Cooling Capacity Control for Multi-Evaporator Vapor Compression Systems

Multi-evaporator vapor compression systems (ME-VCS) simultaneously provide cooling to multiple zones. The thermodynamic conditions in these zones are independent: the heat loads often differ, and the occupants of these spaces often have different desired room temperatures. Therefore, in order to regulate each zone to its desired setpoint temperature, the amount of thermal energy removed by each evaporator must be modulated independently. However, the common evaporating pressure within all evaporators introduces coupling that makes this objective difficult---the valve and piping arrangement imposes the constraint that all evaporators operate at the same temperature. (Systems considered here do not have valves at the outlet of each evaporator and therefore the individual evaporator pressures cannot be independently controlled.) In order to reduce the per-zone cooling, existing control strategies duty cycle the evaporator (alternate between a fully-open and fully-closed valve). However, duty cycling causes periodic disturbances to not only the local zone, but also to many machine temperatures and pressures, and these disturbances are often not transient but instead persist indefinitely. Fluctuations induced by the periodic disturbances can degrade the ability of the machine to regulate zone temperatures with zero steady state error, cause excessively high or low temperatures during peaks of the period, and couple into most machine signals of interest in ways that are difficult to describe with low order dynamical models. As an alternative to duty cycling, an observed behavior of refrigerant mass distribution in multi-path heat exchangers is exploited for control purposes. Multi-path heat exchangers are characterized by an inlet header pipe that splits refrigerant flow to two or more parallel paths through the heat exchanger and collects those paths into a common outlet header pipe. In the paper, we describe the following empirical phenomenon exploited for control: as the inlet valve is decreased, refrigerant mass flow rate entering the heat exchanger is reduced, and at some critical flow rate, refrigerant is shown to preferentially flow in some paths more than others, causing maldistribution. This uneven refrigerant distribution is repeatable and reduces the capacity in a continuous manner. The refrigerant distribution can be detected by temperature sensors along different paths of a multi-path heat exchanger. As some paths are starved for refrigerant they become superheated, and this uneven superheating process is unstable. A feedback controller is designed to provide stability and robustness to per-zone conditions. Finally, setpoints for this controller that relate per-path superheat temperature to overall evaporator capacity is created in such a way as to be robust to changes in local zone temperatures and the overall system evaporating temperature, which provides zone decoupling and ultimately creates a virtual control input for a supervisory controller such as a model predictive controller

Integrated Control of Multi-Zone Buildings with Ventilation and VRF systems in Cooling Mode

The accelerating decarbonization of energy systems to address climate change and the increasing recognition of the role that buildings play in occupants\u27 health have served to further emphasize two long-standing trends in the buildings and HVAC industries: the pursuit of ever-higher energy efficiency for buildings, and the proper management of the overall indoor environment. These two objectives, which are often at odds, are becoming ever more linked due to the emergence of new practices in the buildings industry that require both reductions in energy intensity and the improved management of temperature, humidity, and ventilation. In seeking to improve thermal comfort while reducing power consumption, the dynamics due to interactions between coupled subsystems, such as ventilation systems and VRF systems, become increasingly important, and must be properly designed and managed to achieve the desired system-level performance. We explore one approach to address these challenges by using a model-based process to design an HVAC system for a building including both a multi-zone variable refrigerant flow (VRF) system and a ventilation system. Such an approach is essential because the dynamics of both the VRF system and the ventilation system affect the thermal conditions of each zone; as each system acts as a disturbance to the other, the overall dynamical system can either develop limit cycles or can evolve toward an operating point which consumes more power than is necessary while satisfying specified setpoints. We use the equation-oriented language Modelica to construct detailed multiphysics models of the individual VRF, ventilation, and building systems, and then couple these models together to analyze the overall system properties. We then design a method for coordinating the control of these systems to maintain system performance while minimizing the energy consumption, and demonstrate the efficacy of these methods using realistic dynamic building inputs, such as time-varying occupancy and weather data. While these models have significant advantages in their use for control design, their modularity also provides a promising path for the rapid evaluation of alternate system architectures. This is particularly useful for the system under study, as multiple ventilation systems with different costs and energy performance can be used to provide fresh air to the occupied space. We thus study the performance of the building with the VRF system with three alternate ventilation approaches: a simple fan, an energy recovery ventilator (ERV), and a dedicated outdoor air system (DOAS). Such an methodology illuminates the potential energy impact of each ventilation approach on the overall HVAC system; because the use of the DOAS significantly reduces the load on the VRF system, the total system energy consumption can be reduced by over 50% by using the DOAS as opposed to a simple fan. The final paper will describe and elaborate on such results, providing a concrete demonstration of the benefits of model-based system and control design for HVAC systems in buildings

Comparing Realtime Energy-Optimizing Controllers for Heat Pumps

As the vapor compression machine has become more sophisticated (for example, through the adoption of variable speed compressor technology, electronic expansion valves and variable speed fans), the opportunities to improve efficiency are increasingly realized through the control algorithms that operate machine actuators. However, designing control algorithms that minimize energy consumption is not straightforward: the heat load disturbances to be rejected are not measured, the governing dynamics are nonlinear and interactive, and the machine exhibits strong coupling between the multivariate inputs and outputs. Further, many heat pumps must also operate in cooling mode, forcing compromises in sensor locations and actuator selection. This paper compares two controllers for realtime (online) energy optimization of heat pumps. The first energy-optimizing controller is model-based. A custom multi-physical model of the dynamics of a heat pump is developed in the Modelica modeling language and used to obtain the relationship between control inputs and power consumption as a function of the operating conditions. The gradient of this relationship is computed symbolically and used to derive a gradient descent control law that is shown to drive actuator inputs such that the system power consumption is minimized. To address the concern of modeling error on optimization performance, the controller based on a model of a heat pump will be tested on a physical system in an experimental setting for the submitted paper. We expect the convergence rate to be exponential, and will quantify the sensitivity between modeling errors and the non-optimality of the stabilized system. The second approach is model-free and based on the authors\u27 time-varying (TV) and proportional-integral (PI) extremum seeking control (ESC) algorithms. Briefly, extremum seeking controllers use an estimate of the gradient between a plant\u27s manipulated inputs and an objective signal (i.e., power consumption) to steer the system toward an optimum operating point, under the assumption that this relationship is convex. Whereas traditional ESC methods exhibit slow and non-robust convergence, our TV-ESC and PI-ESC methods have demonstrated higher performance due to the estimation routine that tracks the gradient as a time-varying parameter. We expect this algorithm to converge faster than transitional perturbation-based ESC methods (as we have previously demonstrated), but perhaps slower than the model-based approach. However, we expect this controller to converge to a neighborhood around the true optimum since modeling errors are not applicable in this model-free algorithm. The final paper will compare convergence properties of these two methods through experiments obtained on a commercial four-zone heat pump installed in calorimetric-style testing chambers, and the resultant coefficients-of-performance (COPs) will be measured

Dynamic Charge Management for Vapor Compression Cycles

Because vapor compression air-conditioners and heat pumps consume significant amounts of electrical power in today\u27s residential and commercial buildings, energy optimization of these systems is becoming increasingly important from the perspectives of both environmental conservation and economic value. Corresponding efforts to improve the energy efficiency of these machines require attention to all stages of system design, installation, and operation, due to the myriad factors influencing power consumption. Among the many variables that must be optimized, one particularly salient variable is the mass of refrigerant contained within the cycle, or the refrigerant charge; this variable is strongly coupled to many other variables in the system, including the electrical power consumption, the system pressures, and the degree of subcooling and superheat in the heat exchangers. As such, the mass of refrigerant in the system must be carefully tuned for a given set of operational conditions to maximize the system\u27s energy efficiency. In practice, field-installed vapor compression systems are often not charged with the mass of refrigerant that optimizes energy efficiency for the conditions in which systems actually operate. In accordance with the conventional view of the refrigerant charge as a static system parameter, the mass of refrigerant is often specified to maximize the average energy efficiency over a set of multiple conditions. This approach results in suboptimal energy efficiency at any one of the conditions within the rating set, and furthermore often results in lower energy efficiency at non-rated conditions. Such an impact is especially evident in reversible heat pump cycles because the optimal refrigerant mass for a cycle over a range of conditions in cooling mode is often very different than the optimal refrigerant mass in heating mode. As today\u27s system manufacturers sell equipment across large geographic ranges with a wide range of ambient conditions and operational requirements, the cumulative impact of operating these systems with suboptimal refrigerant charge is generally a much higher rate of energy consumption than would be observed with cycles that incorporate an optimally specified refrigerant charge. In this paper, we describe a system architecture for a vapor compression system that enables the circulating refrigerant charge to be modulated as a function of time, effectively allowing the refrigerant charge to be optimized for a predicted or observed set of operational conditions. This is accomplished by dynamically controlling the amount of refrigerant sequestered in a storage vessel (referred to as a dynamic receiver) that is continuously coupled to the other components of the system. We first explore alternate system architectures that have been previously proposed for similar purposes, and elaborate on the opportunities that are afforded by this particular candidate architecture. A set of first-principles physics-based dynamic models are then developed using the Modelica language, and a candidate controller architecture is discussed that directly optimizes the electrical power consumption by using this new dynamic receiver. Finally, we will compare energy performance of this proposed system with that of conventional system architectures to evaluate its benefits over a range of operational conditions

Model Predictive Control of Variable Refrigerant Flow Systems

Model Predictive Control (MPC) of vapor compression systems (VCSs) offers several advantages over conventional control methods (such as multivariable process control with selector logic) in terms of 1) the resulting closed-loop performance and 2) the control engineering design process. VCSs are multivariable systems and feature constraints on system variables and actuators that must be enforced during steady-state and transient operation. We present the design and validation of an MPC for a split ductless VCS. The design regulates room temperature with zero steady state error for unknown changes in the thermal load and enforces constraints on system variables such as compressor discharge temperature and actuator ranges and rates. We show how the MPC design can evolve during the engineering process by adding and modifying constraints and process variables. The design methodology provides guarantees in terms of closed loop stability and convergence. Importantly, in contrast to other published results on MPC for VCSs, our design makes use of only available temperature measurements and does not require pressure or mass flow measurements which are typically not available in production VCSs

Pseudolinearization Using Spline Functions with Application to the Acrobot

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / MSM-9100618University of Illinois Manufacturing Research CenterOpe

Pseudolinearization Using Spline Functions With Application to the Acrobot

197 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1992.A method for the construction of the pseudolinearizing controller and extended linearizing observer for single-input, multi-output nonlinear systems is presented. The technique uses spline functions to approximate the elements of gradient vectors which arise during the derivation of the pseudolinearizing controller and extended linearizing observer. The construction of both is computer automated and can be accomplished regardless of the complexity of the original nonlinear model. Further, the structure of the controller and observer makes their implementation computationally efficient.The stability of the controller for set-point and time-varying desired trajectories is rigorously investigated. Controller construction is illustrated for a robotic mechanism called the acrobot. The pseudolinearizing controller's regulation of the acrobot is contrasted with two linear controllers via numerical simulation. Trajectory tracking performance and computational efficiency of the controller are verified in three experiments carried out with actual acrobot hardware.The state estimate error for the extended linearizing observer is shown to be locally exponentially stable. A separation principle which allows state estimates generated by the observer to be substituted into the controller is discussed. The observer construction and performance are illustrated via simulation for an extension of the acrobot called the rolling acrobot.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD