Electric Power Systems Research 106 (2014) 214–225 Contents lists available at ScienceDirect Electric Power Systems Research jou rn al hom epage: www.elsevier.com/locate/epsr Calculation of derating factors based on steady-state unbalanced multiphase induction machine model under open phase(s) and optimal winding currents A.S. Abdel-Khalik a , M.I. Masoud b,a,∗ , S. Ahmed c , A. Massoud d a Electrical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria, Egypt b ECE Department, Faculty of Engineering, Sultan Qaboos University, Muscat, Oman c Electrical and Computer Engineering Department, Texas A&M University at Qatar, Doha, Qatar d Electrical Engineering Department, Qatar University, Doha, Qatar a r t i c l e i n f o Article history: Received 14 November 2012 Received in revised form 22 June 2013 Accepted 22 August 2013 Available online 27 September 2013 Keywords: Multiphase induction machine Poly-phase Eleven phase Fault tolerant Current optimization Genetic algorithm a b s t r a c t Multiphase machines have become a promising candidate in high-power applications as they offer many advantages over their three-phase counterparts. The main salient feature is the high fault tolerance capa- bility. During faults, two alternatives for machine operation are possible, namely; open loop control and optimal current control. While the former corresponds to higher torque ripple and unbalanced winding currents, the latter option necessitates unbalanced phase voltages and typically an increased DC-link volt- age to source the required optimal currents. Consequently, an increase in the employed semiconductor device rating is required, which is a critical design factor especially in medium voltage applications. This paper investigates an eleven-phase induction machine with concentric windings under fault conditions. An unbalanced steady-state machine model based on symmetrical components theory is developed as a mathematical tool to estimate different machine currents and total developed torque under open circuit phase(s). The effect of different sequence planes is also included in the derived model. This model is then experimentally verified. It is shown that the application of optimal current control in multiphase induc- tion machines with open circuited phase(s) optimizes torque production while maintaining minimum stator copper loss and torque ripples. This optimization problem usually incorporates solving compli- cated nonlinear equations that increase in complexity with higher numbers of phases. Alternatively, a genetic algorithm is used in this paper to provide a simple method to obtain the optimum currents in the remaining healthy phases. Based on the derived optimal currents, the steady-state model is used to estimate the required DC-link voltage reserve that ensures no machine de-rating. Finally, the required derating factors to avoid machine overheating are calculated for different numbers of disconnected phases when DC-link voltage limitation is introduced. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Multiphase machines have become serious contenders for safety-critical application and high power applications [1–6]. The additional degrees of freedom provided by multiphase machines [1,7,8] enable meeting the stringent requirements typical of high power and/or wide fault tolerance applications in electric ships, hybrid vehicles, pumps, compressors, and electric aircraft. The advantages of multiphase machine drives over conventional three- phase machines include [1,7,9–14]: ∗ Corresponding author at: ECE Department, Faculty of Engineering, Sultan Qaboos University, Muscat, Oman. Tel.: +968 96139466; fax: +968 24413454. E-mail address: m.masoud@ieee.org (M.I. Masoud). • They can be designed with a reduced per-phase voltage, corre- spondingly, reduced semiconductor device voltage rating; which is highly desirable in medium voltage applications; • Enable independent control of the fundamental and spatial har- monics leading to higher torque density [15]; • Can operate as a multi-motor drive system [1]; • Possess additional degrees of freedom that can be exploited to improve fault tolerant capability where the machine can continue running with (n - 3) disconnected phases [1,6]. The most salient feature of multiphase machines is their ability to operate under open-phase conditions. This can occur due to one of the phase terminals being disconnected, internal winding rupture, or one or more of the inverter phase legs failing open (disconnecting). Multiphase machine performance with open circuit faults has been studied in literature [11–14,16–18] and a 0378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2013.08.015