For the simulation of electrical machines and drive systems, the abc-model brings benefits in terms of accuracy, efficiency, and flexibility. In particular, it allows one to naturally include both geometry-and saturation-induced space harmonics. We propose here a novel nonlinear abc-model using current-flux linkage and electromagnetic torque N-dimensional lookup tables (N-D LUTs). The current-flux linkage LUTs are built from the flux linkage-current LUTs using inversion and N-D interpolation. The abc-model is validated by comparison with the circuit-coupled finite-element (FE) model, in both steady and transient state, for balanced and unbalanced operation. It gives the same results as the FE model with a speedup factor of about two orders of magnitude.