This paper presents a model reduction of a boiler-header system. Since it is desirable that the reduced model retains the structure of the full model where the boilers are interconnected with the header, a structured model reduction technique is applied, which takes the entire system into account. This method requires the solution of two linear matrix inequalities to obtain the structured Gramians of the system, but in general it is not possible to guarantee feasibility of these linear matrix inequalities. However for stable systems that are connected in series with a negative feedback-loop with strictly positive real subsystems, we prove that solutions always exist. By showing that the boiler-header system belongs to this class of systems it follows that the structured model reduction method can be applied regardless of the system parameters.