A regional electric-heat supply system was selected as an example to verify the effectiveness of the method. 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. As a result, mathematical descriptions of electricity, heat and hydraulic flow in a multi-energy system were established. This expression modified the Sukhov cooling operator and intuitively revealed the impact factor of transmission loss in hot water pipes. This paper realized a new expression of hot water temperature drop with the thermal supply pipe network. 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. 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.
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