Modern power networks are complex multi-component dynamic system with many operational levels made up of a wide range of renewable energy resources. The low frequency oscillations may undergo and sustain to cause system separation if adequate damping is not provided. This research work presents the mathematical model of Solid Oxide Fuel Cells (SOFC) within transmission network in order to dynamic stability analysis and control. The main contribution is to propose the new linearized Heffron-Philips model of the system under consideration the SOFC power plant to studying of low frequency oscillations. The eigenvalue-based objective function is used to search optimal multi-machine power system stabilizer (PSS) with the Particle Swarm Optimization (PSO) technique under various operating conditions. The effectiveness of the proposed model is tested on three-machine power system integrated with the single SOFC power plant. The time-domain simulation results are promising and illustrate the effectiveness of the proposed stabilizers. It can be damp the low frequency oscillations in the best possible procedure and significantly improves the stability performance of the case study system. (C) 2018 Elsevier Ltd. All rights reserved.