**AUTHORS:**Ibrahim B. M. Taha, Sherif Ghoneim, Mohamed G. Ashmawy

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**ABSTRACT:**
HVDC system is necessary for very long power transmission lines and interconnections between networks of different frequencies. Therefore, it is required to model HVDC transmissions lines and combined them in the AC power flow calculation of the whole AC-DC system. In this paper, the Newton-Raphson method used in AC power flow calculations is modified to be suitable to model the AC-DC systems with inserting the HVDC line in the AC network. The elements of the unknown vector of the AC system are kept unchanged and are extended by a new unknown vector of the DC system variables. The Jacobian matrix of the AC system is modified to include the effect of the DC system which represents the modifications due to the DC line. The modified Jacobian matrix includes the effect of the active and reactive power absorbed at the DC buses, and their dependency on the AC system variables. The modified Newton-Raphson method was implemented on the AC-DC test systems with a power flow calculations using MATLAB script file and the results were presented and discussed for the hybrid AC-DC systems.

**KEYWORDS:**
Newton-Raphson Method, HVDC, AC-DC Load Flow

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