Prior to 1950s, the shunt capacitor banks were placed nearer to themain substation for capacitive reactive power compensation, it helps inimproving the power factor, reduces power losses and improving the voltageprofile. Placement problem of capacitor banks has beenextensively discussed in technical literature especially since 1980’s as thedistribution system planning and operation started getting renewed focus. Sincethen, many solution techniques have been suggestedidentifying the problem as a complex problem which is classified as analytical,numerical, heuristics, Artificial Intelligence (AI) Based and hybrid techniquesand they have been developed to solve the problem.1.
1 Analytical TechniquesAnalytical techniques are early works of optimal capacitor placementin which using the calculus to calculate the minimum losses and maximumsavings. They were based on impractical assumptions like uniform loading,non-discrete capacitor sizes, equal capacitor sizes and constant capacitorlocations. Two-thirds rule was established due to these techniques. A capacitorof rating equal to two-thirds of the peak reactive demand should be installedat a position two-thirds of the distance along the total feeder length formaximum loss reduction.The analytical techniques for capacitorplacement are mainly developed by N. Neagle and D. Samson for optimum singleand multiple capacitor banks in case of uniform and non-uniform distribution ofload 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 bybuilding a voltage-independent reactive current model. S.
Lee and J. Grainger 12 used fixed and switched capacitors which were placed for optimizingthe net savings associated with the reduction of power and energy losses. J.
Grainger and S. Lee 13 proposed a voltage-dependent methodology for shunt capacitorcompensation of primary distribution feeders. M. Kaplan 14 proposed an analytical method to optimize number, location, and sizeof capacitors. Most of the analytical methods discussed above-considered modelingof the capacitor placement locations and sizes as continuous variables.
Therefore, the results might need to be rounded up or down to the nearestpractical value, which may result in an overvoltage problem or loss savingsless than the calculated one. The more recent analytical methods are much moreaccurate and practical for distribution systems such as J. Grainger et al.15-21 where the objectives are a minimizationof power/energy losses, and minimization of peak load.