Prior to 1950s, the shunt capacitor banks were placed nearer to the
main substation for capacitive reactive power compensation, it helps in
improving the power factor, reduces power losses and improving the voltage
profile. Placement problem of capacitor banks has been
extensively discussed in technical literature especially since 1980’s as the
distribution system planning and operation started getting renewed focus. Since
then, many solution techniques have been suggested
identifying the problem as a complex problem which is classified as analytical,
numerical, heuristics, Artificial Intelligence (AI) Based and hybrid techniques
and they have been developed to solve the problem.

1.1 Analytical Techniques

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Analytical techniques are early works of optimal capacitor placement
in which using the calculus to calculate the minimum losses and maximum
non-discrete capacitor sizes, equal capacitor sizes and constant capacitor
locations. Two-thirds rule was established due to these techniques. A capacitor
of rating equal to two-thirds of the peak reactive demand should be installed
at a position two-thirds of the distance along the total feeder length for
maximum loss reduction.

The analytical techniques for capacitor
placement are mainly developed by N. Neagle and D. Samson for optimum single
and multiple capacitor banks in case of uniform and non-uniform distribution of
load to minimize the power loss 9. R. Cook 10 and Y. Bae 11 worked on the same guideline of 9 proposed a more practical algorithm for fixed capacitor bank by
building a voltage-independent reactive current model. S.  Lee and J. Grainger 12 used fixed and switched capacitors which were placed for optimizing
the net savings associated with the reduction of power and energy losses. J.
Grainger and S.  Lee 13 proposed a voltage-dependent methodology for shunt capacitor
compensation of primary distribution feeders.

M. Kaplan 14 proposed an analytical method to optimize number, location, and size
of capacitors. Most of the analytical methods discussed above-considered modeling
of the capacitor placement locations and sizes as continuous variables.
Therefore, the results might need to be rounded up or down to the nearest
practical value, which may result in an overvoltage problem or loss savings
less than the calculated one. The more recent analytical methods are much more
accurate and practical for distribution systems such as J. Grainger et al.
15-21 where the objectives are a minimization
of power/energy losses, and minimization of peak load.

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