International Journal of Electrical Engineering Education 39/4 An efficient power flow algorithm for distribution systems with polynomial load Jianwei Liu, M. M. A. Salama and R. R. Mansour Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada E-mail: m.salama@ece.uwaterloo.ca Abstract A new, efficient power flow algorithm for complex distribution systems is presented. Voltage ratio is used for convergence control. This method has fast convergence ability for the polynomial load model for which the traditional Newton-Raphson method is usually not adaptable. Test results show the robustness of the proposed method. Keywords Newton-Raphson method; polynomial load model; power flow; radial network Power flow analysis is essential for power system planning and operation. With the use of digital computing since the 1960s and its rapid development, many power flow algorithms based on modern computing methods have been introduced. 1–3 The most famous methods include: ladder network methods for radial-type distribution systems using basic circuit theories (KCL and KVL); and the Gauss-Seidel, Newton- Raphson and Decoupled Newton-Raphson methods for transmission grid analysis using the nodal method. All these methods have been successfully applied in indus- try for many years. Well-known conclusions of using these methods are: 3–6 • ladder network methods are quite suitable for one sending end radial networks with high R/X ratio; • nodal analysis methods are suitable for multiple-source systems. Traditionally, most distribution systems are radial or weakly meshed types. 4–7 Faced with the power markets of today, increasing requirements for reliability and out- going distribution generation have meant that the structure of distribution systems has become more complex. 1,8 Thus the power flow analysis in such distribution systems becomes more difficult than before. Most of the above methods were developed based on the assumptions of a static load model. Reliable power delivery needs power flow analysis with a detailed load model. Distributed generation is becoming an attractive solution to meet the fast load increase in the deregulation era. 9 Utilities have to analyse the operation con- ditions of the radial-type systems with distributed sources. Newton-Raphson like methods are not suitable for this purpose because of the high R/X ratio; while traditional ladder network methods also face a great challenge because of the multiple-source conditions. Usually the commercial SCADA/DMS systems treat these systems as independent parts, i.e., HVAC (high voltage a.c.) loop and MVAC (medium voltage a.c.) or LVAC (low voltage a.c.) radial systems. Such rough equivalence will cause inaccuracies in the power flow solutions.