ENERGYPLUS

COPYRIGHT 1996-2011 The Board of Trustees of the University of Illinois and the Regents of the University of California through the Ernest Orlando Lawrence Berkeley National Laboratory. All Rights Reserved. No part of this material may be reproduced or transmitted in any form or by any means without the prior written permission of the University of Illinois or the Ernest Orlando Lawrence Berkeley National Laboratory. EnergyPlus is a Trademark of the US Department of Energy.

EnergyPlus Engineering Reference

The Reference to EnergyPlus Calculations (in case you want or need to know)

Date: May 24, 2012

TABLE OF CONTENTS

5/24/12 i

Overview .......................................................................................................................................... 1

Document Overview ........................................................................................................ 1

General Modeling Overview ............................................................................................ 1

Simulation Manager ........................................................................................................ 1

Warmup Convergence .................................................................................................... 3

Integrated Solution Manager ........................................................................................................... 6

Basis for the Zone and Air System Integration................................................................. 7

Zone Sensible Heat Capacity Multiplier ................................................................... 10

Summary of Predictor-Corrector Procedure .................................................................. 11

Air System Control ........................................................................................................ 11

Moisture Predictor-Corrector ......................................................................................... 16

Moisture Prediction .................................................................................................. 17

Moisture Correction ................................................................................................. 19

Carbon Dioxide Predictor-Corrector .............................................................................. 20

Carbon Dioxide Prediction ....................................................................................... 22

Carbon Dioxide Correction ...................................................................................... 24

Generic Contaminant Predictor-Corrector ..................................................................... 24

Generic Contaminant Prediction .............................................................................. 26

Generic Contaminant Correction ............................................................................. 28

Summary of Time Marching Solution ............................................................................. 29

Summary of Timestep Model Formulation ............................................................... 29

Zone Update Method ............................................................................................... 30

Variable Timestep ................................................................................................... 31

Simultaneous Solution of Plant/System Water Loop ................................................ 32

References .............................................................................................................. 32

Surface Heat Balance Manager / Processes ................................................................................ 34

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Conduction Through The Walls ..................................................................................... 34

Conduction Transfer Function Module ..................................................................... 34

Calculation of Conduction Transfer Functions ......................................................... 35

Conduction Transfer Function (CTF) Calculations in EnergyPlus ............................ 37

Conduction Transfer Function (CTF) Calculations Special Case: R-Value Only Layers ............................................................................................................. 40

References .............................................................................................................. 42

Conduction Finite Difference Solution Algorithm ............................................................ 42

Basic Finite Difference Solution Approach ............................................................... 42

Finite Difference Node Arrangement in Surfaces ..................................................... 46

Conduction Finite Difference Variable Thermal Conductivity ................................... 47

Conduction Finite Difference Source Sink Layers .................................................... 47

References .............................................................................................................. 47

Combined Heat and Moisture Transfer (HAMT) Model .................................................. 48

Overview ................................................................................................................. 48

HAMT Nomenclature ............................................................................................... 48

HAMT Model Description ......................................................................................... 49

References .............................................................................................................. 53

Effective Moisture Penetration Depth (EMPD) Model .................................................... 53

Overview ................................................................................................................. 53

EMPD Model Description......................................................................................... 53

EMPD Value Determination ..................................................................................... 55

EMPD Nomenclature ............................................................................................... 55

References .............................................................................................................. 56

Outside Surface Heat Balance ...................................................................................... 57

External Shortwave Radiation ................................................................................. 57

External Longwave Radiation .................................................................................. 57

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References .............................................................................................................. 60

Atmospheric Variation ............................................................................................. 60

Outdoor/Exterior Convection ................................................................................... 62

Exterior/External Conduction ................................................................................... 73

References .............................................................................................................. 73

Inside Heat Balance ...................................................................................................... 73

Internal Long-Wave Radiation Exchange ................................................................. 74

Internal Short-Wave Radiation ................................................................................. 76

Interior Conduction .................................................................................................. 76

Interior Convection .................................................................................................. 76

Adiabatic Boundary Conditions ..................................................................................... 93

Infrared Radiation Transfer Material .............................................................................. 94

Radiation Exchange Basics ..................................................................................... 96

Radiation Transfer Surface Details .......................................................................... 97

Behavior Checks ..................................................................................................... 97

Transparent Insulation Material (TIM) .......................................................................... 100

Introduction ........................................................................................................... 100

Comparison of Opaque and Transparent Insulation............................................... 101

Types of Transparent Insulation Materials ............................................................. 101

TIM- Basic Mathematical Model............................................................................. 102

Sample Test Run Cases: Comparison ................................................................ 104

References ............................................................................................................ 106

Surface Heat Balance With Moveable Insulation ......................................................... 106

Basic Heat Balance Cases .................................................................................... 106

Heat Balance Cases .............................................................................................. 108

Fortran Algorithm Examples .................................................................................. 110

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Fortran Variable Descriptions ................................................................................ 111

References ............................................................................................................ 114

Ground Heat Transfer Calculations using C and F Factor Constructions ..................... 114

Advanced Surface Concepts ....................................................................................................... 117

Exterior Naturally Vented Cavity ................................................................................. 117

Baffle Heat Balance ............................................................................................... 117

Cavity Heat Balance .............................................................................................. 119

Underlying Heat Transfer Surface ......................................................................... 121

Solar and Shading Calculations ............................................................................. 121

Local Wind Speed Calculations ............................................................................. 121

Convection Coefficients ......................................................................................... 122

Radiation Coefficients ............................................................................................ 122

References ............................................................................................................ 123

Green Roof Model (EcoRoof) ...................................................................................... 123

Overview ............................................................................................................... 123

Green Roof Model Description .............................................................................. 124

Linearization .......................................................................................................... 129

Final Equations ...................................................................................................... 130

Green Roof Nomenclature ..................................................................................... 131

References ............................................................................................................ 132

Climate, Sky and Solar/Shading Calculations ............................................................................. 134

Climate Calculations.................................................................................................... 134

EnergyPlus Design Day Temperature Calculations ............................................... 134

Sky Radiation Modeling ......................................................................................... 135

EnergyPlus Sky Temperature Calculation ............................................................. 136

EnergyPlus Design Day Solar Radiation Calculations ........................................... 136

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Perez Direct/Diffuse Splitting Model ...................................................................... 139

Weather File Solar Interpolation ............................................................................ 139

References ............................................................................................................ 139

Design Week Specification .......................................................................................... 139

Sky Radiance Model ................................................................................................... 140

Sky Diffuse Solar Radiation on a Tilted Surface .................................................... 142

Shadowing of Sky Diffuse Solar Radiation ............................................................. 143

Shadowing of Sky Long-Wave Radiation ............................................................... 144

Shading Module .......................................................................................................... 145

Shading and Sunlit Area Calculations .................................................................... 145

Solar Position ........................................................................................................ 145

Surface Geometry ................................................................................................. 147

Shadow Projection................................................................................................. 149

Homogeneous Coordinates ................................................................................... 152

Polygon Clipping Algorithms .................................................................................. 152

Overlapping Shadows ........................................................................................... 153

Solar Gains ........................................................................................................... 157

Solar Distribution ................................................................................................... 157

Details of the Interior Solar Distribution Calculation ............................................... 159

Ground Reflectances ............................................................................................. 164

Ground Reflectances (Snow) ................................................................................. 164

References ............................................................................................................ 164

Solar Radiation Reflected from Exterior Surfaces ...................................................................... 166

Diffuse Reflection of Beam Solar and Sky Solar Radiation .......................................... 167

Receiving points .................................................................................................... 168

Rays ...................................................................................................................... 168

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Sky Solar Radiation Diffusely Reflected from Obstructions .................................... 169

Sky Solar Radiation Diffusely Reflected from the Ground ...................................... 170

Beam Solar Radiation Diffusely Reflected from Obstructions ................................ 171

Beam Solar Radiation Diffusely Reflected from the Ground ................................... 171

Beam Solar Radiation Specularly Reflected from Obstructions ............................. 172

Daylighting and Window Calculations ......................................................................................... 174

Daylighting Calculations .............................................................................................. 174

Daylight Factor Calculation.......................................................................................... 175

Overview ............................................................................................................... 178

Interior Illuminance Components ........................................................................... 178

Daylight Factors .................................................................................................... 179

Sky Luminance Distributions ................................................................................. 179

Direct Normal Solar Illuminance ............................................................................ 181

Exterior Horizontal Illuminance .............................................................................. 181

Direct Component of Interior Daylight Illuminance ................................................. 182

Internally-Reflected Component of Interior Daylight Illuminance ............................ 184

Transmitted Flux from Sky and Ground ................................................................. 185

Transmitted Flux from Direct Sun .......................................................................... 186

Luminance of Shaded Window .............................................................................. 187

Daylight Discomfort Glare ...................................................................................... 187

Time-Step Daylighting Calculation ............................................................................... 189

Overview ............................................................................................................... 189

Time-Step Sky Luminance ..................................................................................... 191

Interior Illuminance ................................................................................................ 192

Glare Index ............................................................................................................ 193

Lighting Control System Simulation ....................................................................... 194

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References ............................................................................................................ 196

DElight Daylighting Calculations .................................................................................. 197

DElight Daylight Factor Calculation Differences from EnergyPlus Detailed Methods ................................................................................................................ 198

DElight Time-Step Interior Daylighting Calculation Differences from EnergyPlus Detailed Methods ............................................................................... 199

References ............................................................................................................ 200

Daylighting Devices ..................................................................................................... 200

Tubular Daylighting Devices .................................................................................. 200

Daylighting Shelves ............................................................................................... 208

Window Light Well ................................................................................................. 211

Window Calculation Module ........................................................................................ 213

Optical Properties of Glazing ................................................................................. 213

Glass Layer Properties .......................................................................................... 216

Glass Optical Properties Conversion ..................................................................... 216

Simple Window Model ........................................................................................... 217

Glazing System Properties .................................................................................... 222

Calculation of Angular Properties .......................................................................... 225

Calculation of Hemispherical Values ..................................................................... 228

Optical Properties of Window Shading Devices ..................................................... 228

Thermochromic Windows ...................................................................................... 231

Window Heat Balance Calculation ............................................................................... 262

The Glazing Heat Balance Equations .................................................................... 263

Room-Side Convection .......................................................................................... 265

Solving the Glazing Heat Balance Equations ......................................................... 266

Edge-Of-Glass Effects ........................................................................................... 267

Apportioning of Absorbed Short-Wave Radiation in Shading Device Layers ................................................................................................................... 270

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Window Frame and Divider Calculation ................................................................ 271

Beam Solar Reflection from Window Reveal Surfaces .......................................... 277

Shading Device Thermal Model ............................................................................. 286

Heat Balance Equations for Shading Device and Adjacent Glass .......................... 286

Solving for Gap Airflow and Temperature .............................................................. 288

Heat Balance Equations for Between-Glass Shading Device ................................ 294

Airflow Windows .................................................................................................... 298

References ............................................................................................................ 302

Air Heat Balance Manager / Processes ...................................................................................... 304

Convection from Surfaces ........................................................................................... 304

Convection from Internal Sources ............................................................................... 304

Infiltration/Ventilation ................................................................................................... 304

Infiltration ............................................................................................................... 304

Infiltration Design Flow Rate .................................................................................. 304

Infiltration by Effective Leakage Area .................................................................... 305

Infiltration by Flow Coefficient ................................................................................ 306

Ventilation ............................................................................................................. 306

Ventilation Design Flow Rate ................................................................................. 306

Ventilation by Wind and Stack with Open Area ...................................................... 307

Zone Air Balance Outdoor Airflow (ZoneAirBalance:OutdoorAir) ........................... 308

Reference .............................................................................................................. 309

Air Exchange ............................................................................................................... 309

Temperature Difference Controlled Air Exchange .................................................. 310

Density Difference Controlled Air Exchange .......................................................... 311

References ............................................................................................................ 313

Calculation of Zone Air Temperature ........................................................................... 313

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Building System Simulation System Manager / Processes ........................................................ 314

Air Loops ..................................................................................................................... 314

Definition of Air Loop ............................................................................................. 314

Simulation Method ................................................................................................. 314

Component Models ............................................................................................... 314

Iteration Scheme ................................................................................................... 315

Determination of Air Mass Flow Rates ................................................................... 315

Air Loop Simulation ..................................................................................................... 315

Primary Air System Simulation .................................................................................... 316

Input data .............................................................................................................. 317

Initialization Calculations ....................................................................................... 317

Central air system simulation ................................................................................. 319

Outdoor Air System ..................................................................................................... 320

Simulation ............................................................................................................. 320

Outdoor Air Mixer ........................................................................................................ 320

Simulation ............................................................................................................. 321

Zone Equipment Simulation ........................................................................................ 321

Input data .............................................................................................................. 321

Initialization Calculations ....................................................................................... 322

Simulation ............................................................................................................. 322

Air Path Components .................................................................................................. 323

Overview ............................................................................................................... 323

Zone Supply Air Path ............................................................................................. 323

Zone Splitter .......................................................................................................... 324

Zone Supply Plenum ............................................................................................. 324

Zone Return Air Path ............................................................................................. 324

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Zone Mixer ............................................................................................................ 324

Zone Return Plenum ............................................................................................. 325

Plant Load Profile ........................................................................................................ 325

Calculation Model .................................................................................................. 325

Plant/Condenser Loops ............................................................................................... 326

Integration of System and Plant ............................................................................. 326

Current Primary System Modeling Methodology .................................................... 326

Plant Manager ....................................................................................................... 329

Plant Flow Resolver ............................................................................................... 329

Summary of Load Distribution Schemes ................................................................ 336

Summary of Plant Loop Demand Calculation Schemes ......................................... 337

Plant and Condenser Equipment Operation Schemes ........................................... 338

Plant Operation Schemes ...................................................................................... 338

Condenser Operation Schemes............................................................................. 339

Primary-Secondary Loop Systems ........................................................................ 340

Heat Recovery Loop Systems ............................................................................... 342

Plant Pressure Drop Simulation ............................................................................. 343

Steam Systems and Component Models ..................................................................... 347

Steam Loop Assumptions ...................................................................................... 348

Steam To Air Heat Exchanger ............................................................................... 352

Condensate Pump ................................................................................................. 358

Steam Pipe ............................................................................................................ 360

Loop, Equipment Sizing and other Design Data ......................................................................... 362

Sizing Manager ........................................................................................................... 362

Zone Design Loads and Air Flow Rates ...................................................................... 363

Overview ............................................................................................................... 363

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Zone Design Data Arrays ...................................................................................... 363

Zone Design Load Calculation ............................................................................... 365

Updating and Adjusting the Zone Results .............................................................. 366

System Design Loads and Air Flow Rates ................................................................... 367

Overview ............................................................................................................... 367

System Design Data Arrays ................................................................................... 368

System Design Flow Rate and Load Summation and Adjustment ......................... 369

Plant Loop Sizing ........................................................................................................ 375

Introduction ........................................................................................................... 375

Hot and Chilled Water Loop Sizing ........................................................................ 376

Condenser Loop Sizing ......................................................................................... 376

Component Sizing ....................................................................................................... 376

Introduction ........................................................................................................... 376

Fan Sizing ............................................................................................................. 376

Coil:Cooling:Water................................................................................................. 377

Coil:Cooling:Water:DetailedGeometry Sizing......................................................... 380

Coil:Cooling:WaterToAirHeatPump:EquationFit Sizing .......................................... 382

Coil:Cooling:WaterToAirHeatPump:VariableSpeedEquationFit Sizing ................... 384

Coil:Heating:WaterToAirHeatPump:EquationFit Sizing .......................................... 385

Coil:Heating:WaterToAirHeatPump:VariableSpeedEquationFit Sizing ................... 385

Coil:Heating:Water Sizing ...................................................................................... 385

Coil:Heating:Steam Sizing ..................................................................................... 387

Sizing of Gas and Electric Heating Coils ................................................................ 388

DX Coil Sizing ....................................................................................................... 389

DX MultiSpeed Coil Sizing ..................................................................................... 392

Pump Sizing .......................................................................................................... 392

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Electric Chiller Sizing ............................................................................................. 392

Humidifier Sizing ................................................................................................... 393

Cooling Tower Sizing ............................................................................................. 394

Fluid Cooler Sizing ................................................................................................ 396

Evaporative Fluid cooler Sizing ............................................................................. 398

Fan Coil Unit Sizing ............................................................................................... 400

Window Air Conditioner Sizing .............................................................................. 401

Unit Ventilator Sizing ............................................................................................. 401

Packaged Terminal Heat Pump Sizing .................................................................. 402

MultiSpeed Heat Pump Sizing ............................................................................... 403

Single Duct Terminal Units .................................................................................... 403

Indirect Evaporative Cooler Sizing ......................................................................... 405

Zone Outdoor Air Design Data .................................................................................... 405

Design Outdoor Air Calculation.............................................................................. 406

References ............................................................................................................ 407

Demand Limiting .......................................................................................................................... 409

Algorithm ............................................................................................................... 409

Alternative Modeling Processes .................................................................................................. 411

RoomAir Models .................................................................................................... 411

User Defined RoomAir Temperatures .................................................................... 412

One-Node Displacement Ventilation RoomAir Model ............................................. 414

Three-Node Displacement Ventilation RoomAir Model .......................................... 417

Under-Floor Air Distribution Interior Zone Model .................................................... 426

Under-Floor Air Distribtuion Exterior Zone Model .................................................. 435

Cross Ventilation Room Air Model ......................................................................... 442

AirflowNetwork Model .................................................................................................. 460

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Overview ............................................................................................................... 460

Model Description .................................................................................................. 460

Pressure and Airflow Calculations ......................................................................... 461

Node Temperature Calculations ............................................................................ 475

Node Humidity Ratio Calculations ......................................................................... 477

Sensible and Latent Load Calculations .................................................................. 478

Impacts of Supply Air Fan Control on Load: Cycling vs. Continuous ...................... 479

Integration of the AirflowNetwork Model ................................................................ 481

Model Output ......................................................................................................... 481

References ............................................................................................................ 481

Simulation Models Encyclopedic Reference ............................................................................ 483

Air System Distribution Terminals ................................................................................ 483

Constant Volume Single Duct Uncontrolled Air Terminal ....................................... 483

Constant Volume Single Duct Reheat Air Terminal................................................ 483

Variable Air Volume Single Duct Reheat and No Reheat Air Terminals ................. 484

Variable Air Volume Heating and Cooling Single Duct Reheat and NoReheat Air Terminal .......................................................................................... 485

Constant Volume Single Duct Four Pipe Induction Air Terminal ............................ 488

Fan Powered Induction Series and Parallel Single Duct Reheat Air Terminal ................................................................................................................ 490

Variable Air Volume Fan Powered Single Duct Air Terminal .................................. 493

Cooled Beam Unit (AirTerminal:SingleDuct:ConstantVolume:CooledBeam) ....................................... 495

Constant Volume Dual Duct Air Terminal .............................................................. 498

Variable Air Volume Dual Duct Air Terminal .......................................................... 499

Dual Duct Dedicated Outside Air Terminal with VAV Cooling ................................ 501

Boilers ......................................................................................................................... 503

Simple Hot Water Boiler ........................................................................................ 503

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Steam Boiler .......................................................................................................... 505

Chillers ........................................................................................................................ 511

Absorption Chiller .................................................................................................. 511

Indirect Absorption Chiller...................................................................................... 515

Combustion Turbine Chiller ................................................................................... 521

ChillerHeater:Absorption:DirectFired ..................................................................... 523

ChillerHeater:Absorption:DoubleEffect .................................................................. 527

Constant COP Chiller ............................................................................................ 532

Hot Water Heat Recovery from Chillers ................................................................. 533

Electric Chiller Model Based on Fluid Temperature Differences ............................ 535

Electric Chiller Model Based on Condenser Entering Temperature ....................... 536

Electric Chiller Model Based on Condenser Leaving Temperature ........................ 545

Engine Driven Chiller ............................................................................................. 551

Ice Thermal Storage .................................................................................................... 553

Simple Ice Storage Model ...................................................................................... 553

Detailed Ice Storage Model ................................................................................... 555

Coils ............................................................................................................................ 558

Chilled-Water-Based Air Cooling Coil .................................................................... 558

Chilled-Water-Based Detailed Geometry Air Cooling Coil ...................................... 571

Hot-Water-Based Air Heating Coil ......................................................................... 577

Single-Speed Electric DX Air Cooling Coil ............................................................. 580

Multi-Speed Electric DX Air Cooling Coil ............................................................... 601

Two-Speed Electric DX Air Cooling Coil ................................................................ 608

Electric Air Heating Coil ......................................................................................... 609

Gas Air Heating Coil .............................................................................................. 610

Single-Speed Electric Heat Pump DX Air Heating Coil .......................................... 611

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Single-Speed DX Heating Coil Standard Ratings .................................................. 619

Multi-Speed Electric Heat Pump DX Air Heating Coil ............................................. 626

Desuperheater-Recovery-Based Air Heating Coil .................................................. 631

Desuperheater-Recovery-Based Water Heating Coil ............................................. 637

Heat Exchanger Assisted Air Cooling Coil Systems ............................................... 642

Single-Speed Electric Heat Pump DX Water Heating Coil ..................................... 647

Water Source Electric DX Air Cooling Coil ............................................................. 656

Water Source Electric Heat Pump DX Air Heating Coil .......................................... 656

Steam-Based Air Heating Coil ............................................................................... 656

Variable Refrigerant Flow Cooling Coil .................................................................. 656

Variable Refrigerant Flow Heating Coil .................................................................. 663

Variable Speed Water to Air Heat Pump (Heating & Cooling) ................................ 663

HVAC Controllers ........................................................................................................ 679

Control Valve for Water-Based Air System Coils ................................................... 679

Outdoor Air Damper Controller for Air Systems ..................................................... 682

Outdoor Air Damper Controller for Zone Energy Recovery Ventilator .................... 688

Baseboard Heaters ..................................................................................................... 690

Hot Water Baseboard Heater with Only Convection .............................................. 690

Electric Baseboard Heater with Only Convection ................................................... 691

Hot Water Baseboard Heater with Radiation and Convection ................................ 692

Electric Baseboard Heater with Radiation and Convection .......................................... 695

Overview ............................................................................................................... 695

Model Description .................................................................................................. 696

Steam Baseboard Heater with Radiation and Convection...................................... 697

Cooling Towers and Evaporative Fluid Coolers ........................................................... 699

One and Two Speed Cooling Towers and Evaporative Fluid Coolers .................... 699

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Variable Speed Cooling Towers ............................................................................ 705

Cooling Towers with Multiple Cells ........................................................................ 714

Cooling Tower Makeup Water Usage .................................................................... 715

One and Two Speed Fluid Coolers ........................................................................ 718

Demand Controlled Ventilation .................................................................................... 721

Ventilation Rate Procedure .................................................................................... 722

Indoor Air Quality Procedure ................................................................................. 727

Proportional Control ............................................................................................... 727

References ............................................................................................................ 729

Evaporative Coolers .................................................................................................... 729

Direct Evaporative Cooler ...................................................................................... 729

Dry Coil Indirect Evaporative Cooler ...................................................................... 732

Wet Coil Indirect Evaporative Cooler ..................................................................... 734

Two Stage Direct/Indirect Evaporative Cooler ....................................................... 736

Indirect Evaporative Cooler Special Research Model ............................................ 737

Direct Evaporative Cooler Special Research Model ............................................... 741

Air System Fans .......................................................................................................... 743

Overview ............................................................................................................... 743

Model .................................................................................................................... 743

References ............................................................................................................ 762

Air System Compound Component Groups ................................................................. 763

Forced-Air Furnace and Central Air Conditioning .................................................. 763

Unitary Systems .................................................................................................... 773

Unitary System with Changeover-Bypass-Variable Air Volume ............................. 773

Unitary Single Speed Air-To-Air Heat Pump .......................................................... 781

Unitary Multi-Speed Air-To-Air Heat Pump ............................................................ 790

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DX Cooling Package ............................................................................................. 801

DX Heating Package ............................................................................................. 802

Desiccant Dehumidifier Package ........................................................................... 803

Unitary Single Speed Water-To-Air Heat Pump ..................................................... 806

Water To Water Heat Pumps ................................................................................. 813

Equation Fit Water To Water Heat Pump Model .................................................... 813

Parameter Estimation Water-To-Water Heat Pump Model ..................................... 816

Variable Refrigerant Flow Heat Pumps........................................................................ 821

Variable Refrigerant Flow Air Conditioner Model ................................................... 821

Zone Terminal Unit List ......................................................................................... 839

Heat Exchangers ......................................................................................................... 840

Air System Air-To-Air Sensible and Latent Effectiveness Heat Exchanger ............ 840

Air System Air-To-Air Flat Plate Heat Exchanger ................................................... 853

Air System Air-To-Air Balanced Flow Desiccant Heat Exchanger .......................... 853

Plant Loop Deep-Ground-To-Water Vertical U-Tube Field Heat Exchanger ............................................................................................................. 863

Plant Loop Pond-To-Water Heat Exchanger .......................................................... 872

Plant Loop Surface-Ground-To-Water Heat Exchanger ......................................... 877

Plant Loop Water-To-Water Free Cooling Hydronic Heat Exchanger .................... 879

Plant Loop Water Side Economizer ....................................................................... 880

References ............................................................................................................ 884

Air System Humidifiers ................................................................................................ 884

Overview ............................................................................................................... 884

Electric Steam Humidifier ...................................................................................... 884

Zone Internal Gains ..................................................................................................... 887

Sources and Types of Gains ................................................................................. 887

Heat Gain from Lights ............................................................................................ 888

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Heat Gain from People .......................................................................................... 888

Heat Gain from Baseboard Heat............................................................................ 889

Distribution of Radiant Gains ................................................................................. 890

References ............................................................................................................ 891

Pipes ........................................................................................................................... 891

Heat Transfer Pipes (Objects: Pipe:Indoor & Pipe:Outdoor) .................................. 891

Underground Pipe (Object: Pipe:Underground) ..................................................... 894

PipingSystem:Underground Simulation ................................................................. 896

Pumps ......................................................................................................................... 900

Summary of Pump Rules ....................................................................................... 900

Dynamic Pump Pressure Head ............................................................................. 901

Variable Speed Pump ............................................................................................ 901

Pressure-based Flow for Variable Speed Pumps .................................................. 902

Constant Speed Pump .......................................................................................... 903

Pressure-based Flow for Constant Speed Pumps ................................................. 903

Pump Heat Addition to the Loop ............................................................................ 904

Pump Heat Addition to Surrounding Zone ............................................................. 904

Headered Pumps .................................................................................................. 904

Condensate Pumps ............................................................................................... 905

Ideal Loads Air System ............................................................................................... 905

Overview ............................................................................................................... 905

Model .................................................................................................................... 905

References ............................................................................................................ 908

District Cooling ............................................................................................................ 908

District Heating ............................................................................................................ 908

Radiant System Models .............................................................................................. 908

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Low Temperature Radiant System Model .............................................................. 908

High Temperature Radiant Heater Model .............................................................. 933

Refrigeration Equipment .............................................................................................. 936

Overview ............................................................................................................... 936

Refrigeration Compressor Racks ........................................................................... 938

Refrigerated Cases................................................................................................ 945

Walk-In Coolers and Freezers ............................................................................... 958

Air Chillers and Air Chiller Sets .............................................................................. 962

Detailed Refrigeration Systems ............................................................................. 966

Secondary Refrigeration Systems ......................................................................... 981

Transcritical CO2 Refrigeration System ................................................................. 988

References ............................................................................................................ 993

Setpoint Managers ...................................................................................................... 995

Overview ............................................................................................................... 995

Scheduled ............................................................................................................. 996

Outdoor Air Reset .................................................................................................. 996

Single Zone Reheat Heating and Cooling .............................................................. 997

Single Zone Heating Only ...................................................................................... 997

Single Zone Cooling Only ...................................................................................... 998

Single Zone Minimum Humidity ............................................................................. 998

Single Zone Maximum Humidity ............................................................................ 999

Mixed Air ............................................................................................................. 1000

Outdoor Air Pretreat ............................................................................................ 1000

Warmest Zone Supply Air Reset .......................................................................... 1000

Coldest Zone Supply Air Reset ............................................................................ 1001

Return Air Bypass Flow ....................................................................................... 1001

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Warmest Temp Flow ........................................................................................... 1001

Multizone Heating Average .................................................................................. 1002

Multizone Cooling Average .................................................................................. 1003

Multizone Minimum Humidity Average ................................................................. 1004

Multizone Maximum Humidity Average ................................................................ 1005

MultiZone Minimum Humidity Supply Air Reset ................................................... 1006

MultiZone Maximum Humidity Supply Air Reset .................................................. 1006

Follow Outdoor Air Temperature .......................................................................... 1007

Follow System Node Temperature ...................................................................... 1007

Follow Ground Temperature ................................................................................ 1008

Condenser Entering Water Temperature Reset ................................................... 1008

Ideal Condenser Entering Water Temperature Reset .......................................... 1011

Solar Collectors ......................................................................................................... 1012

Flat-Plate Solar Collectors ................................................................................... 1012

Integral-collector-storage (ICS) Solar Collector .................................................... 1015

References: ......................................................................................................... 1025

Photovoltaic Thermal Flat-Plate Solar Collectors ................................................. 1025

Unglazed Transpired Solar Collectors ................................................................. 1028

System Availability Managers .................................................................................... 1041

Overview ............................................................................................................. 1041

Scheduled ........................................................................................................... 1042

Scheduled On ...................................................................................................... 1042

Scheduled Off ...................................................................................................... 1042

Night Cycle .......................................................................................................... 1042

Night Ventilation .................................................................................................. 1043

Differential Thermostat ........................................................................................ 1043

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High Temperature Turn Off .................................................................................. 1044

High Temperature Turn On .................................................................................. 1044

Low Temperature Turn Off .................................................................................. 1044

Low Temperature Turn On .................................................................................. 1044

Hybrid Ventilation Control .................................................................................... 1045

Occupant Thermal Comfort ....................................................................................... 1047

Background on Thermal Comfort Models ............................................................ 1047

Mathematical Models for Predicting Thermal Comfort ......................................... 1049

Fanger Comfort Model ......................................................................................... 1050

Pierce Two-Node Model ...................................................................................... 1053

KSU Two-Node Model ......................................................................................... 1060

Adaptive Comfort Model Based on European Standard EN15251-2007 .............. 1067

Mean Radiant Temperature Calculation .............................................................. 1069

References .......................................................................................................... 1071

Trombe Walls ............................................................................................................ 1071

Passive Trombe Wall ........................................................................................... 1072

Active Trombe Wall ............................................................................................. 1075

Water Thermal Tanks (includes Water Heaters) ........................................................ 1077

Mixed Water Thermal Tank ................................................................................. 1077

Heat Pump Water Heater .................................................................................... 1083

Stratified Water Thermal Tank ............................................................................. 1089

Water Heating Sizing ........................................................................................... 1092

Water Systems .......................................................................................................... 1095

Water Mains Temperatures ................................................................................. 1095

Water Use Equipment and Connections .............................................................. 1096

Unconnected Water Use Equipment .................................................................... 1096

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Zone Heat Gain from Water Use Equipment........................................................ 1098

Connected Water Use Equipment ....................................................................... 1101

Water Use Equipment Calculations ..................................................................... 1103

Drainwater Heat Recovery ................................................................................... 1104

Zone Controls............................................................................................................ 1108

Thermostatic Zone Control .................................................................................. 1108

Zone Thermostats ............................................................................................... 1109

Operative Temperature Control ........................................................................... 1111

Temperature And Humidity Control ..................................................................... 1112

Humidistat ........................................................................................................... 1113

Thermal Comfort Zone Control ............................................................................ 1114

Zone Equipment and Zone Forced Air Units .............................................................. 1116

Air Distribution Terminal Unit ............................................................................... 1116

Simple Duct Leakage Model ................................................................................ 1117

Fan Coil Unit........................................................................................................ 1120

Window Air Conditioner ....................................................................................... 1120

Packaged Terminal Air Conditioner ..................................................................... 1120

Packaged Terminal Heat Pump ........................................................................... 1120

Zone Single Speed Water-To-Air Heat Pump ...................................................... 1120

Zone Air DX Dehumidifier .................................................................................... 1124

Energy Recovery Ventilator ................................................................................. 1129

Unit Heater .......................................................................................................... 1133

Unit Ventilator ...................................................................................................... 1134

Variable Refrigerant Flow Terminal Unit .............................................................. 1136

Ventilated Slab .................................................................................................... 1140

CoolTower ........................................................................................................... 1143

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Earthtube ............................................................................................................. 1147

Thermal Chimney Model ..................................................................................... 1153

Zone Outdoor Air Unit .......................................................................................... 1157

Controls ............................................................................................................... 1158

On-Site Generation .................................................................................................................... 1160

Electric Load Center Distribution Manager ................................................................ 1160

Overview ............................................................................................................. 1160

Electric Load Center Generators ......................................................................... 1165

Inverters .............................................................................................................. 1165

Electrical Storage ................................................................................................ 1165

Electrical Storage Kinetic Battery Model ........................................................... 1166

Electric Load Center Transformers ...................................................................... 1170

Photovoltaic Arrays ................................................................................................... 1173

Simple Model ....................................................................................................... 1173

Equivalent One-Diode Model ............................................................................... 1174

Sandia Photovoltaic Performance Model ............................................................. 1180

Generators ................................................................................................................ 1183

Internal Cumbustion Engine ................................................................................ 1183

Turbine Generator ............................................................................................... 1184

Microturbine Generator ........................................................................................ 1185

Micro-Cogenerator............................................................................................... 1195

Fuel Cell Cogenerator ......................................................................................... 1198

Custom Fuel Supply for Generators .................................................................... 1201

Wind Turbine ....................................................................................................... 1203

Performance Curves and Lookup Tables ................................................................................. 1210

Performance Curves ................................................................................................. 1210

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Curves based on a single independent variable .................................................. 1211

Curves based on two independent variables ....................................................... 1211

Curves based on three independent variables ..................................................... 1214

Pressure drop curve ............................................................................................ 1215

Performance Tables .................................................................................................. 1215

Tables based on a single independent variable ................................................... 1215

Tables based on two independent variables ........................................................ 1218

Economics Calculations ............................................................................................................ 1224

Component Costs ..................................................................................................... 1224

Line Item Costs ................................................................................................... 1224

Adjustments......................................................................................................... 1227

Comparisons ....................................................................................................... 1229

Tariff Computation ..................................................................................................... 1229

Conceptual Framework Variables and Hierarchy .............................................. 1229

Default Order of Computation .............................................................................. 1231

Computation Steps .............................................................................................. 1232

Life-Cycle Cost Computations ................................................................................... 1232

ExpressAsCashFlows .......................................................................................... 1233

ComputePresentValue ........................................................................................ 1233

ComputeTaxAndDepreciation .............................................................................. 1233

Special Modules/Reporting ........................................................................................................ 1235

Environmental Impacts .............................................................................................. 1235

Types of Pollutants .............................................................................................. 1235

Carbon Equivalent ............................................................................................... 1236

Fossil Fuel Emissions Factors ............................................................................. 1237

Off-Site Electricity Generation Emissions ............................................................ 1241

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Other Energy-Related Pollutants and Sources of Other Information .................... 1246

References .......................................................................................................... 1246

Overview Document Overview

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Overview

Document Overview

This document is organized to give you the best possible look into the EnergyPlus calculations. First, the concepts of modeling in EnergyPlus are presented. These include descriptions of the zone heat balance process, air loop/plant loop processes as well as other important processes for the building simulation. Discussions during the modeling process may reference specific object names as found in the Input/Output Reference document. The remainder of the document focuses on individual models.

General Modeling Overview

The EnergyPlus program is a collection of many program modules that work together to calculate the energy required for heating and cooling a building using a variety of systems and energy sources. It does this by simulating the building and associated energy systems when they are exposed to different environmental and operating conditions. The core of the simulation is a model of the building that is based on fundamental heat balance principles. Since it is relatively meaningless to state: based on fundamental heat balance principles, the model will be described in greater detail in later sections of this document in concert with the FORTRAN code which is used to describe the model. It turns out that the model itself is relatively simple compared with the data organization and control that is needed to simulate the great many combinations of system types, primary energy plant arrangements, schedules, and environments. The next section shows this overall organization in schematic form. Later sections will expand on the details within the blocks of the schematic.

Figure 1. EnergyPlus Program Schematic

Simulation Manager

The simulation manager of EnergyPlus is contained in a single module. The main subroutine is shown below. Flow within the entire program is managed using a series of flags. These paired flags, in order (from the highest to the lowest) are:

Overview Simulation Manager

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Table 1. Simulation Flags

BeginSimulationFlag EndSimulationFlag BeginEnvironmentFlag EndEnvironmentFlag(one to many days) BeginDayFlag EndDayFlag BeginHourFlag EndHourFlag BeginTimeStepFlag EndTimeStepFlag

There is also a WarmupFlag to signal that the program is in warmup state. The operation of these flags can be seen in the following subroutine. The advantage of using the flag system is that any subroutine throughout the code can determine the exact state of the simulation by checking the status of the flags.

Overview Warmup Convergence

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SUBROUTINE ManageSimulation ! Main driver routine for this module BeginSimFlag = .TRUE. EndSimFlag = .FALSE. CALL OpenOutputFiles CALL GetProjectData CALL GetEnvironmentInfo ! Get the number and type of Environments DO Envrn = 1, NumOfEnvrn ! Begin environment loop ... BeginEnvrnFlag = .TRUE. EndEnvrnFlag = .FALSE. WarmupFlag = .TRUE. DayOfSim = 0 DO WHILE ((DayOfSim.LT.NumOfDayInEnvrn).OR.(WarmupFlag)) ! Begin day loop ... DayOfSim = DayOfSim + 1 BeginDayFlag = .TRUE. EndDayFlag = .FALSE. DO HourOfDay = 1, 24 ! Begin hour loop ... BeginHourFlag = .TRUE. EndHourFlag = .FALSE. DO TimeStep = 1, NumOfTimeStepInHour ! Begin time step (TINC) loop ... BeginTimeStepFlag = .TRUE. EndTimeStepFlag = .FALSE. ! Set the End__Flag variables to true if necessary. Note that each flag builds on ! the previous level. EndDayFlag cannot be .true. unless EndHourFlag is also .true., etc. ! Note that the EndEnvrnFlag and the EndSimFlag cannot be set during warmup. ! Note also that BeginTimeStepFlag, EndTimeStepFlag, and the ! SubTimeStepFlags can/will be set/reset in the HVAC Manager. IF ((TimeStep.EQ.NumOfTimeStepInHour)) THEN EndHourFlag = .TRUE. IF (HourOfDay.EQ.24) THEN EndDayFlag = .TRUE. IF ((.NOT.WarmupFlag).AND.(DayOfSim.EQ.NumOfDayInEnvrn)) THEN EndEnvrnFlag = .TRUE. IF (Envrn.EQ.NumOfEnvrn) THEN EndSimFlag = .TRUE. END IF END IF END IF END IF CALL ManageWeather CALL ManageHeatBalance BeginHourFlag = .FALSE. BeginDayFlag = .FALSE. BeginEnvrnFlag = .FALSE. BeginSimFlag = .FALSE. END DO ! ... End time step (TINC) loop. END DO ! ... End hour loop. END DO ! ... End day loop. END DO ! ... End environment loop. CALL CloseOutputFiles RETURN END SUBROUTINE ManageSimulation

Warmup Convergence

Since everything in EnergyPlus is based on the foundation of the loads simulation, it stands to reason that any inaccuracies in the loads calculation will result in inaccuracies of similar or larger magnitude in the HVAC calculations. In the presumably limited cases where convergence was not truly achieved before the actual simulation began, it is unknown how much error would be introduced into the results. While simulations that last longer (annual vs. design day) will hopefully have any initial condition problems balanced by the shear number of days in the simulation, shorter simulationsparticularly those used for sizingcould result in relatively large errors. The simulation results could be unreliable and inaccurate when steady periodic conditions are not achieved. Therefore, it is important to properly determine when there is enough temperature and flux history terms to start an EnergyPlus simulation since this has a potential economic and energy impact on buildings that use EnergyPlus in design.

Overview Warmup Convergence

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EnergyPlus determines warmup convergence in the following manner as shown in the Figure 2 below. The process of the convergence checks begins by tracking four parameters such including the maximum zone air temperature, the minimum zone air temperature, the maximum heating load, and the maximum cooling load for individual zone. It is note that these convergence checks are only in effective in simulations with at least one zone since the criteria is solely based on the maximum and minimum values obtained from an individual zone. Differences in these parameters between two consecutive days are then compared with the convergence tolerance values at the end of the day during the warmup period. For example, the maximum and minimum air temperature and the percentage difference of zone load for each zone at 9:00AM during the second to last warmup is compared to the values at 9:00AM last warmup day as follows:

max, maxprev tolT T T < (1)

min, minprev tolT T T < (2)

,h h prevtol

h

q qq

q

< (3)

,c c prevtol

c

q qq

q

< (4)

where Tmax,prev is the maximum zone temperature of previous day, Tmax is the maximum zone temperature of current day, Ttol is the value of temperature tolerance, qh,prev is the maximum heating load of previous day, qh, is the maximum heating load of current day, qtol is the value of load tolerance, qc,prev is the maximum cooling load of previous day, and qc, is the maximum cooling load of current day.

Note that a minimum load of 100W is used to establish a fraction for the maximum loads when they are less than the minimum. This is done to avoid a false negative indication for the percentage load difference that may appear when zonal loads are very small. The convergence checks are repeated until passed for all zones. EnergyPlus assumes that the warmup period has been reached steady-periodic when these four parameters are within tolerance. Finally, temperature and load differences between the last two warmup days for individual zone at each time step in the last warmup day are reported so that users can easily track whether or not the warmup period has converged. The input parameters and output related to the warmup period are discussed in the Input-Output Reference.

Overview Warmup Convergence

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Figure 2. Flows of Warmup Convergence Checks

Integrated Solution Manager Warmup Convergence

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Integrated Solution Manager

EnergyPlus is an integrated simulation. This means that all three of the major parts, building, system, and plant, must be solved simultaneously. In programs with sequential simulation, such as BLAST or DOE-2, the building zones, air handling systems, and central plant equipment are simulated sequentially with no feedback from one to the other. The sequential solution begins with a zone heat balance that updates the zone conditions and determines the heating/cooling loads at all time steps. This information is fed to the air handling simulation to determine the system response; but that response does not affect zone conditions. Similarly, the system information is passed to the plant simulation without feedback. This simulation technique works well when the system response is a well-defined function of the air temperature of the conditioned space. For a cooling situation, a typical supply and demand situation is shown schematically in the Figure 3. Here, the operating point is at the intersection of the supply and demand curves.

Figure 3. Sequential Simulation Supply/Demand Relationship.

However, in most situations the system capacity is dependent on outside conditions and/or other parameters of the conditioned space. The simple supply and demand situation above becomes a more complex relationship and the system curve is not fixed. The solution should move up and down the demand curve. This doesnt happen in sequential simulation methods and the lack of feedback from the system to the building can lead to nonphysical results. For example, if the system provides too much cooling to a conditioned space the excess is reported by the program as "overcooling". Other categories of unmatched loads exist and are similarly reported by the program. While this kind of reporting enables the affected system or plant components to be properly sized, the system designer would, in most cases, prefer to see the actual change in zone temperature. The same mismatches can occur between the system and plant simulations when they are simulated sequentially. To obtain a simulation that is physically realistic, the elements have to be linked in a simultaneous solution scheme. The entire integrated program can be represented as a series of functional elements connected by fluid loops as shown in Figure Schematic of Simultaneous Solution Scheme. In EnergyPlus all the elements are integrated and controlled by the Integrated Solution Manager. The loops are divided into supply and demand sides, and the solution scheme generally relies on successive substitution iteration to reconcile supply and demand using the Gauss-Seidell philosophy of continuous updating.

Integrated Solution Manager Basis for the Zone and Air System Integration

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Figure 4. Schematic of Simultaneous Solution Scheme

In the sections which follow, the various individual functions of the integrated solution will be described.

Basis for the Zone and Air System Integration

The basis for the zone