Improved Power Flow Algorithm for VSC-HVDC System Based on High-Order Newton-Type Method

Table 2

Forward and backward mode.

Forward mode	Backward mode
𝑥3̇=con𝑥1⋅𝑥1̇	𝑝1=𝑝1+𝑥3,1𝑝3
𝑥4̇=𝑥1̇𝑥2+𝑥1𝑥2̇	𝑝1=𝑝1+𝑥4,1𝑝4,; 𝑝2=𝑝2+𝑥4,2𝑝4
𝑥5̇=𝑥5𝑥4̇	𝑝4=𝑝4+𝑥5,4𝑝5
𝑥6̇=𝑥3̇+𝑥5̇	𝑝3=𝑝3+𝑥6,3𝑝6,; 𝑝5=𝑝5+𝑥6,5𝑝6
𝑦̇=𝑥6̇	𝑝7=1