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Mathematical Reference TRNSYS 16 a TRaNsient SYstem S imulation program Volume 5 Mathematical Reference Solar Energy Laboratory, Univ. of Wisconsin-Madison http://sel.me.wisc.edu/trnsys TRANSSOLAR Energietechnik GmbH http://www.transsolar.com CSTB – Centre Scientifique et Technique du Bâtiment http://software.cstb.fr TESS – Thermal Energy Systems Specialists http://www.tess-inc.com TRNSYS 16 – Mathematical Reference About This Manual The information presented in this manual is intended to provide a detailed mathematical reference for the Standard Component Library in TRNSYS 16. This manual is not intended to provide detailed reference information about the TRNSYS simulation software and its utility programs. More details can be found in other parts of the TRNSYS documentation set. The latest version of this manual is always available for registered users on the TRNSYS website (see here below). Revision history • 2004-09 For TRNSYS 16.00.0000 • 2005-02 For TRNSYS 16.00.0037 • 2006-03 For TRNSYS 16.01.0000 • 2007-03 For TRNSYS 16.01.0003 Where to find more information Further information about the program and its availability can be obtained from the TRNSYS website or from the TRNSYS coordinator at the Solar Energy Lab: TRNSYS Coordinator Email: [email protected] Solar Energy Laboratory, University of Wisconsin-Madison Phone: +1 (608) 263 1586 1500 Engineering Drive, 1303 Engineering Research Building Fax: +1 (608) 262 8464 Madison, WI 53706 – U.S.A. TRNSYS website: http://sel.me.wisc.edu/trnsys Notice This report was prepared as an account of work partially sponsored by the United States Government. Neither the United States or the United States Department of Energy, nor any of their employees, nor any of their contractors, subcontractors, or employees, including but not limited to the University of Wisconsin Solar Energy Laboratory, makes any warranty, expressed or implied, or assumes any liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. © 2006 by the Solar Energy Laboratory, University of Wisconsin-Madison The software described in this document is furnished under a license agreement. This manual and the software may be used or copied only under the terms of the license agreement. Except as permitted by any such license, no part of this manual may be copied or reproduced in any form or by any means without prior written consent from the Solar Energy Laboratory, University of Wisconsin-Madison. 5–2 TRNSYS 16 – Mathematical Reference TRNSYS Contributors S.A. Klein W.A. Beckman J.W. Mitchell J.A. Duffie N.A. Duffie T.L. Freeman J.C. Mitchell J.E. Braun B.L. Evans J.P. Kummer R.E. Urban A. Fiksel J.W. Thornton N.J. Blair P.M. Williams D.E. Bradley T.P. McDowell M. Kummert D.A. Arias Additional contributors who developed components that have been included in the Standard Library are listed in their respective section. Contributors to the building model (Type 56) and its interface (TRNBuild) are listed in Volume 6. Contributors to the TRNSYS Simulation Studio are listed in Volume 2. 5–3 TRNSYS 16 – Mathematical Reference 5–4 TRNSYS 16 – Mathematical Reference TABLE OF CONTENTS 5. MATHEMATICAL REFERENCE 5–9 5.1. Controllers 5–11 5.1.1. Type 2: Differential Controller 5–15 5.1.2. Type 8: Three Stage Room Thermostat 5–17 5.1.3. Type 22: Iterative Feedback Controller 5–19 5.1.4. Type 23: PID Controller 5–23 5.1.5. Type 40: Microprocessor Controller 5–28 5.1.6. Type 108: Five Stage Room Thermostat 5–34 5.2. Electrical 5–38 5.2.1. Type 47: Shepherd and Hyman Battery Models 5–39 5.2.2. Type 48: Regulator / Inverter 5–44 5.2.3. Type 50: PV-Thermal Collector 5–47 5.2.4. Type 90: Wind Energy Conversion System 5–49 5.2.5. Type 94: Photovoltaic array 5–67 5.2.6. Type 102: DEGS Dispatch controller 5–77 5.2.7. Type 120: Diesel Engine Generator Set 5–79 5.2.8. Type 175: Power conditioning unit 5–83 5.2.9. Type 180: Photovoltaic array (with data file) 5–85 5.2.10. Type 185: Lead-acid battery with gassing effects 5–91 5.2.11. Type 188: AC-busbar 5–97 5.2.12. Type 194: Photovoltaic array 5–99 5.3 Heat Exchangers 5–107 5.2.1 Type 5: Heat Exchanger 5–109 5.2.2 Type 17: Waste Heat Recovery 5–115 5.2.3 Type 91: Constant Effectiveness Heat Exchanger 5–117 5.3 HVAC 5–119 5.3.1 Type 6: Auxiliary heater 5–121 5.3.2 Type 20: Dual Source Heat Pump 5–123 5.3.3 Type 32: Simplified Cooling Coil 5–127 5.3.4 Type 42: Conditioning Equipment 5–131 5.3.5 Type 43: Part Load Performance 5–133 5.3.6 Type 51: Cooling Tower 5–135 5.3.7 Type 52: Detailed Cooling Coil 5–141 5.3.8 Type 53: Parallel Chillers 5–149 5.3.9 Type 92: ON/OFF Auxiliary Cooling Device 5–153 5.3.10 Type 107: Single Effect Hot Water Fired Absorption Chiller 5–155 5.3.11 Type 121: Simple Furnace / Air Heater 5–161 5–5 TRNSYS 16 – Mathematical Reference 5.4 Hydrogen Systems 5–163 5.4.1 Type 100: Electrolyzer controller 5–165 5.4.2 Type 105: Master level controller for SAPS 5–167 5.4.3 Type 160: Advanced Alkaline Electrolyzer 5–171 5.4.4 Type 164: Compressed gas storage 5–177 5.4.5 Type 167: Multistage compressor 5–179 5.4.6 Type 170: Proton-Exchange Membrane Fuel Cell 5–181 5.4.7 Type 173: Alkaline Fuel Cell 5–189 5.5 Hydronics 5–191 5.5.1 Type 3: Variable Speed Pump or Fan without Humidity Effects 5–193 5.5.2 Type 11: Tee Piece, Flow Diverter, Flow Mixer, Tempering Valve 5–195 5.5.3 Type 13: Pressure Relief Valve 5–199 5.5.4 Type 31: Pipe Or Duct 5–201 5.5.5 Type 110: Variable Speed Pump 5–204 5.5.6 Type 111: Variable Speed Fan/Blower with Humidity Effects 5–206 5.5.7 Type 112: Single Speed Fan/Blower with Humidity Effects 5–208 5.5.8 Type 114: Constant Speed Pump 5–210 5.6 Loads and Structures 5–212 5.6.1 Type 12: Energy/(Degree Day) Space Heating or Cooling Load 5–214 5.6.2 Type 18: Pitched Roof and Attic 5–220 5.6.3 Type 19: Detailed Zone (Transfer Function) 5–224 5.6.4 Type 34: Overhang and Wingwall Shading 5–237 5.6.5 Type 35: Window with Variable Insulation 5–241 5.6.6 Type 36: Thermal Storage Wall 5–243 5.6.7 Type 37: Attached Sunspace 5–249 5.6.8 Type 56: Multi-Zone Building and TRNBuild 5–253 5.6.9 Type 88: Lumped Capacitance BuildingType 5–255 5.7 Obsolete 5–257 5.8 Output 5–259 5.8.1 Type 25: Printer 5–261 5.8.2 Type 27: Histogram plotter 5–263 5.8.3 Type 28: Simulation Summary 5–265 5.8.4 Type 29: Economic analysis 5–272 5.8.5 Type 65: Online plotter 5–280 5.9 Physical Phenomena 5–284 5.9.1 Type 16: Solar Radiation Processor 5–286 5.9.2 Type 30: Collector Array Shading 5–296 5.9.3 Type 33: Psychrometrics 5–300 5.9.4 Type 54: Hourly Weather Data Generator 5–302 5.9.5 Type 58: Refrigerant Properties 5–306 5–6 TRNSYS 16 – Mathematical Reference 5.9.6 Type 59: Lumped capacitance model 5–308 5.9.7 Type63: Thermodynamic properties of substances with NASA CEA2 5–309 5.9.8 Type 64: Shading By External Object with Single Shading Mask 5–311 5.9.9 Type 67: Shading By External Object 5–313 5.9.10 Type 68: Shading By External Object 5–323 5.9.11 Type 69: Effective Sky Temperature 5–325 5.9.12 Type 77: Simple Ground Temperature Profile 5–327 5.9.13 Type 80: Calculation of Convective Heat Transfer Coefficients 5–329 5.10 Solar Thermal Collectors 5–331 5.10.1 Type 1: Flat-plate collector (Quadratic efficiency) 5–333 5.10.2 Type 45: Thermosyphon collector with integral collector storage 5–339 5.10.3 Type71: Evacuated tube solar collector 5–345 5.10.4 Type 72: Performance Map Solar Collector 5–351 5.10.5 Type 73: Theoretical flat-plate collector 5–357 5.10.6 Type 74: Compound Parabolic Concentrating Collector 5–361 5.11 Thermal Storage 5–367 5.11.1 Type 4: Stratified Fluid Storage Tank 5–369 5.11.2 Type 10: Rock bed storage 5–375 5.11.3 Type 38: Algebraic tank (Plug-flow) 5–379 5.11.4 Type 39: Variable volume tank 5–385 5.11.5 Type 60: Stratified fluid storage tank with internal heat exchangers 5–389 5.12 Utility 5–395 5.12.1 Type 9: Data reader (Generic data files) 5–397 5.12.2 Type14: Time dependent forcing function 5–408 5.12.3 Type 21: Time Values 5–410 5.12.4 Type 24: Quantity integrator 5–412 5.12.5 Type 41: Forcing function sequencer 5–414 5.12.6 Type 55: Periodic integrator 5–416 5.12.7 Type 57: Unit conversion routine 5–420 5.12.8 Type 62: Calling Excel 5–426 5.12.9 Type 66: Calling Engineering Equation Solver (EES) Routines 5–428 5.12.10 Type 70: Parameter replacement 5–432 5.12.11 Type 81: 1D interpolation from file 5–435 5.12.12 Type 83: Differentiation of a signal 5–436 5.12.13 Type 84: Moving Average 5–438 5.12.14 Type 89: Weather data reader (standard format) 5–440 5.12.15 Type 93: Input value recall 5–442 5.12.16 Type 95: Holiday calculator 5–444 5.12.17 Type 96: Utility rate schedule processor 5–448 5.12.18 Type 97: Calling CONTAM 5–456 5.12.19 Type 101: Calling FLUENT 5–459 5–7 TRNSYS 16 – Mathematical Reference 5.12.20 Type 155: Calling Matlab 5–461 5.12.21 Type157: Calling COMIS 5–466 5.13 Weather Data Reading and Processing 5–468 5.14.1 Type 15: Weather Data Processor 5–470 5.14.2 Type 109: Combined data reader and solar radiation processor 5–474 5.15.
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