As the traditional GM(1,1) model does not have the property of exponential law coincidence, this paper improves
the grey differential equation of GM(1,1) model from grey derivative and background value respectively. Two kinds of
GM(1,1) power model with power exponential law coincidence are proposed and relevant theoretical proofs are also given.
Two grey differential equations with power exponential law coincidence are transformed into exactly the same form, based
on which parameters can be effectively estimated. Numerical simulation and application examples show that the simulation
and prediction accuracy of GM(1,1) power model is effectively enhanced by using the proposed method.