Multiple linear regression based models for solar collectors

Mathematical modelling is the theoretically established tool to investigate and develop solar thermal collectors as environmentally friendly technological heat producers. In the present survey, recent multiple linear regression (MLR) based collector models are presented and compared with one another and with a physically-based model, used successfully in many applications, by means of measured data. The MLR-based models, called MLR model, SMLR model and IMLR model, prove to be rather precise with a modelling error of 4.6%, 8.0% and 4.1%, respectively, which means that all MLR-based models are more or nearly the same accurate as the well- ried physically-based model. The SMLR model is the most, while the IMLR model is the least easy-to-apply MLR-based model with the lowest and the highest computational demand, respectively. Nevertheless, all MLR-based models have lower computational demand than the physically-based model. Accordingly, the MLR-based models are suggested for fast but accurate collector modelling

Grey-box model for pipe temperature based on linear regression

Developing mathematical models describing pipe (or duct) temperature is of great importance, since pipes are unavoidable elements in most (hydraulic) heating systems, in which some heat transfer fluid flows/circulates between neighbouring working components (such systems are district, central or solar heating systems, etc.). In the present study, the Newton’s law of cooling is completed with a recent explicit equation determining the time delay of pipes. Based on measured data, the gained mathematical model, called physically-based model, describes the outlet (fluid) temperature of pipes with a convenient accuracy with respect to the practice. A further model, called LR model, is worked out based on multiple linear regression. Based on measured data, the LR model can model the outlet temperature of pipes generally more precisely than the physically-based model if the flow rate is nonzero. In addition, the LR model has lower computational demand. Since the physically-based model is still more precise under certain conditions, a third model, called grey-box model, is proposed as a combination of the physically-based and the LR model calculating every time according to the more advantageous one of them. Based on measured data, the grey-box model is the most precise model. In addition, this model has lower computational demand than the physically-based model

Transfer functions of solar heating systems with pipes for dynamic analysis and control design

In view of system efficiency and environmental protection, it is important to harvest solar energy better e.g. by improving solar heating systems. A theoretically founded tool for it is mathematical modelling with the use of system transfer functions. Knowing the transfer functions, the outlet temperature of the system can be determined as a function of the system inputs (solar irradiance, inlet and environment temperatures), the dynamic analysis of the system can be carried out, furthermore, stable feedback control can be designed effectively based on the mathematical methods of control engineering. The designed control can be used e.g. to provide just the minimal required outlet temperature for the consumer and, therefore, to maximize the produced heat with minimal or without any auxiliary heating cost. Although, pipes can affect the operation of solar heating systems considerably, this effect has not been built in the transfer functions of such systems worked out already in the literature. In this study, new transfer functions for solar heating systems with pipes are proposed based on a validated mathematical model. Transfer function based control design is also given generally. As particular applications, the dynamic analysis and the design of a stable P control are presented on a real solar heating system. It is also presented quantitatively that the designed P control is faster and more precise than the most conventional on/off control. Furthermore, the presented methods can be easily adapted for any solar heating system with long pipes equipped with an external heat exchanger

Development of an energetically-based control for solar thermal heating systems

This paper introduces the realization and application of a physicaily-based mathematical model of solar heating systems. The model was realized in TRNSYS 16 simulation environment which is well recognized and frequently-used in scientific researches of transient thermal processes. The mode! is flexible that is it can be easily adapted to a wide range of particular solar heating systems and is a good tool for analyzing and developing them. As an application the model was adopted to the particular solar heating system at the campus of Szent István University, Gödöllő and a new, energetically-based control was evolved and compared with the generally used on/off control method which operates with fixed temperature differences. Based on the relevant simulations it is shown that compared to the ordinary control the energetically-based control provides remarkable savings in auxiliary heating energy. This result should be valid for any systems similar to the particular one in Gödöllő

Black-box model for solar storage tanks based on multiple linear regression

Developing easy-to-use mathematical models for describing temperatures of solar storage tanks is important for the practice, since solar storages are unavoidable elements in solar heating systems, where some heat should be stored in the form of hot fluid. In this paper, a new, general and easy-to-apply black-box model, called LR model (where LR is the abbreviation of linear regression), is proposed for solar storages on the basis of multiple linear regression. This linear model may be the simplest black-box type model, which can follow the transient processes of solar storages precisely. Accordingly, the LR model proves to be more precise than a slightly modified version of a physically-based storage model used successfully for different applications in the literature. The modified physically-based model accounts for the short circuit effect occurring in storages. Comparing measured and simulated data on a real solar storage, both models are validated and their efficiency is discussed in details. The general and simple usability of the LR model is mentioned and future research proposals are given

Multiple linear regression based model for the temperature of the upper, undisturbed part of a solar storage

Developing mathematical models for describing the temperature of solar storage tanks is of great importance for the practice, since the storage tank stores and provides the solar heat directly, in the form of hot water, for the consumer. In this study, a new, general and easy-to-apply multiple linear regression based model, called LR model, is proposed to predict the temperature at the upper, undisturbed part of solar storages. This model is likely one of the simplest linear black-box type models, which can still describe the transient changes of the upper temperature with a satisfactory precision. Comparing measured and simulated data on a real solar storage, the validation and the efficiency of the LR model is presented. The generality and the simple applicability of the model are also mentioned along with future research proposals

Modified effectiveness and linear regression based models for heat exchangers under heat gain/loss to the environment

Developing mathematical models for describing heat exchanger outlet temperatures is of great importance for the practice, since heat exchangers are unavoidable elements in any applications, where heat transfer is needed between hydraulically separated fluid parts. The conventional, well-tried physically-based E model (standing for the known effectiveness-NTU approach) is recalled. This model assumes energy balance between the two sides of a heat exchanger (without any interaction with the environment). Based on studies in the literature, mathematical models with similar simplicity and usability to that of the E model, but under heat gain/loss to the environment, are still lacking in the field. This work intends to contribute to filling this gap with two proposed models, called ME and LR models. Based on measured data, all three models are accurate enough for general engineering/modelling purposes, nevertheless, the partly physically-based, partly empirical ME model is more precise than the E model if the heat gain/loss to the environment is considerable, and the empirical (black-box type) LR model is more precise than both the E and ME models if the heat gain/loss is not negligible. Furthermore, the outlet temperatures can be explicitly expressed from the simple linear algebraic relations characterizing all models alike