The energy demand is growing worldwide, and this has to be met with various energy resources and with advanced energy technologies. Power plant optimization is one of the ways in which the growing energy demand and call for reduction in greenhouse gas emission can be met. The present work investigates the optimal operating condition of a combined cycle cogeneration power plant with solid oxide fuel cell (SOFC) co-fired with coal and natural gas. The study also looks at an efficient way to perform iterative processes used to find exit conditions from the gasifier, fuel cell, gas turbine, and combustion chamber and exit condition from the gas turbine. The maximum fuel cell net work output, combined cycle net work output, combined cycle thermal efficiency, and cogeneration efficiency are determined. The optimal pressure ratio, temperature of operation of the SOFC, and gas turbine inlet temperature is determined using a sequential quadratic program solver based on the Quasi-Newton algorithm. The maximum cogeneration efficiency obtained from the plant configuration investigated in this study is 82.20% at a pressure ratio of 14.31 and SOFC temperature of 1223 K. Copyright © 2011 John Wiley & Sons, Ltd.