Aiming at the problem that the accuracy of the active power estimation algorithm is affected by the increasing colored noise of the novel power system, this paper firstly establishes the active power convolution sum estimation algorithm with non-stationary colored Gaussian noise, and deduces the important terms of noise which influencing the active power estimation algorithm. Secondly, the distribution characteristics of the output noise signal from the active power estimation algorithm are analyzed, then, the analytical formula of theoretical relative limit error of the active power estimation algorithm caused by colored Gaussian noise is derived. Finally, Monte Carlo simulation experiments are used to analyze the relative limit error of the active power estimation algorithm caused by colored Gaussian noise, and the results show that the theoretical relative limit error formula is correct, and the relative limit error formula gives a general method to evaluate the influence of non-stationary colored Gaussian noise on the error of the active power estimation algorithm.