In scenarios where certain probability distribution parameters are absent

the probability-interval hybrid uncertainty power flow calculation can directly obtain the power flow distribution and its associated interval bounds. However

the existing methods rely on sampling and numerical computation

which leads to inefficiency. To address this issue

a probabilistic embedding mixed uncertainty power flow (PEPF) calculation method is proposed

which can efficiently and accurately solve power flows under normal operating conditions without complex sampling. The proposed method targets the stochastic uncertainty of distributed generation and the interval uncertainty of load power. First

it defines a mixed uncertainty analytical model with input variable probabilities as embedded factors

extending power flow calculations from a single operating state to a continuous state space. Subsequently

a cascaded analytical model linking system inputs and power flow calculations is constructed. A linear recursive approach is employed to determine the power series coefficients of state variables

thereby obtaining analytical polynomial expressions of these variables to input probabilities. Finally

by collecting sparse yet highly representative probability sample points

the boundaries of power flow solution distributions can be efficiently determined through direct substitution. The accuracy and effectiveness of the proposed method are verified by using the IEEE 30-bus system and IEEE 141-bus system standard node systems.