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Cyclopedia of civil engineering; a general reference work on surveying, highway construction, railroad engineering, earthwork, steel construction, specifications, contracts, bridge engineering, masonry and reinforced concrete, municipal engineering, hydraulic engineering, river and harbor improvemen online

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low limit, and $20 per kilowatt-year as a high limit. The operating
expenses, labor, oil, waste, repairs, etc., may be expected to cost
from $1 to $5 per kilowatt-year, which places the cost of electric
power at the busbars between the rare low limit of $8.50 per kilo-
watt-year, and the high limit of $25 per kilowatt-year for full load,
24-hour power, for these rates of charging expenses.

Besides the increase in development cost, there is another
item that sometimes enters; and that is an increase in land expense
or land damage, which may be large in settled communities. The




increase in cost is not all due to increase in cost of machinery;
this has probably decreased, not only from better methods of
manufacture and more competition, but also from the use of higher
heads and better wheels and electric generators.

186. Competition. Just how much can be paid profitably for
the development of water power, either now or in the future, will be
measured solely by the power cost of that one of the competing
systems steam, gas, or oil most available in the same locality, or,
if not in the same locality, at some point within the limits of electrical
transmission. To the cost of generating water power, must be
added transmission cost, involving fixed charges on lines, trans-
formers, switchboard, and other equipment, together with their
maintenance and operating charges. All of these together may
add to first cost $30 per kilowatt, and increase the power cost for a
150-mile transmission $5 per kilowatt-year.

After analyzing the details of power cost for oil, gas, and steam
development, Professor Lucke continues :

These costs may now be summarized for comparison, as follows:

Assume: Stations consisting of six units, two in reserve, and four working on 24 hours
rated load, with the exception of the water power. First cost and fixed charges based on capacity
of 150 per cent of output.





First cost per
kw. rating


(160-kw. units)

(600-kw. units)

(5000-kw. units)

Fixed charges,
rate per cent

10 per cent

10 per cent

10 per cent

10 per cent

Fixed charges,
per kw.-year





Operating and
costs per kw.-





Total power
costs per kw.-





From these figures it appears that we have not yet reached the
limit of cost of development of water powers which may be advis-



able. It apparently would pay to spend even more money than $200
per kilowatt, the present maximum for water-power development,
if there were no other considerations entering. Among the chief
considerations of this kind, may be set down that of transportation
of products from the works, and of raw material to the works; but
this must be considered against the question of transmission of
current from the waterfall to a convenient point of transportation.

187. Load. The discussion and the figures presented above
refer to a 24-hour continuous full load, a condition which frequently
is practically fulfilled in the case of electrochemical works, but
rarely in other branches of industry.

Load Factor. The term load factor may be defined as the ratio
of the actual power output of an installation during a 24-hour period
of operation to its 24-hour capacity at full load ; or, in the case of the
consumer, it may be defined as the ratio of average to maximum
load. The term, however, is occasionally employed with a some-
what different significance.

Peak Load. The peak load represents the maximum output,
corresponding to the maximum demand for power from all the
industries served at any one time during a 24-hour period of opera-
tion; or, in the case of the consumer, it represents the maximum use
of power during that period. So short a time as a 1- or 2-minute
interval may be used in estimating peak loads.

The value of the load factor varies between very wide limits in
the different industries, depending on their nature and peculiarities.
Thus, from the census report of the year 1902, the average
load factor of all United States lighting systems was about 23 per
cent, while the street railways had a load factor of about 30 per
cent, and an average of all electric-light and railway systems
amounted to about 26 per cent. From these low values the load
factor varies, for the different industries or combinations of indus-
tries, up to nearly 100 per cent, as stated above.

It is evident that in the case of an installation furnishing power
to an industry using that power fairly uniformly, the load factor
will be higher than under the reverse conditions. It is also clear
that if the power is furnished to a combination of different indus-
tries so selected regarding power demand that the times of high
requirement in some occur simultaneously with the times of low



requirement in others, the result of this correspondence will be a
more or less uniform demand for power from the power company,
and the load factor will be high.

Overload Compensation. The general effect of the load factor
on the cost of power production is evident, for the plant must be
designed and installed to meet peak-load conditions, even though
these conditions obtain for short periods only during each 24 hours.
Accordingly, during the balance of the time, part of the plant must
lie idle or work at less than full load, whereas certain fixed charges
on the total investment, such as interest, taxes, depreciation, and
insurance, continue uniformly. Unless the entire plant representing
the investment is put to its normal maximum use every hour in the
day and every day in the year, it is not working at its theoretic
maximum efficiency, and the cost of power production will be cor-
respondingly increased.

To carry over the peak load, the motor units may be designed
with sufficient overload capacity; storage batteries of sufficient
capacity may be installed, to take the excess over the average load;
auxiliary steam or gas units may be employed, or one or more main
units may be held in reserve, for the same purpose.


188. Basis of Charge. "Since the day when the first commer-
cial electric light entered the field of artificial illuminants, there have
been endeavors to find an equitable way of charging for energy
supplied in the form of electricity. At first, in the absence of any
measuring instruments, the flat rate was the only method. This
was soon found to be impracticable for most cases, and the ampere-
hour meter, followed by various types of integrating and recording
wattmeters, soon brought into use the idea of paying for the exact
amount of energy used, at a given price per ampere-hour or per
kilowatt-hour. This method is still in very general use in its sim-
plest form, but there has been dissatisfaction with it from the time
it started. The fact of the matter is that neither the straight flat
rate nor the straight kilowatt-hour rate is equitable, except when
applied in connection with a definite load factor; and even then it

: Street Railway Journal, June 30 and July 7, 1900.



may not be entirely so, due to uncertainty as to the number of hours
per day that full-load conditions prevail, with corresponding high
efficiency, and to the hours during which operation continues at
light loads, with resultant low efficiency.

189. Load Factor. "It is fully recognized now, however, that
the load factor is the root of the trouble; and unless a system of
charging gives due consideration to it, there will always be inequality
of rates and dissatisfaction on the part of the power company or of
its customers, or of both. This has been shown in all classes of
service incandescent and arc lighting, heating and power purposes,
including railway lines and in power companies and consumers of
all sizes/'

The ratio of the use actually obtained to the theoretical or
possible maximum use, is the load factor of the manufacturing
establishment and of the railway line, just as it is of the power
house or of the transmission system.

"The effect : of load factor on cost of power is thoroughly under-
stood where steam plants are concerned; but it might be supposed,
in the case of hydraulic power, where no furnaces have to be banked,
and inefficiency at light loads becomes unimportant, that the condi-
tions would be different. "Hydraulic turbines of modern design,
however, usually have such characteristics that their overload
capacity is very slight; and it therefore becomes necessary, if peak
loads are to be handled, to provide extra machinery to take care of
these. With no provision for peaks* it is still necessary to hold at
least one generating unit in reserve, and a margin of capacity must be
left unused in the operating turbines for gate travel in regulation,
and to allow for partial clogging of distributors by refuse which acci-
dentally enters the penstocks. As the water is available and costs
no more if used to the full capacity of the plant, it is plain that the
power-selling company will strive vigorously for a uniform load as
high as is practicable for the installed machinery to carry. This
results in making peaks a prohibitive element to power deals where
the hydraulic plant has been some time in the field and has been
able to discriminate in the choice of its customers.

"The plants now operating at Niagara Falls have been particu-
larly fortunate in this respect, one of the oldest having a 24-hour
load line of about 26,000 horsepower, and fluctuations not exceed-



ing 5 per cent of the average load. Needless to say, the portion of
this power supplied for railway and lighting purposes is very small.
Niagara conditions are unique, as the electro chemical plants, which
consume the greater part of the present power, provide an ideal load.

190. Auxiliary Power. "The typical street-railway load neces-
sarily has prominent peaks; and if these cannot be smoothed down
by adjustments of service, it is still possible, where a fair price is
asked for the waiter power, to carry the heaviest part of the all-day
load by means of this, and the remainder by steam engines, gas
engines, or storage batteries, or combinations of engines and batteries.

"The point is frequently raised that power companies under-
taking to supply customers of any sort should be equipped to take
care of all requirements of these customers, including peak loads.
This is done in some cases, the power companies going so far as to
provide steam plants for reserves and peak purposes. The char-
acter of local demands for power will usually determine this matter;
and if the power companies eventually install auxiliary steam plants,
it will be only because they are forced to it by periodic shortages of
water, or inability to obtain customers whose aggregate use of
power results in a high yearly load factor. The power company
wants to sell all of its power all of the time; and in a thriving, pro-
gressive community, it is probable that it finally will come very near
doing this. The load factor will improve as customers increase in
number; and as the load approaches the full capacity of the plant,
the power company will become more discriminating about closing
new contracts, or renewing old ones, that involve conditions tending
toward poor load factor.

"If power companies cannot entertain peak propositions at
all, or if they place prohibitive rates thereon, the purchaser must
then provide the steam plant, or storage battery, or both, to care
for a part of the load. Railway systems supplied with purchased
hydroelectric power afford ideal opportunities for the application of
storage batteries. The batteries can be charged at night with power
that otherwise could not be used ; and the discharge of the load peak
provides power at an extremely low load factor which costs only
the fixed charges, operation, and maintenance of the battery.

191. Penalty. "If it is possible to make contracts for full
power requirements, it is usual for power companies to place some



penalty rate on the peak power, or to arrange the terms of charge
so that there are distinct advantages to the purchaser in keeping
the load line as nearly straight as possible. The most common
method is to sell a solid block of 'firm' power which can be used at a
load factor of 70 per cent to 80 per cent, or better, charging the
minimum flat rate for this, and providing power above the firm
amount on a kilowatt-hour basis, at rates gradually increasing with
the height of the peaks.

"Sometimes provision is made for charging extreme rates for
possible peaks of such height that the railway company has no
expectation of ever reaching them. These clauses should be avoided,
if possible, as the unexpected is constantly happening in the opera-
tion and growth of a railroad. Where measurement of peaks is
dealt with at all, it should be specified that they are not to be counted
unless they continue for 2 minutes or longer. (In some cases 1 min-
ute is specified.) Uncontrollable occurrences, such as the partial
grounding of a feeder, or the performance of a defective car, may
produce peaks of short duration which are of small consequence to
the power company, but might be very costly to the railway com-
pany under an unreasonable power agreement.

"The purchaser should be allowed, without charge, swings
of about 10 per cent (or 5 per cent) above the firm line of purchased
power, provided the kilowatt-hours used above the line do not
exceed those unused below it; since it is impossible to always carry
the load directly on the limiting line, even with the aid of batteries
and the most approved regulating devices.

192. Sliding Rate. "A fair method of charging for power
is on a sliding rate depending on the monthly load factor. The
maximum 2-minute (or 1 -minute) peaks are recorded in kilowatts
each day, and averaged for the month, giving the average maximum
demand for the month. The total number of kilowatt-hours used
during the month, divided by the number of hours in a month,
gives the average hourly rate of consumption for the month. Then
the monthly load factor is obtained by dividing this average by
the maximum demand; and this factor is used as follows in determin-
ing the charge for the month:

Illustrative Examples. "Assuming that a manufacturer has
made a contract to buy 400 horsepower for the operation of his



factory, and that the rate per horsepower-year varies between the
limits of $16 and $43, depending on the load factor, the determi-
nation of his rate per horsepower per year for any given month would
be as follows:

"If the kilowatt-hours consumed during a thirty-day month
are 43,200, then the average demand for power is 43,200 divided
by 720 (the number of hours in the month), equal to 60 kilowatts
or 80 horsepower. Assuming further that his maximum demand
each day was just 400 horsepower, then, of course, his average
maximum demand for the month will be the same amount, and the
load factor is 80 divided by 400 = .2, or, as commonly expressed,
20 per cent. If the rate per horsepower-year varies between $16
and $43, it will be evident that the variable quantity is their differ-
ence, or $27. The rate is therefore equal to the minimum rate
($16), plus the load factor (.2) multiplied by the variable ($27).
In the present case, this will amount to 16 +.2X27 = $21. 40. The
total charge for the month would therefore be $21. 40X400^ 12 =
$713.33, which is equivalent to 1.65 cents per kilowatt-hour, or
$107.00 per horsepower,* for power actually used.

"If the monthly load factor had been 30 per cent (.3) instead
of 20 per cent (.2), the rate per horsepower per year would have
increased to $24.10; but the equivalent cost per kilowatt-hour
would have decreased to 1.24 cents, a reduction of almost 25 per
cent in cost per kilowatt-hour due to increasing the load factor
to 30 per cent.

"This may readily be put in the form of an equation in which
desired rate per horsepower per year is R, minimum rate limit
is A, maximum rate limit is B, and load factor is L', thus

R = A + L(B-A)

"This method is much more equitable than that sometimes
used, of selling all the power on a kilowatt-hour basis with a guar-
antee from the consumer of a specified load factor." With this
system of charging, the method of establishing equitably the limiting
values for horsepower per year (corresponding to $16 and $43, in
the example above) will require very careful consideration.

193. Proportioning the Load. "Very careful consideration
must be given to proportioning the division of load between water

*Cost per kilowatt-hour = cost per horsepower-year^- 6480.




power and steam power. The cost of hydroelectric power at 100
per cent load factor should be somewhere in the neighborhood of
one-third the cost of steam-generated power at 100 per cent load
factor, assuming reasonable first cost of plant and moderate distance
of transmission in the first case, and average cost of coal and labor
in the second. Obviously the bulk of the load should be carried
by the purchased power; but the higher the limiting firm line of
this power is raised, the lower will the load factors of both steam
power and purchased power become, and the cost per kilowatt-
hour of each will increase. In each case, however, there is a certain
critical point to which the firm purchased-power line may be raised
before the total cost (which is of prime importance) of combined
purchased power and steam power will commence to increase.
In raising the firm line of purchased power to this point, the total
cost will be decreasing."


Loads of a Niagara Company. "Curve sheet, Fig. 217,

shows at A A the remarkably straight local load line of one of the

FiK 217. Curve Shoot Showing Load Curves of One of the Niagara Companies

Niagara power companies. At BB is shown the total load line,
including the long-distance load, of the same company. CC shows
a railway load, the shaded portion of which is carried by the railway




company's steam engines and storage batteries. The unevenness
of the power company's total load is not contributed to by the
railway company, except to the extent of a dip during the early
morning hours. The peaks of the railway load would, if included

Fig. 218. Curve Sheet Showing Railway Load Line Represented as C-C on
Curve Sheet, Fig. 217

in the power company total load, distort it considerably, in an unde-
sirable way. The curves are all plotted from the same base line,
and represent the same day."

Railway Load. "Curve sheet, Fig. 218, shows on a more open
vertical scale the same railway load that is represented at CC in




Fig. 217. The firm line of purchased power is here located lower,
with reference to the total load, than has been described as the
economical point. This is partly for the reason that the chart
represents a winter day (the heavy load season of the year). The
total load drops below the firm purchased power line during the
middle of the day at some seasons, and, as the firm line cannot be
shifted back and forth, there are necessarily times when the pro-
portions of purchased power and steam are not the most economical,
as in the instance of this particular day.

Relation of Load Factor to Rates. "Fig. 219 gives the rates per
horsepower in terms of load factor. The curve marked 'Hydro-

Fig. 219. Method of Plotting Costs per Horsepower per Year in Terms of Load Factor,
and Rate per Horsepower per Year|

Electric Plant' is intended to represent rate of power cost after
transmission for some distance, while that marked 'Steam Plant'
represents rate at the power-house switchboard. These curves
are about the best obtainable from any power houses of 5000-
to 10,000-horsepower capacity, with coal from $2.50 to $2.75
per ton."

Fig. 220 shows the same rates as represented in Fig. 219, reduced
to cost per horsepower per year, of power actually used; while
Fig. 221 gives these same costs in terms of kilowatt-hours, of power
actually used.

Since there are approximately 8640 hours per year, and since




1 horsepower is approximately equal to J kilowatt, the values in
Figs. 220 and 221 are mutually convertible by means of the con-
version factor | of 8640 = 6480. Or Fig. 221 may be constructed
directly from the values taken from Fig. 219, by means of the con-
version diagram, Fig. 222. Fig. 223 is interesting in that it shows
in a general way how the fixed charges and operating charges,
and therefore the total cost vary with the load factor. While the

per cent of the total cost
chargeable to operation in-
creases with the load factor,
the actual cost of operation
per kilowatt-year decreases.


195. General. "When-
ever the development of a
water power for the purpose
of selling water or mechanical
or electrical energy is under
consideration, the most im-
portant question to be decided
is: What is the limit of cost
per horsepower that may be
expended for a development
and still leave the plant a
financial success; or what is a
reasonable price to be charged
per horsepower per year?
"A great amount of data has been published in regard to the
cost of hydraulic power and power plants; but, as water powers
present an infinite variety of conditions, such prices of other plants
should be used only with the greatest precaution. A few general
figures applying to conditions now prevailing in the northern
part of the United States and in Canada may be given here.

196. Unit Costs. "A water-power electric plant, including
transmission line and substation, where such are required, but

Fig. 220. Rates of Fig. 196 Reduced to Cost per
Horsepower per Year, of Power Used

*Thurso, "Modern Turbine Practice".




Fig. 221. Rates o

f Fig. 196 Reduced to Cost per Kilowatt-Hour, of Power Used




without the local distribution, should not cost more than $100 per
electrical horsepower, if situated in a remote location or in a farming
district; but $150 to $200 may be expended per electrical horse-
power for power plant, transmission, and substation, if the power
can be sold in a large city or industrial district.

"The price charged for power water per gross horsepower
per year, delivered at or near the customer's turbines, may be taken

lig. 223. Curve Sheet of Power Station with 5500-Kilowatt
Steam Turbo-Generators

at from $5 to $15, the lower figure being for remote locations, low
heads, and large powers, and the higher figure for the reverse con-
ditions. The price of $15 to $25 per mechanical horsepower per
year at the power house, or of $25 to $50 per electrical horsepower
per year delivered to the customer, may be taken as the limits paid
at present. Here, again, the lower rate is for remote locations and
large powers, and the higher for the reverse conditions.



"It is also safe to state that in a climate such as that of the
northern part of the United States, and in Canada, with the long
and severe winters, it does not pay to develop a water power if
the power produced will cost more than 75 per cent of the amount
for which steam power could be produced in the same locality.

"In Canada, with the great number of water powers yet unde-
veloped or only partly utilized, it must be regarded as poor policy
to install a larger plant than can be run at all stages of the wat3r,
or to have a great proportion of power dependent upon storage
lakes during the months of low water.

"A water power requiring an auxiliary steam plant during the
low-water season, can only pay if either the cost of the development
is exceptionally low, or the locality very favorable for the sale of
power, or both."


o u %



The term river improvement may be said to refer to any engineer-
ing work undertaken with a view to bettering the conditions of a

Online LibraryAmerican Technical SocietyCyclopedia of civil engineering; a general reference work on surveying, highway construction, railroad engineering, earthwork, steel construction, specifications, contracts, bridge engineering, masonry and reinforced concrete, municipal engineering, hydraulic engineering, river and harbor improvemen → online text (page 22 of 32)