Reduced Order Modeling for Vapor Compression Systems via Proper Orthogonal Decomposition
Dynamic modeling of Vapor Compression Cycles (VCC) is particularly important for designing and evaluating controls and fault detection and diagnosis (FDD) algorithms. As a result, transient modeling of VCCs has become an active area of research over the past two decades. Although a number of tools have been developed, the computational requirements for dynamic VCC simulations are still significant. A computationally efficient but accurate modeling approach is critically important to accelerate the design and assessment of control and FDD algorithms where a number of iterations with a variety of test input signals are required. Typically, the dynamics of compressors and expansion devices evolve on an order of magnitude faster than those of heat exchangers (HX) within VCC systems. As a result, most dynamic modeling efforts have focused on heat exchanger models. The switched moving boundary (SMB) method, which segments a heat exchanger depending on thermodynamic phase of the refrigerant, i.e. subcooled liquid, two-phase and superheated vapor, and moves control volumes as the length of each phase changes, can reduce the computation time compared with the finite volume (FV) method by solving fewer equations due to a smaller set of control volumes. Despite the computational benefit of the SMB, there is a well-known numerical issue associated with switching the model representations when a phase zone disappears or reappears inside of a heat exchanger. More importantly, the computational load is still challenging for many practical VCC systems. This thesis proposes an approach applying nonlinear model order reduction (MOR) methods to dynamic heat exchanger models to generate reduced order HX models, and then to couple them to quasi-static models of other VCC components to complete a reduced order VCC model. To enable the use of nonlinear model reduction techniques, a reformulated FV model is developed for matching the baseline MOR model structure, by using different pairs of thermodynamic states with some appropriate assumptions. Then a rigorous nonlinear model order reduction framework based on Proper Orthogonal Decomposition (POD) and the Discrete Empirical Interpolation Method (DEIM) is developed to generate reduced order HX models.
The proposed reduced order modeling approach is implemented within a complete VCC model. Reduced order HX models are constructed for a centrifugal chiller test-stand at Herrick Labs, Purdue University, and are integrated with quasi-static models of compressor and expansion valve to form the complete cycle. The reduced cycle model is simulated in the Modelica-based platform to predict load-change transients, and is compared with measurements. The validation results indicate that the reduced order model executes 200 times faster than real time with negligible prediction errors.