6.1 COSTS
The users of
electricity must pay for what they use.
To provide them with electric power, generating stations must be built
and maintained, a transmission and distribution network installed, staff paid
and, of course, fuel burnt (except in natural-energy plants such as
hydroelectric stations). All of these
must be paid for.
The costs of
generation and of transmission and distribution are divided broadly into two
groups: ‘capital’ and ‘running’. Capital
costs cover the acquisition of land, building of power stations and
transmission and distribution networks, buying the prime mover and generating
plant and other equipment such as switchgear and transformers, and setting up
the administrative organisation to run the system.
Money for capital
costs is basically a ‘one-off’ demand, for which finance has to be raised,
usually by borrowing. This means
interest payments and repayment of the capital loan over a definite period.
All plant and
equipment deteriorates with use and with time, and its value must be regularly
scaled down until it is virtually written off except for its scrap value. A Depreciation Fund is raised, which can be
used either to repay the original loan or to replace the worn-out equipment. The build-up of this fund, along with
interest payments, represents a continuing annual charge, called ‘Annual
Capital Cost’.
Under ‘running’ costs
clearly the principal item is fuel. The
amount used is directly proportional to the loading on the station, and it is
therefore necessary for each consumer to pay for the energy actually consumed
in order to meet the fuel cost. Other
running costs include labour and day-to-day overheads such as lighting,
heating, cleaning, cranage and storekeeping, as well as rates and water charges
etc. which are in general not dependent on the station loading.
Maintenance and
replacements are also a continuing charge both on the generating plant itself
and on the distribution system consisting of switchgear, transformers, lines
and substations. These, together with
the other overhead charges referred to above, form part of the broad ‘running’
costs.
In order for the whole
system to be viable, the customers using the electric power must pay not only
for the energy (fuel) which they consume and a share of the other running
costs, but they must also pay a contribution towards the total Annual Capital
Cost.
Running costs are
simple to calculate. Each consumer is
provided with a meter which records the total energy consumed in kWh or MWh
during any accounting period and it is paid for at whatever rate is demanded
per ‘unit’ (kWh).
To assess the proper
contribution towards the Annual Capital Cost, it is assumed that the size of
generating plant and distribution system has already been determined by the sum
total of all the individual consumers’ expected demands (with an allowance for
growth), the unit generally used being kVA.
For example, if one consumer’s expected load demand has been estimated
(by him) to be 10 000kVA, then 10 000kVA of generating and distributing
plant must be provided for his use; this must be based on the consumer’s
expected maximum demand, since that is what the generating plant will, at some
time, have to meet. Each individual
consumer will thus have earmarked a certain proportion of the total generating
capacity, and this is the proportion of the Annual Capital Cost which he will
be expected to pay.
6.2 TARIFFS
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The Authority who
supplies power to the consumer must therefore devise a tariff which will recoup
enough money from all his customers to pay his own costs. This tariff will in general be in two parts -
one part based solely on the energy consumed to meet fuel and other running
costs, the second part based on the maximum demand expected at any time from
that consumer. Large consumers usually
pay this part based on ‘Maximum Demand kVA’, although some Boards prefer to
charge by ‘Maximum Demand kW’; smaller consumers are usually charged on Maximum
Demand kW with a penalty for low power factor.
This element of the tariff is designed to meet each consumer’s
contribution to the Annual Capital Cost.
FIGURE
6.1
TYPICAL MAXIMUM
DEMAND kVA METER
In practice maximum demand is not measured at any given instant but is
averaged over successive periods of 30 minutes.
A kVAh integrating meter of the eddy-current type (a typical one is
shown in Figure 6.1) indicates by a small moving pointer the total kVAh taken
over 30 minutes, after which the pointer resets to zero and starts again. As it moves forward it pushes a free pointer
ahead of it but leaves it behind when it resets to zero. The free pointer stays in that position
unless or until the total kVAh taken during any subsequent 30-minute period
exceeds that at which the pointer was left; the pointer is then pushed further
on to provide a new maximum reading.
When the meter is read, the position of the free pointer indicates the
maximum kVAh taken during the worst 30-minute period and so gives the average
kVA during that period. On this is based
the ‘maximum demand’ charge.
The actual charges, both for kWh units and for kVA maximum demand, are
determined by the Supply Authority and are often negotiated with important
consumers. The following is a greatly
simplified example of such a calculation.
Example
Output = 800MW or
1 000MVA
\ Annual Capital Cost = = £14 000 per MVA
or
£14 per kVA
Fuel cost (say) 3p
per kWh
Other running costs
(say) 1.5p
per kWh
Total Running Cost: 4.5p
per kWh
The minimum tariff
(ignoring profit, etc.) would therefore be:
£14 p.a. per kVA maximum demand and
4.5p per kWh unit.
Thus a factory which
uses 8 000 000 units per year and has a maximum demand of 6 000k VA would pay
annually on the above tariff:
8 x 106 x 4.5p =
£360 000 fuel charge
+ 6 x 103 x £14 = £ 84 000 maximum demand charge
£444
000 total
For domestic consumers, whose bills are
paid quarterly, the tariff is usually simpler, based on a simple charge per
unit (kWh) and a fixed Standing Charge, all payable quarterly.
From the example given
above:
Annual Capital Cost = £14.00 per kW p.a.
or
£3.50 per kW per quarter
Area Electricity
Boards usually offer special reduced terms where the maximum demand occurs
outside the peak period - for example the ‘Economy 7’ tariff. This is to encourage consumers to go in for
‘off-peak’ consumption, for example for water heating. During offpeak periods the consumption is
separately metered.
6.3 POWER CORRECTION AND TARIFFS
It is shown in the
manual ‘Electric Motors’ how low power factor in a motor may be corrected by
the use of capacitors. A powerful reason for doing this is to lower the kVA
demanded by such motors, and thereby to reduce the maximum demand charge under
the tariff.
Since kVA =
 , and since the
kW demand is determined by the process system and cannot be varied, the kVA is
at its lowest value when the kvar is zero, in which case the kVA is equal to
the kW loading. This situation occurs when the power factor has been corrected
to unity.
Such an exact
correction is not however necessary, as Figure 6.2 shows:
FIGURE 6.2
MOTOR POWER FACTOR CORRECTION
Vector OP represents
the active current and so the kW loading of a motor, and PQ represents the
reactive current and so the kvar. Vector
OQ is then the total uncorrected kVA. If
PQ is reduced by power factor correction, the slope of OQ becomes less until,
ideally at unity power factor, OQ lies on top of OP, and the kVA is then at its
minimum value and equal to the kW.
If, however, the kvar
were not made exactly zero, the motor might be slightly under-corrected (PQ’)
or over-corrected (PQ”), in which case OQ’ (or OQ”) does not lie exactly over
OQ but still has some slope. This slope,
however, is small, and the difference in length between OP and OQ’ (or OQ”) is
negligible. There is, therefore, little
.to be gained by achieving exact correction, and indeed, because correcting
capacitors are expensive, there is some virtue in aiming at slight under-correction. A compromise would be reached, and the small
extra maximum demand cost remaining due to under-correction would be set
against the cost of the extra capacitance needed to achieve full correction.
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