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

Analytical techniques are early works of optimal capacitor placement

in which using the calculus to calculate the minimum losses and maximum

savings. They were based on impractical assumptions like uniform loading,

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.