In this paper is proposed a Maximum Power Point (MPP) tracking technique for the Fuel Cell (PC) stacks based on advanced Extremum Seeking (aES) control that improves the basic performances of the ES control schemes: a guaranteed convergence and proved internal robustness. Other features such as higher search speed and improved tracking accuracy are demonstrated for the proposed aES control, besides these features that are necessary in case of unmodeled dynamics. The analysis on the frequency domain reveals the relationships between the main aES control parameters, the values of closed loop gain and dither amplitude, and the design performance indicators, the speed of search and accuracy of MPP finding, respectively. If the dither amplitude is set to be proportional with the magnitude of first harmonics of the processed PC power, then the reference current used in the PC current control loop will have an insignificant ripple after the MPP is caught. Thus, a reduced FC power ripple will appear. Therefore, if the search speed is set to be the same for all ES control schemes, then the proposed aES control outperforms all classical ES control schemes in overall power efficiency. Moreover, the aES search speed will proportionally increase with the loop gain and the dither amplitude. Note that here the dither has the amplitude set by the first harmonic of the FC power, being a time variable that have high value during the searching phase. This accelerates MPP searching up to the FC safe limits. Finally, this means a controllable time to shortly find the next MPP on dynamical operation of the FC stack. First harmonic of the FC power becomes almost zero after MPP is caught. Thus, higher tracking accuracy that means an economy on fuel consumption is obtained. The simulations performed show that above mentioned performances are effective for the aES control operating in both ripple- and dither-based modes of the grid connected PC inverters. Copyright (C) 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.