  This paper proposes a novel method for solving and tracing power flow
solutions with changes of a loading parameter. Different from the conventional
continuation power flow method, which repeatedly solves static AC power flow
equations, the proposed method extends the power flow model into a fictitious
dynamic system by adding a differential equation on the loading parameter. As a
result, the original solution curve tracing problem is converted to solving the
time domain trajectories of the reformulated dynamic system. A non-iterative
algorithm based on differential transformation is proposed to analytically
solve the aforementioned dynamized model in form of power series of time. This
paper proves that the nonlinear power flow equations in the time domain are
converted to formally linear equations in the domain of the power series order
after the differential transformation, thus avoiding numerical iterations. Case
studies on several test systems including a 2383-bus system show the merits of
the proposed method.
