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| Reducing Distribution Line Losses |
One of the main benefits of applying capacitors
is that they can reduce distribution line losses. Losses come from
current through the resistance of conductors. Some of that current
transmits real power, but some flows to supply reactive power. Reactive power
provides magnetizing for motors and other inductive loads. Reactive
power does not spin kWh meters and performs no useful work, but it must
be supplied.
Using capacitors to supply reactive power reduces the amount of current in the line.
Since line losses are a function of the current squared,I2R, reducing reactive power flow on lines significantly reduces losses.
Engineers
widely use the “2/3 rule” for sizing and placing capacitors to
optimally reduce losses. Neagle and Samson (1956) developed a capacitor
placement approach for uniformly distributed lines and showed that the
optimal capacitor location is the point on the circuit where the
reactive power flow equals half of the capacitor var rating. From this,
they developed the 2/3 rule for selecting and placing capacitors. For a
uniformly distributed load, the optimal size capacitor is 2/3 of the var
requirements of the circuit.
The optimal placement of this
capacitor is 2/3 of the distance from the substation to the end of the
line. For this optimal placement for a uniformly distributed load, the
substation source provides vars for the first 1/3 of the circuit, and
the capacitor provides vars for the last 2/3 of the circuit (see Figure 1).
A generalization of the 2/3 rule for applying n capacitors to a circuit is to size each one to 2/(2n+1) of the circuit var requirements. Apply them equally spaced, starting at a distance of 2/(2n+1) of the total line length from the substation and adding the rest of the units at intervals of 2/(2n+1) of the total line length. The total vars supplied by the capacitors is 2n/(2n+1) of the circuit’s var requirements.
So
to apply three capacitors, size each to 2/7 of the total vars needed,
and locate them at per unit distances of 2/7, 4/7 and 6/7 of the line
length from the substation.
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| Figure 1 - Optimal capacitor loss reduction using the two-thirds rule |
Grainger
and Lee (1981) provide an optimal yet simple method for placing fixed
capacitors on a circuit with any load profile, not just a uniformly
distributed load. With the Grainger/Lee method, we use the reactive load
profile of a circuit to place capacitors.
The basic idea is again
to locate banks at points on the circuit where the reactive power
equals one half of the capacitor var rating.
With
this 1/2-kvar rule, the capacitor supplies half of its vars downstream,
and half are sent upstream. The basic steps of this approach are:1. Pick a size
Choose a standard size capacitor. Common sizes range from 300 to 1200 kvar, with some sized up to 2400 kvar. If the bank size is 2/3 of the feeder requirement, we only need one bank. If the size is 1/6 of the feeder requirement, we need five capacitor banks.
2. Locate the first bank
Start from the end of the circuit. Locate the first bank at the point on the circuit where var flows on the line are equal to half of the capacitor var rating.
3. Locate subsequent banks
After a bank is placed, reevaluate the var profile. Move upstream until the next point where the var flow equals half of the capacitor rating. Continue placing banks in this manner until no more locations meet the criteria.
Choose a standard size capacitor. Common sizes range from 300 to 1200 kvar, with some sized up to 2400 kvar. If the bank size is 2/3 of the feeder requirement, we only need one bank. If the size is 1/6 of the feeder requirement, we need five capacitor banks.
2. Locate the first bank
Start from the end of the circuit. Locate the first bank at the point on the circuit where var flows on the line are equal to half of the capacitor var rating.
3. Locate subsequent banks
After a bank is placed, reevaluate the var profile. Move upstream until the next point where the var flow equals half of the capacitor rating. Continue placing banks in this manner until no more locations meet the criteria.
There is no reason we have to stick with the same
size of banks. We could place a 300-kvar bank where the var flow equals
150 kvar, then apply a 600-kvar bank where the var flow equals 300 kvar,
and finally apply a 450-kvar bank where the var flow equals 225 kvar.
Normally, it is more efficient to use standardized bank sizes, but
different size banks at different portions of the feeder might help with
voltage profiles.
The 1/2-kvar method works for any section of
line. If a line has major branches, we can apply capacitors along the
branches using the same method. Start at the end, move upstream, and
apply capacitors at points where the line’s kvar flow equals half of the
kvar rating of the capacitor. It also works for lines that already have
capacitors (it does not optimize the placement of all of the banks, but
it optimizes placement of new banks).
For large industrial loads, the best location is often going to be right at the load.
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| Figure 2 - Placement of 1200-kvar banks using the 1/2-kvar method |
Figure 2
shows the optimal placement of 1200-kvar banks on an example circuit.
Since the end of the circuit has reactive load above the 600-kvar
threshold for sizing 1200-kvar banks, we apply the first capacitor at
the end of the circuit. (The circuit at the end of the line could be one
large customer or branches off the main line.) The second bank goes
near the middle. The circuit has an express feeder near the start.
Another
1200-kvar bank could go in just after the express feeder, but that does
not buy us anything. The two capacitors total 2400 kvar, and the feeder
load is 3000 kvar. We really need another 600-kvar capacitor to zero
out the var flow before it gets to the express feeder.
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Figure
3 -Sensitivity to losses of sizing and placing one capacitor on a
circuit with a uniform load. (The circles mark the optimum location for
each of the sizes shown.)
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Fortunately, capacitor
placement and sizing does not have to be exact. Quite good loss
reduction occurs even if sizing and placement are not exactly
optimum. Figure 3 shows the loss reduction for one fixed capacitor on a circuit with a uniform load. The 2/3 rule specifies that the optimum distance is 2/3 of the distance from the substation and 2/3 of the circuit’s var requirement.
optimum. Figure 3 shows the loss reduction for one fixed capacitor on a circuit with a uniform load. The 2/3 rule specifies that the optimum distance is 2/3 of the distance from the substation and 2/3 of the circuit’s var requirement.
As long as the size and location are somewhat close
(within 10%), the not-quite-optimal capacitor placement provides almost
as much loss reduction as the optimal placement.
Consider the
voltage impacts of capacitors. Under light load, check that the
capacitors have not raised the voltages above allowable standards.
If voltage limits are exceeded, reduce the size of the capacitor banks
or the number of capacitor banks until voltage limits are not exceeded.
If additional loss reduction is desired, consider switched banks as
discussed below.
Energy Losses
Use the average
reactive loading profile to optimally size and place capacitors for
energy losses. If we use the peak-load case, the 1/2-kvar method
optimizes losses during the peak load. If we have a load-flow case with
the average reactive load, the 1/2-kvar method or the 2/3 rule optimizes
energy losses. This leads to more separation between banks and less
kvars applied than if we optimize for peak losses.
If an average
system case is not available, then we can estimate it by scaling the
peak load case by the reactive load factor, RLF:
RLF = Average kvar Demand / Peak kvar Demand
The
reactive load factor is similar to the traditional load factor except
that it only considers the reactive portion of the load. If we have no
information on the reactive load factor, use the total load factor.
Normally, the reactive load factor is higher than the total load factor.
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| Figure 4 - Example of real and reactive power profiles on a residential feeder on a peak summer day with 95% air conditioning |
Figure 4 shows an example of power profiles; the real power (kW) fluctuates significantly more than the reactive power (kvar).
