Piezoelectric vibration harvesters with strong electromechanical coupling coefficients have recently been combined with nonlinear electrical techniques capable of tuning their resonant frequency as a solution to provide energy to wireless sensor nodes from wideband vibrations. To be fully competitive, this approach requires piezoelectric generators with strong global electromechanical coupling coefficients k². However, the presence of non-linear dielectric and piezoelectric losses in piezoelectric materials significantly reduces the power harvested when strongly coupled materials are used. This paper presents a non-linear model that allows for a better consideration of losses for such piezoelectric harvesters. An experimental validation is performed with a strongly coupled cantilever based on a PMN-PT material (k²=16 %). The results reveal the importance of considering non-linear dielectric losses. Indeed, we show thanks to the model that neglecting these losses can induce an 18 % overestimation of the harvested power for the presented prototype driven at 0.5 m/s 2 amplitude ambient acceleration.