家用储水式电热水器的温度设定问题研究  

Research on Temperature Setting of Household Storage Electric Water Heater

作　　者：谢强军[1] 裘哲勇[1] 王淑平[1] XIE Qiangjun;QIU Zheyong;WANG Shuping(School of Sciences,Hangzhou Dianzi University,Hangzhou,Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310038

出　　处：《数学建模及其应用》2023年第4期49-55,共7页Mathematical Modeling and Its Applications

摘　　要：针对家用储水式电热水器洗澡用水的温度设定问题,首先讨论了在非出水和出水两种模式下,热水器温度和加热功率变化与水温、加热时间、加热能耗及出水量的关系,在合理假设下,基于热平衡原理获得能量变化的微分方程模型;其次,基于模型,以某城市为例,分析在不同环境温度、两种模式下的电量消耗情况,进一步,考虑在不同季节电源一直开启时,构建了以积分形式的耗电量为目标函数的优化模型,通过算法求解得到既满足一个人随时洗澡又使电量消耗最小的温度;最后研究了在冬季,实现既能使电量消耗较少,同时使第二个洗澡人等待加热时间也较小的双目标优化问题,求解获得热水器最佳设定温度和最优加热等待时间.In this paper,we consider the temperature setting of household storage electric water heater.Firstly,we discuss the relationships between the temperature of water heater and the water temperature,heating time,heating energy consumption,water output,in the non-effluent and effluent modes.The same goes for heating power changes.Under reasonable assumption,the differential equation model of energy change is obtained based on the principle of heat balance.Secondly,we take a city as an example to analyze the power consumption under different environmental temperatures with two modes.Then,considering the power supply is always on in different seasons,an optimization model with the integral form of power consumption as the objective function is constructed.The optimum temperature that can satisfy a person to take a bath at any time and minimize power consumption is obtained by solving the algorithm.At last,we study the two-objective optimization problem,which can achieve less power consumption and less waiting time for the second bather in winter.And then the optimal set temperature and the optimal waiting time for heating are obtained.

关 键 词：储水式电热水器 温度设定 微分方程模型 目标优化 

分 类 号：O29[理学—应用数学]