Rev. Roum. Sci. Techn.– Électrotechn. et Énerg. Vol. 63, 2, pp. 145–150, Bucarest, 2018 1 University of Craiova, Faculty of Electrical Engineering, acampeanu@em.ucv.ro 2 Technical University of Cluj Napoca, Dedicated to the memory of Academician Andrei Ţugulea DYNAMIC STABILITY OF PERMANENT MAGNET SYNCHRONOUS MACHINE VERSUS SYNCHRONOUS MACHINE WITH ELECTROMAGNETIC EXCITATION AUREL CAMPEANU 1 , RADU MUNTEANU 2 , VASILE IANCU 2 Key words: Permanent magnet, Synchronous motor, Transients, Modeling, Simulation. There has been followed the effect of the two excitation systems upon the dynamic stability of synchronous machine. The dynamic electromagnetic torques, the electrical angular speeds of the main rotating field, and that of the rotor are simulated in detail; the dynamic magnetic stresses are also specified. By simulation, the currents of all the machine windings can be determined, so on this basis, all the electromagnetic and mechanical stresses are specified. The qualitative and quantitative results are useful both in the design stage of synchronous machine and in the industrial practice. 1. INTRODUCTION At present by the side of synchronous machines in classical construction, with electromagnetic excitation (SMEE), [1–3] there are also manufactured, in a large range of power, permanent magnet synchronous machines (PMSM), with known advantages and disadvantages and which are the issue of many researches [4–13]. In order to really obtain competitive performances with PMSM, in the design stage it is absolutely necessary to simulate the specific dynamic processes which are to specify the electromagnetic and mechanical stresses; the parameters and constructive solutions are only finalized on this basis. Generally advanced dynamic mathematical models of synchronous machine (using circuit theory, field models or circuits field) are proved to be a valuable mathematical tool, which provides plausible quantitative results. The simulations are also proved opportune in industrial working for pre- determining the machine behaviour in anticipated dynamic processes. In this paper there are analyzed comparatively the dynamic performances, by using circuit theory, of a certain synchronous machine, which has the rotor with electromagnetic excitation or with permanent magnets; the same damping windings in D, Q axes are considered. The particularities of the dynamic behaviour of high power synchronous machine are analyzed in [14]. 2. DYNAMIC MATHEMATICAL MODELS Park voltage equations for both excitation systems are of the form [15], (see and [4]) A d X d t + BX = U . (1) X is the matrix of the state variables and A, B are matrixes dependent upon the state variables. For PMSM, the hybrid model is considered with T q d q d i i X Ψ Ψ = (2) T // 0 0 1 p D d q d T u u U ψ σ − = . (3) Accordingly, the matrices A, B have the form A = 1 1 −L d σ Dd 1 −σ D 1 1 −σ D −L q σ Qq 1 −σ Q 1 1 −σ Q , (4) B = R s −ω R s ω −L d T d 0 // 1 −σ D T d 0 // 1 −σ D −L q T q 0 // 1 −σ Q T q 0 // 1 −σ Q , (5) where T” d0 , T” q0 , – rotor time constants for open stator winding. For SMEE, the currents of the windings are considered as state variable with T Q D E q d i i i i i X = , (6) T 0 0 E q d u u u U = (7) and accordingly, the matrices A, B A = L d L md L md L q L mq L md L E L DE σ + L md L md L DE σ + L md L D L mq L Q , (8) B = R s −ωL q −ωL mq ωL d R s ωL md ωL md R S R D R Q . (9) The equation of motion is added to the voltage eqs. (1),