Elsevier

Renewable Energy

Volume 100, January 2017, Pages 114-128
Renewable Energy

Modelling and control of solar thermal system with borehole seasonal storage

https://doi.org/10.1016/j.renene.2016.05.091Get rights and content

Highlights

  • The paper addresses the modelling and control of solar thermal system with borehole seasonal storage energy.

  • The discrete model of the integrated energy system is obtained by using energy preserving Cayley-Tustin discretization.

  • A servo control is designed to regulate the system operating at desired thermal level despite environmental disturbances.

Abstract

The paper addresses the problem of controlling a solar thermal storage system with the purpose of achieving a desired thermal comfort level and energy savings. A solar thermal power plant is used for heating district houses with borehole seasonal energy storage. As the energy output from the solar thermal plant with borehole seasonal storage varies, the control system maintains the thermal comfort by using a servo controller. In this work, the modelling of the solar thermal system with borehole seasonal storage is inspired by the Drake Landing Solar Community in Okotoks, Alberta, Canada [1]. The discrete model of the integrated energy system is obtained by using energy preserving Cayley-Tustin discretization. A simple and easily realizable servo control algorithm is designed to regulate the system operating at desired thermal comfort level despite disturbances from the solar thermal plant system, the borehole geo-thermal energy storage system and/or the district heating loop system. Finally, the performance of the servo controller and frequency analysis of the plant is given in simulation results section.

Introduction

The modelling and control of the solar thermal system with borehole seasonal storage is motivated by the need for accurate modelling and analysis of the state of the art community development of the Drake Landing Solar Community (DLSC) in Okotoks, Alberta, Canada [1]. The DLSC contains 52 energy-efficient houses with an innovative heating system which includes a solar thermal power plant, borehole thermal energy storage system (BTES), short term thermal storage system (STTS) and a district heating loop system. Solar thermal energy is collected through roof mounted plate collectors. A heat transfer fluid containing a high concentration of glycol is used to collect solar energy. The energy collected by the glycol loop is transferred to STTS by a heat exchanger, see Fig. 1. Depending on the season and energy requirements, the energy from the STTS can be distributed to the district heating loop or stored in the BTES. The BTES uses a grid of boreholes with single u-tube heat exchangers [2], [3]. Finally, the collected energy is sent to the district heating loop system to heat the energy efficient homes.

A major step towards the completion of the control system is the develo-pment of a process model using detailed energy balances. The solar thermal plant system concentrates solar radiation using mirrors or lenses to heat a fluid [4]. The dynamic model of the solar thermal energy system is of distributed nature. However, the changes of solar radiation on warm sunny or cold cloudy days affect the dynamics of the solar thermal system. Due to this solar radiation variability, many advanced control techniques have been applied to the solar thermal energy system to account for possible problems caused by the solar radiation under variable solar energy supply [5], [6], [7], [8].

The energy collected by a solar thermal plant system is sent to the STTS through heat exchanger. The dynamics of the heat exchanger system is distributed in nature and is modelled by the transport thermal distributed parameter system [9]. The energy from the solar thermal system is transferred to the heat exchanger system through the boundary and the counter-current flows exchange the energy, therefore, the boundary controlled system realization is considered in the modelling of the heat exchanger system.

The BTES uses a grid of boreholes with U-tube heat exchangers to preserve energy as a long-term storage device in the overall system. To fulfill energy requirements in different seasons, the BTES saves energy during the summer months by transferring available thermal energy to the ground and provides energy from the ground during the heating season. The energy balance and dynamics of the BTES is modelled as a transport thermal distributed parameter system [10], [11]. In particular, when it comes to the BTES, environmental temperature fluctuations make a possible sources of disturbances to the BTES system and may affect the time evolution of the model.

In the STTS, water-filled storage tanks act as a thermal buffer between the solar thermal plant system and the district heating loop system [2]. During the summer months, the hot tank utilizes thermal energy from the solar plant. When the temperature of the hot tank rises above the set-point, thermal energy from the hot tank is transferred to the BTES system. During the heating season, the hot tank charges thermal energy from both the solar plant and the BTES. Finally, the collected energy of the STTS is sent to a district heating loop system.

In order to heat the energy efficient homes in the district heating loop system, a backup gas boiler is provided to insure that heat is available to each and every home at all times. One important performance specification is to heat homes to the prespecified temperature (which may fluctuate with seasonal changes in temperature), and therefore a controller for the natural gas boiler system is designed to track the desired temperature set-point. The temperature regulation of the solar thermal system with borehole seasonal storage is characterized by many uncertainties, such as environmental changes, occupancy status changes, and changes in the operating conditions of equipment in the building. Therefore, control systems play an important role in maintaining the performance of the systems in the presence of possible uncertainties and disturbances. The ultimate performance goal is that the proposed controller maintains the temperature at a desired set point and keeps the integrity of the energy demands in the district heating loop system.

Servo controller design is a well-know strategy that computes the required input which asymptotically attenuates error between the output and a reference trajectory or set point to zero [12], [13]. One of the advantages of a servo controller is that it can account for disturbances which may affect the process. We propose a servo control system design for the solar thermal system regulation with borehole seasonal storage, which takes into account measurable disturbances, such as changes in ambient temperature and disturbance predictions, such as weather forecast that may potentially assist in the prediction of the availability of the different energy sources.

From the literature review, most of the modelling of subsystems, such as solar thermal energy system [4], heat exchanger system [9], and BTES system [10], [11] are continuous and distributed in nature. In this work, in order to realize accurate modelling of the subsystems and to design a practical and usable controller, discrete models of the subsystems and a discrete controller design are developed. We utilize Cayley-Tustin time discretization which preserves the infinite-dimensional nature of the distributed parameter system [14]. This transformation preserves the energy equality among the continuous and discrete model which provides a discrete model for controller design and frequency analysis. Other model reduction technique, such as explicit Euler discretization may potentially transfer the stable continuous system into unstable discrete system or require small time steps for approximation. This proposed discretization transforms the system from a continuous to a discrete state space setting without spatial discretization and/or any other type of spatial approximation of the distributed parameter system. In this work, according to the energy balance conservation laws, the processes in solar thermal system with borehole seasonal storage are modelled using ordinary differential equations (ODEs), hyperbolic partial differential equations (PDEs) or coupled PDEs-ODEs equations. In particular, by application of Cayley-Tustin time discretization we maintain the low dimensionality of the overall discrete model. The discrete representation of coupled partial and ordinary differential equations does not include any high order plant representation, which is contrary to the previous proposed methods [15]. In addition, a discrete infinite-dimensional representation of the system realized in this paper provides an insight into frequency response of the subsystems and that of the overall plant. This is of importance, since all well known frequency analysis methods and controller synthesis can be easily applied, and one can obtain appropriate engineering insight into plant operation. Finally, the controller designed for the servo problem is a discrete controller which can be easily realized and implemented in practice.

The paper is organized as follows: section 2 introduces the Cayley-Tustin time discretization. In section 3, we address the model of the solar thermal system with borehole seasonal storage and discretize the subsystems of the overall plant. Section 4 provides the servo controller design and the analysis of the system frequency response. Finally, we demonstrate the performance of the servo control formulations built in previous section through simulation studies.

Section snippets

Time discretization for linear system

According to the energy balance, the processes in the solar thermal system with borehole seasonal storage can be modelled by ordinary differential equations (ODEs), hyperbolic partial differential equations (PDEs) and/or coupled PDEs-ODEs equations. In other words, the overall system contains internally coupled linear finite and infinite dimensional systems, see Fig. 2. The Cayley-Tustin time discretization method is applied to obtain a discrete model version which provides an insight into the

Overview of solar thermal system with borehole seasonal storage

The solar thermal system with borehole seasonal storage modelled in this work uses the solar thermal system, heat exchanger, BTES system, STTS system, natural gas system and the district heating loop system, see Fig. 2. The thermal energy transfers from the solar thermal system to the STTS system through a heat exchanger. The BTES system stores thermal energy to the STTS system directly. Then, the STTS system provides thermal energy to district the heating loop system. Finally, the inlet to the

Controller design and system analysis

Since large disturbances from the solar thermal plant system, borehole thermal energy storage system or the district heating loop system greatly impact system operation, the control system plays an important role in maintaining the system’s performance. In this section, we propose a servo controller design which successfully rejects undesired disturbances and tracks a reference trajectory or a set point.

One of the important analysis tools of the controlled system performance is given by the

Simulation results

In this section, we demonstrate the implementation of the servo control system to improve the overall efficiency of the system. The dynamic model of the collection-storage-district heating loop system is simulated according to the energy balance models developed in the previous section. With plant model available, a servo problem is set up to compute the control input that maintains the energy demand constant and rejects disturbances, with guaranteed asymptotic stabilization despite

Conclusion

In this work, we provided a model of the state-of-the-art in the solar thermal system with borehole seasonal storage mathematically modelled by ordinary differential equations (ODEs), hyperbolic partial differential equation (PDEs) and coupled PDEs-ODEs according to the energy balance. Then, the discrete systems of these integrated systems are obtained by the application of the Cayley-Tustin time discretization method. We developed a simple servo controller design for the solar thermal system

References (18)

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