The MAXIMA consortium has released Deliverable 4.3, which presents a multi‑objective optimal control framework for the project’s permanent‑magnet synchronous motor (PMSM) traction drive. The work targets higher efficiency, improved torque capability and better thermal management by treating the electric machine and traction inverter as a coupled system rather than optimising each component in isolation.
From classical dq models to nonlinear, FEA‑based representation
Starting from conventional dq‑frame PMSM models, the deliverable constructs a nonlinear, control‑oriented representation of the drive that is suitable for embedded implementation. Flux‑linkage maps extracted from finite‑element analysis (FEA) are used to embed magnetic saturation, dq cross‑coupling and temperature‑dependent effects, while stator resistance and permanent‑magnet flux are modelled as explicit functions of temperature. This provides a compact state‑space model that captures the key phenomena needed for accurate operating‑point optimisation in traction applications.
Machine and converter losses in a single framework
Deliverable 4.3 extends the machine model with detailed loss representations for both the PMSM and the two‑level three‑phase voltage‑source inverter. Iron and permanent‑magnet losses are decomposed into hysteresis, eddy‑current and magnet components, expressed as nonlinear functions of electrical speed and operating‑point‑dependent flux level and converted into an equivalent shaft loss torque. In parallel, the inverter model accounts for MOSFET and diode conduction losses via temperature‑dependent parameters, as well as switching and reverse‑recovery losses based on voltage‑scaled energy curves, yielding a total converter loss term consistent with the dq operating point.
Steady‑state optimisation and LUT‑based implementation
On top of this modelling chain, the report formulates steady‑state operating‑point selection in the dq plane as a constrained optimisation problem with a common feasibility region defined by stator current and inverter voltage limits. Within this region, different objectives can be activated, including maximum‑torque‑per‑ampere (MTPA), minimum total drive losses (machine plus converter), maximum‑torque‑per‑voltage in field‑weakening, and system‑level maximum‑efficiency‑per‑ampere strategies. The optimisation is solved offline over a grid of speed, torque, DC‑bus voltage, and temperature conditions, producing multidimensional lookup tables of optimal current references that can be interpolated online within a standard field‑oriented control (FOC) architecture.
Digital Twin‑enabled, temperature‑aware control
The proposed control concept is coupled with a Digital Twin of the drive system, which provides consistent estimates of electromagnetic, thermal, and mechanical states during operation. These estimates enable temperature‑aware scheduling of current references, thermal derating of torque commands as critical stator and rotor temperatures are approached, and long‑term monitoring of component degradation, in particular for permanent magnets and bearings. In this way, the framework extends conventional FOC with a physics‑informed supervisory layer that adapts the drive behaviour to the actual operating state of the system.
Demonstrated gains over a reference drive cycle
A drive‑cycle evaluation using representative operating points of the target application shows that the strategy minimising total system‑level losses achieves the best energy performance. Compared with a baseline that only minimises machine losses, including converter losses in the optimisation reduces total input energy consumption by about 2.5% over the reference cycle, while other strategies such as MTPA, system‑level MEPA and constant‑flux MTPA deliver intermediate gains in the 0.7–1.5% range. These results confirm the practical benefit of system‑level, multi‑objective optimisation for next‑generation PMSM traction drives.