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  1. Renewable Energy Generation: An Introduction Chapter 1 The Electric Power Industry Dr. Wenzhong Gao
  2. Course Syllabus “Introduction to Renewable Energy Generation” is an elective course offered in the School of Engineering and Computer Science, suitable for all undergraduate students in the school. The goal is to let students learn international state of the art of renewable energy and new energy technology. In this course, basic concepts, state of the art, basic principles and related technology for new and renewable energy power generation will be introduced. The following topics will be covered: distributed and clean power generation (wind, solar, fuel cells, etc), energy storage system application, environmental impacts, renewable energy system economics, etc. 2
  3. Course Syllabus • Goal: promote engineering for sustainability, environmentally benign electric power systems, energy efficiency, new power technologies, (reduce loss, waste heat re-use, power gen at load proximity, microgrid, smart grid, etc) • Course intended for upper division engineering students and graduate students • Course is quantitative and applications oriented with emphasis on resource estimation, system sizing, and economic evaluation. 3
  4. Course Syllabus • Overview of today’s power grid (text Chap 1): regulatory and history evolution, how power plants operate. • Economics (text appendix) • Compromise different backgrounds: (text Chapter 2) we review basic concepts of electricity and magnetism. • Intro to electric power concepts (text Chapter 3): power factor, transmission lines, three-phase power, power supplies, power quality. 4 Text:Gilbert M. Masters,Renewable and Efficient Electric Power Systems, Wiley--IEEE Press, 2nd Edition, 2013 References: related papers such as EEE publications
  5. Course Syllabus • Solar Resource (text Chapter 4): estimate insolation at any location and time on earth. • Photovoltaic Materials and Electrical Characteristics (text Chapter 5): Photovoltaic Systems (text Chapter 6) semiconductor physics, PV modeling, applications/designs. • Wind power systems (text Chap 7): wind power production, wind statistics, efficiency limit, speed control. 5
  6. Course Syllabus • Other renewable Energy Systems and Distributed Generation (DG, text Chapter 8): CSP, wave energy, tidal power, micro- hydro, biomass, geothermal. • Smart Grid and emerging technologies (text Chapter 9): energy storages, DSM, economics of energy efficiency, CHP, micro turbines, fuel cells. • Advanced topics / projects / case studies 6
  7. Modern Power System • Large central units  high-voltage transmission lines distribution networks  electricity customers • US grid: over 275,000 miles of high-voltage electric transmission lines; ~1 terawatt (TW) of electrical power; customer base of over 300 Million people. • Resistive losses in transmission lines are now estimated to be about 10% annually (which is 0.1 TW of power dissipated as heat!). -- inefficiency • Power industry pollution in US: ¾ of SOx, 1/3 of CO2 and NOx, ¼ of particulate matter and toxic heavy metals -- • (research the above quantities to be still right!) • (if we double voltage, how much loss reduction? analogy between computer storage and power) 7
  8. Energy use and resource • World energy consumption, supplied by: oil, coal, natural gas, biomass and waste, nuclear, hydro, other renewables. • Finite resources: global reserves • Energy security and disparity of use • Environmental impact of energy use: CO2, greenhouse, global warming, climate change; • Cost of electricity and environmental cost, environmental levy, carbon tax, carbon trade? • Efficient energy use: save, consume less, the most cost effective way for sustainability • Possible solutions? CO2 capture and sequestration, carbon neutral ways of power generation, efficiency 8
  9. Structure of Power Systems • Generation source of power, ideally with a specified voltage and frequency • Transmission, transmits power; ideally as a perfect conductor • Distribution • Utilization (load), consumes power; ideally with a constant resistive value 9
  10. Structure of Power Systems 10 161kV, 3 transmission line Boiler or reactor Turbine Alternator Unit trans- former CB CB Power Trans. CB CB Power trans- former CB CB CB CB Generation Substation Substation Three-phase 345kV transmission line CB = Circuit Breaker 20kV 161kV bus Distribution lines 7.16kV, 1 distribution line Distribution transformer 120/240V, 1 to consumer Utilization
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  13. Wind Energy Needed: goal - 20%30 13
  14. Wind power increase 14 Wind power plant in Xinjiang, China Increasing wind power capacity worldwide  Wind power experiences a steady increase in recent decade as the worldwide installed wind power capacity attained 430 GW in 2015.  The largest onshore wind farms, located in Gansu, China, generated electric power up to 6000 MW.  The ongoing research plans to develop single wind turbines with the capacity of 10 – 20 MW for the offshore use  The efficiency of wind power generation depends largely on the performance of wind turbine control with the increased turbine capacity and flexibility of structures.
  15. RE generation from technologies that are commercially available today, in combination with a more flexible electric system, is more than adequate to supply 80% of total U.S. electricity generation in 2050—while meeting electricity demand on an hourly basis in every region of the country. http:// 2010 2050 A Transformation of the U.S. Electricity System 15
  16. Example Power Grid 16
  17. Brief Background on the Electric Utility Industry • First real practical uses of electricity began with the telegraph (around the civil war) and then arc lighting in the 1870’s (Broadway, the “Great White Way”). • Central stations for lighting (incandescent lamp) began with Edison in 1882, using a dc system (safety was key), but transitioned to ac within several years. Chicago World’s fair in 1893 was key demonstration of electricity (Edison vs. Westinghouse) • High voltage ac started being used in the 1890’s with the Niagara power plant transferring electricity to Buffalo; also 30kV line in Germany • Frequency standardized in the 1930’s 17
  18. Regulation and Large Utilities • Electric usage spread rapidly, particularly in urban areas. Samuel Insull (originally Edison’s secretary, but later from Chicago) played a major role in the development of large electric utilities and their holding companies. • Insull was also instrumental in start of state regulation in 1890’s,leading to the concept of regulated utilities with monopoly franchises: (1) Franchise territories; (2) Price controlled by Public Utility Commissions (PUCs). • Public Utilities Holding Company Act (PUHCA) of 1935 essentially broke up inter-state holding companies. 18
  19. Regulation and Large Utilities • This gave rise to electric utilities that only operated in one state • PUHCA was repealed in 2005 (Energy Policy Act 2005) • For most of the last century electric utilities operated as vertical monopolies 19
  20. Regulatory and Power Market History, 1970’s •1970’s brought inflation, increased fossil-fuel prices, calls for conservation and growing environmental concerns •Increasing rates replaced decreasing ones •As a result, U.S. Congress passed Public Utilities Regulator Policies Act (PURPA) in 1978, which mandated utilities must purchase power from independent generators located in their service territory (modified 2005). •PURPA introduced some competition, but its implementation varied greatly by state 20
  21. PURPA and Renewables •PURPA, through favorable contracts, caused the growth of a large amount of renewable energy in the 1980’s (about 12,000 MW of wind, geothermal, small scale hydro, biomass, and solar thermal) •These were known as “qualifying facilities” (QFs) •California added about 6000 MW of QF capacity during the 1980’s, including 1600 MW of wind, 2700 MW of geothermal, and 1200 MW of biomass •By the 1990’s the ten-year QFs contracts written at rates of $60/MWh in 1980’s, and they were no longer profitable at the $30/MWh 1990 values so many sites were retired or abandoned 21
  22. History, cont’d – 1990’s & 2000’s •Major opening of industry to competition occurred as a result of National Energy Policy Act of 1992 •This act mandated that utilities provide “nondiscriminatory” access to the high voltage transmission • FERC Oder 888 (in 1996) – encouraged formation of nonprofit independent system operators (ISO) to control the operation of transmission facilities owned by traditional utilities. • FERC Order 2000 (in 1999) – create regional transmission organizations (RTOs) to break up the vertically integrated utilities 22
  23. The seven ISO/RTOs deliver two-thirds of the U.S. electricity ISO/RTOs in the US 23
  24. History, cont’d – 1990’s & 2000’s •Major opening of industry to competition occurred as a result of National Energy Policy Act of 1992 •This act mandated that utilities provide “nondiscriminatory” access to the high voltage transmission •Goal was to set up true competition in generation •Result over the last few years has been a dramatic restructuring of electric utility industry (for better or worse!) •Energy Bill 2005 repealed PUHCA; modified PURPA 24
  25. National Energy Policy Act of 1992 • Production tax credit (PTC) : At the time it provided an inflation-adjustable 1.5 ¢/kWh income tax credit for the first 10 years of production. As of 2012, the PTC rate was 2.2 ¢/kWh. • Over time the PTC has been extended, usually for just a few years at a time. • The alternative to the PTC has been a 30% investment tax credit (ITC), which at times Congress has allowed to be paid as an upfront cash payment delivered when the project is placed in service. •Another tax incentive for businesses is the right to use a rapid depreciation schedule called the Modified Accelerated Cost Recovery System (MACRS) 25
  26. Vertical Monopolies • Within its service territory each utility was the only game in town • Neighboring utilities functioned more as colleagues than competitors • Utilities gradually interconnected their systems so by 1970 transmission lines crisscrossed North America, with voltages up to 765 kV • Economies of scale keep resulted in decreasing rates, so most every one was happy 26
  27. Generation Transmission Distribution Customer Service • Within a particular geographic market, the electric utility had an exclusive franchise • In return for this exclusive franchise, the utility had the obligation to serve all existing and future customers at rates determined jointly by utility and regulators • It was a “cost plus” business Vertical Monopolies 27
  28. The Goal: Customer Choice 28
  29. History, cont’d – 1990’s & 2000’s •Goal was to set up true competition in generation •Result over the last few years has been a dramatic restructuring of electric utility industry (for better or worse!) •Energy Bill 2005 repealed PUHCA; modified PURPA 29
  30. Power System Restructuring 30
  31. Power System Restructuring •In this structure, Generation Companies (GENCOs) will be separately owned and compete to sell energy to customers, and may no longer be controlled by the same entities that control the transmission system. •Transmission Companies (TRANSCOs) will move power from place to place over the high-voltage lines. •Distribution Companies (DISTCOs) will move power at the retail level and may aggregate retail loads. 31
  32. US Utilities 32
  33. • Nonutility generators have become a significant portion of total electricity generated in the United States. Utilities and Nonutilities 33
  34. NORTH AMERICAN INTERCONNECTIONS •Transmission of U.S. electric power is divided into three quite separate power grids, which are further subdivided into 10 North American Electric Reliability Council Regions. •ECAR, East Central Area Reliability Coordination Agreement; ERCOT, Electric Reliability Council of Texas; FRCC, Florida Reliability Coordinating Council; MAAC, Mid-Atlantic Area Council; MAPP, Mid-Continent Area Power Pool; MAIN, Mid- America Interconnected Network; NPCC, Northeast Power Coordinating Council; SERC, Southeastern Electric Reliability Council; SPP, Southwest Power Pool; WSCC, Western Systems Coordinating Council. (EIA 2001). 34
  35. North American Electricity Grid • Three separate interconnection grids—the Eastern Interconnect, the Western Interconnect, and Texas. • Interconnections between the grids are made using high voltage DC (HVDC) links. • North American Electric Reliability Corporation (NERC): eight regional councils. Established after 1965 Northeast Blackout • Responsible for overseeing operations in the electric power industry and for developing and enforcing mandatory reliability standards. • Western Electricity Coordinating Council (WECC) covers the 12 states west of the Rockies and the Canadian provinces of British Columbia and Alberta. 35
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  37. Current Midwest Electric Grid as an Example 37
  38. • Primary energy sources: fossil fuels (coal, natural gas, some oil) for 70% of US electricity; nuclear and hydro 30%; plus small other renewables • Efficiency from primary energy to end-use energy: ~1/3 • See figure in next slide, T and D loss 3.1% out of 34.7% Gross Generation Power Industry Statistics 38
  39. Energy sources for U.S. electricity in 2010 (based on EIA Monthly Energy Review, 2011). Power Industry Statistics 39
  40. Only about one-third of the energy content of fuels ends up as electricity delivered to customers (losses shown are based on data in the 2010 EIA Annual Energy Review). Power Industry Statistics 40
  41. Energy Flow Chart (Sankey Diagrams) 2013 41
  42. Energy Flow Chart (Sankey Diagrams) 2014 42
  43. Energy Flow Chart (Sankey Diagrams) • A quad is a unit of energy equal to 1015 (a short-scale quadrillion) BTU, or 1.055 × 1018 joules (1.055 exajoules or EJ) in SI units. • The unit is used by the U.S. Department of Energy in discussing world and national energy budgets. The global primary energy production in 2004 was 446 quad, equivalent to 471 EJ. • Some common types of an energy carrier approximately equal 1 quad are: • 8,007,000,000 Gallons (US) of gasoline • 293,083,000,000 Kilowatt-hours (kWh) • 33.434 gigawatt-years (GWy) • 36,000,000 Tonnes of coal • 970,434,000,000 Cubic feet of natural gas • 5,996,000,000 UK gallons of diesel oil • 25,200,000 Tonnes of oil • 252,000,000 Tonnes of TNT or five times the energy of the Tsar Bomba nuclear test. • 13.3 Tonnes of Uranium-235 43
  44. • Distribution of retail sales of electricity by end use. Residential and commercial buildings account for over two-thirds of sales. Total amounts in billions of kWh (TWh) are 2010 data. Industry Statistics 44
  45. •All power systems have three major components: Load, Generation, and Transmission/Distribution. •Load: Consumes electric power •Generation: Creates electric power. •Transmission/Distribution: Transmits electric power from generation to load. •A key constraint is since electricity can’t be effectively stored, at any moment in time the net generation must equal the net load plus losses Power System Structure 45
  46. Example: Daily Variation for CA 46
  47. Example: Weekly Variation 47
  48. Example: Weekly Variation 48
  49. Balancing Electricity Supply and Demand 49 Bathtub analogy that incorporates the roles that different kinds of power plants provide as well as the potential for demand response
  50. Grid Stability 50 After a sudden loss of generation, automatic controls try to bring frequency to an acceptable level within seconds. Operator-dispatched power takes additional time to completely recover. From Eto et al., 2010.
  51. Balancing Authority (BA) Areas • Transmission lines that join two areas are known as tie- lines. • The net power out of an area is the sum of the flow on its tie-lines. • The flow out of an area is equal to total gen - total load - total losses = tie-flow 51
  52. Area Control Error (ACE) • The area control error is the difference between the actual flow out of an area, and the scheduled flow. • Ideally the ACE should always be zero. • Because the load is constantly changing, each utility must constantly change its generation to “chase” the ACE. 52
  53. Automatic Generation Control • BAs use automatic generation control (AGC) to automatically change their generation to keep their ACE close to zero. • Usually the BA control center calculates ACE based upon tie- line flows; then the AGC module sends control signals out to the generators every couple seconds. 53
  54. Generator Costs • There are many fixed and variable costs associated with power system operation. • The major variable cost is associated with generation. • Cost to generate a MWh can vary widely. • For some types of units (such as hydro and nuclear) it is difficult to quantify. • Many markets have moved from cost-based to price-based generator costs 54
  55. Economic Dispatch • Economic dispatch (ED) determines the least cost dispatch of generation for an area. • For a lossless system, the ED occurs when all the generators have equal marginal costs. IC1(PG,1) = IC2(PG,2) = … = ICm(PG,m) 55
  56. Frequency Control • Steady-state operation only occurs when the total generation exactly matches the total load plus the total losses • too much generation causes the system frequency to increase • too little generation causes the system frequency to decrease (e.g., loss of a generator) • AGC is used to control system frequency 56
  57. 8760 Example: Annual System Load 57
  58. Load Duration Curve • A very common way of representing the annual load is to sort / rank the one hour values, from highest to lowest. This representation is known as a “load duration curve.” 58 6000 5000 4000 3000 2000 1000 0 DEMAND (MW) 0 1000 HRS 7000 8760 Load duration curve tells how much generation is needed
  59. State Variation in Electric Rates 59
  60. Renewable Portfolio Standards • Individual state-by-state enacted Renewable Portfolio Standards (RPS) that require retail power suppliers to provide a certain minimum percentage of electricity from specified renewable power sources, including wind power. These have been a powerful motivator behind the rapid growth of wind and solar energy systems. 60
  61. Renewable Portfolio Standards (September 2009) 61
  62. Renewable Portfolio Standards (March 2013) 62 REC
  63. In the News: California to go to 33% Renewable Portfolio Standard (RPS) •On Friday the California legislature passed a bill to raise their RPS value from 20% by 2010 to 33% by some future date. •Governor Schwarzenegger plans to veto the bill because it is overly complex, and (in his opinion) unnecessarily restricts the import of renewable energy from other states •He would implement the 33% by executive order; this order would also apply to municipal utilities in the state like LAPW •Presently San Diego Gas and Electric is only getting 6% from renewables and is unlikely to meet the 2010 date 63
  64. Duck Curve 64 64 The CAISO Duck Chart Source: CAISO 2013 As the solar penetration increases, the net load profile becomes more and more like a “duck” shape.
  65. Electric Power Infrastructure: Generation 65
  66. Thermodynamic cycles for Heat Engines • Rankine Cycle: Working fluid (water) changes between gas and liquid (condensed); baseload plants • Brayton cycle: the working fluid remains a gas throughout the cycle; gas turbines, peaking plants • Combined-cycle plants: new generation of thermal power plants use both cycles to get higher efficiency 66
  67. Carnot Efficiency for Heat Engines • Steam turbines, gas turbines, ICE convert heat into mechanical work, then to electric generator. These heat engines generate 90% of US electricity. • Fundamental limit to the max possible energy- conversion efficiency? • Based on the theory of Entropy, Carnot found the limit of a heat engine operating between a hot and cold thermal reservoir: • Example: for 1000 K source and 300 K sink, the limit would be 70%. 67 H C T T  1 max 
  68. Basic Steam Power Plant 68
  69. Basic Steam Power Plant 69 2 types cooling: (1) once-through cooling, requires more water / thermal pollution ; (2) Cooling tower, evaporation into atmosphere
  70. Coal-fired Steam Power Plant 70
  71. • City Water Light and Power (CWLP) is building a new 200 MW, • $500 million, pulverized coal power plant at their existing Dallman plant location of Lake Springfield • Final testing is taking place this month, well ahead of schedule (4/10) Modern Coal Power Plant Dallman 4, Under Construction 71
  72. • Located in Southern Illinois near St. Louis, construction started in October 2007 with completion expected is 2011/2 •Largest Coal-Fired Plant •under construction •in the United States; now 25% complete • $4 Billion, 1600 MW Prairie State Energy Campus Under Construction 72
  73. Combustion gas turbines 73
  74. •Brayton Cycle: Working fluid is always a gas •Most common fuel is natural gas Maximum Efficiency 550 273 1 42% 1150 273      •Typical efficiency is around 30 to 35% Basic Gas Turbine 74
  75. Source: Masters Gas Turbine 75
  76. 76
  77. • Efficiencies of up to 60% can be achieved, with even higher values when the steam is used for heating Combined Cycle Power Plants 77
  78. Combine cycle 78
  79. Combine cycle 79
  80. • Overall Thermal Efficiency = 33% (Electricity) + 53% (Heat) = 86% Combined Heat and Power 80
  81. Polyphase Synchronous Generators 81
  82. Polyphase Synchronous Generators • A Single-phase synchronous generator: • For two pole-machines, how fast would the rotor turn to have 60Hz AC? • Ns = rotor shaft rotation rate = 1 revolution per cycle/cycle x 60 cycles/sec x 60 sec/min = 3600 rpm • If we have p-poles, the rotor would need to be slower: • Ns = 120f/p, where f is frequency (60Hz), p is number of poles • (why? Since in each revolution the rotor turns, the AC will have p/2 cycles) 82
  83. Voltage and current can be created by (a) moving a conductor through a magnetic field, or (b) moving the magnetic field past the conductors. The armature windings indicate current flow into the page with an “x” and current out of the page with a dot (the x is meant to resemble the feathers of an arrow moving away from you; the dot is the point of the arrow coming toward you). A Simple Generator 83
  84. Changing flux in the stator creates an emf voltage across the windings. A Simple Generator 84
  85. As the permanent-magnet rotor turns, it causes magnetic flux within the iron stator to vary (approximately) sinusoidally. The windings around the stator therefore see a time-varying flux, which creates a voltage across their terminals. A Simple Generator 85
  86. Operation Principle The rotor of the generator is driven by a prime-mover A dc current is flowing in the rotor winding which produces a rotating magnetic field within the machine The rotating magnetic field induces a three-phase voltage in the stator winding of the generator 3-phase ac: 120 degree apart Polyphase Synchronous Generators 86
  87. Field windings on (a) 2-pole, round rotor and (b) 4-pole, salient rotor Single-Phase Synchronous Generators 87
  88. (a) A 2-pole machine has one N and one S pole on the rotor and on the stator. (b) A 4-pole machine has 4 poles on the rotor and 4 on the stator Single-Phase Synchronous Generators 88
  89. Three-Phase Synchronous Generators (a) A 2-pole, 3-phase synchronous generator. (b) Three-phase stator output voltage. • A 4-pole, 3-phase, wye-connected, synchronous generator with a 4-pole rotor. • The dc rotor current needs to be delivered to the rotor through brushes and slip rings. 89
  90. •Large plants predominate, with sizes up to about 1500 MW. •Coal is most common source (45%), followed by natural gas(24%), nuclear (20%) and renewables (10%). •New construction is mostly natural gas, with economics highly dependent upon the gas price •Generated at about 20 kV for large plants Generation 90
  91. Loads •Can range in size from less than one watt to 10’s of MW •Loads are usually aggregated for system analysis •The aggregate load changes with time, with strong daily, weekly and seasonal cycles • Load variation is very location dependent 91
  92. Some notations • Power: Instantaneous consumption of energy • Power Units • Watts = voltage x current for dc (W) • kW – 1 x 10^3 Watt • MW – 1 x 10^6 Watt • GW – 1 x 10^9 Watt • Installed U.S. generation capacity is about 900 GW ( about 3 kW per person) 92
  93. Some concepts / notations • Energy: Integration of power over time; energy is what people really want from a power system. • Energy content. The energy content of a fuel (also referred as heating value) is the heat released when a known quantity of fuel is burned under specific conditions. The typical energy content of natural gas in the U.S. is roughly 1,027 BTU/cf depending on gas composition. • U.S. electric energy consumption is about 3600 billion kWh (about 13,333 kWh per person, which means on average we each use 1.5 kW of power continuously) 93
  94. Some notations • Energy Units • Joule = 1 Watt-second (J) • kWh – Kilowatthour (3.6 x 10^6 J) • BTU – 1055 J; 1 MBTU=0.293 MWh • Other energy relations: • 1 MWh=3.413MBTU (10^6BTU); • 1BTU=1055joules • 1 Quad= 10^15 BTUs 94
  95. Heat Rate •The thermal efficiency of a power plant is often expressed as a heat rate, which is the thermal energy input (Btu or kJ) required to deliver 1 kWh of electrical output (1 Btu/kWh = 1.055 kJ/kWh) at the busbar. The smaller the heat rate, the higher the efficiency. •Heat rate = 3.412 MBtu/MWh/efficiency •3600 kJ in a kWh 95
  96. Heat Rate •Example, a 33% efficient plant has a heat rate of 10.24 Mbtu/MWh •The heat rate is an average value that can change as the output of a power plant varies. • Fuel costs are usually specified as a fuel cost, in $/Mbtu, times the heat rate, in MBtu/MWh •Do Example 1.1, material balance 96 IGCC Coal plant Heat Rate is 9,000 Btu/kWh NGCC plant heat rate is 7,000 Btu / kWh
  97. Exercise Consider an average PC plant with a heat rate of 10,340 Btu/kWh burning a typical U.S. coal with a carbon content of 24.5 kgC/GJ (1 GJ = 109 J). About 15% of thermal losses are up the stack and the remaining 85% are taken away by cooling water. a. Find the efficiency of the plant. b. Find the rate of carbon and CO2 emissions from the plant in kg/kWh. c. If CO2 emissions eventually are taxed at $10 per metric ton (1 metric ton = 1000 kg), what would be the additional cost of electricity from this coal plant (₡/kWh)? d. Find the minimum flow rate of once-through cooling water (gal/kWh) if the temperature increase in the coolant returned to the local river cannot be more than 20°F. e. If a cooling tower is used instead of once-through cooling, what flow rate of water (gal/kWh) taken from the local river is evaporated and lost. Assume 144 Btu are removed from the coolant for every pound of water evaporated. 97
  98. Solution 98
  99. Solution 99
  100. Determining operating costs •In determining whether to build a plant, both the fixed costs and the operating (variable) costs need to be considered. •Once a plant is build, then the decision of whether or not to operate the plant depends only upon the variable costs •Variable costs are often broken down into the fuel costs and the O&M costs (operations and maintenance) •Fuel costs are usually specified as a fuel cost, in $/Mbtu, times the heat rate, in MBtu/MWh •Heat rate = 3.412 MBtu/MWh if 100%efficiency •Example, a 33% efficient plant has a heat rate of 10.24 100
  101. Fixed Charge Rate (FCR) •The capital costs for a power plant can be annualized by multiplying the total amount by a value known as the fixed charge rate (FCR) •The FCR accounts for fixed costs such as interest on loans, acceptable returns to investors, fixed operation and maintenance costs, and taxes. •The FCR varies with interest rates, and is now below 10%. •For comparison this value is often expressed as $/yr-kW •Annual fixed costs ($/yr) = PR(kW)Xcapital cost ($/kW) X FCR (%/yr) [this is for the entire plant] •Annual Payments on a loan ($/yr) = P($)X CRF (%/yr) • CRF = i(1+i)^n / [(1+i)^n-1] 101
  102. Annualized Operating Costs •The operating costs can also be annualized by including the number of hours a plant is actually operated •Assuming full output the value is •Variable ($/yr-kW) = [Fuel($/Btu) * Heat rate (Btu/kWh) + O&M($/Kwh)]*(operating hours per year) 102
  103. Coal Plant Example – Electricity pricing •Assume capital costs of $4 billion for a 1600 MW coal plant with a FCR of 10% and operation time of 8000 hours per year. Assume a heat rate of 10 Mbtu/MWh, fuel costs of 1.5 $/Mbtu, and variable O&M of $4.3/MWh. What is annualized cost per kWh? Variable ($/yr-kW) =[Fuel($/Btu) * Heat rate (Btu/kWh) + O&M($/Kwh)] * (operating hours per year) 103
  104. Coal Plant Example • Assume capital costs of $4 billion for a 1600 MW coal plant with a FCR of 10% and operation time of 8000 hours per year. Assume a heat rate of 10 Mbtu/MWh, fuel costs of 1.5 $/Mbtu, and variable O&M of $4.3/MWh. What is annualized cost per kWh? Fixed Cost($/kW) = $4 billion/1.6 million kW=2500 $/kW Annualized capital cost = $250/kW-yr Annualized operating cost = (1.5*10+4.3)*8000/1000 = $154.4/kW- yr Cost = $(250 + 154.4)/kW-yr /(8000h/yr) = $0.051/kWh 104
  105. Capacity Factor (CF) • The term capacity factor (CF) is used to provide a measure of how much energy a plant actually produces compared to the amount assuming it ran at rated capacity for the entire year. CF = Actual yearly energy output / (Rated Power * 8760) • The CF varies widely between generation technologies, 105 8760 8760 ) ( 8760 0 year per P at Op of Hrs Equivalent P dt t p CF rated rated    
  106. Generator Capacity Factors 106 Source: EIA Electric Power Annual, 2007 The capacity factor for solar is usually less than 25% (sometimes substantially less), while for wind it is usually between 20 to 40%). A lower capacity factor means a higher cost per kWh
  107. Appendix A Energy Economics Tutorial 107
  108. Screening curve • A very simple mode of the economics of a given power plant takes all of the costs and puts them into two categories: fixed cost and variable costs. • Fixed costs are monies that must be spent even if the power plant is never turned on. • Variable costs are the added costs associated with actually running the plant. • The first step in finding the optimum mix of power plants is to develop screening curves that show annual revenues required to pay fixed and variable costs as a function of hours per year that the plant is operated. 108
  109. Screening curve • The capital costs of a power plant can be annualized by multiplying it by a quantity called fixed charging rate (FCR). Fixed ($/yr-kW) = Capital cost ($/kW) * Fixed charge rate (yr-1) • The variable costs, which are also annualized, depend on the unit cost of fuel, the O&M rate for actual operation of the plant, and the number of hours per year the plant is operated. Variable ($/yr-kW) = [Fuel ($/Btu) * Heat rate (Btu/kWh) + O&M ($/kWh)] *h/yr 109
  110. Screening curve example • Cost of Electricity from a Coal-Fired Steam Plant. Find the annual revenue required for a pulverized-coal steam plant using parameters given in Table 3.3. Assume a fixed charge rate of 0.16/yr and assume that the plant operates at the equivalent rate of full power for 8000 hours per year. What should be the price of electricity from this plant? 110
  111. Screening curve (224 150.80)$ / Price 1 $0.0469 / 4.69 / 8000 / yr kW kW kWh cents kWh kWh yr       111 • Fixed cost = $1400/kW * 0.16/yr = $224/kW-yr • The variable cost for fuel and O&M, operating 8000 hours at full power, would be • Variable = ($1.50/10^6 Btu * 9700 Btu/kWh + 0.0043 $/kWh) * 8000 hr/yr = 0.01885 $/kWh * 8000 hr/yr = $150.80 /kW-yr • For a 1-kW plant, • Electricity generated = 1 kW * 8000 hr/yr = 8000 kWh/yr • Capacity factor (CF) = 8000 / 8760 = 91.32 % • CF = Annual output (kWh/yr) / [Rated power (kW)* 8760 hr/yr]
  112. Screening curves 112 • The average cost of electricity is the slope of the line drawn from the origin to point on the revenue curve that corresponds to the capacity factor. The data shown are for the coal plant in Example 3.3 Slope: $150.80 / 8000 = $0.0189
  113. Screening curves 113 • Screening curves for coal-steam, combustion turbine, and combined-cycle plants based on data in Table 3.3. For plants operated less than 1675 h/yr, combustion turbines are least expensive; for plants operated more than 6565 h/yr, a coal-steam plant is cheapest; otherwise, a combined-cycle plant is least expensive
  114. Load-Duration curve 114 • A load-duration curve is simply the hour-by-hour curve rearranged from chronological order into an order based on magnitude. The area under the curve is the total kWh/yr.
  115. Load-Duration curve Example 115 Tells how many hours per year the load MW is equal to or above a particular value.
  116. 116 • Plotting the crossover points from screening curves onto the load-duration curve to determine an optimum mix of power plants
  117. 117 Mapping those capacity factors onto the screening curves indicates new coal plants delivering electricity at 8.6 ¢/kWh, the NGCC plants at 11.6 ¢/kWh, and the CTs delivering power at 27.7 ¢/kWh.
  118. Load-Duration curve Example 118 Tells how many hours per year the load MW is equal to or above a particular value.
  119. Load-Duration curve 119 • Plotting the crossover points from screening curves onto the load-duration curve to determine an optimum mix of power plants
  120. END 120