  In this paper, we propose an efficient continuation method for locating
multiple power flow solutions. We adopt the holomorphic embedding technique to
represent solution curves as holomorphic functions in the complex plane. The
holomorphicity, which provides global information of the curve at any regular
point, enables large step sizes in the path-following procedure such that
non-singular curve segments can be traversed with very few steps. When
approaching singular points, we switch to the traditional predictor-corrector
routine to pass through them and switch back afterward to the holomorphic
embedding routine. We also propose a warm starter when switching to the
predictor-corrector routine, i.e. a large initial step size based on the poles
of the Pad\'{e} approximation of the derived holomorphic function, since these
poles reveal the locations of singularities on the curve. Numerical analysis
and experiments on many standard IEEE test cases are presented, along with the
comparison to the full predictor-corrector routine, confirming the efficiency
of the method.
