ORIGINAL CONTRIBUTION Transmission Line Adapted Analytical Power Charts Solution Japhet D. Sakala 1 • James S. J. Daka 1 • Ditiro Setlhaolo 1 • Alec Pulu Malichi 2 Received: 20 May 2015 / Accepted: 15 July 2016 Ó The Institution of Engineers (India) 2016 Abstract The performance of a transmission line has been assessed over the years using power charts. These are graphical representations, drawn to scale, of the equations that describe the performance of transmission lines. Vari- ous quantities that describe the performance, such as sending end voltage, sending end power and compensation to give zero voltage regulation, may be deduced from the power charts. Usually required values are read off and then converted using the appropriate scales and known rela- tionships. In this paper, the authors revisit this area of circle diagrams for transmission line performance. The work presented here formulates the mathematical model that analyses the transmission line performance from the power charts relationships and then uses them to calculate the transmission line performance. In this proposed approach, it is not necessary to draw the power charts for the solution. However the power charts may be drawn for the visual presentation. The method is based on applying derived equations and is simple to use since it does not require rigorous derivations. Keywords Virtual receiving end  Sending end and combined power charts  Transmission line performance Introduction Power charts, also known as circle diagrams, have been over the years used to analyse the performance of a transmission line graphically [1–5], that is, for a given load supplied at a specified voltage, the receiving end power chart may be used to find the sending end voltage, mag- nitude and load angle, and the compensation that is required for a zero voltage regulation. The sending end power chart may then be drawn to determine the sending end apparent power, the sending end angle between voltage and current and hence the sending end power factor. The transmission line losses and efficiency may be found from a combined receiving end and sending end power chart [5]. The authors acknowledge that earlier work championed the foundation work of power charts which became part of the established analytical tools [3, 6, 7]. The contribution of this paper is the presentation of an analytical method for adapting the equations that are used to draw power charts to equations that calculate the performance of the trans- mission line without necessarily drawing the charts. The main advantage of the method is that the required quanti- ties are calculated, instead of being read from a chart and this avoids both drawing the chart(s) and reading off the values. Background A transmission line of length l with series impedance per unit length z and a shunt admittance per unit length y may be represented by its ABCD constants where A ¼ D ¼ cosh cl; B ¼ Z C sinh cl; C ¼ 1 Z C sinh cl & James S. J. Daka dakajsj@mopipi.ub.bw 1 Department of Electrical Engineering, University of Botswana, Gaborone, Botswana 2 Department of Electrical and Electronics Engineering, University of Zambia, Lusaka, Zambia 123 J. Inst. Eng. India Ser. B DOI 10.1007/s40031-016-0260-6