Multistability, multiscroll chaotic attractors and angle instability in multi-machine swing dynamics

The modelling and nonlinear analysis of a multi-machine system using swing dynamics is explored in this paper. Four identical machines (synchronous generators) in parallel is considered as a special case. Some interesting and unique nonlinear characteristics such as (1) different dynamic transitions via period doubling bifurcation, (2) angular instability via multiscroll chaotic attractor and (3) the presence of coexisting attractors (multistability) are revealed. Nonlinear tools such as Lyapunov exponents, bifurcation diagrams, time series and phase portrait responses are utilized to explain and validate the different dynamic behaviours. Furthermore, an adaptive second order PI sliding mode control is used to suppress the chaotic oscillations in multi-machine system. Numerical simulations are carried out in the MATLAB environment which confirm that the objective is accomplished successfully.