Nonlinear Modeling of a Plate Heat Exchanger of a District Heating System

The integration of renewable and residual energy sources requires a detailed level of knowledge of district heating components such as thermal pipes, pipes, pumps, and heat exchanger of a substation. The thermal energy stored in these components can be utilized to match the heat demand and heat generation in time for next generation district heating networks. The goal of this paper is to provide accurate substation models that can be utilized for controlled energy exchange between primary and secondary networks. The proposed method introduces an efficient, user-friendly, combined parametric and nonparametric nonlinear data-driven modeling technique illustrated on a plate heat exchanger which is installed in the district heating network of the Vrije Universiteit Brussel. A fair comparison between a physics-based white-box and a data-driven black-box modeling techniques is provided. The white-box model is developed on the first principle modeling approach of the heat balance equations, which allows calculating the temperature evolution and heat transfer in the plate heat exchanger. As for the data-driven modeling approach, there are four interrelated consecutive steps. First, the measurement is processed to obtain a frequency response function model. Second, a linear parametric (state-space) model is estimated. Third, a polynomial nonlinear model is built. Last, a decoupled model structure is obtained based on the previously obtained PNLSS model. The proposed black-box method outperforms the white-box techniques in terms of prediction capabilities and computational needs.