For urban electrical and thermal energy supply and consumption terminals, the multi-energy system is a way to realize the energy conversion and consumption efficiently, cleanly and economically. To further study the power flow character of multi-energy systems, additional factors such as electric-thermal coupling equipment, thermal flow rules should be taken into consideration. The traditional Newton-Raphson iteration method which has been commonly used for electrical power flow calculation must be expanded to electric-thermal mixed power flow. This paper realized a new expression of hot water temperature drop with the thermal supply pipe network. This expression modified the Sukhov cooling operator and intuitively revealed the impact factor of transmission loss in hot water pipes. As a result, mathematical descriptions of electricity, heat and hydraulic flow in a multi-energy system were established. With the modified Sukhov cooling operator, the mathematical model of the expanded Newton-Raphson fast iterative solution algorithm, together with its Jacobian matrix elements affected by the electro-thermal coupling relationship was derived. A regional electric-heat supply system was selected as an example to verify the effectiveness of the method. Results showed that the transmission loss in electrical grid is related with the power load while in thermal pipes it was mainly related with the ambient temperature.
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