The most economical power factor: A practical design formula for distribution circuits

Abstract

The use of power factor corrective devices on distribution circuits is justified, under certain conditions, by rather substantial savings in investment charges and by a reduction in the power losses of the system. The object of the present paper is to develop a practical working formula for calculating the most economical corrected power factor for a distribution circuit. Most economical conditions are assumed when the total of such annual circuit costs as are directly affected by a change in power factor, is a minimum. The usual methods for computing separately, the saving in I <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> R losses and the decrease in investment charges due to power factor improvement, are inadequate. Particularly in the design of new circuits and extensions has the need for a more accurate method for calculating optimum power factor and conductor sizes been expressed. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> Since these equations were originally worked out, two other solutions for the most economical corrected power-factor angle have been published, each having been obtained independently of the other. Menjelou <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> obtained his formula in the form: α sin θ = 1 β tan θ in which θ is the power-factor angle and α and β are constants computed from the circuit costs. Stevenson <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> obtained a similar expression: sin θ = δ − η tan θ the difference lying in the constants to be evaluated. The equation developed in this paper reduces to the simple form: sin θ = unit cost ratio That is, the sine of the most economical corrected power-factor angle is determined by the ratio of the annual cost of condenser capacity per reactive kilovolt-ampere of correction to the annual cost (fixed charges plus value of losses) per kilovolt-ampere delivered, of that portion of the supply circuit which is directly affected by the change in power factor. When the unit cost ratio is greater than the sine of the original power-factor angle, it is found that no investment in corrective equipment is economically justified. The equation is set up in such a form that solutions are readily obtained for the most economical size of conductor as determined by the Kelvin law, and for the required kilovolt-ampere rating of the transformers and condensers. A method is suggested for including generating station costs with those of the individual circuit under consideration. In evaluating circuit costs, the effects of load factor and the shape of the typical daily load curve upon capital investment and power losses have been worked out after the methods used by Gear and Williams <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> and by Reyneau and Seelye <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> . Equations for evaluating the circuit constants are included in the appendix. Several illustrative examples are worked out.