Analytical solution and its application for the dynamic characteristics of a heat recovery steam generator in gas–steam combined cycle

•An analytical solution of dynamic characteristics for HRSG is derived from the differential equations.•The equilibrium state, time-impact factor and dynamic amplitude are clearly expressed in the solution.•The exponential term (αγ + βγ) can quantify the changing rate of a dynamic process in heating surfaces.•A dynamic forecasting model of HRSG is constructed and validate based on analytical solution. This paper presents a study from the perspective of analytical solutions to analyze the dynamic characteristics of a Heat Recovery Steam Generator (HRSG) and explore its practical applications. The study employs the lumped parameter method to simplify the metal heat storage and temperature changes within HRSGs. Differential equations, based on the principles of mass and energy conservation, are formulated to describe the heating surfaces within HRSGs. Analytical solutions are derived, and the essential parameters in these expressions are discussed for their physical significance. Using these analytical solutions, the dynamic heat transfer processes for heating surfaces in a typical HRSG under various starting conditions are investigated. The findings reveal that a larger heat transfer factor or a smaller heat capacity factor of HRSG metal (or a larger ratio of these factors) results in a faster thermal equilibrium during the heat transfer process. Additionally, a dynamic forecasting model is developed based on these analytical solutions. The Particle Swarm Optimization (PSO) algorithm is applied as a parameter identification technique to fine-tune the model's initial parameters, which may be incomplete in real start-up processes. To validate the model, real-time on-site measurement data from a cold start-up of a non-supplementary fired HRSG is used. The results demonstrate the model's strong predictive capabilities, with an average absolute error ranging from 0.5 °C to 2 ℃, highlighting its high accuracy. Comparing the model with a thermal equilibrium model, it is evident that during the cold start-up of an HRSG, the heating surfaces exhibit dynamic characteristics, transitioning from a non-steady state in the first 3000 s to a quasi-steady state between 3000 and 7000 s.