Monitoring energy efficiency of condensing boilers via hybrid first-principle modelling and estimation

The operating principle of condensing boilers is based on exploiting heat from flue gases to pre-heat cold water at the inlet of the boiler: by condensing into liquid form, flue gases recover their latent heat of vaporization, leading to 10-12% increased efficiency with respect to traditional boilers. However, monitoring the energy efficiency of condensing boilers is complex due to their nonlinear dynamics: currently, (static) nonlinear efficiency curves of condensing boilers are calculated at quasi-stationary regime and 'a posteriori', i.e. from data collected during chamber tests: therefore, with this static approach, it is possible to monitor the energy efficiency only at steady-state regime. In this work we propose a novel model-based monitoring approach for condensing boilers that extends the operating regime for which monitoring is possible: the approach is based on a hybrid dynamic model of the condensing boiler, where state-dependent switching accounts for dynamically changing condensing/non condensing proportions. Monitoring the energy efficiency over the boiler's complete dynamic regime is possible via switching estimators designed for the different condensing/non condensing modes. By using real-world boiler efficiency data we show that the proposed approach results in a (dynamic) nonlinear efficiency curve which gives a more complete description of the condensing boilers operation than static nonlinear efficiency curves: in addition, the dynamic curve can be derived 'a priori', i.e. from first principles, or from data collected during normal boiler operation (without requiring special chamber tests).