0.0

˙QTotalHeating=˙QTotal

where:

˙QTotalCooling = output variable ‘Packaged Terminal Air Conditioner Total Zone Cooling Rate, W’

˙QTotalHeating = output variable ‘Packaged Terminal Air Conditioner Total Zone Heating Rate, W’

In addition to heating and cooling rates, the heating and cooling energy supplied to the zone is also calculated for the time step being reported. The following example for total zone cooling energy is representative of what is done for the sensible and latent energy as well as the heating counterparts.

QTotalCooling=˙QTotalCooling⋅TimeStepSys⋅3600

where:

QTotalCooling = output variable ‘Packaged Terminal Air Conditioner Total Zone Cooling Energy, J’

TimeStepSys= HVAC system simulation time step, hr## Packaged Terminal Heat Pump[LINK]

## Overview[LINK]

The input object ZoneHVAC:PackagedTerminalHeatPump provides a model for a packaged terminal heat pump (PTHP) that is a compound object made up of other components. Each PTHP consists of an outdoor air mixer, direct expansion (DX) cooling coil, DX heating coil, supply air fan, and a supplemental heating coil. While the figure below shows the PTHP with draw through fan placement, blow through fan placement can also be modeled by moving the supply air fan before the DX cooling coil. The packaged terminal heat pump coordinates the operation of these components and is modeled as a type of zone equipment (Ref. ZoneHVAC:EquipmentList and ZoneHVAC:EquipmentConnections).

Schematic of a Packaged Terminal Heat Pump (Draw Through Fan Placement)

The PTHP conditions a single zone and is controlled by a thermostat located in that zone. The PTHP operates to meet the zone sensible cooling or sensible heating requirements as dictated by the thermostat schedule. The model calculates the required part-load ratio for the heat pump’s coils and the supply air fan to meet the cooling/heating requirements. The heating or cooling energy provided by the PTHP is delivered to the zone via the zone air inlet node.

The PTHP 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.

Output variables reported by the PTHP object include the supply air fan part-load ratio, the compressor part-load ratio, and the electric consumption of the PTHP. Additional output variables report the total zone heating rate and the total zone cooling rate provided by the heat pump. The sensible and latent components of zone cooling are also available as output variables. Reporting of other variables of interest for the PTHP (DX coil cooling rate, DX coil heating rate, crankcase heater power, fan power, etc.) is done by the individual system components (fan, DX cooling coil, DX heating coil, and supplemental heating coil).

## Model Description[LINK]

As described previously, the PTHP conditions a single zone and is controlled by a zone thermostat (ZoneControl:Thermostat). Each simulation time step, EnergyPlus performs a zone air heat balance to determine if cooling or heating is required to meet the thermostat setpoints, excluding any impacts from PTHP operation. PTHP performance is then modeled with all heating/cooling coils off but the supply air fan operates as specified by the user. If the zone air heat balance plus the impact of PTHP operation with coils off results in no requirement for heating or cooling by the PTHP coils, or if the PTHP is scheduled off (via its availability schedule), then the PTHP coils do not operate and the compressor part-load ratio output variable is set to 0. If the model determines that cooling or heating is required and the PTHP is scheduled to operate, the model calculates the average air flow rate through the unit and the part-load ratio of the cooling and heating coils in order to meet the thermostat setpoint temperature.

The remainder of this section describes the calculations performed during the latter situation, when cooling or heating coil operation is required. For any HVAC simulation time step, the PTHP can only be cooling or heating, not both. Because the PTHP cycles its coil(s) on and off to meet the required load, the coil(s) operate for a portion of the time step and are off for the rest of the time step. If the user specifies continuous fan operation (supply air fan operating mode schedule value > 0), then the supply air fan continues to operate at a user-specified flow rate even during periods when the coils cycle off. If the user specifies AUTO fan operation (supply air fan operating mode schedule value = 0), then the supply air fan cycles on and off with the coils. The model accounts for these variations in air flow through the PTHP within a simulation time step when it determines the total cooling or heating energy delivered to the zone, the average supply air conditions and air flow rate, and the energy consumed by the heat pump.

## Cooling Operation[LINK]

If EnergyPlus determines that the heat pump must supply cooling to the zone in order to meet the zone air temperature setpoint, then the model first calculates the PTHP’s sensible cooling rate to the zone under two conditions: when the unit runs at full-load (steady-state) conditions and when the DX cooling coil is OFF. If the supply air fan cycles on/off with the compressor, then the sensible cooling 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 rate will not be zero when the cooling coil is OFF. Calculating the sensible cooling rate involves modeling the supply air fan (and associated fan heat), the outdoor air mixer, and the DX cooling coil. The DX heating coil and the gas or electric 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 and DX cooling coil OFF), the sensible cooling rate delivered to the zone by the PTHP is calculated as follows:

˙Qcooling,max=(˙mSA,fullload)(hout,fullload−hzoneair)HRmin

˙Qcooling,min=(˙mSA,coiloff)(hout,coiloff−hzoneair)HRmin

where:

˙Qcooling,max = maximum PTHP sensible cooling rate with cooling coil ON, W

˙QSA,fullload = supply air mass flow rate at full-load (steady-state) conditions, kg/s

hout,fullload= enthalpy of air exiting the PTHP at full-load conditions, J/kghzoneair= enthalpy of zone (exhaust) air, J/kgHRmin =enthalpies evaluated at a constant humidity ratio, the minimum humidity ratio of the PTHP exiting air or the zone (exhaust) air˙Qcooling,min = minimum PTHP sensible cooling rate with cooling coil OFF, W

˙QSA,coiloff = supply air mass flow rate with the cooling coil OFF, kg/s

hout,coiloff= enthalpy of air exiting the PTHP with the cooling coil OFF, J/kgWith the calculated PTHP sensible cooling rates and the zone sensible cooling load to be met, the compressor part-load ratio for the PTHP is approximately equal to:

PartLoadRatio=MAX⎛⎜ ⎜⎝0.0,ABS(˙Qzone,cooling−˙Qcooling,min)ABS(˙Qcooling,max−˙Qcooling,min)⎞⎟ ⎟⎠

where:

PartLoadRatio = compressor part-load ratio required to meet the zone load

˙Qzone,cooling = required zone sensible cooling rate to meet setpoint, W

Since the part-load performance of the DX cooling coil is frequently non-linear (Ref: DX Cooling Coil Model), and the supply air fan heat varies based on cooling coil operation for the case of cycling fan/cycling coil (AUTO fan), the actual part-load ratio for the cooling coil compressor and fan are determined through iterative calculations (successive modeling of the individual PTHP component models) until the PTHP’s cooling output (including on/off cycling effects) matches the zone cooling load requirement within the cooling convergence tolerance that is specified.

If the PTHP is specified to operate with cycling fan/cycling coil (AUTO fan), then the user-defined supply air flow rate during cooling operation (volumetric flow rate converted to mass flow rate) is multiplied by the final PartLoadRatio value to determine the average supply air mass flow rate for the HVAC system simulation time step. For this case, the air conditions (temperature, humidity ratio and enthalpy) at nodes downstream of the cooling coil represent the full-load (steady-state) values when the coil is operating. If the supply air fan is specified to operate continuously (fan ON), then the supply air mass flow rate is calculated as the average of the air mass flow rate when the compressor is on and the air mass flow rate when the compressor is off. 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 mixed inlet air conditions when the coil is OFF). Additional discussion regarding the calculation of the average supply air flow and supply air conditions is provided later in this section.

## Heating Operation[LINK]

Calculations of the PTHP’s sensible heating rate delivered to the zone at full load and with the DX heating coil OFF are identical to the calculations described above for cooling operation.

˙Qheating,max=(˙mSA,fullload)(hout,fullload−hzoneair)HRmin

˙Qheating,min=(˙mSA,coiloff)(hout,coiloff−hzoneair)HRmin

where:

˙Qheating,max = maximum PTHP sensible heating rate with DX heating coil ON, W

˙Qheating,min = minimum PTHP sensible heating rate with DX heating coil OFF, W

With the calculated PTHP sensible heating rates and the zone sensible heating load to be met, the compressor part-load ratio for the PTHP is approximately equal to:

PartLoadRatio=MAX⎛⎜ ⎜⎝0.0,ABS(˙Qzone,heating−˙Qheating,min)ABS(˙Qheating,max−˙Qheating,min)⎞⎟ ⎟⎠

where:

PartLoadRatio = compressor part-load ratio required to meet the zone load

˙Qzone,heating = required zone sensible heating rate to meet setpoint, W

Iterative calculations (successive modeling of the individual PTHP component models) are used to determine the final heating part-load ratio to account for the non-linear performance of the DX heating coil at part-load conditions and the variation in supply air fan heat for the case of cycling fan/cycling coil (AUTO fan). If DX heating coil operating at full load is unable to meet the entire zone heating load (e.g., the DX heating coil capacity is insufficient or the coil is scheduled OFF, or the outdoor temperature is below the PTHP’s minimum outdoor dry-bulb temperature for compressor operation), the supplemental heating coil is activated to meet the remaining zone heating load to the extent possible.

## Average Air Flow Calculations[LINK]

The packaged terminal heat pump operates based on user-specified (or autosized) air flow rates. The PTHP’s supply air flow rate during cooling operation may be different than the supply air flow rate during heating operation. In addition, the supply air flow rate when no cooling or heating is required but the supply air fan remains ON can be different than the air flow rates when cooling or heating is required. The outdoor air flow rates can likewise be different in these various operating modes. The model takes these different flow rates into account when modeling the heat pump, and the average air flow rate for each simulation time step is reported on the inlet/outlet air nodes of the various PTHP components in proportion to the calculated part-load ratio of the DX coil compressor.

The average supply air and outdoor air mass flow rates through the heat pump for the HVAC simulation time step are calculated based on the part-load ratio of the DX cooling coil or DX heating coil (whichever coil is operating) as follows:

˙mSA,avg=˙mSA,compon(PartLoadRatio)+˙mSA,compoff(1−PartLoadRatio)

˙mOA,avg=˙mOA,compon(PartLoadRatio)+˙mOA,compoff(1−PartLoadRatio)

where:

˙mSA,avg = average supply air mass flow rate during the time step, kg/s

˙mSA,compon = supply air mass flow rate when the DX coil compressor is ON, kg/s

PartLoadRatio= part-load ratio of the DX coil compressor (heating or cooling)˙mSA,compoff = supply air mass flow rate when the DX coil compressor is OFF, kg/s

˙mOA,avg = average outdoor air mass flow rate during the time step, kg/s

˙mOA,compon = average outdoor air mass flow rate when the DX coil compressor is ON, kg/s

˙mOA,compoff = average outdoor air mass flow rate when the DX coil compressor is OFF, kg/s

The supply air and outdoor air flow rates when the DX cooling or DX heating coil compressor is ON are specified by the user (e.g., supply air volumetric flow rate during cooling operation, supply air volumetric flow rate during heating operation, outdoor air volumetric air flow rate during cooling operation, and outdoor air volumetric air flow rate during heating operation) and are converted from volumetric to mass flow rate. If the user has specified cycling fan operation (supply air fan operating mode schedule value = 0), then the supply air and outdoor air mass flow rates when the DX compressor is OFF are zero. If the user has specified constant fan operation (supply air fan operating mode schedule value > 0), then the user-defined air flow rates when no cooling or heating is needed are used when the DX compressor is OFF.

There is one special case. If the user has specified constant fan operation (supply air fan operating mode schedule value > 0) and they specify that the supply air volumetric flow rate when no cooling or heating is needed is zero (or field is left blank), then the model assumes that the supply air and outdoor air mass flow rates when the DX coil compressor is OFF are equal to the corresponding air mass flow rates when the compressor was last operating (ON).

## Calculation of Outlet Air Conditions[LINK]

When the supply air fan cycles on and off with the PTHP coils (AUTO fan), the calculated outlet air conditions (temperature, humidity ratio, and enthalpy) from the DX heating or DX cooling coil at full-load (steady-state) operation are reported on the appropriate coil outlet air node. The air mass flow rate reported on the air nodes is the average air mass flow rate proportional to the part-load ratio of the DX coil compressor (see Average Air Flow Calculations above).

When the supply air fan operates continuously while the PTHP coils cycle on and off (fan ON), the air mass flow rate reported on the air nodes is the average air mass flow rate proportional to the part-load ratio of the DX coil compressor (see Average Air Flow Calculations above). Since the air flow rate can be different when the coil is ON compared to when the coil is OFF, then the average outlet air conditions from the DX heating or DX cooling coil are reported on the appropriate coil outlet air node.

Refer to the sections in the document that describe the DX heating and DX cooling coils for further explanation on how they report their outlet air conditions.

## Calculation of Zone Heating and Cooling Rates[LINK]

At the end of each HVAC simulation time step, this compound object reports the heating or cooling rate and energy delivered to the zone, as well as the electric power and consumption by the heat pump. In terms of thermal energy delivered to the zone, the sensible, latent and total energy transfer rate to the zone is calculated as follows:

˙QTotal=(˙mSA,avg)(hout,avg−hzoneair)

˙QSensible=(˙mSA,avg)(hout,avg−hzoneair)HRmin

˙QLatent=˙QTotal−˙QSensible

where:

˙QTotal = total energy transfer rate to the zone, W

˙QSensible = sensible energy transfer rate to the zone, W

˙QLatent = latent energy transfer rate to the zone, W

˙mSA,avg = average mass flow rate of the supply air stream, kg/s

hout,avg= enthalpy of the air being supplied to the zone, J/kgSince each of these energy transfer rates can be calculated as positive or negative values, individual reporting variables are established for cooling and heating and only positive values are reported. The following calculations are representative of what is done for each of the energy transfer rates:

IF (˙QTotal

< 0.0 )THEN˙QTotalCooling = ABS (˙QTotal )

˙QTotalHeating =

0.0ELSE

˙QTotalCooling =

0.0˙QTotalHeating = ˙QTotal

where:

˙QTotalCooling = output variable ‘Packaged Terminal Heat Pump Total Zone Cooling Rate, W’

˙QTotalHeating = output variable ‘Packaged Terminal Heat Pump Total Zone Heating Rate, W’

In addition to heating and cooling rates, the heating and cooling energy supplied to the zone is also calculated for the time step being reported. The following example for total zone cooling energy is representative of what is done for the sensible and latent energy as well as the heating counterparts.

QTotalCooling=˙QTotalCooling∗TimeStepSys∗3600.

where:

QTotalCooling = output variable ‘Packaged Terminal Heat Pump Total Zone Cooling Energy, J’

TimeStepSys= HVAC system simulation time step, hr## Zone Single Speed Water-To-Air Heat Pump[LINK]

## Overview[LINK]

The input object ZoneHVAC:WaterToAirHeatPump provides a zone equipment model for a water-to-air heat pump that is a “virtual” component consisting of an on/off fan component, a water-to-air heat pump cooling coil, a water-to-air heat pump heating coil, and a gas or electric supplemental heating coil. The specific configuration of the blowthru heat pump is shown in the following figure. For a drawthru heat pump, the fan is located between the water-to-air heat pump heating coil and the supplemental heating coil. In addition, a water-to-air heat pump has a water loop connection on its source side. The water loop can be served by a condenser loop (like GHE for Ground source systems), or by a cooling tower/ boiler plant loop (for water loop systems).

Source Side and Load Side Configuration of a Zone WaterToAir Heat Pump

There are two models for zone water-to-air heat pump cooling and heating coils, i.e. Single-Speed and Variable-Speed Equation Fit models. Cooling and heating coils are modeled using the Equation Fit model described here.

## Single Speed Equation-Fit Model:[LINK]

This section describes the equation-fit model for Water-to-Air heat pump (Object names: Coil:Cooling:WaterToAirHeatPump:EquationFit and Coil:Heating:WaterToAirHeatPump:EquationFit). This documentation is derived from the M.S. dissertation of Tang (2005) which is available on the Oklahoma State University web site . The model uses five non-dimensional equations or curves to predict the heat pump performance in cooling and heating mode. The methodology involves using the generalized least square method to generate a set of performance coefficients from the catalog data at indicated reference conditions. Then the respective coefficients and indicated reference conditions are used in the model to simulate the heat pump performance. The variables or inlet conditions that influenced the water-to-air heat pump performance are load side inlet water temperature, source side inlet temperature, source side water flow rate and load side water flow rate. The governing equations for the cooling and heating mode are as following:

Cooling Mode:

PowercPowerc,ref=C1+C2[TwbTref]+C3[Tw,inTref]+C4[˙Vair˙Vair,ref]+C5[˙Vw˙Vw,ref]

QhQh,ref=E1+E2[TdbTref]+E3[Tw,inTref]+E4[˙Vair˙Vair,ref]+E5[˙Vw˙Vw,ref]

PowerhPowerh,ref=F1+F2[TdbTref]+F3[Tw,inTref]+F4[˙Vair˙Vair,ref]+F5[˙Vw˙Vw,ref]

Heating Mode:

˙mwater,ss=ρwater(˙Vwater,rated)(WaterRemovalModFac)(24hr/dy)(3600sec/hr)(1000L/m3)

Pdehumid,ss=˙Vwater,rated(WaterRemovalModFac)(1000W/kW)EFrated(EFModFac)(24hr/day)Pdehumid,avg=Pdehumid,ss(RTF)+(Poff−cycle∗(1−RTF))

Assuming no losses, the source side heat transfer rate for cooling and heating mode is calculated as following;

Qsource,c=Qtotal+Powerc

Qsource,h=Qh−Powerh

where:

A1−F5 = Equation fit coefficients for the cooling and heating mode

Tref = 283K

Tw,in = Entering water temperature, K

Tdb = Entering air dry-bulb temperature, K

Twb = Entering air wet-bulb temperature, K

˙Vair = Load side air volumetric flow rate, m3/s

˙Vw = Source side water volumetric flow rate, m3/s

Qtotal = Total cooling capacity, W

Qsens = Sensible cooling capacity, W

Powerc = Power consumption (cooling mode), W

Qsource,c = Source side heat transfer rate (cooling mode), W

Qh = Total heating capacity, W

Powerh = Power consumption (heating mode), W

Qsource,h = Source side heat transfer rate (heating mode), W

The inlet conditions or variables are divided by the reference conditions. This formulation allows the coefficients to fall into smaller range of values. Moreover, the value of the coefficient indirectly represents the sensitivity of the output to that particular inlet variable. The reference conditions used when generating the performance coefficients must be the same as the reference conditions used later in the model. The reference temperature Tref is fixed at 283K. Temperature unit of Kelvin is used instead of Celsius to keep the ratio of the water inlet temperature and reference temperature positive should the water inlet temperature drop below the freezing point.

For cooling mode, the reference conditions; reference load side air volumetric flow rate (˙Vair,ref) ,reference source side water volumetric flow rate(˙Vw,ref) ,reference sensible capacity (Qsens,ref) and reference power input (Powerc,ref) are the conditions when the heat pump is operating at the highest cooling capacity or reference cooling capacity(Qtotal,ref) indicated in the manufacturer’s catalog. Note that the reference conditions for heating mode might differ from the reference conditions specified for the cooling mode.

## Coefficient estimation procedure:[LINK]

The generalized least square method is used to generate the coefficients. This method utilizes an optimization method which calculates the coefficients that will give the least amount of differences between the model outputs and the catalog data. A set of coefficients for the cooling mode is generated which includes A1-A5 for total cooling capacity, B1-B6 for sensible cooling capacity, and C1-C5 for power consumption. The same procedure is repeated for the heating mode to generate the coefficients E1-E5 (total heating capacity) and F1-F5 (power consumption). An information flow chart showing the inputs, reference conditions, performance coefficients and outputs are shown in the figure below:

Information Flow Chart for Water-to-Air Heat Pump Equation Fit Model (Tang 2005)

## Zone Air DX Dehumidifier[LINK]

## Overview[LINK]

This model, object name ZoneHVAC:Dehumidifier:DX, simulates the thermal performance and electric power consumption of conventional mechanical dehumidifiers. These systems use a direct expansion (DX) cooling coil to cool and dehumidify an airstream. Heat from the DX system’s condenser section is rejected into the cooled/dehumidified airstream, resulting in warm dry air being supplied from the unit. In EnergyPlus, this object is modeled as a type of zone equipment (ref. ZoneHVAC:EquipmentList and ZoneHVAC:EquipmentConnections).

Mechanical Dehumidifier Schematic

The model assumes that this equipment dehumidifies and heats the air. If used in tandem with another system that cools and dehumidifies the zone air, then the zone dehumidifier should be specified as the lowest cooling priority in the ZoneHVAC:EquipmentList object for best control of zone temperature and humidity levels. With this zone equipment prioritization, the other cooling and dehumidification system would operate first to meet the temperature setpoint (and possibly meet the high humidity setpoint as well). If additional dehumidification is needed, then the zone dehumidifier would operate. The sensible heat generated by the dehumidifier is carried over to the zone air heat balance for the next HVAC time step.

## Model Description[LINK]

The user must input water removal, energy factor and air flow rate at rated conditions (26.7°C, 60% RH). Three performance curves must also be specified to characterize the change in water removal and energy consumption at part-load conditions:

1) Water removal curve (function of inlet air temperature and relative humidity)

2) Energy factor curve (function of inlet air temperature and relative humidity)

3) Part load fraction correlation (function of part load ratio)

· The water removal modifier curve is a biquadratic curve with two independent variables: dry-bulb temperature and relative humidity of the air entering the dehumidifier. The output of this curve is multiplied by the Rated Water Removal to give the water removal rate at the specific entering air conditions at which the dehumidifier is operating (i.e., at temperature/relative humidity different from the rating point conditions). If the output of this curve is negative, then a warning message is issued and it is reset to 0.0.

WaterRemovalModFac=a+b(Tin)+c(Tin)2+d(RHin)+e(RHin)2+f(Tin)(RHin)

where

Tin= dry-bulb temperature of the air entering the dehumidifier, °CRHin= relative of the air entering the dehumidifier, % (0-100)· The energy factor modifier curve is a biquadratic curve with two independent variables: dry-bulb temperature and relative humidity of the air entering the dehumidifier. The output of this curve is multiplied by the Rated Energy Factor to give the energy factor at the specific entering air conditions at which the dehumidifier is operating (i.e., at temperature/relative humidity different from the rating point conditions). If the output of this curve is negative, then a warning message is issued and it is reset to 0.0.

EFModFac=a+b(Tin)+c(Tin)2+d(RHin)+e(RHin)2+f(Tin)(RHin)

· The part load fraction (PLF) correlation curve is a quadratic or a cubic curve with the independent variable being part load ratio (PLR = water removal load to be met / dehumidifier steady-state water removal rate). The part load ratio is divided by the output of this curve to determine the dehumidifier runtime fraction. The part load fraction correlation accounts for efficiency losses due to compressor cycling.

∙Qheating=∙Qheating,rated(HCapFTemp)(HCapFAirFlow)(HCapFWaterFlow)

or

IF(CondenserPumpHeatIncludedInRatedHeatingCapacityandRatedCOP)∙Qheating,total=∙QheatingELSE∙Qheating,total=∙Qheating+Ppump(Fracpumptowater)ENDIF

where

PLR=part−loadratio=(waterremovalloadtobemetdehumidifiersteady−statewaterremovalrate)

The part load fraction correlation should be normalized to a value of 1.0 when the part load ratio equals 1.0 (i.e., no efficiency losses when the dehumidifier runs continuously for the simulation timestep). For PLR values between 0 and 1 (0 < = PLR < 1), the following rules apply:

0.7 < = PLF < = 1.0 and PLF > = PLR

If PLF < 0.7 a warning message is issued, the program resets the PLF value to 0.7, and the simulation proceeds. The runtime fraction of the dehumidifier is defined as PLR/PLF. If PLF < PLR, then a warning message is issued and the runtime fraction of the dehumidifier is set to 1.0.

Mechanical dehumidifier typically have long runtimes with minimal compressor cycling. So, a typical part load fraction correlation might be:

PLF = 0.95 + 0.05(PLR)

If the user wishes to model no efficiency degradation due to compressor cycling, the part load fraction correlation should be defined as follows:

PLF = 1.0 + 0.0(PLR)

All three part-load curves are accessed through EnergyPlus’ built-in performance curve equation manager (Curve:Quadratic, Curve:Cubic and Curve:Biquadratic). It is not imperative that the user utilize all coefficients shown in curve equations above if their performance equation has fewer terms (e.g., if the user’s PartLoadFrac performance curve is linear instead of quadratic, simply enter the values for a and b, and set coefficient c equal to zero).

For any simulation time step when there is a water removal load to be met, the dehumidifier is available to operate (via availability schedule), and the inlet air dry-bulb temperature is within the minimum and maximum dry-bulb temperature limits specified in the input file for this object, the water removal rate for the dehumidifier is calculated as follows:

˙mair,avg=ρair(˙Vair,rated)(PLR)

where

˙mwater,ss = dehumidifier steady-state water removal rate, kg/s

ρwater = density of water, kg/m3

˙Vwater,rated = rated water removal rate (user input), L/day

The Zone Dehumidifier Part-Load Ratio (output variable) is then calculated, with the result constrained to be from 0.0 to 1.0:

PLR=waterremovalloadtobemet˙mwater,ss,0.0≤PLR≤1.0

The steady-state and average electrical power consumed by the dehumidifier are calculated next using the following equations:

Pdehumid,ss=˙Vwater,rated(WaterRemovalModFac)(1000)EFrated(EFModFac)(24)

Pdehumid,avg=Pdehumid,ss(RTF)+(Poff−cycle(1−RTF))

where the 1000 and 24 are for conversion between kW and W, and days and hours, and:

Pdehumid,ss = dehumidifier steady-state electric power, W

Pdehumid,avg = Zone Dehumidifier Electric Power, W (output variable)

RTF=PLRPLF=ZoneDehumidifierRuntimeFraction(outputvariable)

E