Hybrid 2 Theory Manual

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HYBRID2- A HYBRID SYSTEM SIMULATION MODEL

THEORY MANUAL

J. F. ManwellA. Rogers

G. HaymanC. T. Avelar

J. G. McGowanU. Abdulwahid

K. Wu

Renewable Energy Research LaboratoryDepartment of Mechanical EngineeringUNIVERSITY OF MASSACHUSETTS

June 30, 2006

submitted to

National Renewable Energy Laboratory

Subcontract No. XL-1-11126-1-1

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Abstract

This report describes the theoretical basis for Hybrid2, a computer simulation model for hybridpower systems. Hybrid power systems are designed for the generation and use of electricalpower. They are independent of a large, centralized electricity grid and incorporate more thanone type of power source. They may range in size from relatively large island grids to individualhousehold power supplies.

This hybrid system computer model, developed at the University of Massachusetts and theNational Renewable Energy Laboratory, is a comprehensive, flexible, user friendly model thatallows a wide range of choices of system components and operating strategies. In general, ahybrid system might contain alternating current (AC) diesel generators, direct current (DC) dieselgenerators, an AC distribution system, a DC distribution system, loads, renewable power sources,energy storage, power converters, rotary converters, coupled diesel systems, dump loads, loadmanagement options, or a supervisory control system. Each of these can be modeled with theHybrid2 code with a structure designed to mirror as closely as possible the structure of actualhybrid power systems. The code itself is based on a combined time series/probabilistic method.

This manual describes the operation of hybrid power systems and describes the theory behind theHybrid2 computer code. It is intended to allow the user to understand the details of thecalculations and considerations involved in the modeling process. This theory manual is acompanion volume to the Hybrid2 User Manual (NREL/TP-440-21272), which describes thepractical aspects of using the model. In addition to providing a detailed description of thestructure of Hybrid2, this work discusses the principles of the model, including the details of thegoverning energy balance relationships. The individual module algorithms in the code(includingpower system, loads, renewable resource characterization, and economics) are described. Inaddition, major sections of the report are devoted to detailed summaries and documentation of thecode component and subsystem algorithms.

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Table of Contents

ABSTRACT...................................................................................................................... V

TABLE OF CONTENTS ............................................................................................... VI

LIST OF FIGURES .......................................................................................................XV

FORWARD ................................................................................................................ XVII

NOMENCLATURE..................................................................................................... XIX

1. INTRODUCTION......................................................................................................... 1

1.1OVERVIEW ................................................................................................................. 11.2HOW TO USE THE MANUAL ........................................................................................ 1

2. BACKGROUND ........................................................................................................... 3

2.1EXECUTIVE SUMMARY ............................................................................................... 3

2.2WHAT IS A HYBRID POWERSYSTEM? ........................................................................ 32.2.1 Hybrid Power Systems ....................................................................................... 42.2.2 AC Diesel Generators ........................................................................................ 42.2.3 DC Diesel Generators........................................................................................ 62.2.4 Distribution System............................................................................................ 62.2.5 DC Distribution ................................................................................................. 62.2.6 Loads.................................................................................................................. 62.2.7 Renewable Power Sources................................................................................. 6

Wind Turbines ........................................................................................................ 6Photovoltaic Panels................................................................................................. 7Other Renewable Power Sources............................................................................ 7

2.2.8 Storage ............................................................................................................... 72.2.9 Power Converters .............................................................................................. 72.2.10 Rotary Converters............................................................................................ 82.2.11 Synchronous Condensers ................................................................................. 82.2.12 Coupled Diesel Systems ................................................................................... 82.2.13 Dump Load....................................................................................................... 82.2.14 Load Management ........................................................................................... 92.2.15 Supervisory Control System............................................................................. 92.2.16 Hybrid Power Systems - Renewable Sources and Fuel Savings.................... 10

2.3HYBRID POWERSYSTEM MODELING ....................................................................... 11

3. STRUCTURE OF HYBRID2 MODEL .................................................................... 13

3.1EXECUTIVE SUMMARY ............................................................................................. 133.2STRUCTURE OF HYBRID2 ......................................................................................... 13

3.2.1 Simulation Preparation.................................................................................... 153.2.2 Simulation Engine............................................................................................ 163.2.3 Overview of Program Flow ............................................................................. 17

Project Definition.................................................................................................. 17Power System Definition ...................................................................................... 21Power System Control Definition......................................................................... 21

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Site/Resource Characteristics Definition .............................................................. 21Power System Components Definition................................................................. 21Initialize Load Data Files...................................................................................... 22Initialize Resource Data Files ............................................................................... 22Prepare Output Load Files .................................................................................... 22

Input Load Data .................................................................................................... 23Calculate Renewable Power ................................................................................. 23Calculate Net Loads.............................................................................................. 23Diesel Only ("Base Case") Calculations............................................................... 23Storage/No Storage ............................................................................................... 23Transfer of Excess Power ..................................................................................... 24Storage/Diesel Calculations .................................................................................. 24Storage/Coupled Diesel (Shaft Bus) ..................................................................... 25Storage / No Diesel Calculations .......................................................................... 25AC Diesel /No Storage Calculations..................................................................... 26Deferrable Loads................................................................................................... 26

Heat and Optional Loads ...................................................................................... 26Dump Load ........................................................................................................... 26Detailed Output..................................................................................................... 26Summaries............................................................................................................. 27Next Time Step ..................................................................................................... 27Battery Life ........................................................................................................... 27Totals and Averages.............................................................................................. 27Summary Output................................................................................................... 27

4. PRINCIPLES OF HYBRID2 CODE ........................................................................ 28

4.1EXECUTIVE SUMMARY ............................................................................................. 284.2BACKGROUND -HYBRID SYSTEM OPERATION ......................................................... 284.3OVERVIEW OF PRINCIPLES OF HYBRID2CODE ......................................................... 304.4PRINCIPLES OF HYBRID2CODE ................................................................................ 30

4.4.1 Time Series/Probabilistic Method.................................................................... 30Details of the Time Series/Probabilistic Method.................................................. 31Application of Statistics in Hybrid2 ..................................................................... 34Theoretical Basis for Time Series/Probabilistic Method ...................................... 34

4.4.2 Energy Balance................................................................................................ 37Energy Balance Overview .................................................................................... 37Theory of Energy Balance .................................................................................... 38

4.4.3 Time Step.......................................................................................................... 38

5. MODULE ALGORITHMS AND PROGRAM OUTPUT...................................... 395.1EXECUTIVE SUMMARY ............................................................................................. 395.2POWERSYSTEM MODULE ........................................................................................ 39

5.2.1 Executive Summary.......................................................................................... 395.2.2 Description of Bus System ............................................................................... 405.2.3 Overview of Power Transfer Between Buses................................................... 41

Power Transfer with No Net Load Variability ..................................................... 41Power Transfer with Net Load Variability ........................................................... 41

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5.2.4 Theory of Power Transfer Between Buses Losses ........................................... 44Converter Rated Power Limit ............................................................................... 48Converter No Load Limit...................................................................................... 48Transfer Losses ..................................................................................................... 48Bus Net Loads After Transfer............................................................................... 49

Special Conditions ................................................................................................ 495.3LOADS MODULE....................................................................................................... 505.3.1 Executive Summary.......................................................................................... 505.3.2 Overview of Loads ........................................................................................... 51

Primary Loads....................................................................................................... 51Deferrable Loads................................................................................................... 51Optional and Heat Loads ...................................................................................... 51Dump Load ........................................................................................................... 52Unmet Load .......................................................................................................... 52

5.3.3 Details of Loads ............................................................................................... 52Primary Loads....................................................................................................... 52

Inputs..................................................................................................................... 52Deferrable Loads................................................................................................... 53Inputs..................................................................................................................... 53Block Average Deferrable Loads.......................................................................... 54Running Average Deferrable Loads ..................................................................... 55Comparison of Block Average and Running Average Deferrable Loads............. 56Optional Loads...................................................................................................... 57Inputs..................................................................................................................... 57Block Average Optional Loads............................................................................. 58Running Average Optional Loads ........................................................................ 58Comparison of Block Average and Running Average Optional Loads................ 58Heat Load.............................................................................................................. 59Inputs..................................................................................................................... 59Dump Load ........................................................................................................... 59Unmet Load .......................................................................................................... 60

5.4RENEWABLE RESOURCE MODULE............................................................................ 605.4.1 Executive Summary.......................................................................................... 605.4.2 Overview of Renewable Resource Characterization ....................................... 605.4.3 Details of Renewable Resource Characterization ........................................... 61

Wind Resource Characterization .......................................................................... 61Inputs..................................................................................................................... 61Solar Resource Characterization........................................................................... 62Inputs..................................................................................................................... 63

5.5ECONOMICS MODULE .............................................................................................. 635.5.1 Executive Summary.......................................................................................... 635.5.2 Model Overview............................................................................................... 64

Major Input ........................................................................................................... 64Output ................................................................................................................... 66

5.5.3 Economic Model Theory.................................................................................. 67Overall Model Basis and Overview...................................................................... 67

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Economics of New Hybrid Power Systems.......................................................... 68Economics of Retrofit Systems............................................................................. 78

5.6BASE CASE MODULE................................................................................................ 815.7PROGRAM OUTPUT................................................................................................... 81

5.7.1 Executive Summary.......................................................................................... 81

5.7.2 Performance Summary Files............................................................................ 815.7.3 Economics Summary Files............................................................................... 865.7.4 Detailed Files................................................................................................... 87

5.8DATA FILE GAP FILLER............................................................................................ 885.8.1 Executive Summary.......................................................................................... 885.8.2 Overview .......................................................................................................... 895.8.3 Description of Gap Filler................................................................................. 89

Markov Chain Method.......................................................................................... 905.8.4 Gap Filling in Solar Data ................................................................................ 915.8.5 Examples .......................................................................................................... 91

5.9DATA SYNTHESIZER................................................................................................. 95

5.9.1 Executive Summary.......................................................................................... 955.9.2 Overview .......................................................................................................... 955.9.3 Description of Data Synthesizer ...................................................................... 95

Step 1: Data Inputs................................................................................................ 97Step 2: Markov Process Transition Probability Matrix ........................................ 97Step 3: Generation of Time Series Using the Transition Probability Matrix ....... 98Step 4: Calculation of Actual Mean and Standard Deviation of Time Series ...... 98Step 5: Adjusting Time Series to Correct Mean and Standard Deviation ............ 98Step 6: Diurnal Scaling of Time Series................................................................. 98

5.9.4 Generation of the Transition Probability Matrix............................................. 98Overview............................................................................................................... 98Background ......................................................................................................... 101Target Long Term Probability Vector ................................................................ 101Weighting Matrix................................................................................................ 102Initial Probability Vector .................................................................................... 102Predicted Long Term Probability Vector............................................................ 102Autocorrelation Analysis .................................................................................... 103

5.9.5 Special Conditions ......................................................................................... 104Wind Speed......................................................................................................... 104Load .................................................................................................................... 105Solar Radiation.................................................................................................... 105

5.9.6 Comparisons of Predictions........................................................................... 106Wind Data ........................................................................................................... 107Load Data............................................................................................................ 108Solar Data............................................................................................................ 110

5.9.7 References ...................................................................................................... 112

6. COMPONENT ALGORITHMS............................................................................. 113

6.1WIND TURBINE PERFORMANCE MODEL ................................................................. 1136.1.1 Executive Summary........................................................................................ 1136.1.2 Model Overview............................................................................................. 114

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Major Input ......................................................................................................... 114Output ................................................................................................................. 114Major Modifiers.................................................................................................. 114

6.1.3 Detailed Parameter Description.................................................................... 115Modeling Input.................................................................................................... 115

Simulation Input.................................................................................................. 115Output ................................................................................................................. 115Modifiers............................................................................................................. 116

6.1.4 Model Theory ................................................................................................. 117Mean Wind Power .............................................................................................. 117Variability of Wind Power.................................................................................. 118Wind Turbine Power Curve Generation and Adjustment................................... 118Wind Speed......................................................................................................... 122Height Correction................................................................................................ 125Wind Speed Scale Factor .................................................................................... 125Air Density.......................................................................................................... 125

6.2PHOTOVOLTAIC PERFORMANCE MODEL ................................................................ 1266.2.1 Executive Summary........................................................................................ 1266.2.2 Model Overview............................................................................................. 127


6.2.3 Detailed Parameter Description.................................................................... 127Modeling Input.................................................................................................... 127Simulation Input.................................................................................................. 128Output ................................................................................................................. 128Modifiers............................................................................................................. 129

6.2.4 Model Theory ................................................................................................. 130Basic Photovoltaic Panel Model ......................................................................... 131Temperature Effects............................................................................................ 132Determination of PV Model Parameters............................................................. 132Determining Cell Temperature ........................................................................... 134Application of Theory to Find PV Panel Operating Characteristics................... 135Maximum Power Point Tracking........................................................................ 137Photovoltaic Panels/Battery Integration ............................................................. 138

6.3DIESEL GENERATORPERFORMANCE MODEL ......................................................... 1386.3.1 Executive Summary........................................................................................ 1386.3.2 Model Overview............................................................................................. 139



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6.3.4 Model Theory ................................................................................................. 140Fuel Consumption Characterization ................................................................... 140Minimum Run Time ........................................................................................... 141Minimum Power Level ....................................................................................... 141Back Drive Capability......................................................................................... 141

6.4BATTERY PERFORMANCE MODEL .......................................................................... 1426.4.1 Executive Summary........................................................................................ 1426.4.2 Model Overview............................................................................................. 142



6.4.4 Model Theory ................................................................................................. 144Capacity Model................................................................................................... 145Voltage Model .................................................................................................... 146Charge Transfer Model ....................................................................................... 147Battery Losses Model ......................................................................................... 148Battery Life ......................................................................................................... 149Battery Use and the Probabilistic Method .......................................................... 151Temperature Effects............................................................................................ 151

6.5DUMP PERFORMANCE MODEL................................................................................ 1526.5.1 Executive Summary........................................................................................ 1526.5.2 Model Overview............................................................................................. 152



6.5.4 Model Theory ................................................................................................. 1536.6CONVERTERPERFORMANCE MODEL...................................................................... 154

6.6.1 Executive Summary........................................................................................ 1546.6.2 Power Converter Model Overview ................................................................ 155

Major Inputs........................................................................................................ 155Major Outputs .................................................................................................... 155Major Modifiers.................................................................................................. 155

6.6.3 Detailed Parameter Description.................................................................... 155Modeling Input.................................................................................................... 155Simulation Input.................................................................................................. 155Output ................................................................................................................. 156

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Modifiers............................................................................................................. 1566.6.4 Model Theory ................................................................................................. 156

6.7COUPLED DIESEL MODEL ...................................................................................... 1576.7.1 Executive Summary........................................................................................ 1576.7.2 Model Overview............................................................................................. 158



6.7.4 Model Theory ................................................................................................. 159

7. SUBSYSTEM ALGORITHMS ............................................................................... 162

7.1MULTIPLE WIND TURBINES AND POWERSMOOTHING ........................................... 1627.1.1 Executive Summary........................................................................................ 1627.1.2 Model Overview............................................................................................. 162

Major Input ......................................................................................................... 162Restrictions ......................................................................................................... 163Output ................................................................................................................. 163Major Modifiers.................................................................................................. 163


7.1.4 Model Theory ................................................................................................. 164Total Mean Wind Power..................................................................................... 164Variability of Total Wind Power ........................................................................ 164

7.2PHOTOVOLTAIC ARRAY PERFORMANCE................................................................. 1687.2.1 Executive Summary........................................................................................ 1687.2.2 Photovoltaic Array Overview ........................................................................ 169

Major Inputs........................................................................................................ 169Output ................................................................................................................. 170Modifiers............................................................................................................. 170

7.2.3 Details of Solar Insolation Calculations........................................................ 170Model Input......................................................................................................... 170

Simulation Input.................................................................................................. 170Model Output ...................................................................................................... 171Modifiers............................................................................................................. 171

7.2.4 Theory of Solar Insolation Calculations........................................................ 1717.2.5 Multiple Panels in Photovoltaic Arrays......................................................... 178

7.3BATTERY BANK..................................................................................................... 1787.3.1 Executive Summary........................................................................................ 1787.3.2 Overview of Battery Bank Model................................................................... 178

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Major Inputs........................................................................................................ 178Major Outputs ..................................................................................................... 179

7.3.3 Details of Battery Calculations...................................................................... 1797.4DISPATCH MODEL.................................................................................................. 179

7.4.1Executive Summary..................................................................................... 179

7.4.2 Dispatch Overview ..................................................................................... 180Battery Dispatch ............................................................................................... 180Diesel Dispatch................................................................................................. 181Battery and Diesel Dispatch ........................................................................... 182

7.4.3 Detailed Dispatch Description .................................................................. 182Battery Dispatch Theory.................................................................................. 183Diesel Dispatch Theory ................................................................................... 184Battery and Diesel Dispatch Theory.............................................................. 187

7.5DIESEL FUEL USE................................................................................................... 1897.5.1 Executive Summary........................................................................................ 1897.5.2 Overview of Fuel Use Calculations ............................................................... 189

Single Diesel Operation ...................................................................................... 189Multiple Diesel Operation................................................................................... 1897.5.3 Details of Fuel Use Calculations................................................................... 190

Single Diesel Operation ...................................................................................... 190Multiple Diesel Operation................................................................................... 191

REFERENCES.............................................................................................................. 192

APPENDICES............................................................................................................... 195

APPENDIX 1-PROOF OF EQUATION 6.1.11................................................................... 195APPENDIX 2-PROOF OF EQUATION 6.2.13................................................................... 196APPENDIX 3FLOW CHARTS....................................................................................... 198

APPENDIX 4PSEUDO-GRID MODEL........................................................................... 233Executive Summary................................................................................................. 233Model Overview...................................................................................................... 233

Major input.......................................................................................................... 233Output ................................................................................................................. 233

Detailed Parameter Description............................................................................. 233Modeling Input.................................................................................................... 233Simulation Input.................................................................................................. 233Output ................................................................................................................. 233

Model Theory .......................................................................................................... 234APPENDIX 5OVERVIEW OF ECONOMIC EVALUATION OF PSEUDO-GRID OPERATION 235

Model Overview...................................................................................................... 235Economic Inputs ................................................................................................. 235Economic Outputs............................................................................................... 235

Detailed Parameter Description............................................................................. 235Economic Inputs ................................................................................................. 235Economic Outputs............................................................................................... 236

APPENDIX 6ELECTRICAL WIND WATER PUMP MODEL ............................................... 237Executive Summary................................................................................................. 237

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Model Overview...................................................................................................... 237Major input.......................................................................................................... 237Output ................................................................................................................. 237

Detailed Parameter Description............................................................................. 237Modeling Input.................................................................................................... 237

Simulation Input.................................................................................................. 239Output ................................................................................................................. 239Model Theory .......................................................................................................... 241

Overview of Operation of VVVF System .......................................................... 241Rotor Model ........................................................................................................ 243Gearbox Model ................................................................................................... 244The Permanent Magnet Alternator Model .......................................................... 245Induction Motor Model....................................................................................... 245Load Model......................................................................................................... 247Overall Electrical Model..................................................................................... 247Algorithm for Finding the Steady State .............................................................. 251

References ............................................................................................................... 255APPENDIX 7-SOLARINSOLATION DATA FIT-AUTOMATIC ADDITIONAL TIMECORRECTION FITTING .................................................................................................. 257

Introduction............................................................................................................. 257Problem Statement .................................................................................................. 257Solution and Implementation .................................................................................. 257

APPENDIX 8-NOTES REGARDING A MODEL FORPVPANEL PERFORMANCE............... 259Background ............................................................................................................. 259Inputs to Revised Model.......................................................................................... 259PV Model ................................................................................................................ 259Cell Temperature .................................................................................................... 262

INDEX............................................................................................................................ 263

FOR MORE INFORMATION.................................................................................... 267

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List of Figures

Figure 2.1. Hybrid Power System Configuration. ............................................................. 5Figure 2.2. Functions of Supervisory Control. ................................................................ 10

Figure 3.1. Schematic of Components and Subsystems in Hybrid2................................ 14Figure 3.2. Hybrid2 Engine Flow Chart (1 of 3). ............................................................ 18Figure 3.3. Continuation of Hybrid2 Engine Flow Chart (2 of 3). .................................. 19Figure 3.4. Continuation of Hybrid2 Engine Flow Chart (3 of 3). .................................. 20

Figure 4.1. Sample Fluctuating Load, Wind Power and Net Load.................................. 29Figure 4.2. Schematic of Energy Balance........................................................................ 37

Figure 5.1. Power System Configurations in Hybrid2..................................................... 40Figure 5.2. Histograms of Bus Power before and after Power Transfer (Example 1)..... 43Figure 5.3. Histograms of Bus Power before and after Power Transfer (Example 2)..... 43

Figure 5.4. Histograms of Bus Power before and after Power Transfer (Example 3)..... 44Figure 5.5. Diagram of Load Priority .............................................................................. 51Figure 5.6. Gap Filling in Noisy Data.............................................................................. 92Figure 5.7. Close Up of Filled Gap in Noisy Data........................................................... 93Figure 5.8. Gap Filling in Solar Data............................................................................... 93Figure 5.9. Close Up of Filled Gap in Solar Data............................................................ 94Figure 5.10 Flow Chart of Data Synthesis Procedure...................................................... 96Figure 5.12 Time Series of Real Wind Data................................................................... 107Figure 5.13 Time Series of Synthetic Wind Data ........................................................... 107Figure 5.14 Distribution of Real and Synthetic Wind Data............................................ 108Figure 5.15 Autocorrelation of Real and Synthetic Wind Data...................................... 108

Figure 5.16 Time Series of Real Load Data ................................................................... 109Figure 5.17 Time Series of Synthetic Load Data............................................................ 109Figure 5.18 Distribution of Real and Synthetic Load Data ............................................ 109Figure 5.19 Autocorrelation of Real and Synthetic Load Data ...................................... 110Figure 5.20 Diurnal Averages of Real and Synthetic Load Data ................................... 110Figure 5.21 Time Series of Real Solar Data ................................................................... 111Figure 5.22 Time Series of Synthetic Solar Data ........................................................... 111Figure 5.23 Distribution of Real and Synthetic Solar Clearness Index .......................... 111Figure 5.24 Autocorrelation of Real and Synthetic Solar Clearness Index.................... 112

Figure 6.1. Sample Wind Turbine Power Curve............................................................ 113

Figure 6.2. Sample Wind ............................................................................................... 123Figure 6.3. Histogram of Wind Data ............................................................................. 123Figure 6.4. Correlation vs. Lag ...................................................................................... 124Figure 6.5. Modified Power Curves............................................................................... 124Figure 6.6. Typical Current-Voltage Performance Curve for a PV Panel ..................... 130Figure 6.7. Equivalent Circuit of PV Generator ............................................................ 131Figure 6.8. Load Matching............................................................................................. 136Figure 6.9. Sample Diesel Engine Fuel Consumption with Linear Fit.......................... 139

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Figure 6.10. Battery Model............................................................................................ 144Figure 6.11. Sample Battery Discharge Voltage vs. Charge Removed. ........................ 146Figure 6.12. Battery Cycle Life vs. Depth of Discharge ............................................... 150Figure 6.13. Coupled Diesel and Shaft Bus Schematic ................................................. 157

Figure 7.1. Spatial Effects on Power Variability ........................................................... 168Figure 7.2. Diagram of Solar Radiation Calculation Scheme........................................ 169

Figure A6-1. Schematic of electric wind water pump with gearbox and capacitance.... 237Figure A6-2. Input window for electrical wind water pump model. .............................. 239Figure A6-3. Output window for electrical wind water pump model............................. 240Figure A6-4. Schematic of electric wind water pump with gearbox and capacitance.... 241Figure A6-5. Plot of power coefficient versus tip speed ratio for rotor model............... 244Figure A6-6. Single phase equivalent circuit of PMA.................................................... 245Figure A6-7. Single phase equivalent circuit of induction machine............................... 246Figure A6-8. Equivalent circuit of electrical model with series capacitance. ................ 247

Figure A6-9. Equivalent circuit of electrical model with parallel capacitance............... 248Figure A6-10. Rotor power for 2 wind speeds (dashed) with alternator shaft power. ... 252Figure A6-11. Motor and pump power versus slip for a) f = 90 Hz and b) f = 110 Hz.. 253Figure A6-12. Thevenin equivalent circuit with load. .................................................... 254Figure A6-13. Thevenin equivalent circuit used by Brown and Hamilton..................... 254Figure A6-14. Motor power versus slip for series capacitance, with approximate smax.

................................................................................................................................. 255Figure A7-1. Sample user interface for the Solar Insolation Data Fit ............................ 258

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ForwardJune, 2006

Since initial completion of Hybrid2 and the associated Theory and Users Manual, additionalcapabilities have been added to the code, both in the form of additional functionality integral tothe code and as utilities linked to the code. This most recent Theory Manual includesdocumentation related to all of these additions. The additional capabilities and the associateddocumentation include:

Data Synthesizer

The Hybrid2 time series data synthesizer generates realistic time series data for input to Hybrid2.It can be accessed through the Tools menu in the main window. It is useful when no data existand when representative data can be useful for an analysis. The Hybrid2 time series datasynthesizer may be applied to wind speed, solar radiation, electrical load, or temperature. Typicalinputs are means, standard deviations (or maximum and minimum), type of probabilitydistribution expected for histograms of the data, autocorrelation at a specified lag, and the numberof points desired. The output is a time series with the desired summary characteristics. For certaindata, a sinusoidal diurnal pattern (or longer, in the case of wind) may also be superimposed.Documentation about the data synthesizer can be found in Section 5.9 of the theory Manual.

Heating Loads and Thermal StorageHybrid2 now includes the option of including heating loads and thermal storage as systemcomponents. A heating load is a special category of an optional load and may be used to representan electrical space heating load. It may be an AC or a DC load and requires inputs related to theambient temperature, target room temperature and to the relevant heat loss coefficient. Thermalenergy may also be stored to meet the heating load, but it cannot be converted back intoelectricity. Documentation about the heat load and storage algorithms can be found in Section 5of the Theory Manual.

Switchable rotary converter and synchronous condenserRotary converters may be used in hybrid power systems to convert power between DC and AC.Synchronous condensers may be used to provide reactive power to AC loads. The option nowexists in Hybrid 2 for these to be switched off when not in use. This decreases no-load losses.Mention of switchable rotary converters and synchronous condensers can be found in Section 2 ofthe Theory Manual.

Solar Insolation Data FitThe solar insolation data fit algorithm, which is now a part of Hybrid2, checks solar data toensure that the time stamp of the data is correct. The algorithm uses a statistical approach todetermine when local solar noon occurs in the solar insolation data file and to confirm if the timestamp in the file is correct. If not, the code offers the user the option to correct the time stamp.

Documentation about the solar insolation data fit can be found in the appendices of the theoryManual.

Variable Voltage, Variable Frequency Wind Turbine GeneratorThe variable voltage, variable frequency electrical wind water pump system modeled is an add-onutility to Hybrid 2. It can be accessed through the Tools menu in the main window. It is a modelof a variable speed electric water pumping wind turbine system. The model consists of a windturbine rotor mechanically coupled to a permanent magnet alternator (PMA) through a gearbox,

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an induction motor electrically coupled to the PMA with a series or parallel capacitance, and aload directly connected to the motor. The load may be a water pump, but can be any type of loadthat can be described by a torque versus speed curve. The utility will determine the steady stateoperating points of the system at a range of user-specified wind speeds. Documentation about thevariable voltage, variable frequency electrical wind water pump system can be found in theappendices of the Theory Manual.

Grid Inter-TieHybrid power systems are not always totally isolated from a main grid. Islands that are relativelyclose to the mainland or close to other islands are examples of such systems. Designers for theselocations may want to investigate the option of connecting to the grid in lieu of using dieselgenerators. This connection may be used as a source of supplemental power and a sink for excesspower. The Grid Inter-tie capabilities of Hybrid2 allow it to model the purchase of neededelectricity and sale of excess electricity via a connection to a larger grid. These capabilities havebeen achieved by using the diesel model and an optional load to model the exchanges of energythrough the grid inter-tie. Thus, in the software, the grid inter-tie capabilities are referred to as aPseudo-Grid. The Pseudo-Grid properties can be entered through the Power System Moduleinterface. Documentation about the Pseudo-Grid can be found in the appendices of the Theory

Manual.

Improved PV Panel Performance ModelAn improved PV panel performance model is now being used in Hybrid2. The model does abetter job than the original one of modeling the current-voltage (I-V) curves of PV panels atdifferent temperatures and at different insolation levels. Mention of details of the new PV panel

model can be found the appendices of the Theory Manual.

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Nomenclature

This is a partial listing of symbols used in this report. It is divided according to Chapter.

Chapter 4

DI,I

erf(.)

LS

to the primary load (both buses), kW

= Deferrable inventory input, kW= Deferrable inventory output, kWDI,O

erator(s) (either bus), kWDL = Power delivered from the diesel genDP = Power dissipated in dump load, kW

excess of dump load capacity, kWDPEx = Extra power in

= Error function.rrection factorFWP = Wind power turbulence coT

= Losses (both buses), kW

LD = Power delivered to the deferrable load (both buses), kW

LO = Power delivered to the optional load (both buses), kW

LP = Power deliveredL = Mean load, kW

Ne value of the net load, kW

= Instantaneous value of net load, kW.

Nmax = Maximum acceptabl

N = Mean net load, kWP = Disregarded net load probability, -DNL PV V array (either bus), kW= Power supplied by P

SI = Storage input, kW

SO = Storage output, kW

S = Mean photovoltaic power, kWU = Unmet load, kW

V = Mean wind speed, m/sW e(s) (both buses), kW= Power delivered from all the wind turbin

W = Mean wind power, kW.W1 = Mean power of one wind machine, kWy

= Standard deviation of the wind power, kW

= Argument of error function, -L = Standard deviation of load, kWN = Standard deviation of the net load, kWW V = Standard deviation of wind speed, m/s

Chapter 5, Sections 5.2 Power System and 5.3 Loadsa nL

= Constant limiting range of integratio

i

L = Converter loss during transfer, kW.

= Sampled load, kW

transfer

L = Average load over time step, kWn = Number of measured values for the lo

ad within the time step

N

N1

2 = Instantaneous net load on bus 2, kW

= Instantaneous net load on bus 1, kW

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N1, at = Net load on bus 1 after transfer, kW

N1,b = Net load on bus 1 before transfer, kWt

,at = Net load on bus 2 after transfe

r, kWN2N2,bt fer, kW= Net load on bus 2 before trans

N1

= Mean net load on bus 1, kW

N2 = Mean net load on bus 2, kWp(.) = Probability density functions, assumed to be Gaussian, -

P1 = Average power transferred from2 bus 1 to bus 2, kW

P2 = Average power transferred from bus1 2 to bus 1, kW

, kW

x

P = Average power transferred after converter size limit is considered2= Rated power of co

1,new

Rc nverter, kW

= Random variable; net load on bus 1= Random variable; net load on bus 2; argument of error functiony(

y = Mean value of y

yy< = Fractional meana han "a"value of y when y less t

yy = Fractional mean value oa f y when y equal to or greater than "a"

z robability density function; net load afteretween buses.

= Random variable; argument of ptransfer of power b

z = Mean value of zu = Variable of integration

= Standard deviation of load, kWL x = Standard deviation of x

on bus 1, kW

Chapte

12 = Standard deviation of net load on bus 2, k

= Standard deviation of net load

W

r 5, Section 5.5 EconomicsC(n) = System operating costs in year n, $/yearCA = Annual payment on loan for equipmen

t, $/year

se), $/year

, $/year

in year

n,B base case), $/year

ase case), $/year

costs, $

) in year n, $/year

B(n) n (base case), $/year

(base case), $

CA,B = Annual payment on loan for equipment (base ca

A /yeaC ,L = Levelized annual payment for equipment, $ rCA, = Levelized annual payment for equipment (base case)L,BCAdm = Annual administrative cost, $/

CAdmi = Annual administrative costs (

)CB(n = System operating costs in year n (b

CBat = Battery bank capital costs, $

CBatI

= Battery installation costs, $

CBOS = Balance of system costs, $

CC = Power converters capital

CCap(n = Payment for equipment capital costs

CCap, = Payment for equipment capital costs in year

n costs, $CCI = Power converters installatio

CD = Diesel capital costs, $

CD,B = Diesel capital costs

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cDef = Cost of energy to deferrable load, $/kWh

e), $

mp sts, $I $

to existing grid, $

) ar

B(n)

f capital cost

$/year

e cost (base case), $/year

ys st, $/year

s,B ance costs (base case), $/year

, $

COECOE' = Level odified for direct comparisons, $/kWh

h

rofit system, $/kWh

e in retrofit system, modified for direct

oltaics, $

and/or trackers, $

$$

i for ith wind turbine, $

CDI = Diesel installation costs, $CDI,B = Diesel installation costs (base cas

Cdp = Down payment, $Cdp,B = Down payment, base case, $

CDu = Dump load capital coCDump = Dump load installation costs,

CE = Equipment related costs, $

CExt = Installed cost of line extension

cF = Cost of fuel, $/unit

CF(n = Cost of fuel in year n, $/ye

CF, = Cost of fuel in year n (base case), $/year

CF,L = Levelized cost of fuel, $/yearCF,L,B = Levelized cost of fuel (base case), $/yearCI = Total installation costs, $cI = System installation overhead cost fraction,-

CM(n) = Total non-fuel operation and maintenance cost in year n, $/year

CM,B(n) = Total non-fuel operation and maintenance cost in year n (base case), $/year

cM,Bat = Battery annual operation and maintenance costs, fraction o

cM,D = Diesel related operation and maintenance costs, $/kWh

CM,L = Total levelized non-fuel operation and maintenance cost,

CM,L,B = Total levelized non-fuel operation and maintenanc

CM,S = General system operation and maintenance co

CM,Sy = General system operation and mainten

cM,W = Wind turbine operation and maintenance costs, $/kWh

CMPPT = Capital cost of maximum power point tracker

CO = Installed cost of optional load equipment, $= Levelized cost of energy, $/kWh

ized cost of energy, mCOEB = Levelized cost of energy, (base case) $/kW

COER = Levelized cost of energy difference in ret

COE = Levelized cost of energy differencR'

comparisons, $/kWhcOpt = Cost of energy to optional load, $/kWh

cPrim = Cost of energy to primary load, $/kWh

CPV = Capital cost of photovoltaics, $

CPVI = Installation cost of photov

CPVR = Capital cost of photovoltaics racksCR(n) = Total yearly replacement costs, $/year

CR,B(n) = Yearly replacement cost for diesels (base case), $/year

CR,Di = Diesel overhaul costs, $

CR,L = Levelized diesel overhaul costs,

CR,L,B = Levelized diesel overhaul costs (base case),

CR,W = Total overhaul cost

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CR,X = Yearly replacem(n) ent cost for component "X", $/year

C wind turbines, $

C wind turbines, $

d turbines, $

ind turbines, $

I,AC urbines, $

nd turbines, $

C bines, $

DC

dD(n)

(n) $

CS = System installed capital cost, $CS,B = System installed capital cost (base case), $CSh = Shipping costs, $

CT = Tariff costs, $

CW = Total wind turbine capital cost, $CWD,AC = Capital cost of domestically purchased A

CWD,DC = Capital cost of domestically purchased D

CWF,AC = Capital cost of internationally purchased AC win

CWF,DC = Capital cost of internationally purchased DC w

CW = Installation cost of AC wind t

CWI,DC = Installation cost of DC wi

CWT,A = Capital cost of tower for AC wind tur

C T, = Capital cost of tower for DC wind tW urbines, $

= Discount rate, fraction/year= Depreciation in year n, $

DB = Depreciation in year n (base case),DPP = Discounted payback period, years

F = Average hourly total diesel fuel consumption, units/hrF = Average hourly total diesel fuel consuB

/year

mption (base case), fuel units/hr

ipment, -

(n) $/year

ear

fference in year n, $/year

(base case)

ear n, $/year

C nnected WTGs, kW

Pr (n) r n, $/year

PrL

f = Fuel inflation rate, fractionfdp = Capital cost down payment fraction, -

s stem equf = Fractional salvage value of sy

g = General inflation rate, fraction/year i = Loan interest rate, fraction/yearI(n) = Revenue in year n, $/yearIB(n) = Revenue in year n (base case), $/year

Inet(n) = Net revenue in year n, $/year Inet,B = Net revenue in year n (base case),

INet,R(n) = Net revenue difference in year n (retrofit), $/y

IR(n) = Retrofit system revenue di

N = Financial life of system, yearsND = Number of diesel generator sets

ND,B = Number of diesel generator sets

NW = Number of wind turbinesPr(n) = Profit from retrofit system in yPR,AC = Total rated power of AC connected WTGs, kW

PR,Bat = Nominal battery capacity, kW

PR,C = Rated power of the converters, kWPR,D = Rated power of diesels, kW

PR,D = Total rated power of DC co

PR,Dump = Rated power of dump load, kW

PR,PV = Rated power of photovoltaics, kW

B = Profit from base case system in yea

=Levelized system profit, $

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PrL,R(n) m in year n, $/yearPr (n) r n, $

=Levelized profit difference in retrofit syste

R = Retrofit system profit difference in yea

PD = Average power from diesels, kW

PD = Average power to deferrable load, kWef

POver = Average overload power, kW

P = Average overload power (base case), kWOver,B

POpt = Average power to optional load, kW

PPrim = Average power to primary load, kW

P = Average power from photovoltaics, kWPVPW = Average wind power, kW

stment, fraction/yearr = Rate of return on investS = Salvage value of sy

SB = Salvage value of syem equipment, $

ipment (base case), $

R retrofit, years

x credit rate, $/kWh

verter replacements, years

mp ments, years

ements, years

ne i

T B(n

XX(n)X

XNPW = Net present worth of cost or income, $XPW(n) e in year n, $

at

ed wind turbines, -

ed wind turbines, -

nted payback period, -

stem equipment (base case), $

SL Levelized salvage value of system equipment, $=

SL Levelized salvage value of system equ,B =SPP = Simple payback period, yearsSPP = Simple payback period for

t = Corporate tax rate, -TBat = Battery life, years

tc = Renewable energy production ta

TDi = Operating time of diesel engine i, hrs

TE = Equipment depreciation time, years

TG = Loan grace period, years

TL = Loan period, years

TR,C = Period between power con

TR,Di = Diesel overhaul interval, yearst i = Period between diesel overhauls, hrsR,DTR,Du = Period between dump load replace

V replacTR,P = Time between photovoltaics

TR,Wi = Time between overhauls for wind turbi

TSim = Simulation length, hours

Tx(n) = Tax payment in year n, $x ) = Tax payment in year n (base case), $

= Arbitrary cost or income, $= Arbitrary system cost in year n, $

L = Levelized cost or income, $

= Present worth of cost or incom

B = Battery size scale factor, - = Scale factor for AC connectW,AC = Scale factor forDC connectW,DC = Ratio used in finding discou

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Chapter 5, Section 5.8 Gap Filler

Cj,k[ ] = Cumulative transition probability matrixN

Nj,k rom bin j to bin kr mber between 0 and 1, -Tj,k = Probability of making a transition from bin j to bin k

j = Index ranging from 1 tok = Index ranging from 1 to N

N = Number of binsNj = Total transitions from bin j= Number of transitions f= Random nu

Tj,k[ ] = Transition Probability MatrixXh = Greatest value oigh f data

xi = Time series data, ith value

Xlow = Lowest value of data

x{ } = Set of time series data . = Bin width

Chapter 6, Section 6.1 Wind Turbinesf = Frequency, Hzflo = Lower limit of integration of power spectral density, Hzflo,1 = Frequency corresponding to 1/ t1, Hzflo,2 = Frequency corresponding to 1/ t2 , Hz

ower spectral density, Hz-

te = Site altitude, mH 2 e LlapsePP

) ng times long,

p ) ed based on averaging times long,

f = Upper limit oup f integration of p

FW = Wind power turbulence factor,PTFv = Fraction of variance, -H = Height above ground level, m

Hsi1,H = Heights above ground level used adjustm nt of wind speed, m

= Turbulence integral length scale, m= Adiabatic lapse rate, -0.00638 K/m.= Power, kW

i = Sampled value of power, kWt2p1(V = Probability density function of wind speed based on averagi

-t12(V = Probability density function of wind spe

-

Pt = Power curve based on averaging times1 (.) t1 long, kW

on averaging timesP = Power curve based2 (.) t2 long, kWtP = Mean wind power over time step, kP

W

r = Mean atmospheric pressure at site, mm HgsitePrSL i ons,0 ti , 760 mm Hg.

ulent wind speed, (m/s)2/Hz

L,0

= Atmospheric pressure at standard cond

S(f) = Power spectral density of turb

T SL = Sea level temperature, K

TS = Temperature at standard conditions, K

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Tsite = Site mean temperature, KT nd speed, -VV

V1 2

I = Turbulence intensity of wi= Wind speed, m/s= Sampled value of wind speed, m/si

, V = Wind speed at heights 1 and 2, m/s

V = Mean wind speed over time step, m/s.V1 t= Wind speed averaged over time period 1 .Z0 = Surface roughness height, m

curve estimate, sec

wer curve is adjusted, sec

. long, m/s

Chapter 6, Section 6.2 Photovoltaic Panels

= Power law exponent, -.t1 = Averaging time step used in powert2 = Averaging time step to which po

= Air density at site, kg/m2

0 = Air density at standard conditions (293 K), kg/m2P = Standard deviation of wind power, kWV = Standard deviation of wind speed, m/s

V1 = Standard deviation of wind speed based on averaging times t1

2

CT i s, W/m2

A = PV panel curve f

taic panel, m

itting parameter.

Ac = Area of photovol

Aref = PV panel curve Fitting Parameter at Reference Conditions

O g condit onGT,N = Solar irradiance at normal operatin

GT,SOC = Solar irradiance at standard conditions, W/m2

G = Average solar irradiance on a horizontal surface, W/m2

GT

= Average solar irradiance incident on the PV panel, W/m2,

f ditions, A

,ref rrent at reference conditions, A

N ltaic panel, -

ance in PV cell, Ohms

ons, K

V T1 T2Tc,SOC

I = Current, AI0 = Diode reverse saturation current

I0,re = Current at Reference Con

ID = Diode current, AIL = Light current, A

IL,ref = Light current at reference conditions, W/m2Imp = Maximum power point current, AImp = Maximum power point cu

Isc = PV panel short circuit current, A

s = Number of cells in series in photovo

Rs = Series resistRsh = Shunt resistance in PV cell, Ohms

Ta = Ambient temperature, K

Tc,NOCT = PV cell temperature at normal operating conditi

m

, = Temperatures near the reference temperature

p = Maximum power point voltage, V

= PV panel temperature at standard conditions, K

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T

Tc,ref = PV panel temperature at reference conditions, K

p,ref ditions, V

Voc,ref = Open circuit voltage at reference conditions, Von the panel surface, -

Chapte

c = PV panel temperature, K

= PV panel loss coefficient, W/C m2UL

V = Voltage, VVm = Maximum power point voltage at reference con

Voc = Open circuit voltage, V

= Absorbed radiation fractionc = Efficiency of the panel in converting sunlight to electricityI,sc = Short circuit current temperature coefficient, A/CV,oc = Open circuit voltage temperature coefficient, V/C

er the cells, - = Transmittance of covers ov

r 6, Section 6.3 Diesel Generatorsa = No load fuel consumption, fuel units/hr

b = Slope of fuel vs. power curve, fuel units/kWhfuel units/hr

Chapter 6, Section 6.4 Batteries

F = Fuel consumption,

voltage to state of charge, Vvs. cycle depth of discharge

o state of charge, -to charge/discharge cycles, -

ax

onstant, -

ing to specified fractional depth of discharge, -

eed

qmq0

= Total battery charge at beginning of time step, Ah

q1 ge, Ah

0

R0 = Kinetic Battery Model internal resistance,

A = Constant relating internal battery,...,a5a1 = Constants used in fit of cycles to failure

c = Kinetic Battery Model capacity ratio, -C = Constant relating internal battery voltage to state of charge, VCF = Battery cycles to failure, -

D = (i) Constant relating internal battery voltage tD = (ii) Damage done to battery due

E = Battery internal voltage, VE0 = Fully charged internal battery voltage, V

I = Battery current, AIc = Charging current, A

Ic,max = Maximum charging current, A

Id = Discharge current, A

Id,m = Maximum discharge current, A

k = Kinetic Battery Model rate cLchg = Power loss in charging, W

Ni = Number of cycles correspond

PN = Power required from battery in time step, W

ax = Maximum battery capacity, Ah

= Kinetic Battery Model "available" char

q1, = Available charge at the beginning of time step, Ahq2 = Kinetic Battery Model "bound" charge, A

q2,0 = Bound charge at the beginning of time step, Ah

R = Fractional depth of discharge, -

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V = Battery terminal voltage, Vof state of charge and current), V

tage, V

V(q,I) = Voltage (as functionVnom = Nominal battery vol

X = Non-dimensional state of charge of battery, -

t = Length of time step of model, hr

Chapter 6, Section 6.6 Power ConvertersconB = Constant relating input to output of power verter

out

l

PNL

P t

Chapter 7, Section 7.1 Multiple Wind Turbines

Bin = Constant relating input to output of power converter (referred to input)

B = Constant relating input to output of power converter (referred to output)

Ln = No load loss of power converter, kW

Pin = Input power, kW

= No load power, kW

ou = Output power, kW

PR = Rated input or output power of converter, kW

R = Rated efficiency of power converter, -

a cay constant, taken to be 50k ming linearity),

LN

= Coherence de= Constant relating wind speed to wind turbine power (assu

kW/(m/s)= Integral length scale of turbulence, m= Number of wind turbines in array, -

P1 = Mean power from 1 wind turbine, kWPN = Mean power from N wind turbines, kW

) wind at one point, (m/s)2/HzS1(f = Power spectra of fluctuating

S = Power spectra of fluctuating wind at N points, (m/s)2/HzN(f)

V = Mean wind speed, m/s.x ij = Spacing between p ntsoi i and j, m

ij

2 f( ) = Coherence, -P,1 = Standard deviation of power from one wind turbine, kW

rom N wind turbines, kW

Chapte

P,N = Standard deviation of power fV = Standard deviation of wind speed, m/s

r 7, Section 7.2 Photovoltaic ArrayAi = Anisotropy index, given byA i = Gb / Go , -B = Term in Equation of Time, given by B = (n-1) 360/365, -

.,C5 azimuth, -

for the Equation of Time, hrs.

C1,.. = Constants used in calculation of solar or surface

E = Correction

= Modulating factor(Gb / G )1/2 ,

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Go = Average solarirradiance on horizontal surface outside earth's atmosphere,

G 2)

W/m2

sc = Solar constant (1367 W/m

G = Average (over time step) of total solar irradiance on horizontal surface, W/m2

Gb = Average (over time step) of beam component of solar irradiance, W/m2

= Avera diffuse component of solar irradiance, W/m2Gd ge (over time step) of

G = Average (over time steT p) of total solar irradiance on tilted surface, W/m2

kT e step) of clearness index, given by kT = G / G0= Average (over tim , -L sis, degLst deg

nR horizontal, -tsol = Solar time, hrststd

= Longitude of the site under analy= Standard meridian for the local time zone,

= Julian day

b = Ratio of beam radiation on slope to that on

= Standard time, hrs

= PV array slope, deg = PV array surface azimuth angle, deg s = Solar azimuth angle, deg = Declination angle of sun, deg = Angle of incidence of beam radiation on surface, deg

ar to the

g

eg

Chapte

z = Zenith angle (the angle between the sun's rays and a line perpendiculearth's surface), deg

g = Ground reflectance, - = Site latitude, deg = Hour angle, deges = Sunrise hour angle, de2 = Hour angle at the end of a time step, deg1 = Hour angle at the start of a time step, d

r 7, Section 7.4 Dispatch, 7.5 Diesel uel UseFa1 = No load fuel consumption of 1st diesel, fuel units/hr

l in the ith configuration, fuel units/hr

diesel, fuel units/kWh

th diesel in the ith configuration, fuel

Fi,m = Minimum allowed fuel consumption for configuration, fuel units/hr= Minimum fuel consumption at power level L in configuration, fuel units/hr

i = Configuration number, -j = Ordered index of states, -k = Dummy index, -L = Load on diesels, kWNd = Number of diesels, -

p(N) = Probability density function of net load, -.

a ,k = No load fuel consumption of the kth dieseib = Incremental fuel consumption of 1st1

bi,k = Slope of fuel vs. power curve for the k

units/kWh

Fm(L)

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Plo,j = Lower power level

P = Minimum allowed power level of the kthdiesel in the ith configuration, kW

Minimum allowed power level of the kthdiesel, kW

of the jth state, kW

m,i,k

Pm,k =

Pmin = Total minimum power of ith

configuration, kW

Pmin,1 = Minimum power level of 1st diesel, kW

PR,1 = Rated power level of 1st diesel, kW

PR,k = Ordered rated diesel power, kW

Pup,j = Upper power level of the jth

state, kW

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1. Introduction

1.1 Overview

Hybrid power systems are designed for the generation and use of electrical power. They areindependent of a large centralized electricity grid, incorporate more than one type of powersource, and are typically found in remote locations. Diesel generators are portable, modular, andhave a high power-to-weight ratio, which makes them an ideal power source for these hybridpower systems. In an effort to conserve expensive diesel fuel, hybrid systems often include someother power source such as wind, solar, or hydropower. To maximize the use of the renewableresource, the size and operation of the hybrid system components need to be matched to the loadand the available renewable resource. This is best accomplished by using computer models.

These models of hybrid systems allow the user to easily consider a number of systemconfigurations and operating strategies to optimize the system design. Hybrid2, a hybrid systemcomputer model designed at the University of Massachusetts and the National Renewable EnergyLaboratory, is a comprehensive, flexible, user-friendly model that allows a wide range of choicesof system components and operating strategies. A hybrid system might contain alternating

current (AC) diesel generators, direct current (DC) diesel generators, an AC distribution system, aDC distribution system, loads, renewable power sources (wind turbines or photovoltaic powersources), energy storage, power converters, rotary converters, coupled diesel systems, dumploads, load management options, or a supervisory control system. Each of these can be modeledwith the Hybrid2 code.

The Hybrid2 model has been developed to assist a designer in sizing hybrid power systemhardware and in selecting operating options on the basis of overall system performance andeconomics when site specific conditions and load profiles are known. It cannot, however, tell thedesigner how to implement the necessary system controls and to provide for adequate voltage orfrequency regulation. Other analytical tools may be needed for the detailed design of the hybridpower system. Nonetheless, Hybrid2 can be of great value in narrowing the options and reducing

the need for more detailed analysis.

This manual describes the operation of hybrid power systems and describes the theory behind theHybrid2 computer code. It is intended to allow the user to understand the details of thecalculations and considerations involved in the modeling process. This theory manual is acompanion volume to the user manual, which describes the practical aspects of using the model.Each chapter of this theory manual begins with an executive summary summarizing the contentsof the chapter. This is followed with more detailed information. In Chapters 6 and 7, theexecutive summary is followed by an overview of the inputs needed for the section of the modelbeing discussed, details of model inputs, and finally, the theory behind the section of the modelunder consideration.

1.2 How to Use the Manual

Each of the main features of the Hybrid2 model is described in the following chapters. Thechapters and major sections begin with an executive summary. They then describe the variousaspects of the model in more depth. For an overview of the model, it is suggested that the userread only the executive summaries. The user who is interested in the details may wish to bypassthe executive summaries and read the remainder of the chapters instead. Chapter 2 describes allof the components and the component features that are included in the hybrid systems modeledon Hybrid2. Chapter 3 describes the overall model structure as it is implemented in the code.

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Chapter 4 includes an explanation of odeling method used on Hybrid2.Chapter 5 details calculations and inp etermine power flows in the system,

ads, and to calculate system economics. Chapter 6 describes thecomponent (such as wind turbines, photovoltaic cells, or

he

the principles behind the muts used in the code to d

to handle the various types of lomodels used to model each systemdiesels) and the inputs to those models. Chapter 7 includes the algorithms used to model toperation of multiple individual components that are grouped into subsystems (such as wind

farms or PV panels).

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2. Background

2.1 Executive Summary

This manual describes the theory behind the Hybrid2 computer code, which analyzes theoperation of hybrid power systems. The Hybrid2 computer code structure was designed to mirroas closely as possible the structure of actual hybrid power systems. Before proceeding, it isuseful to review the main features of hybrid power systems and to put this model into theof ongoing hybrid power system modeling efforts.

r

context

this

l

er system might contain AC diesel generators, DC diesel generators, an AC

tions, fornput to economic analyses. Dynamic models are used

essment of system stability, and determination of power

g

st of

mirroructure of actual hybrid power systems. Before addressing the

Hybrid power systems are designed for the generation and use of electrical power. They areindependent of a large, centralized electricity grid and incorporate more than one type of powersource. They may range in size from relatively large island grids of many megawatts toindividual household power supplies on the order of one kilowatt (kW). Larger, systems (greaterthan 100 kW nominal capacity) are normally based on alternating current (AC) of fixedfrequency. Larger isolated AC systems include at least the following: conventional ACgenerators, an electrical distribution system, and distributed AC loads. A hybrid system ofsize could also include additional power sources such as renewables (wind turbines, photovoltaic

panels, hydroelectric generators) and storage. Medium-size systems (greater than 10 kW nominacapacity) may also be based primari

Documents

Hybrid 2 Theory Manual