## 1 Introduction  
As a clean and renewable energy source, geothermal energy is characterized by a stable energy supply, large storage capacity, and wide distribution. As such, the use of geothermal systems for building heating has been increasing worldwide in recent decades. As it has no carbon footprint, ground source heat pump (GSHP) heating technology has a significant potential for continued development. The application of this technology will help mitigate smoke and haze occurring during winter in northern China, which results from coal combustion heating. Generally, according to the ground depth of heat extraction, GSHP roughly includes two categories of the shallow-depth GSHP and the medium-depth GSHP (MD-GSHP). As shallow-depth GSHP heating technology occupies a large area and has difficulty maintaining the thermal balance of the soil, the promotion and application of this technology has been limited. In 2012, medium-depth GSHP heating technology was proposed by some scientists in China, and it has been rapidly promoted in Shaanxi, Henan, and Beijing in northern China. For medium-depth GSHP heating technology, a closed-cycle water system is adopted to extract heat from the high-temperature rock and soil layer 2-3 km underground; this is achieved by drilling holes and installing medium-depth buried pipe heat exchangers in them. Then, heat from water as a heat transfer fluid (HTF) drives a high-temperature heat pump to heat the buildings [1]. Compared with shallow-depth GSHP technology, the underground heat-exchanging area of the buried pipe exchanger for MD-GSHP is smaller; this benefit comes in addition to the higher heat pump efficiency. Furthermore, MD-GSHP is not sensitive to ground temperature and other surrounding conditions [2]. At present, increasing amounts of attention have been paid to medium-depth GSHP systems in China. Numerical simulations on the heating coefficient of performance and optimization of the system have been conducted. The optimization of the MD-GSHP system was primarily carried out on the two kinds of variables of operating parameters, including the circulation flow and operation stop ratio, and the design parameters, including the space between boreholes, the nominal diameter of the buried pipe, the run-stop ratio, etc. Taking an 8000 m\({}^{2}\) residential building in Harbin, China, as a case study, [PERSON] [3] emulated the operational energy efficiency of the GSHP units and the water system of the ground source side in the GSHP system at constant and variable flowrates under certain operating variables. [PERSON] et al. [4] analyzed the variations in the unit, buried pipe, and heating terminal under three operation conditions of intermittent mode GSHP through an experimental study on the operation modes of the MD-GSHP system in some severely cold regions. [PERSON] et al. [5] tested the operational performance and energy efficiency of the medium-depth GSHP system in Xi'an. In their study, the energy efficiency of the medium-depth GSHP system and the heat transfer performance of the geothermal heat exchanger were revealed by the results of short-term and annual field tests. [PERSON] et al. [6] quantified the life cycle impacts of six heating and cooling configurations from shallow to medium-depth geothermal wells with connected, decentralized heat pumps and district heating and cooling in the State of Geneva. [PERSON] et al. [7] adopted the residential community heating in Fuxin City, Liaoning Province as an example and established a simulation model by TRNSYS software. In addition, they investigated the effect of variables that could determine the annual costs of the medium-depth double U-shaped buried pipe heat pump system through simulation and orthogonal tests. [PERSON] [8] took the medium-depth GSHP system in Handan City, Hebei Province as an engineering case, along with proposing a simulation model of the medium-depth GSHP system.