Rank Exponent-Based Reduction of Higher Order Electric Vehicle Systems

Electric vehicles (EVs) are gaining an ever-growing popularity in the society as the green vehicles of the next future, i.e., vehicles independent of oil and not producing greenhouse gases. The modelling of these vehicles is made complex by their higher-order nature. Hence, reduction methods are more and more proposed in the literature. To the best of the authors' knowledge, this is the first paper proposing to exploit both the rank exponent (RE)-based reduced order (RO) modeling of higher-order electric vehicle system (HOEVS) of order five, and the error minimization based reduction approach by employing the grey-wolf optimization (GWO) algorithm. The Markov parameters (MaPas) and time moments (TiMos) of HOEVS, and its ROEV model (ROEVM) are exploited for obtaining the desired ROEVM of order two. For error minimization, a weight associated objective function is framed by utilizing HOEVS's and ROEVM's MaPas and TiMos. The weight ascertainment is done based on transient and step responses of desired ROEVM with respect to HOEVS. The GWO algorithm is then employed to optimize the weighted objective function under defined constraints. Firstly, steady state matching constraint is employed to ensure that ROEVM accurately captures the steady state behavior of HOEVS. Secondly, the Hurwitz stability criterion is incorporated as a constraint to guarantee the stability of ROEVM. To validate the effectiveness of the presented approach, a comparative analysis with other reduction methods has been carried out, in terms of the step, impulse, Nichols, Bode, and error plots along with time domain specifications and error indices. The responses and tabulated data showcase the superiority of the proposed method, thus confirming the efficacy and efficiency of our approach in reducing the order of electric vehicle systems.