Masters G.M. Renewable and Efficient Electric Power Systems

Подождите немного. Документ загружается.

278 ECONOMICS OF DISTRIBUTED RESOURCES

Expansion

Valve

Condenser

Evaporator

Absorber

Generator

Strong water-

LiBr solution

Weak water-

LiBr solution

Water vapor

Heat

Source

gen

Heat rejection

to environment

Cold

Refrigerated space

Liquid

water

Waste heat

abs

Figure 5.18 Lithium bromide absorption chiller schematic. The compressor in a standard

compressive refrigeration system has been replaced with a generator and absorber that

perform the same function but do so with heat instead of mechanical power.

generator is ready to pass through the condenser and the rest of the conventional

refrigeration system. Meanwhile, the lithium bromide returns to the absorber,

never having left the system. The absorption of refrigerant into the absorbent is

an exothermic reaction, so waste heat is released from the absorber as well as

the condenser.

The COP of an absorption refrigeration system is given by

COP

Desired output (cooling)

Required input (heat + very little electricity)

≈

gen

(5.47)

For a good LiBr system, the COP is currently about 1.0 to 1.1, but new “triple

effect” absorption units promise COPs better than 1.5.

A competing absorption cycle chiller uses water as the absorbent and uses

ammonia as the refrigerant. These NH

–H

O chillers date back to the mid-1850s

and were originally popular as ice makers. While their COPs are not as good as

those based on LiBr, they do create lower temperatures and, because they operate

with higher pressures, the piping and equipment can be physically smaller.

As is suggested in Fig. 5.19, the advantage of absorption cooling coupled with

cogeneration is the smoothing of the demand for thermal energy throughout the

year, which signiﬁcantly improves the economics of CHP electricity.

5.6.4 Desiccant Dehumidiﬁcation

Another technology that can take advantage of thermal energy to provide cool-

ing is based on the ability of some materials, called desiccants, to dehumidify air

COOLING, HEATING, AND COGENERATION 279

Total thermal load

Heating load

Absorption

cooling load

Jan Mar Jun Sep Dec

Monthly Thermal Load

Figure 5.19 Absorption cooling helps smooth the annual thermal demand for a building.

by adsorbing water vapor onto their surfaces. The cooling load associated with

cooling outside air, or recirculated indoor air, is a combination of (a) sensible

cooling, in which the temperature of air is lowered, and (b) latent cooling, in

which water vapor is removed. Especially in humid climates, the latent cooling

load is by far the most important. In the usual compressive refrigeration sys-

tem, air is dehumidiﬁed by cooling it well below its dew point to condense out

some of the water vapor, and then it is reheated to a comfortable supply tem-

perature. All of that takes considerable compressor power. When an inexpensive

source of relatively low-temperature heat is available, however, desiccants offer

an alternative, less electricity-intensive approach.

Desiccants, such as natural or synthetic zeolites, powdered silica gels, and

certain solid polymers, have a strong afﬁnity for moisture, which means that

when contact is made, water vapor readily condenses, or adsorbs, onto their

surfaces. The resulting release of latent heat raises the desiccant temperature, so

the overall result of an air stream passing through a desiccant is dehumidiﬁcation

with an increase in air temperature. The accumulating moisture in the desiccant

must of course be removed, or desorbed, and that is accomplished by driving a

very hot air stream through the desiccant in a process called regeneration. The

sorption and desorption of moisture is often done with a rotating wheel, as shown

in Fig. 5.20.

The remaining components in a desiccant air-conditioning system are there

to provide sensible cooling to the now hot, dry supply air and to provide the

heat needed to regenerate the desiccant. It is this latter step that dominates the

energy requirement of a desiccant system, and that is why the availability of an

inexpensive source of heat becomes so important for these systems. Waste heat

from an industrial process, thermal energy from a cogeneration facility, or heat

from a solar collector system all could provide the necessary thermal input to

these systems. An example of a desiccant cooling system is shown in Fig. 5.21.

280 ECONOMICS OF DISTRIBUTED RESOURCES

Desorption

Exhaust

air 120°F

Warm, 80°F

humid, outside air

Sorption

Rotationg

desiccant

wheel

Hot, dry air

ready to be

cooled

120°F

250°F Heated

regeneration air

Figure 5.20 Desiccant wheel as part of a dehumidiﬁcation and cooling system.

Desiccant

wheel

Heat

exchanger

Sensible

cooling

Thermal

input

Hot water heater

65°F

75°F

95°F

90°F

120°F

250°F 120°F

80°F

Figure 5.21 A desiccant refrigeration system for space cooling and domestic hot water.

Temperatures are illustrative.

5.7 DISTRIBUTED BENEFITS

There are a number of subtle but important beneﬁts associated with distributed

generation, which have only recently begun to be appreciated and assessed

(Swisher, 2002). In addition to direct energy savings, increased fuel efﬁciency

with cogeneration, and reduced demand charges for larger customers, there are a

number of other DG attributes that can signiﬁcantly add value, including

Option Value: Small increments in generation can track load growth more

closely, reducing the costs of unused capacity.

Deferral Value: Easing bottlenecks in distribution networks can save utili-

ties costs.

DISTRIBUTED BENEFITS 281

Engineering Cost savings: Voltage and power factor improvements and

other ancillary beneﬁts provide grid value.

Customer Reliability Value: Reduced risk of power outages and better power

quality can provide major beneﬁts to some customers.

Environmental Value: Reduced carbon emissions for CHP systems will

have value if/when carbon taxes are imposed; for fuel cells, since they

are emission-free, ease of permitting has value.

5.7.1 Option Values

In the context of distributed generation, the option part of option value refers to

the choice of the incremental size of new generation capacity; that is, the buyer

has the option to purchase a large power plant that will satisfy future growth for

many years, or a series of small ones that will each, perhaps, only satisfy growth

for a year or two. The value part refers to the economic advantages that go with

small increments, which are better able to track load growth.

Figure 5.22 illustrates the comparison between adding fewer, larger increments

of capacity versus smaller, but more frequent, increments. Smaller increments,

such as distributed generation, better track the changing load and result in less idle

capacity on line over time. The advantage is especially apparent when forecasted

load growth doesn’t materialize and a large incremental power plant may result

in long-term overbuilt capacity that remains idle but still incurs costs.

Install large

resoure

Install large

resource

MW Capacity

Install DG resource

Time

Idle capacity of large resource

Idle capacity of DG resource

Overbuilt capacity

Electric Load

Figure 5.22 Smaller distributed generation increments better track the changing electric

load with less idle capacity than fewer, larger plants. Less idle capacity translates into

decreased costs. Based on Swisher (2002).

282 ECONOMICS OF DISTRIBUTED RESOURCES

Idle capacity

Generation Capacity

1 Large plant

Small, plants, 1 per yr

Order new plant at

= 0, pay for it at

= 1 when it comes on line..

0 1 2 3 4 5 .....

Time (yrs)

•

Figure 5.23 Comparing the present worth of a single large plant capable of supplying

N years of growth with N plants, each satisfying 1 year of growth. For simplicity, both

are assumed to have 1-year construction lead times.

One way to quantify the cost advantage of the option value is to do a present

worth analysis of the capital cost of a single large plant compared with a series

of small ones. Figure 5.23 shows a comparison of one large power plant, which

can supply N years of load growth, with N small plants, each able to supply

one year’s worth of growth. Let us begin by assuming that it only takes 1 year

between the time a plant is ordered and the time it comes on line, so at time

t = 0, either a large plant or a small plant must be ordered. Finally, assume that

full payment for a plant is due when it comes on line.

Let

Annual growth in demand = P (kW)

Cost of a small plant = P

($/kW) × P (kW)

Cost of a large plant = P

($/kW) × NP (kW)

Discount rate = d(yr

−1

)

The present value of the single large plant (P V

) is its initial cost discounted

back 1 year to t = 0:

NP

(1 + d)

(5.48)

For the sequence of N small plants, the present value of N payments of

P , w ith the ﬁrst one at t = 1 year, is given by

= P

P PVF(d, N ) (5.49)

DISTRIBUTED BENEFITS 283

where PVF(d, N ) is the present value function used to ﬁnd the present value of

aseriesofN equal annual payments starting at t = 1. If we equate the present

values of the large plant and the N small ones, we get

NP

(1 + d)

= P

P PVF(d, N ) (5.50)

and, using (5.9) for PVF(d,N)gives

($/kW)

(1 + d)PVF(d, N )

(1 + d)



d(1 + d)

(1 + d)

− 1



= N



d(1 + d)

N−1

(1 + d)

− 1



(5.51)

Equation (5.51) is the ratio of the small-plant-to-large-plant capital costs ($/kW)

that makes them equivalent on a present worth basis.

Example 5.16 Present Value Beneﬁt of Small Increments of Capacity. Use

(5.51) to ﬁnd the present value advantage of eight small plants, each supplying

1 year’s worth of growth, over one large plant satisfying 8 years of growth. Use

a discount rate of 10%/yr. Each plant takes 1 year to build. If the large one costs

$1000/kW, how much can the small ones cost to be equivalent?

Solution. Using (5.51), we obtain

($/kW)

= 8



0.1(1 + 0.1)

(1 + 0.1)

− 1



= 1.363

This means the small DG plants can cost $1363/kW and they still would be

equivalent to the single large one at $1000/kW.

Even though the calculation in Example 5.16 is impressive enough as it stands,

it omits another important advantage of smaller plants. Large plants tie up capital

for a longer period of time before the plant can be designed, permitted, built,

and turned on. That longer lead time costs money, so let’s modify our analysis

to include it.

Imagine the initial cost of the large plant being spread over years 1 through L,

where L is the lead time. Also, suppose payments on the N small plants begin

in year L, as shown in Fig. 5.24. We continue to assume the small plants can

284 ECONOMICS OF DISTRIBUTED RESOURCES

= 0 …

$/yr

L payments of

∆

P N/L

payments of P

∆P

One Large Plant

Small Plants

1 2 (years) (L + N − 1)

Figure 5.24 The payments made on one large plant spread over the L years of lead

time that it takes to bring it on line, and annual payments made on N small plants. The

ﬁrst of each type comes on line in year L.

be built in one year. The present value of the payments made on the large plant

costing P

NP spread out over L years is given by

NP

· PVF(d, L) (5.52)

And, for the N small plants, each costing P

P over years L to L +N − 1,

we have

(1 + d)

L−1

P · PVF(d, N )] (5.53)

where the term in the brackets ﬁnds the present value of the series of payments,

discounted back to year L − 1, and the initial term discounts that back to t = 0.

Setting the present value of the large plant (5.52) equal to the present value of

the series of small ones (5.53) results in the following ratio of capital costs for

small and large plants, including the extra lead time for the large one:

($/kW)

N(1 + d)

L−1

PVF(d, L)

PVF(d, N)

(5.54)

where N is the number of small plants, each taking 1 year to build and satisfying

1yrofgrowth;L represents the years of lead time for the single large plant; and

d is the discount rate (yr

−1

Example 5.17 Option Value of Small Plants Including Short Lead-Time

Advantage. Find the capital cost that could be paid for eight small plants, each

sized to supply one year of load growth and each taking 1 year to build, com-

pared with one large plant that supplies 8 years of growth. The large plant costs

$1000/ kW and has a lead time of 4 years to build. Use a discount rate of 10%/yr.

DISTRIBUTED BENEFITS 285

Solution. To use(5.54) we need

PVF(d, L) =

(1 + d)

− 1

d(1 + d)

(1 + 0.1)

− 1

0.1(1 + 0.1)

= 3.1698

and

PVF(d, N) =

(1 + 0.1)

− 1

0.1(1 + 0.1)

= 5.3349

($/kW)

N(1 + d)

L−1

PVF(d, L)

PVF(d, N)

8(1 + 0.1)

4−1

3.1698

5.3349

= 1.582

The capital cost of the small plants can be $1582/kW, and they would still be

equivalent to one large plant costing $1000/kW.

Table 5.10 has been derived from (5.54) to show the cost premium that smaller

plants can enjoy and still have the same present value as a single larger one. An

additional advantage of the small plants is that they will have less unused capacity

if load doesn’t grow as fast as forecast.

Another advantage of meeting projected demand with incremental capacity

additions is the reduced need for working capital to build the plants. Putting

enormous amounts of capital into a huge, billion-dollar power plant and then

TA BLE 5.10 Capital Cost Premium that N Smaller

Plants Can Have Versus One Larger One and Still

Have the Same Present Value

NL= 1yr 2yr 3yr 4yr 5yr

1 0% 5% 10% 16% 22%

2 5% 10% 16% 22% 28%

3 10% 15% 21% 27% 34%

4 15% 20% 27% 33% 40%

5 20% 26% 32% 39% 46%

6 25% 32% 38% 45% 53%

7 31% 37% 44% 52% 60%

8 36% 43% 50% 58% 66%

9 42% 49% 57% 65% 73%

10 48% 55% 63% 72% 81%

L is years of lead time to build the larger plant. Assumes dis-

count rate of 10%/yr and a 1-year lead time for small plants.

Source: Swisher (2002).

286 ECONOMICS OF DISTRIBUTED RESOURCES

waiting 5 or so years to start earning revenue could be perceived by the capital

markets to be a riskier investment than would be the case for a series of short-

lead-time, modular units. The reduced risk in the modular approach can translate

into lower cost of capital, providing another ﬁnancial advantage to distributed

generation.

5.7.2 Distribution Cost Deferral

The utility distribution system, which sends power to every house and store in

town, is a very expensive asset that is typically greatly underutilized except in

certain critical locations during certain times of the day and year. As Fig. 5.25

attests, distribution systems constitute a signiﬁcant fraction—on the order of

half in recent years—of annual utility construction cost. Running power lines

up and down every street to serve residential customers is expensive, and it

is one reason why residential electric rates are so much higher than those for

large, industrial facilities with dedicated feeders. In terms of the overall cost of

running a utility, including construction costs, fuel, administrative costs, billing,

and operations and maintenance, the distribution system accounts for about 20%

of the total.

As Fig. 5.26 indicates, distribution system assets are not only expensive, but

they are often utilized far less than is the case for generation. For example,

only one-third of the time is this particular feeder operating above 50% of its

capacity—or conversely, two-thirds of the time there is more than twice as much

distribution capacity as is needed. Compare this with generation, where that level

of underutilization never occurs.

Distribution systems are plagued by bottlenecks. When a new housing devel-

opment or shopping center gets built, distribution feeders and the local substation

may have to be upgraded even though their current capacity may be exceeded

for only a few hours each day during certain months of the year. The effect of

that localized growth can ripple from feeder to substation to transmission lines

to power plants.

General/Misc

100%

80%

60%

40%

20%

Distribution

Transmission

Generation

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Figure 5.25 Allocation of U.S. investor-owned utilities’ construction expenditures. From

Lovins et al. (2002).

DISTRIBUTED BENEFITS 287

100

0 102030405060708090100

Percentage of the Year (%)

Load Factor

Percentage (%)

Distribution Asset Utilization

Electric Generation Asset Utilization

Figure 5.26 Comparing the load–duration curve for a typical feeder in the distribution

system of a large utility with a curve for generation assets. The distribution system assets

are utilized far less than the generation system. From Ianucci (1992).

Studies of area-and-time (ATS) costs can pinpoint those portions of a distri-

bution network where the marginal cost of delivering another kilowatt makes

distributed generation and demand-side management particularly cost effective.

Figure 5.27, for example, shows an extreme case in which an ATS study iden-

tiﬁed a particular feeder in which the marginal cost of peak power rose to over

$3.50/kWh during a few hours a day over just a few weeks each year. At such a

site, almost any distributed generation or energy conservation system would be

cost effective.

On-site generation by utility customers can help avoid or delay the need for

distribution system upgrades, leading to more efﬁcient use of existing facili-

ties. Customers in portions of the distribution grid where capacity constraints

are imminent could in the future be provided with incentives to generate some

of their own power (or shed some of their load), especially at times of peak

power demand. Area-and-time-based differential pricing of grid services could

well become an important driver of distributed generation.

5.7.3 Electrical Engineering Cost Beneﬁts

Besides capacity deferrals, distributed generation can also decrease costs in the

distribution network by helping to improve the efﬁciency of the grid. Power

injected into the grid by local distributed generation resources helps to reduce

losses in several ways.

Without DG, the current supplied to a distribution network by the transmission

system must be sufﬁcient to satisfy all of the loads, from one end to the other.

When current ﬂows through conductors, there is voltage drop due to Ohm’s law,