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This paper presents a comprehensive model for miniature vibration-powered piezoelectric generators and analyses modes of operation and control of a buck-boost converter for the purpose of tracking the generators optimal working points. The model describes the generator's power dependence with the mechanical acceleration and frequency, and helps in the definition of the load behaviour for power optimization. Electrical behaviour of the input of buck-boost converter in discontinuous current mode turns out to be in perfect agreement with the considered optimization criteria with a very simple, sensorless control. Experimental results show that the converter controlled by a very low consumption circuit effectively maximizes the power flow into a 4.8 V rechargeable battery connected to the converter output. The converter's efficiency is above 84% for input voltages between 1.6 and 5.5 V, and for output powers between 200 muW and 1.5 mW. The presented circuit and control can be used as well for power optimization of electromagnetic energy harvesting devices.