Masters G.M. Renewable and Efficient Electric Power Systems

Подождите немного. Документ загружается.

138 THE ELECTRIC POWER INDUSTRY

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.

Variab le ($/yr-kW) = [Fuel ($/Btu) × Heat rate (Btu/kWh)

+ O&M ($/kWh)] × h/yr (3.19)

In (3.19) it is assumed that the plant runs at full rated power while it is operated,

but no power at other times. Adjusting for less than full power is an easy mod-

iﬁcation that will be introduced later. Also, (3.19) assumes that the fuel cost is

ﬁxed, but it too is easily adjusted to account for fuel escalation and inﬂation. For

our purposes here, these modiﬁcations are not important. They will, however,

be included in the economic analysis of power plants presented in Chapter 5.

Table 3.3 provides some representative costs for some of the most commonly

used power plants.

Example 3.3 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?

Solution From (3.18) the annual ﬁxed revenue required would be

Fixed costs = $1400/kW × 0.16/yr = $224/kW-yr

TA BLE 3.3 Example Cost Parameters for Power Plants

Technology Fuel

Capital

Cost

($/kW)

Heat

Rate

(Btu/kWh)

Fuel

Cost

($/million Btu)

Var i abl e

O&M

(¢/kWh)

Pulverized coal steam Coal 1400 9,700 1.50 0.43

Advanced coal steam Coal 1600 8,800 1.50 0.43

Oil/gas steam Oil/Gas 900 9,500 4.60 0.52

Combined cycle Natural gas 600 7,700 4.50 0.37

Combustion turbine Natural gas 400 11,400 4.50 0.62

STIG gas turbine Natural gas 600 9,100 4.50 0.50

New hydroelectric Water 1900 — 0.00 0.30

Source: Based on data from Petchers (2002) and UCS (1992).

BASELOAD, INTERMEDIATE AND PEAKING POWER PLANTS 139

The variable cost for fuel and O&M, operating 8000 hours at full power, would be

Variab le = ($1.50/10

Btu × 9700 Btu/kWh + 0.0043$/kWh) ×8000 hr/yr

= $150.80/kW-yr

For a 1-kW plant,

Electricity generated = 1kW× 8000 hr/yr = 8000 kWh/yr

Price = 1kW×

(224 + 150.80)$/yr-kW

8000 kWh/yr

= $0.0469/kWh = 4.69¢/kWh

In the above example, it was assumed that in a year with 8760 hours, the plant

would operate at full power for 8000 hours and no power for 760 hours. The

same 8000 kWh/yr could, of course, be the result of operating all 8760 hours,

but not always at the full rated output. The resulting price of electricity would

be the same in either case. One way to capture this subtlety is to introduce the

notion of a capacity factor (CF):

Annual output (kWh/yr) = Rated power (kW) × 8760 h/yr × CF (3.20)

Solving (3.20) for CF gives another way to interpret capacity factor as the ratio

of average power to rated power:

CF =

Average power (kW) × 8760 h/yr

Rated power (kW) × 8760 h/yr

Average power

Rated power

(3.21)

Figure 3.27 shows how total revenues required for the coal plant in Example 3.3

vary as a function of its capacity factor (or as a function of hours per year at full

power). Under the circumstances in the example, the average cost of electricity

($0.0469/kWh) is the slope of a line drawn to the point on the curve corresponding

to the 8000 hours of operation (CF = 0.9132). Clearly, the average cost increases

as CF decreases, which helps explain why peaking power plants that operate only

a few hours each day have such high average cost of electricity.

When plots like that shown in Fig. 3.27 are drawn on the same axes for

different power plants, the resulting screening curves provide the ﬁrst step in

determining the optimum mix of different power plant types. The screening curve

for the pulverized coal plant in Fig. 3.27, along with analogous curves for the

combined-cycle plant and the combustion turbine described in Table 3.3, are

shown in Fig. 3.28. What these screening curves show is that the combustion

turbine, which is cheap to build but expensive to operate, is the least-cost option

as long as it doesn’t operate more than 1675 h/yr (CF ≤ 0.19), making it the

best choice for peaking power plants. The coal-steam plant, with its high capital

cost and low fuel cost, is the least expensive as long as it runs at least 6565 h/yr

140 THE ELECTRIC POWER INDUSTRY

800070006000500040003000200010000

100

150

200

250

300

350

400

Equivalent Hours Per Year at Rated Power

Capacity factor

Revenue required ($/kW-yr)

0 0.2 0.4 0.6 0.8

1.00.913

Slope = Variable costs

$0.0189/kWh

Slope = Average cost

$0.0469/kWh

Fixed

costs

$224/kW-yr

8760

Figure 3.27 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.

800070006000500040003000200010000

100

200

300

400

500

600

Revenue Required ($/yr-kW)

Equivalent Hours Per Year at Rated Power

0 0.19 0.5 0.75 1.0

Capacity Factor

Coal-steam

Combustion

turbine

Combined-cycle

6565 hrs1675 hrs

Figure 3.28 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.

BASELOAD, INTERMEDIATE AND PEAKING POWER PLANTS 141

(CF ≥ 0.75), making it an ideal baseload plant. The combined cycle plant is the

cheapest option if it runs somewhere between 1675 and 6565 h/yr (0.19 ≤ CF ≤

0.75), which makes it well suited as an intermediate load plant.

3.9.2 Load–Duration Curves

We can imagine a load–time curve, such as that shown in Fig. 3.26, as being a

series of one-hour power demands arranged in chronological order. Each slice

of the load curve has a height equal to power (kW) and width equal to time

(1 h), so its area is kWh of energy used in that hour. As suggested in Fig. 3.29,

if we rearrange those vertical slices, ordering them from highest kW demand to

lowest through an entire year of 8760 h, we get something called a load–duration

curve. The area under the load–duration curve is the total kWh of electricity used

per year.

A smooth version of a load-duration curve is shown in Fig. 3.30. Notice that

the x axis is still measured in hours, but now a different way to interpret the curve

presents itself. The graph tells how many hours per year the load is equal to or

above a particular value. For example, in Fig. 3.30, the load is above 3000 MW

123456

………hour number in the year... 8760

kW Demand

HOUR-BY-HOUR

LOAD CURVE...

Area of each rectangle is

kWh of energy in that

hour…

Total area is kWh/yr

LOAD CURVE

REORDERED FROM

HIGHEST TO

LOWEST..

Total area is still kWh/yr

kW Demand

Highest

Lowest

“LOAD−DURATION CURVE”

……… 8760

Highest

Lowest

Figure 3.29 A load–duration curve is simply the hour-by-hour load curve rearranged

from chronological order into an order based on magnitude. The area under the curve is

the total kWh/yr.

142 THE ELECTRIC POWER INDUSTRY

6000

5000

4000

3000

2000

1000

0 1000 HRS 7000 8760

INTERPRETING THE CURVE...

THE LOAD IS ALWAYS BETWEEN 2000 MW AND 6000 MW

THE LOAD IS GREATER THAN 5000 MW FOR 1000 HOURS/YR

THE LOAD IS GREATER THAN 3000 MW FOR 7000 HOURS/YR

THE LOAD IS BETWEEN 3000 MW AND 5000 MW FOR 6000 HOURS (7000-1000)

Demand (MW)

Figure 3.30 Interpreting a load–duration curve.

for 7000 h each year, and it is above 5000 MW for only 1000 h/yr. It is always

above 2000 MW and never above 6000 MW.

By entering the crossover points in the resource screening curves into the

load-duration curve, it is easy to come up with a ﬁrst-cut estimate of the opti-

mal mix of power plants. For example, the crossover between gas turbines and

combined-cycle plants in Fig. 3.28 occurs at 1675 hours of operation, while the

crossover between combined-cycle and coal-steam plants is at 6565 hours. Those

are entered into the above load–duration curve and presented in Fig. 3.31. The

screening curve tells us that coal plants are the best option as long as they

operate for more than 6565 h/yr, and the load–duration curve indicates that the

demand is at least 3500 MW for 6565 h. Therefore we should have 3500 MW

of baseload, coal-steam plants in the mix. Combined-cycle plants need to operate

at least 1675 h/yr and less than 6565 h to be most cost-effective. The screen-

ing curve tells us that 1200 MW of these intermediate plants would operate

within that range. Since combustion turbines are the most cost effective as long

as they don’t operate more than 1675 h/yr, and the load is between 4700 MW

and 6000 MW for 1675 h, the mix should contain 1300 MW of peaking gas

turbines.

The generation mix shown on a load-duration curve allows us to ﬁnd the

average capacity factor for each type of generating plant in the mix, which

will determine the average cost of electricity for each type. Figure 3.32 shows

rectangular horizontal slices corresponding to energy that would be generated by

each plant type if it operated continuously. The shaded portion of each slice is

the energy actually generated. The ratio of shaded area to total rectangle area is

the capacity factor for each. The baseload coal plants operate with a CF of about

91%, the intermediate-load combined-cycle plants operate with a CF of about

47%, and the peaking gas turbines have a CF of about 10%. Those capacity

factors, combined with cost parameters from Table 3.3, allow us to determine

the cost of electricity from each type of plant.

BASELOAD, INTERMEDIATE AND PEAKING POWER PLANTS 143

1675 6565

4700

0 8760

6000

3500

1000

4000

1300-MW Combustion turbines

1200-MW Combined-cycle

3500-MW Coal-steam

Hours

800070006000500040003000200010000

100

200

300

400

500

600

Revenue Required ($/yr-kW)

Coal-steam

Combustion

turbine

Combined-cycle

6565 h1675 h

Demand (MW)

Figure 3.31 Plotting the crossover points from screening curves (Fig. 3.28) onto the

load–duration curve (Fig. 3.30) to determine an optimum mix of power plants.

The process and results for our example utility are summarized in Table 3.4.

The baseload plants deliver energy at 4.69¢/kWh, the intermediate plants for

6.23¢/kWh, and the combustion-turbine peakers for 12.87¢/kWh. The peaker

plant electricity is so much more expensive in part because they have lower

efﬁciency while burning the more expensive natural gas, but mostly because

their capital cost is spread over so few kilowatt-hours of output since they are

used so little.

Using screening curves for generation planning is merely a ﬁrst cut at deter-

mining what a utility should build to keep up with changing loads and aging

existing plants. Unless the load–duration curve already accounts for a cushion

of excess capacity, called the reserve margin, the generation mix just estimated

144 THE ELECTRIC POWER INDUSTRY

4700

0 8760

6000

3500

1300-MW CT

Hours

1200-MW CC

CF ≈ 0.10

CF ≈ 0.47

Demand (MW)

3500-MW Coal-steam CF ≈ 0.91

Figure 3.32 The fraction of each horizontal rectangle that is shaded is the capacity factor

for that portion of the generation facilities.

TA BLE 3.4 Unit Cost of Electricity from the Three Types of Generation for the

Example Utility

Generation Type

Rated

Power

(MW) CF

Fixed

Cost

(million

$/yr)

Var i abl e

($/kWh)

Output

(billion

kWh/yr)

Total

Cost

(billion

$/yr)

Unit

Cost

(¢/kWh)

Coal-steam 3500 0.91 784.0 0.0189 27.99 1.312 4.69

Combined-cycle 1200 0.47 115.2 0.0390 4.94 0.308 6.23

Combustion turbine 1300 0.10 83.2 0.0556 1.14 0.147 12.87

Electricity from the peakers is expensive because peakers are used so little.

would have to be augmented to allow for plant outages, sudden peaks in demand,

and other complicating factors.

The process of selecting which plants to operate at any given time is called

dispatching. Since costs already incurred to build power plants (sunk costs) must

be paid no matter what, it makes sense to dispatch plants in order of their oper-

ating costs, from lowest to highest. Renewables, with their intermittent operation

but very low operating costs, should be dispatched ﬁrst whenever they are avail-

able; so even though their capacity factors may be low, they are part of the

baseload. A special case is hydroelectric plants, which must be operated with

multiple constraints including the need for proper ﬂows for downstream ecosys-

tems, water supply, and irrigation while maintaining sufﬁcient reserves to cover

dry seasons. Hydro is especially useful as a dispatchable source that may sup-

plement baseload, intermittent, or peak loads, especially when existing facilities

are down for maintenance or other reasons.

TRANSMISSION AND DISTRIBUTION 145

3.10 TRANSMISSION AND DISTRIBUTION

While the generation side of electric power systems usually receives the most

attention, the shift toward utility restructuring, along with the emergence of dis-

tributed generation systems, is causing renewed interest in the transmission and

distribution (T&D) side of the business.

Figure 3.33 shows the relative capital expenditures on T&D over time com-

pared with generation by U.S. investor-owned utilities. The most striking feature

of the graph is the extraordinary period of power plant construction that lasted

from the early 1970s through the mid-1980s, driven largely by huge spending for

nuclear power stations. Except for that anomalous period, T&D construction has

generally cost utilities more than they have spent on generation. In the latter half

of the 1990s, T&D expenditures were roughly double that of generation, with

most of that being spent on the distribution portion of T&D.

The utility grid system starts with transmission lines that carry large blocks

of power, at voltages ranging from 161 kV to 765 kV, over relatively long

distances from central generating stations toward major load centers. Lower-

voltage subtransmission lines may carry it to distribution substations located

closer to the loads. At substations, the voltage is lowered once again, to typi-

cally 4.16 to 24.94 kV and sent out over distribution feeders to customers. An

example of a simple distribution substation is diagrammed in Fig. 3.34. Notice

the combination of switches, circuit breakers, and fuses that protect key com-

ponents and which allow different segments of the system to be isolated for

maintenance or during emergency faults (short circuits) that may occur in the

system.

1925 1930 1935 1940 1945 1950 1955 1960

Year

Transmission and distribution Generation

$US billion

1965 1970 1975 1980 1985 1990 1996 1998

Figure 3.33 Transmission and distribution (T&D) construction expenditures at U.S.

investor-owned utilities compared with generation. Except for the anomalous spurt in

power plant construction during the 1970s and early 1980s, T&D costs have generally

exceeded generation. From Lovins et al. (2002), using Edison Electric Institute data.

146 THE ELECTRIC POWER INDUSTRY

Subtransmission

System

34.5 kV − 138 kV

Substation

Disconnect

Fuse

Distribution.

Substation

Transformer

Lightning

Arrestors

Overcurrent

Relay

Bus Breaker

Main Bus

Overcurrent

Relay

Feeder

Breakers

Feeder

Disconnect

Voltage

Regulators

Radial

Distribution

Feeders

4.16 kV −

24.94 kV

Figure 3.34 A simple distribution station. For simplication, this is drawn as a one-line

diagram, which means that a single conductor on the diagram corresponds to the three

lines in a three-phase system.

3.10.1 The National Transmission Grid

The United States has close to 275,000 miles of transmission lines, most of which

carry high-voltage, three-phase ac power. Investor owned utilities (IOUs) own

three-fourths of those lines (200,000 miles), with the remaining 75,000 miles

owned by federal, public, and cooperative utilities. Independent power produc-

ers do not own transmission lines so their ability to wheel power to customers

depends entirely on their ability to have access to that grid. As will be described

in the regulatory section of this chapter, Federal Energy Regulatory Commission

(FERC) Order 2000 is attempting to dramatically change the utility-ownership

of the grid as part of its efforts to promote a fully competitive wholesale power

market. Order 2000 encourages the establishment of independent regional trans-

mission organizations (RTOs), which could shift transmission line ownership to

a handful of separate transmission companies (TRANSCOs), or it could allow

continued utility ownership but with control turned over to independent system

operators (ISOs).

As shown in Fig. 3.35, the transmission network in the United States is orga-

nized around three major power grids: the Eastern Interconnect, the Western

Interconnect, and the Texas Interconnect. Texas is unique in that its power does

not cross state lines so it is not subject to control by the Federal Energy Reg-

ulatory Commission (FERC). Within each of these three interconnection zones,

utilities buy and sell power among themselves. There are very limited inter-

connections between the three major power grids. After a major blackout in

the Northeastern United States in 1965, the North American Electric Reliabil-

ity Council (NERC) was formed to help coordinate bulk power policies that

affect the reliability and adequacy of service within 10 designated regions of the

U.S. grid.

While almost all power in the United States is transmitted over three-

phase ac transmission lines, there are circumstances in which high-voltage

TRANSMISSION AND DISTRIBUTION 147

Texas Interconnect

Western

Interconnect

Eastern

Interconnect

ERCOT

FRCC

SERC

SPP

WSCC

MAPP

NPCC

ECAR

MAAC

MAIN

Figure 3.35 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).

dc (HVDC) lines have certain beneﬁts. They are especially useful for inter-

connecting the power grid in one part of the country to a grid in another

area since problems associated with exactly matching frequency, phase, and

voltages are eliminated in dc. An example of such a system is the 600-

kV, 6000-MW Paciﬁc Intertie between the Paciﬁc Northwest and South-

ern California. Similar situations occur between countries, and indeed many

of the HVDC links around the world are used to link the grid of one

country to another—examples include: Norway–Denmark, Finland–Sweden,

Sweden–Denmark, Canada–United States, Germany–Czechoslovakia, Aus-

tria–Hungary, Argentina–Brazil, France–England, and Mozambique–South

Africa. The control and interfacing simplicity of dc makes HVDC links particu-

larly well suited for connecting ac grids that operate with different frequencies,

as is the case, for example, in Japan, with its 50-Hz and 60-Hz regions.

HVDC links require converters at both ends of the dc transmission line to

rectify ac to dc and then to invert dc back to ac. The converters at each end

can operate either as a rectiﬁer or as an inverter, which allows power ﬂow