Realtime Optimization of MPC Setpoints using Time-Varying Extremum Seeking Control for Vapor Compression Machines

Recently, model predictive control (MPC) has received increased attention in the HVAC community, largely due to its ability to systematically manage constraints while optimally regulating signals of interest to setpoints. For example, in a common formulation of an MPC control problem for variable compressor speed vapor compression machines, the setpoints often include the zone temperature and the evaporator superheat temperature. However, the energy consumption of vapor compression systems has been shown to be sensitive to these setpoints. Further, while superheat temperature is often preferred because it can be easily correlated to heat exchanger efficiency (and therefore cycle efficiency), direct measurement of superheat is not always available. Therefore, identifying alternate signals in the control of vapor compression machines that correlate to efficiency is desired. Conventionally, methods for maximizing the energy efficiency rely on the use of mathematical models of the physics of vapor compression systems. These model-based approaches attempt to describe the influence of commanded inputs on the thermodynamic behavior of the system and the consumed electrical energy, and they are used to predict the combination of inputs that both meet the heat load requirements and minimize energy consumption. However, these models of vapor compression systems rely on simplifying assumptions in order to produce a mathematically tractable representation. Further, they are difficult to derive and calibrate, and often do not describe variations over long time scales, such as those due to refrigerant losses or accumulation of debris on the heat exchangers. In this paper, we consider a model-free extremum seeking algorithm that adjusts setpoints provided to a model predictive controller. While perturbation-based extremum seeking methods have been known for some time, they suffer from slow convergence rates---a problem emphasized by the long time constants associated with thermal systems. Our method uses a new algorithm (time-varying extremum seeking), which has dramatically faster and more reliable convergence properties. In particular, we regulate the compressor discharge temperature using an MPC controller with setpoints selected from a model-free time-varying extremum seeking algorithm. We show that the relationship between compressor discharge temperature and power consumption is convex (a requirement for this class of realtime optimization), and use time-varying extremum seeking to drive these setpoints to values that minimize power. The results are compared to the traditional perturbation-based extremum seeking approach. Further, because the required cooling capacity (and therefore compressor speed) is a function of measured and unmeasured disturbances, the optimal compressor discharge temperature setpoint must vary according to these conditions. We show that the energy optimal discharge temperature is tracked with the time-varying extremum seeking algorithm in the presence of disturbances

Numerical Simulation of Fault Impacts for Commercial Walk-in Freezers

Refrigeration systems can undergo many faults that could negatively affect their operation and performance. This paper describes a modeling process to simulate the fault impacts on the operation of a commercial walk-in freezer using semi-empirical models. These models often require less modeling effort than full forward models and could be used in scenarios where detailed information is missing, such as in field-measured systems. An important characteristic of a typical walk-in refrigeration system is the existence of a liquid-line receiver after the condenser, which significantly changes the behavior of the cycle, in comparison to a receiver-less system. Component models described in this paper consist of: a compressor, two heat exchangers, pipelines, receiver, and thermostatic expansion valve. The semi-empirical component models are partially based on physics, and partially based on some empirical coefficients. They are able to predict several dependent variables, including mass flow rates, heat transfer rates, power consumption, and pressures. In this paper, the individual component models are presented and trained with a limited set of faulted and fault-free experimental data. The faults are: heat exchanger fouling, liquid-line restriction, and compressor valve leakage. The results show that models for major components, such as compressor and heat exchangers, give good predictions for some of the most important performance indices. Modeling challenges and future research are outlined

Icing Mitigation via High-pressure Membrane Dehumidification in an Aircraft Thermal Management

Icing, or the formation of ice from water via freezing or water vapor via desublimation, is a phenomenon that commonly occurs within air cycle-based refrigeration systems and requires thermal control that limits system performance. In aircraft applications icing frequently occurs in the heat exchangers and turbine(s) that are part of the air cycle machine, the refrigeration unit of the environmental control system. Traditionally, water vapor is removed from an air cycle machine via condensing in a heat exchanger and subsequent high-pressure water separation. This approach is not capable of removing all of the vapor present at low altitude conditions, corresponding to a high risk of icing. To mitigate icing under these conditions, a membrane dehumidifier is considered to separate the water vapor that remains after condensing and liquid water separation. Three distinct investigations are conducted as part of this work. The first is aimed at modeling approaches for desublimation frosting, or frost growth on sufficiently cold flat surfaces. This results in a novel, analytical, and non-restrictive solution well-suited for representing frost growth and densification in moist air heat exchangers. The second investigation concerns membrane dehumidification and module design. A custom component model is developed and verified under aircraft conditions, then the Pareto frontier of volumetrically efficient membrane modules is characterized via a multi-objective optimization study. The final investigation evaluates three two-wheel air cycle subsystem architectures with differing dehumidification approaches: (1) condenser-based, (2) membrane dehumidifier-based, and (3) combined. Steady-state simulations are run for each of these over a range of flow rates and altitudes. The results demonstrate that incorporating a membrane dehumidifier reduces the turbine inlet saturation temperature, which mitigates icing in the turbine and reduces the required bypass flow, thus increasing the cooling capacity