  This paper proposes a semi-implicit version of continuous Newton method (CNM)
for power flow analysis. The proposed method succeeds the numerical robustness
from the implicit CNM (ICNM) framework while prevents the iterative solution of
nonlinear systems, hence revealing higher convergence speed and computation
efficiency. The intractability of ICNM consists in its nonlinear implicit
ordinary-differential-equation (ODE) nature. We circumvent this by introducing
intermediate variables, hence converting the implicit ODEs into differential
algebraic equations (DAEs), and solve the DAEs with a linear scheme, the
stiffly accurate Rosenbrock type method (SARM). A new 4-stage 3rd-order
hyper-stable SARM, together with a 2nd-order embedded formula to control the
step size, is constructed. Case studies on system 9241pegase verified the
alleged performance.
