Fig.1 Discretization model for thermal pipe

Fig.2 Cross section of pipe segment j

Fig.3 Equivalent circuit thermal model for pipe segment

Fig.4 Equivalent circuit thermal model for pipe

Fig.5 Equivalent circuit hydraulic model for pipe segment

Fig.6 Equivalent circuit hydraulic model for pipe

Fig.7 Mass flow balance of junction

Fig.8 Equivalent circuit model for junction

Fig.9 Variation of heating input power of heat pump unit with water supply temperature and ambient temperature

Fig.10 Variation of COP of heat pump unit with water supply temperature and ambient temperature

Fig.11 Equivalent circuit model for heat pump

Fig.12 Framework for modeling of electric and heating multi-energy system

Fig.13 Flowchart of simulation of electric and heating multi-energy system

Fig.14 Irrelevance of different discrete steps

Fig.15 Relative computation time for different discrete steps

Fig.16 Pipe model responses to temperature change compared with physical reality

Fig.17 Comparison of mass flow rate changes between proposed pipe model and Dymola model

Fig.18 Comparison of temperature changes between proposed pipe model and Dymola model

Fig.19 One-line diagram of multi-carrier energy system

Fig.20 Nodes temperature change during heat network regulation

Fig.21 Number of heat pumps in operation

Fig.22 Power nodes voltage change during heat network regulation

Fig.23 Phase A voltage at node 2

Fig.24 Zoomed-in view of phase A voltage at node 2

Fig.25 Simulation results obtained with full electromagnetic transients model with time-step size of 0.1 s

Fig.26 Nodes temperature change of heat network before and after heat pump unit startup

Fig.27 Nodes voltage when the heat pump unit is connected to different nodes of the grid

Fig.28 Ambient temperature and soil temperature

Fig.29 Daily variation of temperature at each node of the heat network

Fig.30 Daily variation of the input power of heat pump unit

Fig.31 Daily variation of part of the nodes of the power grid