Convex parameter estimator for grey-box models, applied to characterise heat flows in greenhouses

Abstract

An algorithm is presented to identify model parameters in grey-box models. The solver is convex, so the global optimum is guaranteed. The method is applied to estimate bulk transfer coefficients in greenhouses from easily monitored data. This model covers the most important processes, such as conduction losses to the environment, heat exchange with neighbouring compartments, heating from the sun and lighting installations, and ventilation losses. Screen positions are also included in the model. Each process is parameterised, so that the specific situation of each greenhouse can be identified. Greenhouse experiments are often repeated in the same greenhouse or performed in parallel. If some model parameters are assumed to remain identical in these experiments, this can be incorporated in the optimiser making it more robust. The estimator is exemplified using measurements from two compartments in a greenhouse; one equipped with LED lighting, the other equipped with HPS lighting. It showed that effective conduction parameters for the greenhouse and screens were similar to values found in literature (5.8 and 5 W m−2 K−1, respectively). The model also predicted that both lighting systems provide the same amount of sensible heat at the height of the plants, despite the HPS system consuming 43% more energy. A vertical temperature measurement confirmed that both lighting systems produced the same amount of heat at the height of the plants. The LED system dispersed heat more evenly over height, while the HPS system heated the upper layers more.