Fuel Cell Characteristic Curve Approximation Using the Bézier Curve Technique

Abstract

Accurate modelling of the fuel cell characteristics curve is essential for the simulation analysis, control management, performance evaluation, and fault detection of fuel cell power systems. However, the big challenge in fuel cell modelling is the multi-variable complexity of the characteristic curves. In this paper, we propose the implementation of a computer graphic technique called Bézier curve to approximate the characteristics curves of the fuel cell. Four different case studies are examined as follows: Ballard Systems, Horizon H-12 W stack, NedStackPS6, and 250 W proton exchange membrane fuel cells (PEMFC). The main objective is to minimize the absolute errors between experimental and calculated data by using the control points of the Bernstein–Bézier function and de Casteljau’s algorithm. The application of this technique entails subdividing the fuel cell curve to some segments, where each segment is approximated by a Bézier curve so that the approximation error is minimized. Further, the performance and accuracy of the proposed techniques are compared with recent results obtained by different metaheuristic algorithms and analytical methods. The comparison is carried out in terms of various statistical error indicators, such as Individual Absolute Error (IAE), Relative Error (RE), Root Mean Square Error (RMSE), Mean Bias Errors (MBE), and Autocorrelation Function (ACF). The results obtained by the Bézier curve technique show an excellent agreement with experimental data and are more accurate than those obtained by other comparative techniques.

Experimental Analysis of a Fuzzy Scheme against a Robust Controller for a Proton Exchange Membrane Fuel Cell System

“…Additionally, because of the groundbreaking innovation of fuel cell electric vehicles (FCEV) and large capacity stationary fuel cells (LCSFC), the interest has been growing exponentially since 2007 [5]. This is principally due to their emissions level that could reach up to 0% (depending on the type and fuel) and a high efficiency that yields up to 60% [6,7].…”

Application of Support Vector Machine to Obtain the Dynamic Model of Proton-Exchange Membrane Fuel Cell

“…The FC model comparison based on artificial intelligence and electrical circuit models is shown in Table 1. The models presented in [1,3,[5][6][7][8][9][10][11][12][13] are not viable for analyzing the complete polarization curve of an FC, owing to only considering a linear steady-state response based only on the PEMFC ohmic polarization curve, ignoring the voltage-current dynamic response. On the other hand, most models contemplate an analytical approach based on equations that describe the physical system of the FC [3,9,10,[14][15][16][17][18].…”

Dynamic Modeling of a Proton-Exchange Membrane Fuel Cell Using a Gaussian Approach

“…The FC models comparison, based on analytical and numerical procedures, is shown in Table 1. The models presented in [7,16,[18][19][20][21][22] consider a linear steady-state response, ignoring the voltage-current dynamic response. Therefore, these models are not viable for the analysis of the dynamic FC process.…”