A Study of Synchronous Machine Model Implementations in Matlab/Simulink Simulations for New and Renewable Energy Systems Z. Chen, F. Blaabjerg, F.Iov Institute of Energy Technology, Aalborg University, Aalborg, DK-9220, Denmark Abstract-A direct phase model of synchronous machines implemented in MATLAB/SIMULINK is presented. The effects of the machine saturation have been included. Simu- lation studies are performed under various conditions. It has been demonstrated that the MATLAB/SIMULINK is an effective tool to study the complex synchronous machine and the implemented model could be used for studies of various applications of synchronous machines including in renew- able and DG generation systems. I. INTRODUCTION Synchronous machines have been widely used in power systems, they are not only the main generation units in large scale conventional power stations, but also in small and remote stand alone systems. Various new types of synchronous generators are being developed for newly emerging renewable and distributed generation (DG) systems, including multi-pole machine for wind power conversion systems. These machines play a very important role to achieve a high efficiency and reliable power system with good power quality. A detailed and accurate model is essential to investigate the performance of a synchronous machine and its control strategies. Various modelling and simulation techniques have been reported to study the belabour of synchronous ma- chines, dqO reference frame models of synchronous gen- erators are widely used due to the simplicity, however, these models have some limitations [1,2], for example in studying unbalanced and nonlinear loading conditions. On the other hand, a direct phase model is possible to provide a more accurate solution [3] and has the potential to study the performance of various new type of synchronous gen- erators. Also, various conditions, such as sudden applica- tion and removal of balanced and unbalanced loads, con- nection of power electronic converters and symmetrical and asymmetrical faults, can be easily investigated. Currently Matlab/Simulink is a widely used simula- tion tool for dynamic systems. A wide range of compo- nents will be involved for modelling large dynamic sys- tems, for example, power system, including prime mov- ers, generators, transformers, power electronic converters. Matlab/Simulink is an effective tool for such applications [4]. This paper presents important aspects regarding the implementations of a direct phase synchronous machine model. It first briefs the synchronous machine model in both abc frame and qdO frame, then discusses the satura- tion considerations, the saturation is considered in q-d frame as usual way, however, an mathematical expression is used to relate the current and inductance, then the in- ductance may be directly found with the fluxes, which are used as the state variables in the simulation model. The model of synchronous machine has been implemented in MATLAB/SIMULINK. The effects of nonlinearity of the machine have been included in the model. Simulation studies are performed under various conditions. It has been demonstrated that the MATLAB/SIMULINK im- plemented model has the potential to be used for studies of various applications of synchronous machines such as in renewable and DG generation systems. II. SYNCHRONOUS MACHINE MODELS Both direct phase model and commonly used dqO frame model that is used for considering the saturation effects are briefed in this section. A. Direct phase model The six circuits of an idealized synchronous machine, 3 phase windings, a field winding and two equivalent damper coils, are shown in Fig. 1. kQ a O01r / a b, (o, f kD .ryy)n C, Fig. 1. Diagram of idealized synchronous machine. The performance of a synchronous generator can be described by the voltage equations in direct phase quanti- ties for the three armature phases, the field and two equivalent damper coils. The position of the rotor at any instant is specified with reference to the axis of phase a by the angle Or. In terms of flux linkage, the voltage equa- tions for the six circuits can be expressed in phase frame as: [V]=[R].[i]+ d[A] dt where [V] = [Va Vb VC 0 0 Vf 1 [i] [ia 2b Pc 'Q 'D D r f [R]= diagonal[r, rb r, rQ rD rfT The flux is related to the current by: (1) 1960