Preface
The phenomenal growth and new developments in wind and solar power technologies
have made the second edition of this book necessary. It reflects the need for an
expanded, revised, and updated version of the well-received first edition in just 5
years. During that time, the capital and energy costs of wind power have declined
by 20%. Today, the cost of electricity from grid-connected wind farms is below 4
cents/kWh, and that from photovoltaic (PV) parks below 20 cents/kWh. The goal
of ongoing research programs funded by the U.S. Department of Energy (DOE) and
the National Renewable Energy Laboratory (NREL) is to bring wind energy cost
below 3 cents/kWh and the PV energy cost below 15 cents/kWh by 2010. In capital
and energy costs, wind now competes on its merits with the conventional power
technologies, and has become the least expensive source of electrical power —
traditional or new — in many parts of the world. It is also abundant and environmentally
clean, bringing many indirect social benefits not fully reflected in the market
economics. For these reasons, wind power now finds importance in the energy
planning in all countries around the world. According to the DOE, prime wind
locales of the world have the potential of supplying more than ten times the global
energy needs. In the U.S., the DOE has established 21 partnerships with public and
private bodies to develop turbines to generate economical power in low-wind-speed
regions that would open up much larger areas of the country for rapid development
of wind power. The Electric Power Research Institute (EPRI) estimates that wind
energy will grow from less than 1% at present to as much as 10% of the U.S.
electricity demand by 2020.
Around the world, the wind power generation capacity has seen an average
annual growth rate of 30% during the period from 1993 to 2003. More than 8,000
MW of new wind capacity was added globally in 2003 with an investment value of
$9 billion. This brought the total cumulative wind capacity to 40,000 MW. The most
explosive growth occurred in Germany. Offshore wind farms are bringing a new
dimension to the energy market. Many have been installed, and many more, each
exceeding 300-MW capacity, are being installed or are in the planning stage. Most
offshore farms are less than 10 km from the shore in less than 10 m depth of water.
Denmark’s plan to install 750 MW of new wind capacity by 2008, bringing its total
to 4,000 MW for supplying 25% of the country’s electricity, includes aggressive
offshore plans. U.S. wind capacity is projected to reach 12,000 MW by 2015. Utilities
and wind power developers have announced plans for more than 5,000 MW of new
capacity in 15 states by 2006. Hydro-Quebec plans 1,000 MW of new capacity to
be added between 2006 and 2012. In these new installations, 3-MW turbines are
being routinely installed in many countries, with 5-MW machines available today
for large offshore farms; 7-MW units are in prototype tests.
On the solar PV side, the cost of PV electricity is still high: between 15 and 25
cents/kWh. With the consumer cost of utility power ranging from 10 to 15
cents/kWh, PV cannot economically compete directly with utility power as yet,
except in remote markets where utility power is not available and transmission line
cost would be prohibitive. Many developing countries have large areas falling in
this category, and that is where the most PV growth is taking place, such as in India
and China. The worldwide solar PV is about $7 billion in annual business, mainly
driven by Germany.
Worldwide, PV installations grew at an average annual rate of 25 to 30% during
the period from 2000 to 2004. By the end of 2004, the cumulative PV capacity was
2,030 MW, with 1,000 MW in the U.S. The annual production of PV modules was
530 MW in 2004 and is projected to reach 1,600 MW by 2010. The present module
prices are $6 to $7 per watt for 1-kW modules and $3 to $4 per watt for 1-MW
plants. The emerging thin-film and concentrating PV cells are expected to reduce
the module prices substantially in the near future.
After the restructuring of U.S. electrical utilities as mandated by the Energy
Policy Act (EPAct) of 1992, industry leaders expected the power generation business,
both conventional and renewable, to become more profitable in the long run. Their
reasoning is that the generation business has been stripped of regulated prices and
opened to competition among electricity producers and resellers. The transmission
and distribution business, on the other hand, is still regulated. The American experience
indicates that free business generates more profits than regulated business.
Such is the experience in the U.K. and Chile, where the electrical power industry
had long been structured similarly to the U.S. EPAct of 1992. Moreover, the renewable
power price would be falling as the technology advances, whereas the price of
the conventional power would rise with inflation, making the wind and PV even
more profitable in the future.
North America’s darkest blackout in 2003 with its estimated $10 billion in
damage is bringing a new and sharp focus to distributed power generation. Because
overloaded transmission lines caused the blackout, and it would take decades before
new lines can be planned and built, the blackout has created a window of opportunity
for distributed power generation from wind and PV. As most large-scale wind farms
are connected to the grid lines, PV systems are expected to benefit more in distributed
power generation growth.
Contents
PART A
Wind Power Systems
Chapter 1
Introduction ………………………………………………………………………………3
1.1 Industry Overview ……………………………………………………………………………..3
1.2 Incentives for Renewables…………………………………………………………………..5
1.3 Utility Perspective………………………………………………………………………………6
1.3.1 Modularity for Growth…………………………………………………………..7
1.3.2 Emission Benefits………………………………………………………………….8
1.3.3 Consumer Choice ………………………………………………………………….8
References………………………………………………………………………………………………….10
Chapter 2
Wind Power…………………………………………………………………………….11
2.1 Wind Power in the World………………………………………………………………….11
2.2 U.S. Wind Power Development………………………………………………………….15
2.3 Europe and the U.K………………………………………………………………………….19
2.4 India ……………………………………………………………………………………………….21
References………………………………………………………………………………………………….23
Chapter 3
Wind Speed and Energy …………………………………………………………..25
3.1 Speed and Power Relations ……………………………………………………………….25
3.2 Power Extracted from the Wind…………………………………………………………27
3.3 Rotor-Swept Area …………………………………………………………………………….30
3.4 Air Density ……………………………………………………………………………………..30
3.5 Global Wind Patterns………………………………………………………………………..31
3.6 Wind Speed Distribution …………………………………………………………………..33
3.6.1 Weibull Probability Distribution ……………………………………………34
3.6.2 Mode and Mean Speeds……………………………………………………….36
3.6.3 Root Mean Cube Speed ……………………………………………………….39
3.6.4 Mode, Mean, and RMC Speeds…………………………………………….39
3.6.5 Energy Distribution ……………………………………………………………..41
3.6.6 Digital Data Processing………………………………………………………..43
3.6.7 Effect of Hub Height……………………………………………………………44
3.6.8 Importance of Reliable Data …………………………………………………46
3.7 Wind Speed Prediction ……………………………………………………………………..47
3.8 Wind Energy Resource Maps…………………………………………………………….48
3.8.1 U.S. Wind Resource Map …………………………………………………….48
3.8.2 U.K. and Europe Wind Resources …………………………………………52
3.8.3 Mexico Wind Resource Map ………………………………………………..54
3.8.4 Wind Mapping in India………………………………………………………..55
3.8.5 Wind Mapping — Other Countries ……………………………………….57
References………………………………………………………………………………………………….60
Chapter 4
Wind Power Systems ……………………………………………………………….61
4.1 System Components …………………………………………………………………………61
4.1.1 Tower …………………………………………………………………………………63
4.1.2 Turbine……………………………………………………………………………….65
4.1.3 Blades ………………………………………………………………………………..66
4.1.4 Speed Control……………………………………………………………………..68
4.2 Turbine Rating …………………………………………………………………………………69
4.3 Power vs. Speed and TSR…………………………………………………………………70
4.4 Maximum Energy Capture ………………………………………………………………..74
4.5 Maximum Power Operation ………………………………………………………………75
4.5.1 Constant-TSR Scheme …………………………………………………………75
4.5.2 Peak-Power-Tracking Scheme ………………………………………………75
4.6 System-Design Trade-offs …………………………………………………………………76
4.6.1 Turbine Towers and Spacing…………………………………………………76
4.6.2 Number of Blades ……………………………………………………………….78
4.6.3 Rotor Upwind or Downwind ………………………………………………..79
4.6.4 Horizontal vs. Vertical Axis ………………………………………………….79
4.7 System Control Requirements……………………………………………………………80
4.7.1 Speed Control……………………………………………………………………..80
4.7.2 Rate Control ……………………………………………………………………….81
4.8 Environmental Aspects ……………………………………………………………………..82
4.8.1 Audible Noise……………………………………………………………………..82
4.8.2 Electromagnetic Interference (EMI) ………………………………………83
4.8.3 Effects on Birds…………………………………………………………………..83
4.8.4 Other Impacts ……………………………………………………………………..84
4.9 Potential Catastrophes ………………………………………………………………………84
4.9.1 Fire…………………………………………………………………………………….84
4.9.2 Earthquake………………………………………………………………………….85
4.10 System-Design Trends………………………………………………………………………86
References………………………………………………………………………………………………….86
Chapter 5
Electrical Generators………………………………………………………………..87
5.1 DC Generator…………………………………………………………………………………..87
5.2 Synchronous Generator …………………………………………………………………….89
5.3 Induction Generator ………………………………………………………………………….89
5.3.1 Construction ……………………………………………………………………….90
5.3.2 Working Principle………………………………………………………………..90
5.3.3 Rotor Speed and Slip …………………………………………………………..92
5.3.4 Equivalent Circuit………………………………………………………………..94
5.3.5 Efficiency and Cooling…………………………………………………………97
5.3.6 Self-Excitation Capacitors…………………………………………………….97
5.3.7 Torque-Speed Characteristic …………………………………………………99
5.3.8 Transients………………………………………………………………………….100
5.4 Doubly Fed Induction Generator ……………………………………………………..102
5.5 Direct-Driven Generator ………………………………………………………………….102
References………………………………………………………………………………………………..103
Chapter 6
Generator Drives ……………………………………………………………………105
6.1 Speed Control Regions ……………………………………………………………………106
6.2 Generator Drives…………………………………………………………………………….108
6.2.1 One Fixed-Speed Drive………………………………………………………108
6.2.2 Two Fixed-Speed Drive………………………………………………………111
6.2.3 Variable-Speed Gear Drive …………………………………………………113
6.2.4 Variable-Speed Power Electronics ……………………………………….113
6.2.5 Scherbius Variable-Speed Drive…………………………………………..114
6.2.6 Variable-Speed Direct Drive ……………………………………………….115
6.3 Drive Selection ………………………………………………………………………………116
6.4 Cutout Speed Selection …………………………………………………………………..116
References………………………………………………………………………………………………..118
Chapter 7
Offshore Wind Farms……………………………………………………………..119
7.1 Offshore Projects ……………………………………………………………………………121
7.2 Legal Aspects in the U.S …………………………………………………………………122
7.3 Environmental Impact……………………………………………………………………..125
7.4 Offshore Costs ……………………………………………………………………………….126
7.5 Power Transmission to Shore…………………………………………………………..127
7.5.1 AC Cable ………………………………………………………………………….128
7.5.2 DC Cable………………………………………………………………………….128
7.6 Ocean Water Composition……………………………………………………………….129
7.7 Wave Energy and Power………………………………………………………………….130
7.8 Ocean Structure Design…………………………………………………………………..133
7.8.1 Forces on Ocean Structures ………………………………………………..133
7.9 Corrosion……………………………………………………………………………………….134
7.10 Foundation …………………………………………………………………………………….134
7.10.1 Monopile…………………………………………………………………………..135
7.10.2 Gravitation ………………………………………………………………………..135
7.10.3 Tripod ………………………………………………………………………………135
7.11 Materials ……………………………………………………………………………………….136
7.12 Maintenance…………………………………………………………………………………..138
References………………………………………………………………………………………………..139
PART B
Photovoltaic Power Systems
Chapter 8
Photovoltaic Power ………………………………………………………………..143
8.1 PV Projects ……………………………………………………………………………………148
8.2 Building-Integrated PV System………………………………………………………..151
8.3 PV Cell Technologies ……………………………………………………………………..152
8.3.1 Single-Crystalline Silicon …………………………………………………..153
8.3.2 Polycrystalline and Semicrystalline Silicon ………………………….153
8.3.3 Thin-Film Cell…………………………………………………………………..153
8.3.4 Amorphous Silicon…………………………………………………………….155
8.3.5 Spheral Cell ………………………………………………………………………155
8.3.6 Concentrator Cell ………………………………………………………………156
8.3.7 Multijunction Cell ……………………………………………………………..157
8.4 Solar Energy Maps …………………………………………………………………………157
8.5 Technology Trends………………………………………………………………………….159
Reference …………………………………………………………………………………………………161
Chapter 9
Photovoltaic Power Systems……………………………………………………163
9.1 PV Cell …………………………………………………………………………………………163
9.2 Module and Array…………………………………………………………………………..164
9.3 Equivalent Electrical Circuit ……………………………………………………………166
9.4 Open-Circuit Voltage and Short-Circuit Current ………………………………..167
9.5 I-V and P-V Curves………………………………………………………………………..168
9.6 Array Design………………………………………………………………………………….170
9.6.1 Sun Intensity……………………………………………………………………..171
9.6.2 Sun Angle …………………………………………………………………………172
9.6.3 Shadow Effect …………………………………………………………………..172
9.6.4 Temperature Effects …………………………………………………………..174
9.6.5 Effect of Climate ……………………………………………………………….175
9.6.6 Electrical Load Matching……………………………………………………175
9.6.7 Sun Tracking …………………………………………………………………….176
9.7 Peak-Power Operation …………………………………………………………………….179
9.8 System Components ……………………………………………………………………….180
Reference …………………………………………………………………………………………………181
PART C
System Integration
Chapter 10
Energy Storage ………………………………………………………………………185
10.1 Battery…………………………………………………………………………………………..185
10.2 Types of Battery …………………………………………………………………………….187
10.2.1 Lead-Acid …………………………………………………………………………187
10.2.2 Nickel-Cadmium ……………………………………………………………….188
10.2.3 Nickel-Metal Hydride ………………………………………………………..188
10.2.4 Lithium-Ion……………………………………………………………………….189
10.2.5 Lithium-Polymer ……………………………………………………………….189
10.2.6 Zinc-Air ……………………………………………………………………………189
10.3 Equivalent Electrical Circuit ……………………………………………………………189
10.4 Performance Characteristics …………………………………………………………….191
10.4.1 C/D Voltages……………………………………………………………………..191
10.4.2 C/D Ratio………………………………………………………………………….192
10.4.3 Energy Efficiency ………………………………………………………………192
10.4.4 Internal Resistance …………………………………………………………….193
10.4.5 Charge Efficiency ………………………………………………………………193
10.4.6 Self-Discharge and Trickle-Charge………………………………………194
10.4.7 Memory Effect ………………………………………………………………….194
10.4.8 Effects of Temperature ……………………………………………………….195
10.4.9 Internal Loss and Temperature Rise …………………………………….196
10.4.10 Random Failure …………………………………………………………………198
10.4.11 Wear-Out Failure ……………………………………………………………….199
10.4.12 Battery Types Compared…………………………………………………….200
10.5 More on the Lead-Acid Battery ……………………………………………………….200
10.6 Battery Design ……………………………………………………………………………….203
10.7 Battery Charging…………………………………………………………………………….204
10.8 Charge Regulators…………………………………………………………………………..204
10.8.1 Multiple Charge Rates ……………………………………………………….205
10.8.2 Single-Charge Rate ……………………………………………………………205
10.8.3 Unregulated Charging ………………………………………………………..205
10.9 Battery Management……………………………………………………………………….206
10.9.1 Monitoring and Controls…………………………………………………….206
10.9.2 Safety……………………………………………………………………………….207
10.10 Flywheel………………………………………………………………………………………..208
10.10.1 Energy Relations ……………………………………………………………….208
10.10.2 Flywheel System Components…………………………………………….210
10.10.3 Benefits of Flywheel over Battery ……………………………………….213
10.11 Superconducting Magnet…………………………………………………………………214
10.12 Compressed Air ……………………………………………………………………………..217
10.13 Technologies Compared ………………………………………………………………….219
References………………………………………………………………………………………………..220
Chapter 11
Power Electronics…………………………………………………………………..221
11.1 Basic Switching Devices …………………………………………………………………221
11.2 AC–DC Rectifier…………………………………………………………………………….224
11.3 DC–AC Inverter……………………………………………………………………………..225
11.4 Cycloconverter ……………………………………………………………………………….227
11.5 Grid Interface Controls……………………………………………………………………228
11.5.1 Voltage Control …………………………………………………………………228
11.5.2 Frequency Control……………………………………………………………..229
11.6 Battery Charge/Discharge Converters ……………………………………………….229
11.6.1 Battery Charge Converter……………………………………………………230
11.6.2 Battery Discharge Converter ……………………………………………….232
11.7 Power Shunts …………………………………………………………………………………233
References………………………………………………………………………………………………..234
Chapter 12
Stand-Alone Systems ……………………………………………………………..235
12.1 PV Stand-Alone……………………………………………………………………………..235
12.2 Electric Vehicle ………………………………………………………………………………236
12.3 Wind Stand-Alone ………………………………………………………………………….238
12.4 Hybrid Systems………………………………………………………………………………239
12.4.1 Hybrid with Diesel …………………………………………………………….239
12.4.2 Hybrid with Fuel Cell ………………………………………………………..241
12.4.3 Mode Controller ………………………………………………………………..247
12.4.4 Load Sharing …………………………………………………………………….248
12.5 System Sizing ………………………………………………………………………………..249
12.5.1 Power and Energy Estimates ………………………………………………250
12.5.2 Battery Sizing……………………………………………………………………251
12.5.3 PV Array Sizing ………………………………………………………………..252
12.6 Wind Farm Sizing…………………………………………………………………………..254
References………………………………………………………………………………………………..255
Chapter 13
Grid-Connected Systems…………………………………………………………257
13.1 Interface Requirements……………………………………………………………………258
13.2 Synchronizing with the Grid ……………………………………………………………261
13.2.1 Inrush Current …………………………………………………………………..261
13.2.2 Synchronous Operation ………………………………………………………263
13.2.3 Load Transient…………………………………………………………………..264
13.2.4 Safety……………………………………………………………………………….264
13.3 Operating Limit ……………………………………………………………………………..265
13.3.1 Voltage Regulation …………………………………………………………….265
13.3.2 Stability Limit …………………………………………………………………..266
13.4 Energy Storage and Load Scheduling……………………………………………….268
13.5 Utility Resource Planning Tools ………………………………………………………269
13.6 Wind Farm–Grid Integration ……………………………………………………………270
13.7 Grid Stability Issues ……………………………………………………………………….271
13.7.1 Low-Voltage Ride-Through ………………………………………………..271
13.7.2 Energy Storage for Stability ……………………………………………….272
13.8 Distributed Power Generation ………………………………………………………….273
References………………………………………………………………………………………………..274
Chapter 14
Electrical Performance……………………………………………………………277
14.1 Voltage Current and Power Relations ……………………………………………….277
14.2 Component Design for Maximum Efficiency…………………………………….278
14.3 Electrical System Model …………………………………………………………………280
14.4 Static Bus Impedance and Voltage Regulation …………………………………..281
14.5 Dynamic Bus Impedance and Ripples ………………………………………………283
14.6 Harmonics……………………………………………………………………………………..284
14.7 Quality of Power…………………………………………………………………………….285
14.7.1 Harmonic Distortion Factor ………………………………………………..286
14.7.2 Voltage Transients and Sags ……………………………………………….287
14.7.3 Voltage Flickers…………………………………………………………………288
14.8 Renewable Capacity Limit ………………………………………………………………290
14.8.1 System Stiffness ………………………………………………………………..290
14.8.2 Interfacing Standards………………………………………………………….293
14.9 Lightning Protection ……………………………………………………………………….295
14.10 National Electrical Code
®
………………………………………………………………..297
References………………………………………………………………………………………………..297
Chapter 15
Plant Economy ………………………………………………………………………299
15.1 Energy Delivery Factor……………………………………………………………………299
15.2 Initial Capital Cost………………………………………………………………………….301
15.3 Availability and Maintenance…………………………………………………………..302
15.4 Energy Cost Estimates…………………………………………………………………….303
15.5 Sensitivity Analysis ………………………………………………………………………..305
15.5.1 Effect of Wind Speed …………………………………………………………305
15.5.2 Effect of Tower Height……………………………………………………….305
15.6 Profitability Index …………………………………………………………………………..307
15.6.1 Wind Farm Screening Chart ……………………………………………….308
15.6.2 PV Park Screening Chart ……………………………………………………308
15.6.3 Stand-Alone PV vs. Grid Line…………………………………………….311
15.7 Hybrid Economics ………………………………………………………………………….312
15.8 Project Finance ………………………………………………………………………………313
References………………………………………………………………………………………………..316
Chapter 16
The Future …………………………………………………………………………….317
16.1 World Electricity Demand up to 2015 ………………………………………………317
16.2 Kyoto Treaty ………………………………………………………………………………….318
16.3 Future of Wind Power …………………………………………………………………….320
16.4 PV Future………………………………………………………………………………………326
16.5 Wind and PV Growth ……………………………………………………………………..327
16.6 Declining Production Cost ………………………………………………………………329
16.7 Market Penetration………………………………………………………………………….331
16.8 Effect of Utility Restructuring………………………………………………………….333
16.8.1 Energy Policy Act of 1992………………………………………………….334
16.8.2 Impact on Green Power ……………………………………………………..336
16.8.3 Green-Power Marketing ……………………………………………………..336
16.9 Strained Grids ………………………………………………………………………………..337
References………………………………………………………………………………………………..338
PART D
Ancillary Power Technologies
Chapter 17
Solar Thermal System…………………………………………………………….341
17.1 Energy Collection …………………………………………………………………………..342
17.1.1 Parabolic Trough ……………………………………………………………….342
17.1.2 Central Receiver ………………………………………………………………..342
17.1.3 Parabolic Dish …………………………………………………………………..343
17.2 Solar-II Power Plant ……………………………………………………………………….343
17.3 Synchronous Generator …………………………………………………………………..345
17.3.1 Equivalent Electrical Circuit ……………………………………………….348
17.3.2 Excitation Methods ……………………………………………………………348
17.3.3 Electric Power Output………………………………………………………..349
17.3.4 Transient Stability Limit …………………………………………………….351
17.4 Commercial Power Plants ……………………………………………………………….352
17.5 Recent Trends ………………………………………………………………………………..353
References………………………………………………………………………………………………..354
Chapter 18
Ancillary Power Systems………………………………………………………..355
18.1 Heat-Induced Wind Power……………………………………………………………….355
18.2 Marine Current Power …………………………………………………………………….355
18.3 Ocean Wave Power…………………………………………………………………………358
18.4 Piezoelectric Generator……………………………………………………………………360
18.5 Jet-Assisted Wind Turbine……………………………………………………………….361
18.6 Solar Thermal Microturbine …………………………………………………………….362
18.7 Thermophotovoltaic System …………………………………………………………….363
References………………………………………………………………………………………………..364
Chapter 19
Contrarotating Wind Turbines………………………………………………….365
19.1 Introduction……………………………………………………………………………………365
19.2 Potential Applications……………………………………………………………………..366
19.3 Mathematical Model……………………………………………………………………….367
19.3.1 Velocity Components …………………………………………………………368
19.3.2 Force Components……………………………………………………………..369
19.4 Prototype Design ……………………………………………………………………………371
19.4.1 Design Method ………………………………………………………………….372
19.4.2 Selection of Sensors …………………………………………………………..375
19.5 Prototype Tests……………………………………………………………………………….377
19.5.1 Generator Performance Tests ………………………………………………377
19.5.2 Turbine Performance Tests………………………………………………….377
19.5.3 Field-Test Instrumentation ………………………………………………….379
19.5.4 Discussion of Field-Test Data……………………………………………..382
19.5.5 Buffeting…………………………………………………………………………..386
19.6 Wind Farm Power Density ………………………………………………………………388
19.7 Retrofit Implementation and Payback……………………………………………….389
19.7.1 Dual Wind Turbines Back-to-Back in Tandem ……………………..389
19.7.2 Contrarotating Rotors on a Single Generator………………………..390
19.7.3 Retrofit Cost and Payback Period………………………………………..390
19.8 Conclusions……………………………………………………………………………………390
Acknowledgment ………………………………………………………………………………………392
References………………………………………………………………………………………………..392
Appendices
Appendix 1: National Electrical Code
®
(Article 705) ……………………………………395
Appendix 2: Sources of Further Information on Renewable Energy……………….401
Solar Energy Information Sources ………………………………………………………………403
Manufacturers of Solar Cells and Modules in the U.S. …………………………………403
Wind Energy Information Sources………………………………………………………………405
University Wind Energy Programs in the U.S………………………………………………406
Periodicals on Wind Energy……………………………………………………………………….408
International Wind Energy Associations ………………………………………………………410
Wind Power System Suppliers in the U.S. …………………………………………………..412
European Wind Energy Manufacturers and Developers…………………………………414
Research and Consultancy………………………………………………………………………….419
National Associations ………………………………………………………………………………..422
Acronyms…………………………………………………………………………………………………427
Prefixes:……………………………………………………………………………………………………428
Conversion of Units…………………………………………………………………………………..429
Further Reading ………………………………………………………………………………………..431
Index
……………………………………………………………………………………………………433
