This paper presents a functional observer based technique for estimating gaseous partial pressures in triple phase boundary of a high-order solid oxide fuel cell. Triple phase boundary is a nanoscale region in solid oxide fuel cells where direct measurement of partial pressure of individual gases is not possible. For a reliable and a safe operation those quantities must be monitored. This paper reports a novel functional observer based dynamic state estimation approach that utilizes a system decomposition algorithm to provide a functional observer with minimum order. Therefore, the proposed technique has a simpler structure than conventional state observer based schemes. Case studies of the proposed technique, implemented on a complex nonlinear power system, show accurate and smooth estimations in comparison to full-order state observer based techniques in terms of tracking of nonlinear partial pressures.