*Article* **An Improved Mixed AC**/**DC Power Flow Algorithm in Hybrid AC**/**DC Grids with MT-HVDC Systems**

### **Fazel Mohammadi 1,\*, Gholam-Abbas Nazri 2 and Mehrdad Saif 1**


Received: 30 November 2019; Accepted: 19 December 2019; Published: 31 December 2019

**Abstract:** One of the major challenges on large-scale Multi-Terminal High Voltage Direct Current (MT-HVDC) systems is the steady-state interaction of the hybrid AC/DC grids to achieve an accurate Power Flow (PF) solution. In PF control of MT-HVDC systems, different operational constraints, such as the voltage range, voltage operating region, Total Transfer Capability (TTC), transmission reliability margin, converter station power rating, etc. should be considered. Moreover, due to the nonlinear behavior of MT-HVDC systems, any changes (contingencies and/or faults) in the operating conditions lead to a significant change in the stability margin of the entire or several areas of the hybrid AC/DC grids. As a result, the system should continue operating within the acceptable limits and deliver power to the non-faulted sections. In order to analyze the steady-state interaction of the large-scale MT-HVDC systems, an improved mixed AC/DC PF algorithm for hybrid AC/DC grids with MT-HVDC systems considering the operational constraints is developed in this paper. To demonstrate the performance of the mixed AC/DC PF algorithm, a five-bus AC grid with a three-bus MT-HVDC system and the modified IEEE 39-bus test system with two four-bus MT-HVDC systems (in two different areas) are simulated in MATLAB software and different cases are investigated. The obtained results show the accuracy, robustness, and effectiveness of the improved mixed AC/DC PF algorithm for operation and planning studies of the hybrid A/DC grids.

**Keywords:** improved mixed AC/DC power flow; multi-terminal high voltage direct current (MT-HVDC) systems; operational constraints; voltage-sourced converter (VSC)-high voltage direct current (HVDC) station
