IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 2, JUNE 2004 245 Double Winding, High-Voltage Cable Wound Generator: Steady-State and Fault Analysis Marguerite Touma-Holmberg, Member, IEEE, and Kailash Srivastava, Senior Member, IEEE Abstract—This paper describes a detailed circuit representation of synchronous machines equipped with two similar or dissimilar armature windings. The equivalent circuit at steady state is pre- sented. The self and mutual leakage inductances of the two sets of three-phase stator windings are evaluated by the finite element method as well as an analytical method. The simulation results from a steady-state analysis as well as a fault analysis are verified experimentally on the world’s first high-voltage generator Power- former installed in Porjus, Sweden, rated at 45 kV and 11 MVA. Index Terms—Double winding, fault, inductance, leakage, Pow- erformer, steady state, synchronous. I. INTRODUCTION S YNCHRONOUS machines with two similar armature windings have been designed and installed even in the first quarter of the 20th century to permit the electrical segregation of bus sections in large stations. By loading the windings inde- pendently, the advantages of a higher generator reactance and, hence, lower fault currents were obtained, while yet retaining adequate synchronizing power [1]. The generated voltages in the two windings were substantially equal in magnitude as well as in phase. Later on, Robert et al. [2] demonstrated that the stray losses due to the phase harmonics could be substantially reduced if the two windings were displaced 30 from each other. Leijon et al. [3] presented a new concept of rotating ma- chines that enable direct connection of synchronous generators to the transmission network without any intervening step-up transformers. Such a synchronous machine is called Power- former. Powerformer has the possibility of simultaneous direct connection to several different grid voltages through different stator windings. Such a secondary stator winding can also be used for power supply at the standard medium and low-voltage levels to feed power plant auxiliaries. In pump-storage plants, the second winding can be used to start up the water pump. In turbo power plants, the second winding can be used to start up the gas turbine, thereby avoiding an extra motor. Fuchs et al. [4] analyzed a double winding alternator by or- thogonal transformations. The effect of the leakage inductances and damper windings were not considered. Schiferl et al. [5] de- scribed a detailed circuit model of a six-phase salient pole syn- Manuscript received November 13, 2002. M. Touma-Holmberg is with the ALSTOM Power, Vasteras SE-721 76, Sweden (e-mail: meh@work.utfors.se). K. Srivastava is with the ABB, Vasteras SE-721 78, Sweden (e-mail: kailash.srivastava@secrc.abb.se). Digital Object Identifier 10.1109/TEC.2004.827024 Fig. 1. Phasor diagram of a double winding synchronous machine. chronous motor with ac-dc stator connections including stator self and mutual leakage inductances. This paper presents a detailed circuit model of a double winding three-phase salient pole synchronous machine. The self and mutual leakage inductances of the two sets of the three-phase stator windings are calculated by the finite element method (FEM) as well as an analytical method due to Richter [6]. The calculated results from a steady-state analysis as well as a fault analysis are verified against the measurements performed on the world’s first double winding Powerformer installed at Porjus Hydropower station in Sweden. II. EQUIVALENT CIRCUIT REPRESENTATION The schematic representation of a double winding three-phase synchronous machine is shown in Fig. 1. The six stator windings are arranged so that two sets of three- phase balanced systems labeled and are formed. The magnetic axes of these two systems are displaced by an ar- bitrary angle . The stator windings of both systems and are sinusoidally distributed windings, displaced by , with and equivalent turns and resistances and , respectively. The rotor is equipped with a field winding and two damper windings. The field winding referred to as the winding has equivalent turns with a resistance . The damper winding referred to as the winding is along the direct axis, which is called the -axis. The damper winding referred to as the winding is along the quadrature axis, which is called the -axis. The -axis is ahead of the -axis by an angle in 0885-8969/04$20.00 © 2004 IEEE