Economic model predictive control of Li‐ion battery cyclic aging via online rainflow‐analysis

Abstract

Cycle identification via the rainflow-algorithm is implemented online in a model predictive controller (MPC) for Li-ion batteries. This is achieved by externalization of the cycle identification from the optimization problem. The limitation for cyclic aging estimation due to short prediction horizons is overcome by updating and utilizing a State of Charge memory. Furthermore, a comprehensive plant model for Li-ion batteries is presented with novel submodels for calendric and cyclic aging. The novel MPC is implemented in the ACADO Toolkit and tested with the aforementioned plant model. Simulation results indicate that-even without tuning-the novel MPC clearly outperforms a rule-based controller and an extensively tuned MPC from literature.

Economic nonlinear model predictive control of fatigue for a hybrid wind-battery generation system

“…This includes identifying the reversals (extrema) in the given cyclic stress trajectory, to obtain the number of cycles and corresponding cycle characteristics, such as cycle mean, weight, and amplitude. A detailed account of calculating cyclic damage for wind turbine tower root stress and for battery is presented in [7,9,10]. The standard RFC approach calculates, for given stress samples σ(k), the total damage due to both half-and full-cycles, and then discards all the stress samples [11].…”

“…As a consequence, an improper consideration of stress history can lead to the under-evaluation of the resulting cyclic fatigue damage. To this extent, a one step time discrete RFC algorithm, explained in detail in [10], is utilized, where residue samples from the past are stored and merged with incoming stress sample prior to Rainflow analysis. The impact of residue in improving closed-loop economic performance has also been shown in [7], where a stress history-aware controller performs better than a blinded controller (unaware of the stress history).…”

“…represents the mapping of ordinary differential equations governing the continuous dynamics of the system. The PORFC concept has been explained in detail in our previous work [10]. The output of the pre-processing PORFC approach is the time-varying cycle mean σ PORFC m,c1/2…”

“…In the objective function of the MPC, the PORFC parameters p P ORF C are used to timecontinuously calculate the cyclic damage over the horizon and accumulate it via integration. Consequently, the cyclic damage term of PORFC is defined by a time-integral over two cost terms, where each represents one potential cycle-contribution of a stress sample [10]. The rate of cyclic damage…”

“…An electrical equivalent circuit model of a 1MW/1MWh Li-ion battery has been considered in this work. This section summarizes the modeling approach which is presented in detail in [10]. The battery model consists of three sub-models: electrical, thermal, and degradation.…”