Mathematical Analysis of Optimal Operating Conditions in Heating Systems

Hindawi Mathematical Problems in Engineering Volume 2019, Article ID 4264562, 16 pages https://doi.org/10.1155/2019/4264562 Research Article Mathematical Analysis of Optimal Operating Conditions in Heating Systems Chan Kong, Yong Sun, Hongxi Zhang, and Yongjiang Shi College of Energy and Environmental Engineering, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou 075000, Hebei, China Correspondence should be addressed to Yongjiang Shi; Received 7 January 2019; Accepted 31 March 2019; Published 6 May 2019 Academic Editor: Ali Ramazani Copyright © 2019 Chan Kong 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. With changes in the outdoor air temperature, the heat consumption of buildings also changes. Timely adjustment of the heating systems to ensure optimal operating conditions is extremely significant to save energy. In this study, the operation conditions of a heating system were analyzed numerically, and the existence, uniqueness, and stability of the optimal operation conditions of the heating system were proved. An operation optimization model that could obtain the optimal operation conditions was also established, and the correctness of the model was verified experimentally. Experimental results showed that when the flow rate was 0.606 m3 /h, the supply water temperature was 67.13∘ C, water return temperature was 65.90∘ C, and the pump consumed the least amount of electricity. The experimental results and model calculation results showed that the operating cost is lower when the system flow rate is low and the supply water temperature is high under the same heat dissipation and indoor temperature. 1. Introduction In the operation of heating systems, besides controlling and adjusting the operation parameters, it is necessary to adjust the heat supply according to the season, outdoor temperature, and heat demands of users [1]. The purpose is to make the heat dissipation from dissipating equipment adapt to the changing heat load, protect users from excessively high or low room temperatures, ensure that the user heat demand is met, and avoid unnecessary heat wastage to realize economic operation of heating systems [2]. Until now, several studies have been carried out on the optimized operation of heating systems, focusing on the establishment of mathematical models of water supply temperature, flow rate and outdoor temperature, and regulation of water supply temperature and flow rate. Atli Benonysson et al. [3] found that, in order to adapt to the change of heat load, frequent regulation of water supply temperature can reduce the operating costs, but they did not precisely state the frequency at which the water supply temperature was regulated. Guillaume Sandou and Sorin Olaru [4] applied the particle swarm optimization method to control district heating pipe networks and found that the optimization effect was different when the water supply temperature was adjusted at different frequencies. In addition, selection of the control cycle was an important part of the modeling problem [5]. Jonas Gustafsson et al. [6] controlled the radiator system and found that, compared with the traditional control, the larger temperature difference between the primary supply and return water could reduce the energy consumption of the pump and improve the overall fuel efficiency. Pengfei Jie et al. [7] established a dynamic model of the heating system network; based on this model, the peak valley method and correspondence analysis method were introduced, respectively, and two important parameters related to the dynamic characteristics of the heating system, i.e., delay time and relative attenuation degree, could also be calculated. It is concluded that the delay time is approximately equal to the time of heat media flow. These findings provide basis for the optimized operation and management of heating systems. Aibin Yan and Jun Zhao et al. [8] established the hydraulic model and found that, compared with the traditional central circulation pump, the distributed variable speed pump in the heating system could save at least 20% energy. In particular, when the distributed variable speed pump was used with low flow, more power could be saved. P. Lauenburg et al. [9] 2 developed a control algorithm for the radiator system based on field experiments and computer simulation. By determining the optimal combination of the water supply temperature and flow rate in the heating system, a low primary return water temperature was obtained, thereby reducing the operation costs. X. S. Jiang et al. [10] proposed an integrated regional direct heating energy system model that integrates wind energy, solar energy, natural gas, and electric energy. By establishing the objective function of the optimal control strategy with complex operation constraints, the fuel consumption was minimized and the operating efficiency of the system was improved. In other studies [11–13], the heat storage capacity of the district heating system was adapted to the large amounts of renewable energy conversion in the system, thus improving the system operation flexibility and economy. Based on outdoor temperature prediction and process data history, Laakkonen et al. [14] modeled delay as a distribution function and developed a robust optimizer to minimize pumping cost and heat loss; by optimizing the water supply temperature and flow rate, the heating system could run efficiently and smoothly. M. Leśko et al. [15] have presented different approaches to a simplified modeling of district heating networks for optimization purposes. Yiwen Jian et al. [16] analyzed an existing water temperature regulation mode and its impact on indoor environment and energy utilization on the basis of field investigation. By comparing the relationship among outdoor temperature, indoor temperature, indoor reference temperature, and water supply temperature, a method for optimizing water supply temperature based on simulation was proposed. Hence, it can be seen that many researchers have worked in the field of optimized operation of heating system, but none have provided theoretical proofs regarding the properties of the optimal operating conditions of the heating system. Moreover, the optimal operation conditions will have different values under different constraints and objective functions. Therefore, in this study, optimization of the operation of heating systems by adjusting the operating conditions according to load changes was performed, and the optimal operating conditions that can minimize the operating costs of the heating system were determined. To improve the operating efficiency and reduce the operating costs of the heating system, mathematical analysis of the operating conditions was carried out. First, the existence, uniqueness, and stability o (...truncated)