Stability Analysis Of Motion For Self-excited Induction Generator Systems

With advantages of the low cost, robust structure, easy maintainance, good transient performance and self-protection from thort circuit, induction generators are applicable widely to grid-connected, microgrid and stand-alone accasions. Especially for special generation or remote communities and small businesses where there is no access to the grid, they are preferable generators, playing an increasing important role in efficient exploitation of the new energy resources.Modeling of induction generators is an essential approach to analyzing the operating performance. The physical structure of the object can be simulated by a mathematical model, which brings in errors never avoided through supposing conditions. It is the main drawback of the quantity analysis. While the quality analysis lays emphasis on studing the characteristic of quality with the object, which is the sign distinguished from others and the basis of theoretical analysis for the operating performance of the system. But it has something what in subjective. An appropriate integration of the advantages from both the quality analysis and the quantity analysis majors in the quality analysis of the operating mechanism and supplementaries in the quantity analysis by computation and experimented demonstrations. Through the perfectly united approach above, the operating essence of induction generator systems can be revealed effectually.Considering the problem that there is no available approach to computing analytically the transient and steady-state operating performance of induction generator systems at present, the physical model and its mathematical model of induction generator systems in three-phase coordinate frame can be transformed equivalently into the one in another reference frame. And it is obtained the equivalent physical model and its mathematical model of the induction generator in the two-phase stationary reference frame. By introducing nonlinear dynamical system theory and the Law of Energy Conversion and Constant, a holistic theoretical analysis approach based on Lyapunov stability theory is proposed. Through the approach, the self-excited induction generator system is analyzed for voltage buidup transient and loaded steady-state operating performance separately. The clitical condition for the transient stability and its analytical formulas are obtained by transient analysis, whose correctness is demonstrated by example analysis and comparation, explainning its convenience. The steady-state conditions including the limit cycle and steady-state operating point conditions are obtained by steady-state analysis. To solve the steady-state conditions, an equivalent transformation analytical computation method is proposed. Through the analytical formulas of steady-state operating points, it is obtained analytic solutions of the steady-state conditions. Calculation examples are used to test and verify one only analytic solution, which can be commonly used to compute analytically the torque and power, as well as the design of reactive compensator and so on.The transient processe analysis of load connection and disconnection for self-excited induction generators is performed by use of the holistic analysis approach based on Lyapunov stability theory, thus the theoretical approach for transient processes of load switches is proposed to analyze the whole procedures, both of which are considered to be two motions of different properties in the view of the physical essence by the proposed approach in this study.As is known from the above analysis, the motion morphology of steady states are referred as an orbit with a fixed period:limit cycle, whose stability can determine that of the steady states. The external parameters of the generator circuits realize changing the transient and steady-state operating performance by changing the dynamical magnetizing inductance. Through introduced Lyapunov Index, the transient and steady-state operating stability and its degree of the self-excited induction generator system can be unitedly described and analyzed by the theoretical analysis approach proposed. The larger of the absolute value of the minus Lyapunov Index, the more stable are the transient states, the faster does the transient states reach steady sates or zero state, the shorter is the time of the transient response. The bigger of the absolute value of the positive Lyapunov Index, the greater is the sensitivity dependence of the transient system on the initial state, the more unstable are the transient states, the more stable are the corresponding steady states, and the faster is the buildup transient response.Experimental results display as follows. The buildup transient process for the speed fixed of the self-excited induction generator becomes faster with the capacitance increase. The steady-state stator frequency becomes smaller with the capacitance increase, larger with the rotor speed or load resistance increase, while other steady-state state parameters become larger with the capacitance, rotor speed or load resistance increase. The experimental results indicate as follows. The capacitance, rotor speed or load resistance change the nonlinear characteristics of self-excited induction generator systems through changing dynamic magnetizing inductance, coinciding with the theoretical results well. The steady-state values of self-excited induction generators are affected greatly by the remanent magnetism or capacitance store energy and the line loss or iron loss. The more the intial remanent magnetism or capacitance store energy, the larger is the difference between the steady-state experimental and theoretical results. The lower the load resistance is, the smaller is the closed circuit totle equivalent resistance, and the larger is the system line loss or iron loss, so that the experimental results will be lower than the theoretical results. Thus verifies further the correctness of the theoretical analysis approach, analytical conditions and their analytic formulas from the experimental level.The paper establishes systematically a mechanism analysis approach for the whole transient and steady states of induction generator systems. Significantly different from the former analysis scheme based on the numerical and iterative computations, the approach is more applicable to the optimization design and performance evaluation for configurations and operational safeguard procedures in induction generator systems, so as to provide a novel theoretical foundation for improving the conversion efficiency and operational reliability of the new energy generation systems.