Engineering Reference — EnergyPlus 8.3

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Chillers[LINK]

Absorption Chiller[LINK]

The input object Chiller:Absorption provides a model for absorption chillers that is an empirical model of a standard absorption refrigeration cycle. The condenser and evaporator are similar to that of a standard chiller, which are both water-to-water heat exchangers. The assembly of a generator and absorber provides the compression operation. Low-pressure vapor from the evaporator is absorbed by the liquid solution in the absorber. A pump receives low-pressure liquid from the absorber, elevates the pressure of the liquid, and delivers the liquid to the generator. In the generator, heat from a high temperature source (hot water or steam) drives off the vapor that has been absorbed by the solution. The liquid solution returns to the absorber through a throttling valve whose purpose is to provide a pressure drop to maintain the pressure difference between the generator and absorber. The heat supplied to the absorber can be waste heat from a diesel jacket, or the exhaust heat from diesel, gas, and steam turbines. For more information on absorption chillers, see the Input/Output Reference Document (Object: Chiller:Absorption).

The part-load ratio of the absoprtion chiller’s evaporator is simply the actual cooling effect produced by the chiller divided by the maximum cooling effect available.

PLR=˙Qevap˙Qevap,rated

where

PLR = part-load ratio of chiller evaporator

˙Qevap = chiller evaporator load [W]

˙Qevap,rated = rated chiller evaporator capacity [W]

This absorption chiller model is based on a polynomial fit of absorber performance data. The Generator Heat Input Part Load Ratio Curve is a quadratic equation that determines the ratio of the generator heat input to the demand on the chiller’s evaporator (Qevap).

GeneratorHeatInputRatio=C1PLR+C2+C3(PLR)

The Pump Electric Use Part Load Ratio Curve is a quadratic equation that determines the ratio of the actual absorber pumping power to the nominal pumping power.

ElectricInputRatio=C1+C2PLR+C3PLR2

Thus, the coefficient sets establish the ratio of heat power in-to-cooling effect produced as a function of part load ratio. The ratio of heat-power-in to cooling-effect-produced is the inverse of the coefficient of performance.

If the operating part-load ratio is greater than the minimum part-load ratio, the chiller will run the entire time step and cycling will not occur (i.e. CyclingFrac = 1). If the operating part-load ratio is less than the minimum part-load ratio, the chiller will be on for a fraction of the time step equal to CyclingFrac. Steam (or hot water) and pump electrical energy use are also calculated using the chiller part-load cycling fraction.

CyclingFrac=MIN(1,PLRPLRmin)

˙Qgenerator=GeneratorHeatInputRatio(˙Qevap)(CyclingFrac)

˙Qpump=ElectricInputRatio(Ppump)(CyclingFrac)

where

CyclingFrac = chiller part-load cycling fraction

PLRmin = chiller minimum part-load ratio

˙Qgenerator = generator input power [W]

˙Qpump = absorbtion chiller pumping power [W]

The evaporator water mass flow rate is calculated based on the Chiller Flow Mode as follows.

Constant Flow Chillers:

˙mevap=˙mevap,max

Variable Flow Chillers:

ΔTevap=Tevap,inTevap,SP

˙mevap=˙QevapCp,evap(ΔT)

where

˙mevap = chiller evaporator water mass flow rate (kg/s)

˙mevap,max = chiller design evaporator water mass flow rate (kg/s)

ΔTevap = chiller evaporator water temperature difference (ºC)

Tevap,in = chiller evaporator inlet water temperature (ºC)

Tevap,SP = chiller evaporator outlet water setpoint temperature (ºC)

Cp = specific heat of water entering evaporator (J/kg•ºC)

The evaporator outlet water temperature is then calculated based on the cooling effect produced and the evaporator entering water temperature.

Tevap,out=Tevap,in+˙QevapCp,evap(˙mevap)

where

Tevap,out = chiller evaporator outlet water temperature [ºC]

Tevap,in = chiller evaporator inlet water temperature [ºC]

Cp,evap = specific heat of chiller evaporator inlet water [J/kg/ºC]

˙mevap = chiller evaporator water mass flow rate [kg/s]

The condenser heat transfer and condenser leaving water temperature are also calculated.

˙Qcond=˙Qevap+˙Qgenerator+˙Qpump

Tcond,out=Tcond,in+˙QcondCp,cond(˙mcond)

where

˙Qcond = chiller condenser heat transfer rate [W]

Tcond,out = chiller condenser outlet water temperature [ºC]

Tcond,in = chiller condenser inlet water temperature [ºC]

Cp,cond = specific heat of chiller condenser inlet water [J/kg/ºC]

˙mcond = chiller condenser water mass flow rate [kg/s]

The absorption chiller can model the impact of steam or hot water entering the generator, although the connection of the steam (hot water) nodes to a plant is not actually required. The calculations specific to the generator depend on the type of fluid used and are described here in further detail.

Steam Loop Calculations[LINK]

When a steam loop is used and the inlet and outlet node names are specified (i.e. the nodes are connected to a steam loop), the generator outlet node steam mass flow rate and temperature are calculated based on the generator input power, latent heat of steam, the specific heat of water, and the amount of subcooling in the steam generator. The model assumes dry saturated steam enters the absorption chiller’s generator and exits the generator as a subcooled liquid. The temperature leaving the generator is calculated based on the user entered amount of liquid subcooling in the generator. The effect of subcooling of the liquid (condensate) in the pipe returning to the boiler is not modeled.

˙msteam=˙Qgeneratorhfg+cp,water×ΔTsc

Tgenerator,out=Tgenerator,inΔTsc

where

˙msteam = chiller steam mass flow rate [kg/s]

hfg = latent heat of steam [J/kg]

cp,water = specific heat of saturated water in the generator [J/Kg ºK]

ΔTsc = amount of subcooling in steam generator [ºC]

Tgenerator,out = generator steam outlet node temperature [ºC]

Tgenerator,in = generator steam inlet node temperature [ºC]

Hot Water Loop Calculations[LINK]

When a hot water loop is used and the inlet and outlet node names are specified (i.e. the nodes are connected to a hot water loop), the generator outlet node temperature is calculated based on the generator input power, mass flow rate of water, and the specific heat of water entering the hot water generator. The calculations are based on the Chiller Flow Mode as follows.

Constant Flow Chillers:

˙mgenerator=˙mgenerator,max

Variable Flow Chillers:

˙mgenerator=˙QgeneratorCp,water(ΔTgenerator)

Tgenerator,out=Tgenerator,in˙Qgenerator˙mgenerator(Cp,water)

where

˙mgenerator = generator hot water mass flow rate [kg/s]

˙mgenerator,max = generator design hot water mass flow rate (kg/s)

ΔTgenerator = generator design hot water temperature difference (ºC)

Indirect Absorption Chiller[LINK]

The Chiller:Absorption:Indirect object is an enhanced version of the absorption chiller model found in the Building Loads and System Thermodynamics (BLAST) program. This enhanced model is nearly identical to the existing absorption chiller model (Ref. Chiller:Absorption) with the exceptions that: 1) the enhanced indirect absorption chiller model provides more flexible performance curves and 2) chiller performance now includes the impact of varying evaporator, condenser, and generator temperatures. Since these absorption chiller models are nearly identical (i.e., the performance curves of the enhanced model can be manipulated to produce similar results to the previous model), it is quite probable that the Chiller:Absorption model will be deprecated in a future release of EnergyPlus.

The indirect absorption chiller’s condenser and evaporator are similar to that of a standard chiller, which are both water-to-water heat exchangers. The assembly of a generator and absorber provides the compression operation. A schematic of a single-stage absorption chiller is shown in the figure below. Low-pressure vapor from the evaporator is absorbed by the liquid solution in the absorber. A pump receives low-pressure liquid from the absorber, elevates the pressure of the liquid, and delivers the liquid to the generator. In the generator, heat from a high temperature source (hot water or steam) drives off the vapor that has been absorbed by the solution. The liquid solution returns to the absorber through a throttling valve whose purpose is to provide a pressure drop to maintain the pressure difference between the generator and absorber. The heat supplied to the generator can be either hot water or steam, however, connection to an actual plant loop is not required. For more information on indirect absorption chillers, see the Input/Output Reference Document (Object: Chiller:Absorption:Indirect).

Schematic Diagram of a Single-Stage Absorption Chiller

Schematic Diagram of a Single-Stage Absorption Chiller

The chiller cooling effect (capacity) will change with a change in condenser water temperature. Similarly, the chiller cooling effect will change as the temperature of the evaporator water changes. The chiller cooling effect will also change with a change in or generator inlet water temperature and only applies when Hot Water is used as the generator heat source. A quadratic or cubic equation is used to modify the rated chiller capacity as a function of both the condenser and generator inlet water temperatures and the evaporator outlet water temperature. If any or all of the capacity correction factor curves are not used, the correction factors are assumed to be 1.

CAPFTevaporator=a+b(Tevaporator)+c(Tevaporator)2+d(Tevaporator)3

CAPFTcondenser=e+f(Tcondenser)+g(Tcondenser)2+h(Tcondenser)3

CAPFTgenerator=i+j(Tgenerator)+k(Tgenerator)2+l(Tgenerator)3 (Hot Water only)

where

CAPFTevaporator = Capacity correction (function of evaporator temperature) factor

CAPFTcondenser= = Capacity correction (function of condenser temperature) factor

CAPFTgenerator = Capacity correction (function of generator temperature) factor

Tevaporator = evaporator outet water temperature [C]

Tcondenser = condenser inlet water temperature [C]

Tgenerator = generator inlet water temperature [C]

˙Qevap,max = maximum chiller capacity [W]

˙Qevap,rated = rated chiller capacity [W]

The part-load ratio of the indirect absoprtion chiller’s evaporator is simply the actual cooling effect required (load) divided by the maximum cooling effect available.

PLR=˙Qevap˙Qevap,max

where

PLR = part-load ratio of chiller evaporator

˙Qevap = chiller evaporator operating capacity [W]

The generator’s heat input is also a function of several parameters. The primary input for determining the heat input requirements is the Generator Heat Input function of Part-Load Ratio Curve. The curve is a quadratic or cubic equation that determines the ratio of the generator heat input to the chiller’s maximum capacity (Q~evap, max~) and is soley a function of part-load ratio. Typical generator heat input ratios at full load (i.e., PLR=1) are between 1 and 2. Two additional curves are available to modifiy the heat input requirement based on the generator inlet water temperature and the evaporator outlet water temperature.

GeneratorHIR=a+b(PLR)+c(PLR)2+d(PLR)3

GenfCondT=e+f(Tgenerator)+g(Tgenerator)2+h(Tgenerator)3

GenfEvapT=i+j(Tevaporator)+k(Tevaporator)2+l(Tevaporator)3

where

GeneratorHIR = ratio of generator heat input to chiller operating capacity

GenfCondT = heat input modifier based on generator inlet water temperature

GenfEvapT = heat input modifier based on evaporator outlet water temperature

The Pump Electric Use function of Part-Load Ratio Curve is a quadratic or cubic equation that determines the ratio of the actual absorber pumping power to the nominal pumping power.

ElectricInputRatio=a+b(PLR)+c(PLR)2+d(PLR)3

If the chiller operating part-load ratio is greater than the minimum part-load ratio, the chiller will run the entire time step and cycling will not occur (i.e. CyclingFrac = 1). If the operating part-load ratio is less than the minimum part-load ratio, the chiller will be on for a fraction of the time step equal to CyclingFrac. Generator heat input and pump electrical energy use are also calculated using the chiller part-load cycling fraction.

CyclingFrac=MIN(1.PLRPLRmin)

˙Qgenerator=GeneratorHIR(˙Qevap,max)(GenfCondT)(GenfEvapT)(CyclingFrac)

˙Qgenerator=ElectricInputRatio(Ppump)(CyclingFrac)

where

CyclingFrac = chiller part-load cycling fraction

PLRmin = chiller minimum part-load ratio

˙Qgenerator = generator heat input [W]

˙Qpump = chiller pumping power [W]

The evaporator water mass flow rate is calculated based on the Chiller Flow Mode as follows.

Constant Flow Chillers:

˙mevap=˙mevap,max

Variable Flow Chillers:

ΔTevap=Tevap,inTevap,SP

˙mevap=˙QevapCp,evap(ΔTevap)

where

˙mevap = chiller evaporator water mass flow rate (kg/s)

˙mevap,max = chiller design evaporator water mass flow rate (kg/s)

ΔTevap = chiller evaporator water temperature difference (ºC)

Tevap,in = chiller evaporator inlet water temperature (ºC)

Tevap,SP = chiller evaporator outlet water setpoint temperature (ºC)

Cp,evap = specific heat of water entering evaporator (J/kg ºC)

The evaporator outlet water temperature is then calculated based on the cooling effect produced and the evaporator entering water temperature.

Tevap,out=Tevap,in+˙QevapCp,evap(˙mevap)

where

Tevap,out = chiller evaporator outlet water temperature [ºC]

Tevap,in = chiller evaporator inlet water temperature [ºC]

Cp,evap = specific heat of chiller evaporator inlet water [J/kg/ºC]

˙mevap = chiller evaporator water mass flow rate [kg/s]

The condenser heat transfer and condenser leaving water temperature are also calculated.

˙Qcond=˙Qevap+˙Qgenerator+˙Qpump

Tcond,out=Tcond,in+˙QcondCp,cond(˙mcond)

where

˙Qcond = chiller condenser heat transfer rate [W]

Tcond,out = chiller condenser outlet water temperature [ºC]

Tcond,in = chiller condenser inlet water temperature [ºC]

Cp,cond = specific heat of chiller condenser inlet water [J/kg/ºC]

˙mcond = chiller condenser water mass flow rate [kg/s]

The absorption chiller can model the impact of steam or hot water entering the generator, although the connection of the steam (hot water) nodes to a plant is not actually required. The calculations specific to the generator depend on the type of fluid used and are described here in further detail.

Steam Loop Calculations[LINK]

When a steam loop is used and the inlet and outlet node names are specified (i.e. the nodes are connected to a steam loop), the generator outlet node steam mass flow rate and temperature are calculated based on the generator heat input, latent heat of steam, the specific heat of water, and the amount of subcooling in the steam generator. The model assumes dry saturated steam enters the generator and exits the generator as a subcooled liquid. The temperature leaving the generator is calculated based on the user entered amount of liquid subcooling in the generator. The effect of subcooling of the liquid (condensate) in the pipe returning to the boiler is also modeled using the user entered abount of steam condensate loop subcooling.

˙msteam=˙Qgeneratorhfg+cp,water×ΔTsc

Tgenerator,out=Tgenerator,inΔTsc

Tloop,out=Tgenerator,outΔTsc,loop

where

˙msteam = chiller steam mass flow rate [kg/s]

hfg = latent heat of steam [J/kg]

cp,water = specific heat of water [J/Kg ºC]

ΔTsc = amount of subcooling in steam generator [ºC]

ΔTsc,loop = amount of condensate subcooling in steam loop [ºC]

Tgenerator,out = generator steam outlet node temperature [ºC]

Tgenerator,in = generator steam inlet node temperature [ºC]

Hot Water Loop Calculations[LINK]

When a hot water loop is used and the inlet and outlet node names are specified (i.e. the nodes are connected to a hot water loop), the generator outlet node temperature is calculated based on the generator heat input, mass flow rate of water, and the specific heat of water entering the hot water generator. The calculations are based on the Chiller Flow Mode as follows.

Constant Flow Chillers:

˙mgenerator=˙mgenerator,max

Variable Flow Chillers:

˙mgenerator=˙QgeneratorCp,water(ΔTgenerator)

Tgenerator,out=Tgenerator,in˙Qgenerator˙mgenerator(Cp,water)

where

˙mgenerator = generator hot water mass flow rate [kg/s]

˙mgenerator,max = generator design hot water mass flow rate (kg/s)

ΔTgenerator = generator design hot water temperature difference (ºC)

Combustion Turbine Chiller[LINK]

The input object Chiller:CombustionTurbine provides a chiller model that is the empirical model from the Building Loads and System Thermodynamics (BLAST) program. Fitting catalog data to a third order polynomial equations generates the chiller performance curves. Three sets of coefficients are required to model the open centrifugal chiller as discussed in the section, titled, ‘Electric Chiller Based on BLAST Centrifugal Chiller Model’.

The gas turbine-driven chiller is an open centrifugal chiller driven directly by a gas turbine. The BLAST model of an open centrifugal chiller is modeled as standard vapor compression refrigeration cycle with a centrifugal compressor driven by a shaft power from an engine. The centrifugal compressor has the incoming fluid entering at the eye of a spinning impeller that throws the fluid by centrifugal force to the periphery of the impeller. After leaving the compressor, the refrigerant is condensed to liquid in a refrigerant to water condenser. The heat from the condenser is rejected to a cooling tower, evaporative condenser, or well water condenser depending on which one is selected by the user based on the physical parameters of the plant. The refrigerant pressure is then dropped through a throttling valve so that fluid can evaporate at a low pressure that provides cooling to the evaporator. The evaporator can chill water that is pumped to chilled water coils in the building. For more information, see the Input/Output Reference Document.

This chiller is modeled like the electric chiller with the same numerical curve fits and then some additional curve fits to model the turbine drive. Shown below are the definitions of the curves that describe this model.

The chiller’s temperature rise coefficient which is defined as the ratio of the required change in condenser water temperature to a given change in chilled water temperature, which maintains the capacity at the nominal value. This is calculated as the following ratio:

TCEntrequiredTCEntratedTELvrequiredTELvrated

Where:

TCEntrequired = Required entering condenser air or water temperature to maintain rated capacity.

TCEntrated = Rated entering condenser air or water temperature at rated capacity.

TELvrequired = Required leaving evaporator water outlet temperature to maintain rated capacity.

TELvrated = Rated leaving evaporator water outlet temperature at rated capacity.

The Capacity Ratio Curve is a quadratic equation that determines the Ratio of Available Capacity to Nominal Capacity. The defining equation is:

AvailToNominalCapacityRatio=C1+C2Δtemp+C3Δ2temp

Where the Delta Temperature is defined as:

ΔTemp=TempCondInTempCondInDesignTempRiseCoefficient(TempEvapOutTempEvapOutDesign)

TempCondIn = Temperature entering the condenser (water or air temperature depending on condenser type).

TempCondInDesign = Temp Design Condenser Inlet from User input above.

TempEvapOut = Temperature leaving the evaporator.

TempEvapOutDesign = Temp Design Evaporator Outlet from User input above.

TempRiseCoefficient = User Input from above.

The following three fields contain the coefficients for the quadratic equation.

The Power Ratio Curve is a quadratic equation that determines the Ratio of Full Load to Power. The defining equation is:

FullLoadtoPowerRatio=C1+C2AvailToNominalCapRatio+C3AvailToNominalCapRatio2

The Full Load Ratio Curve is a quadratic equation that determines the fraction of full load power. The defining equation is:

FracFullLoadPower=C1+C2PartLoadRatio+C3PartLoadRatio2

The Fuel Input Curve is a polynomial equation that determines the Ratio of Fuel Input to Energy Output. The equation combines both the Fuel Input Curve Coefficients and the Temperature Based Fuel Input Curve Coefficients. The defining equation is:

FuelEnergyInput=PLoad(FIC1+FIC2RLoad+FIC3RLoad2)(TBFIC1+TBFIC2ATair+TBFIC3AT2air)

Where FIC represents the Fuel Input Curve Coefficients, TBFIC represents the Temperature Based Fuel Input Curve Coefficients, Rload is the Ratio of Load to Combustion Turbine Engine Capacity, and ATairis the difference between the current ambient and design ambient temperatures.

The Exhaust Flow Curve is a quadratic equation that determines the Ratio of Exhaust Gas Flow Rate to Engine Capacity. The defining equation is:

  • ExhaustFlowRate=GTCapacity(C1+C2ATair+C3AT2air) * **

Where GTCapacity is the Combustion Turbine Engine Capacity, and ATair is the difference between the current ambient and design ambient temperatures.

The Exhaust Gas Temperature Curve is a polynomial equation that determines the Exhaust Gas Temperature. The equation combines both the Exhaust Gas Temperature Curve Coefficients (Based on the Part Load Ratio) and the (Ambient) Temperature Based Exhaust Gas Temperature Curve Coefficients. The defining equation is:

ExhaustTemperature=(C1+C2RLoad+C3RLoad2)(TBC1+TBC2ATair+TBC3AT2air)273.15

Where C represents the Exhaust Gas Temperature Curve Coefficients, TBC are the Temperature Based Exhaust Gas Temperature Curve Coefficients, RLoad is the Ratio of Load to Combustion Turbine Engine Capacity, and ATair is the difference between the actual ambient and design ambient temperatures.

The Recovery Lubricant Heat Curve is a quadratic equation that determines the recovery lube energy. The defining equation is:

RecoveryLubeEnergy=PLoad(C1+C2RL+C3RL2)

Where Pload is the engine load and RL is the Ratio of Load to Combustion Turbine Engine Capacity

The UA is an equation that determines the overall heat transfer coefficient for the exhaust gasses with the stack. The heat transfer coefficient ultimately helps determine the exhaust stack temperature. The defining equation is:

UAToCapacityRatio=C1GasTurbineEngineCapacityC2

Chiller Basin Heater[LINK]

This chiller’s basin heater (for evaporatively-cooled condenser type) operates in the same manner as the Engine driven chiller’s basin heater. The calculations for the chiller basin heater are described in detail at the end of the engine driven chiller description (Ref. Engine Driven Chiller).

ChillerHeater:Absorption:DirectFired[LINK]

Overview[LINK]

This model (object name ChillerHeater:Absorption:DirectFired) simulates the performance of a direct fired two-stage absorption chiller with optional heating capability. The model is based on the direct fired absorption chiller model (ABSORG-CHLR) in the DOE-2.1 building energy simulation program. The EnergyPlus model contains all of the features of the DOE-2.1 chiller model, plus some additional capabilities.

This model simulates the thermal performance of the chiller and the fuel consumption of the burner(s). This model does not simulate the thermal performance or the power consumption of associated pumps or cooling towers. This auxiliary equipment must be modeled using other EnergyPlus models (e.g. Cooling Tower:Single Speed).

Model Description[LINK]

The chiller model uses user-supplied performance information at design conditions along with five performance curves (curve objects) for cooling capacity and efficiency to determine chiller operation at off-design conditions. Two additional performance curves for heating capacity and efficiency are used when the chiller is operating in a heating only mode or simultaneous cooling and heating mode.

Cooling[LINK]

The following nomenclature is used in the cooling equations:

AvailCoolCap=available full-load cooling capacity at current conditions [W]

CEIR=user input “Electric Input to Cooling Output Ratio”

CEIRfPLR=electric input to cooling output factor, equal to 1 at full load, user input “Electric Input to Cooling Output Ratio Function of Part Load Ratio Curve Name”

CEIRfT=electric input to cooling output factor, equal to 1 at design conditions, user input “Electric Input to Cooling Output Ratio Function of Temperature Curve Name”

CFIR=user input “Fuel Input to Cooling Output Ratio”

CFIRfPLR=fuel input to cooling output factor, equal to 1 at full load, user input “Fuel Input to Cooling Output Ratio Function of Part Load Ratio Curve Name”

CFIRfT=fuel input to cooling output factor, equal to 1 at design conditions, user input “Fuel Input to Cooling Output Ratio Function of Temperature Curve Name”

CondenserLoad=condenser heat rejection load [W]

CoolCapfT=cooling capacity factor, equal to 1 at design conditions, user input “Cooling Capacity Function of Temperature Curve Name”

CoolElectricPower=cooling electricity input [W]

CoolFuelInput=cooling fuel input [W]

CoolingLoad=current cooling load on the chiller [W]

CPLR=cooling part-load ratio = CoolingLoad / AvailCoolCap

HeatingLoad=current heating load on the chiller heater [W]

HFIR=user input “Fuel Input to Heating Output Ratio”

HPLR=heating part-load ratio = HeatingLoad / AvailHeatCap

MinPLR=user input “Minimum Part Load Ratio”

NomCoolCap=user input “Nominal Cooling Capacity” [W]

RunFrac=fraction of time step which the chiller is running

Tcond=entering or leaving condenser fluid temperature [C]. For a water-cooled condenser this will be the water temperature returning from the condenser loop (e.g., leaving the cooling tower) if the entering condenser fluid temperature option is used. For air- or evap-cooled condensers this will be the entering outdoor air dry-bulb or wet-bulb temperature, respectively, if the entering condenser fluid temperature option is used.

Tcw,l=leaving chilled water temperature [C]

Five performance curves are used in the calculation of cooling capacity and efficiency:

  1. Cooling Capacity Function of Temperature Curve

  2. Fuel Input to Cooling Output Ratio Function of Temperature Curve

  3. Fuel Input to Cooling Output Ratio Function of Part Load Ratio Curve

  4. Electric Input to Cooling Output Ratio Function of Temperature Curve

  5. Electric Input to Cooling Output Ratio Function of Part Load Ratio Curve

The cooling capacity function of temperature (CoolCapfT) curve represents the fraction of the cooling capacity of the chiller as it varies by temperature. This a biquadratic curve with the input variables being the leaving chilled water temperature and either the entering or leaving condenser fluid temperature. The output of this curve is multiplied by the nominal cooling capacity to give the full-load cooling capacity at specific temperature operating conditions (i.e., at temperatures different from the design temperatures). The curve should have a value of 1.0 at the design temperatures and flow rates specified in the input data file by the user. The biquadratic curve should be valid for the range of water temperatures anticipated for the simulation.

CoolCapfT=a+bTcw,l+cT2cw,l+dTcond+eT2cond+fTcw,lTcond

The available cooling capacity of the chiller is then computed as follows:

AvailCoolCap=NomCoolCapCoolCapfT(Tcw,l,Tcond)

The fuel input to cooling output ratio function of temperature (CFIRfT) curve represents the fraction of the fuel input to the chiller at full load as it varies by temperature. This a biquadratic curve with the input variables being the leaving chilled water temperature and either the entering or leaving condenser fluid temperature. The output of this curve is multiplied by the nominal fuel input to cooling output ratio (CFIR) to give the full-load fuel input to cooling capacity ratio at specific temperature operating conditions (i.e., at temperatures different from the design temperatures). The curve should have a value of 1.0 at the design temperatures and flow rates specified in the input data file by the user. The biquadratic curve should be valid for the range of water temperatures anticipated for the simulation.

CFIRfT=a+bTcw,l+cT2cw,l+dTcond+eT2cond+fTcw,lTcond

The fuel input to cooling output ratio function of part load ratio (CFIRfPLR) curve represents the fraction of the fuel input to the chiller as the load on the chiller varies at a given set of operating temperatures. The curve is normalized so that at full load the value of the curve should be 1.0. The curve is usually linear or quadratic.

CFIRfPLR=a+bCPLR+cCPLR2

The fraction of the time step during which the chiller heater is operating is computed as a function of the cooling and heating part-load ratios and the user-input minimum part-load ratio:

RunFrac=MIN(1.0,MAX(HPLR,CPLR)/MinPLR)

The cooling fuel input to the chiller is then computed as follows:

CoolFuelInput=AvailCoolCapRunFracCFIRCFIRfT(Tcw,l,Tcond)CFIRfPLR(CPLR)

The electric input to cooling output ratio as function of temperature (CEIRfT) curve represents the fraction of electricity to the chiller at full load as it varies by temperature. This a biquadratic curve with the input variables being the leaving chilled water temperature and either the entering or leaving condenser fluid temperature.

CEIRfT=a+bTcw,l+cT2cw,l+dTcond+eT2cond+fTcw,lTcond

The electric input to cooling output ratio function of part load ratio (CEIRfPLR) curve represents the fraction of electricity to the chiller as the load on the chiller varies at a given set of operating temperatures. The curve is normalized so that at full load the value of the curve should be 1.0. The curve is usually linear or quadratic.

CEIRfPLR=a+bCPLR+cCPLR2

The cooling electric input to the chiller is computed as follows:

CoolElectricPower=NomCoolCapRunFracCEIRCEIRfT(Tcw,l,Tcond)CEIRfPLR(CPLR)

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

The condenser load is computed as follows:

CondenserLoad=CoolingLoad+CoolFuelInputHFIR+CoolElectricPower

Heating[LINK]

The following nomenclature is used in the heating equations:

AvailHeatCap=available full-load heating capacity at current conditions [W]

CPLRh=cooling part-load ratio for heating curve = CoolingLoad / NomCoolCap

HeatCapfCPLR=heating capacity factor as a function of cooling part load ratio, equal to 1 at zero cooling load, user input “Heating Capacity Function of Cooling Capacity Curve Name”

HeatCoolCapRatio=user input “Heating to Cooling Capacity Ratio”

HeatElectricPower=heating electricity input [W]

HeatFuelInput=heating fuel input [W]

HeatingLoad=current heating load on the chiller [W]

HEIR=user input “Electric Input to Heating Output Ratio”

HFIR=user input “Fuel Input to Heating Output Ratio”

HFIRfHPLR=fuel input to heating output factor, equal to 1 at full load, user input “Fuel Input to Heat Output Ratio During Heating Only Operation Curve Name”

HPLR=heating part-load ratio = HeatingLoad / AvailHeatCap

MinPLR=user input “Minimum Part Load Ratio”

NomCoolCap=user input “Nominal Cooling Capacity” [W]

RunFrac=fraction of time step which the chiller is running

TotalElectricPower=total electricity input [W]

TotalFuelInput=total fuel input [W]

Cooling is the primary purpose of the Direct Fired Absorption Chiller so that function is satisfied first and if energy is available for providing heating that is provided next.

The two performance curves for heating capacity and efficiency are:

  1. Heating Capacity Function of Cooling Capacity Curve

  2. Fuel-Input-to Heat Output Ratio Function

The heating capacity function of cooling capacity curve (HeatCapfCool) determines how the heating capacity of the chiller varies with cooling capacity when the chiller is simultaneously heating and cooling. The curve is normalized so an input of 1.0 represents the nominal cooling capacity and an output of 1.0 represents the full heating capacity. An output of 1.0 should occur when the input is 0.0.

HeatCapfCPLR=a+bCPLRh+cCPLRh2

The available heating capacity is then computed as follows:

AvailHeatCap=NomCoolCapHeatCoolCapRatioHeatCapfCPLR(CPLRh)

The fuel input to heat output ratio curve (HFIRfHPLR) function is used to represent the fraction of fuel used as the heating load varies as a function of heating part load ratio. It is normalized so that a value of 1.0 is the full available heating capacity. The curve is usually linear or quadratic and will probably be similar to a boiler curve for most chillers.

HFIRfHPLR=a+bHPLR+cHPLR2

  • The fuel use rate when heating is computed as follows:

HeatFuelInput=AvailHeatCapHFIRHFIRfHPLR(HPLR)

The fraction of the time step during which the chiller is operating is computed as a function of the cooling and heating part-load ratios and the user-input minimum part-load ratio:

RunFrac=MIN(1.0,MAX(HPLR,CPLRh)/MinPLR)

The heating electric input to the chiller is computed as follows:

HeatElectricPower=NomCoolCapHeatCoolCapRatioHEIRRunFrac

If the chiller is delivering heating and cooling simultaneously, the parasitic electric load will be double-counted, so the following logic is applied:

IF(HeatElectricPowerCoolElectricPower)THENHeatElectricPower=0.0ELSEHeatElectricPower=HeatElectricPowerCoolElectricPowerENDIF

The total fuel and electric power input to the chiller is computed as shown below:

TotalElectricPower=HeatElectricPower+CoolElectricPowerTotalFuelInput=HeatFuelInput+CoolFuelInput

ChillerHeater:Absorption:DoubleEffect[LINK]

Overview[LINK]

This model (object name ChillerHeater:Absorption:DoubleEffect) simulates the performance of an exhaust fired two-stage (double effect) absorption chiller with optional heating capability. The model is based on the direct fired absorption chiller model (ABSORG-CHLR) in the DOE-2.1 building energy simulation program. The EnergyPlus model contains all of the features of the DOE-2.1 chiller model, plus some additional capabilities. The model uses the exhaust gas output from Microturbine.

This model simulates the thermal performance of the chiller and the thermal energy input to the chiller. This model does not simulate the thermal performance or the power consumption of associated pumps or cooling towers. This auxiliary equipment must be modeled using other EnergyPlus models (e.g. Cooling Tower:Single Speed).

Model Description[LINK]

The chiller model uses user-supplied performance information at design conditions along with five performance curves (curve objects) for cooling capacity and efficiency to determine chiller operation at off-design conditions. Two additional performance curves for heating capacity and efficiency are used when the chiller is operating in a heating only mode or simultaneous cooling and heating mode.

Cooling[LINK]

The following nomenclature is used in the cooling equations:

AvailCoolCap=available full-load cooling capacity at current conditions [W]

CEIR=user input “Electric Input to Cooling Output Ratio”

CEIRfPLR=electric input to cooling output factor, equal to 1 at full load, user input “Electric Input to Cooling Output Ratio Function of Part Load Ratio Curve Name”

CEIRfT=electric input to cooling output factor, equal to 1 at design conditions, user input “Electric Input to Cooling Output Ratio Function of Temperature Curve Name”

TeFIR=user input “Thermal Energy Input to Cooling Output Ratio”

TeFIRfPLR=thermal energy input to cooling output factor, equal to 1 at full load, user input “Thermal Energy Input to Cooling Output Ratio Function of Part Load Ratio Curve Name”

TeFIRfT=thermal energy input to cooling output factor, equal to 1 at design conditions, user input “Thermal Energy Input to Cooling Output Ratio Function of Temperature Curve Name”

CondenserLoad=condenser heat rejection load [W]

CoolCapfT=cooling capacity factor, equal to 1 at design conditions, user input “Cooling Capacity Function of Temperature Curve Name”

CoolElectricPower=cooling electricity input [W]

CoolThermalEnergyInput=cooling thermal energy input [W]

CoolingLoad=current cooling load on the chiller [W]

CPLR=cooling part-load ratio = CoolingLoad / AvailCoolCap

HeatingLoad=current heating load on the chiller heater [W]

HFIR=user input “Thermal Energy Input to Heating Output Ratio”

HPLR=heating part-load ratio = HeatingLoad / AvailHeatCap

˙mExhAir = exhaust air mass flow rate from microturbine (kg/s)

MinPLR=user input “Minimum Part Load Ratio”

NomCoolCap=user input “Nominal Cooling Capacity” [W]

RunFrac=fraction of time step which the chiller is running

Ta,o = exhaust air outlet temperature from microturbine entering the chiller (oC)

Tabs,gen,o = Temperature of exhaust leaving the chiller (the generator component of the absorption chiller)

Tcond = entering condenser fluid temperature [°C]. For a water-cooled condenser this will be the water temperature returning from the condenser loop (e.g., leaving the cooling tower). For air- or evap-cooled condensers this will be the entering outdoor air dry-bulb or wet-bulb temperature, respectively.

Tcw,l = leaving chilled water temperature [°C]

The selection of entering or leaving condense fluid temperature can be made through the optional field-Temperature Curve Input Variable.

Five performance curves are used in the calculation of cooling capacity and efficiency:

  1. Cooling Capacity Function of Temperature Curve

  2. Thermal Energy Input to Cooling Output Ratio Function of Temperature Curve

  3. Thermal Energy Input to Cooling Output Ratio Function of Part Load Ratio Curve

  4. Electric Input to Cooling Output Ratio Function of Temperature Curve

  5. Electric Input to Cooling Output Ratio Function of Part Load Ratio Curve

The cooling capacity function of temperature (CoolCapfT) curve represents the fraction of the cooling capacity of the chiller as it varies with temperature. This a biquadratic curve with the input variables being the leaving chilled water temperature and the entering condenser fluid temperature. The output of this curve is multiplied by the nominal cooling capacity to give the full-load cooling capacity at specific temperature operating conditions (i.e., at temperatures different from the design temperatures). The curve should have a value of 1.0 at the design temperatures and flow rates specified in the input data file by the user. The biquadratic curve should be valid for the range of water temperatures anticipated for the simulation.

CoolCapfT=a+bTcw,l+cT2cw,l+dTcond+eT2cond+fTcw,lTcond

The available cooling capacity of the chiller is then computed as follows:

AvailCoolCap=NomCoolCapCoolCapfT(Tcw,lTcond)

The thermal energy input to cooling output ratio function of temperature (TeFIRfT) curve represents the fraction of the thermal energy input to the chiller at full load as it varies with temperature. This a biquadratic curve with the input variables being the leaving chilled water temperature and the entering condenser fluid temperature. The output of this curve is multiplied by the nominal thermal energy input to cooling output ratio (TeFIR) to give the full-load thermal energy input to cooling capacity ratio at specific temperature operating conditions (i.e., at temperatures different from the design temperatures). The curve should have a value of 1.0 at the design temperatures and flow rates specified in the input data file by the user. The biquadratic curve should be valid for the range of water temperatures anticipated for the simulation.

TeFIRfT=a+bTcw,l+cT2cw,l+dTcond+eT2cond+fTcw,lTcond

The thermal energy input to cooling output ratio function of part load ratio (TeFIRfPLR) curve represents the fraction of the thermal energy input to the chiller as the load on the chiller varies at a given set of operating temperatures. The curve is normalized so that at full load the value of the curve should be 1.0. The curve is usually linear or quadratic.

TeFIRfPLR=a+bCPLR+cCPLR2

The fraction of the time step during which the chiller heater is operating is computed as a function of the cooling and heating part-load ratios and the user-input minimum part-load ratio:

RunFrac=MIN(1.0,MAX(HPLR,CPLR)/MinPLR)

The cooling thermal energy input to the chiller is then computed as follows:

CoolThermalEnergyInput=AvailCoolCapRunFracTeFIRTeFIRfT(Tcw,l,Tcond)TeFIRfPLR(CPLR)

To make sure that the exhaust mass flow rate and temperature from microturbine are sufficient to drive the chiller, the heat recovery potential is compared with the cooling thermal energy input to the chiller (CoolThermalEergyInput). The heat recovery potential should be greater than the CoolThermalEnergyInput. Heat recovery potential is calculated as:

QRecovery=˙mExhAirCpAir(Ta,oTAbs,gen,o)

Tabs,gen,ois the minimum temperature required for the proper operation of the double-effect chiller. It will be defaulted to 176°C.

The electric input to cooling output ratio as function of temperature (CEIRfT) curve represents the fraction of electricity to the chiller at full load as it varies with temperature. This a biquadratic curve with the input variables being the leaving chilled water temperature and either the entering or leaving condenser fluid temperature.

CEIRfT=a+bTcw,l+cT2cw,l+dTcond+eT2cond+fTcw,lTcond

The electric input to cooling output ratio function of part load ratio (CEIRfPLR) curve represents the fraction of electricity to the chiller as the load on the chiller varies at a given set of operating temperatures. The curve is normalized so that at full load the value of the curve should be 1.0. The curve is usually linear or quadratic.

CEIRfPLR=a+bCPLR+cCPLR2

The cooling electric input to the chiller is computed as follows:

CoolElectricPower=NomCoolCapRunFracCEIRCEIRfT(Tcw,l,Tcond)CEIRfPLR(CPLR)

All five of these cooling performance curves are accessed through EnergyPlus’ built-in performance curve equation manager (objects Curve:Linear, Curve:Quadratic and Curve:Biquadratic). It is not imperative that the user utilize all coefficients in the performance curve equations if their performance equation has fewer terms (e.g., if the user’s TeFIRfPLR performance curve is linear instead of quadratic, simply enter the values for a and b, and set coefficient c equal to zero). A set of curves derived from manufacturer’s data are also provided in the dataset (ExhaustFiredChiller.idf) is provided with E+ installation.

The condenser load is computed as follows:

CondenserLoad=CoolingLoad+CoolThermalEnergyInput/HFIR+CoolElectricPower

Heating[LINK]

The following nomenclature is used in the heating equations:

AvailHeatCap=available full-load heating capacity at current conditions [W]

CPLRh=cooling part-load ratio for heating curve = CoolingLoad / NomCoolCap

HeatCapfCPLR=heating capacity factor as a function of cooling part load ratio, equal to 1 at zero cooling load, user input “Heating Capacity Function of Cooling Capacity Curve Name”

HeatCoolCapRatio=user input “Heating to Cooling Capacity Ratio”

HeatElectricPower=heating electricity input [W]

HeatThermalEnergyInput= heating thermal energy input [W]

HeatingLoad=current heating load on the chiller [W]

HEIR=user input “Electric Input to Heating Output Ratio”

HFIR=user input “Thermal Energy Input to Heating Output Ratio”

HFIRfHPLR=thermal energy input to heating output factor, equal to 1 at full load, user input “Thermal Energy Input to Heat Output Ratio During Heating Only Operation Curve Name”

HPLR=heating part-load ratio = HeatingLoad / AvailHeatCap

MinPLR=user input “Minimum Part Load Ratio”

NomCoolCap=user input “Nominal Cooling Capacity” [W]

RunFrac=fraction of time step which the chiller is running

TotalElectricPower=total electricity input [W]

TotalThermalEnergyInput=total thermal energy input [W]

Cooling is the primary purpose of the Exhaust Fired Absorption Chiller so that function is satisfied first and if energy is available for providing heating that is provided next.

The two performance curves for heating capacity and efficiency are:

  1. Heating Capacity Function of Cooling Capacity Curve

  2. Thermal-Energy-Input-to Heat Output Ratio Function

The heating capacity function of cooling capacity curve (HeatCapfCPLR) determines how the heating capacity of the chiller varies with cooling capacity when the chiller is simultaneously heating and cooling. The curve is normalized so an input of 1.0 represents the nominal cooling capacity and an output of 1.0 represents the full heating capacity. An output of 1.0 should occur when the input is 0.0.

HeatCapfCPLR=a+bCPLRh+cCPLRh2

The available heating capacity is then computed as follows:

AvailHeatCap=NomCoolCapHeatCoolCapRatioHeatCapfCPLR(CPLRh)

The thermal energy input to heat output ratio curve (HFIRfHPLR) function is used to represent the fraction of thermal energy used as the heating load varies as a function of heating part load ratio. It is normalized so that a value of 1.0 is the full available heating capacity. The curve is usually linear or quadratic and will probably be similar to a boiler curve for most chillers.

HFIRfHPLR=a+bHPLR+cHPLR2

  • The thermal energy use rate when heating is computed as follows:

HeatThermalEnergyInput=AvailHeatCap.HFIR.HFIRfHPLR(HPLR)

The fraction of the time step during which the chiller is operating is computed as a function of the cooling and heating part-load ratios and the user-input minimum part-load ratio:

RunFrac=MIN(1.0,MAX(HPLR,CPLRh)/MinPLR)

The heating electric input to the chiller is computed as follows:

HeatElectricPower=NomCoolCapHeatCoolCapRatioHEIR.RunFrac

If the chiller is delivering heating and cooling simultaneously, the parasitic electric load would be double-counted, so the following logic is applied:

IF(HeatElectricPowerCoolElectricPower)THENHeatElectricPower=0.0ELSEHeatElectricPower=HeatElectricPowerCoolElectricPowerENDIF

The total thermal energy and electric power input to the chiller is computed as shown below:

TotalElectricPower=HeatElectricPower+CoolElectricPower

TotalThermalEnergyInput=HeatThermalEnergyInput+CoolThermalEnergyInput

References[LINK]

Personal communications with various absorption chiller manufacturers, March 2011.

Absorption Chillers and Heat Pumps, Keith Herold, Reinhard Radermacher and Sanford A. Klein (Mar 18, 1996).

Absorption systems for combined heat and power: The problem of part-load operation, ASHRAE Transactions, 2003, Vol 109, Part1.