kW and kWh analysis

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

11. 11

12. 12

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:// www.nrel.gov http://www.eere.energy.gov
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

36. 36

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. https://en.wikipedia.org/wiki/Quad_(unit)
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
•http://www.prairiestateenergycampus.com/default.asp
$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