Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 2976731, 15 pages

http://dx.doi.org/10.1155/2016/2976731

## Simplified Building Thermal Model Used for Optimal Control of Radiant Cooling System

School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China

Received 10 November 2015; Accepted 26 January 2016

Academic Editor: Hiroyuki Mino

Copyright © 2016 Lei He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

MPC has the ability to optimize the system operation parameters for energy conservation. Recently, it has been used in HVAC systems for saving energy, but there are very few applications in radiant cooling systems. To implement MPC in buildings with radiant terminals, the predictions of cooling load and thermal environment are indispensable. In this paper, a simplified thermal model is proposed for predicting cooling load and thermal environment in buildings with radiant floor. In this thermal model, the black-box model is introduced to derive the incident solar radiation, while the genetic algorithm is utilized to identify the parameters of the thermal model. In order to further validate this simplified thermal model, simulated results from TRNSYS are compared with those from this model and the deviation is evaluated based on coefficient of variation of root mean square (CV). The results show that the simplified model can predict the operative temperature with a CV lower than 1% and predict cooling loads with a CV lower than 10%. For the purpose of supervisory control in HVAC systems, this simplified RC thermal model has an acceptable accuracy and can be used for further MPC in buildings with radiation terminals.

#### 1. Introduction

Model predictive control (MPC) is a powerful control technique, which can be used in both local and supervisory control in HVAC systems. For example, it was employed to control the zone air temperature serving as a local controller of the VAV damper [1]. Yuan and Perez [2] employed MPC to regulate the temperature within the limits and supply adequate fresh air in a VAV system. Most importantly, the superiority of MPC lies in saving energy as a supervisory controller of HVAC systems. Henze et al. [3] used this technique to generate the optimal setpoint of zone air temperature and the optimal charging and discharging profile of thermal storage for energy saving. Široký et al. [4] applied MPC and weather prediction in a building heating system for energy conservation. MPC is an advanced concept for HVAC systems; therefore it has been widely studied in recent years, which can be found in a review carried out by Afram and Janabi-Sharifi [5].

MPC uses a system model to predict the future states of the system. In the model predictive control of the building thermal process, an accurate building thermal model is a precondition, which is used for the calculation of cooling load, diagnosis of building thermal properties, and prediction of indoor thermal comfort. Generally, the model used for calculating the building thermal process can be classified into three categories: physical model, black-box model, and gray-box model. Among these three models, the physical model is most widely used, and there are various software tools using the physical model to simulate the heat transfer process, such as DOE-2, HAPE-20, BLAST, TAS, HVACSIM+, TRNSYS, SPARK, and ESP-r [6, 7]. For improving the accuracy, the physical model is generally solved by the impulse response method or the finite difference method. As a result of high order of the method used, physical model has large calculation costs, but it is a detailed method to represent the physical process. By contrast, the black-box model driven by data cannot reflect the physical thermal process, but it is less time-consuming. However, since the black-box model is determined by the sample data for model training, this model gets inaccurate results when the predicting data exceeds the scope of sample data. Combining the advantages of physical model and black-box model, the gray model was developed. This model has the characteristics of fewer calculation costs, less time consumption, and part revelation of the physical thermal process [8]. Since the models for MPC have to be less time-consuming, in comparison with the other two models, the simplified gray-box model with lower model order is more suitable for the MPC solution.

As a simplified gray-box model, the lumped parameter model always combines with other models to construct the MPC controller. Hazyuk et al. [9] adopted this model and state space model to construct MPC for intermittent heating buildings. In their study, the results showed that the forecasting error was below 10%. To maximize the MPC performance, both improving the calculation accuracy and reducing the calculation time of lumped parameter model are valid approaches. For improving the calculation accuracy, it is crucial to identify the model parameters. Based on the simplified thermal response model [10], the least square method was used to identify parameters of a solar house [11]. They found that the model parameters had the quality of nonuniqueness and it was unsuitable for evaluating the building thermal performance. However, the model can adjust the parameters using the sample data, so it is suitable for the building energy management system. Gouda et al. [12] used the sequence quadratic programming method to identify the model parameters of various constructions and to compare different order models. The results showed that second-order model balanced the computational accuracy and calculation consumption moderately. The genetic algorithm with data recorded by building management system was employed to identify the RC model parameters in frequency-domain [13, 14]. Based on the time domain and frequency-domain analysis, a method to simplify the RC model was established [15], and this method has higher applicability than the method based on electrical analogy [16]. Besides the real building operation data, the data acquired from the simulation tools can be used to identify the model parameters as well. O’Neill et al. [17] adopted EnergyPlus [18] to test the forecast model consisting of 3R2C and Extended Kalman Filter. Similarly, a cost-effective building thermal model was verified by EnergyPlus [19]. What is more, EnergyPlus and MATLAB were integrated by BCVTB [20] to develop a cooling load prediction model for optimizing HVAC control, and the model parameters were recognized using the data calculated by simulation tool [21, 22]. The above researches show that the lumped parameter model has a strong ability to forecast the indoor temperature and the cooling load, which is suitable for the MPC. However, for the building equipped with radiant terminals, there are some differences from the building with air-based system. In the building with radiant terminals, the long wave radiation between interior surfaces cannot be neglected and the control variable of indoor environment is usually the operative temperature. What is more, in the building with all-air system, the incident solar radiation on the interior surfaces firstly warms up the construction. Then the cooling load is generated by convective heat exchange. By contrast, the incident solar radiation on the radiant cooling surface is directly absorbed. Due to the above differences, the long wave radiation among the indoor surfaces and the incident solar radiation on the envelope surfaces cannot be calculated by these models and they are incapable of evaluating wall surface temperatures accurately. Based on the above reasons, these models in the literature [11–13, 15, 19, 21] are inapplicable for the MPC in buildings with radiant terminals.

In order to optimize the operation of the air-conditioning system with radiant terminals by MPC technology, this paper presents a prediction model for a building with radiant floor. This model consists of three parts: simplified RC model, black-model, and semiempirical model. The simplified RC model is used to describe the heat transfer process of the building, and the black-box model is used to forecast the incident solar radiation on the envelope surfaces, while the semiempirical model is adopted to calculate the long wave radiation between interior surfaces. The model parameters are recognized by the genetic algorithm, and the sampling data for the recognition is derived from TRNSYS. Finally, the model is used in a case study to predict the indoor operative temperature and the cooling load of both radiant terminals and ventilation system.

#### 2. Simplified Building Thermal Model

The RC model adopts different model structures to represent building elements with various heat conduction and thermal storage. In most studies, the optimization method is employed to simplify the RC model and to determine the model parameters. It is verified that the second-order RC model can reduce the calculation time without any compromise of calculation accuracy compared to the higher-order model [11]. Similarly, Gouda et al. [12] proved that the optimized 2nd-order model could simulate both lightweight and heavyweight buildings with the minimal accuracy loss. Thus, the low-order RC model is used to describe the thermal process of building envelope in this paper. The mean radiant temperature is adopted for calculating the long wave radiation between interior wall surfaces, and a black-box model is used to predict the solar radiation on the envelope surfaces.

##### 2.1. Lumped Parameter Model of Envelopes

Both 3R2C model and 2R1C model are adopted to build the thermal network model of the building, as shown in Figure 1. All the enclosure structures are assumed to be connected to the outdoor environment, and the thermal mass such as interior walls and furniture in the room are neglected in the model. Due to the different orientations of the building, solar radiations on the different surfaces are distinct, leading to the different surface temperatures. To accurately calculate the operative temperature, heat transmissions from the external walls and the roof are separately calculated (1)–(4), and the heat storage performance of window (5) is considered by 2R1C model. The radiant surface is calculated as a surface with a constant temperature. The energy balance for indoor air is shown in (6). The heat gains from internal equipment and occupants are calculated in (6):