Abstract: To address the uncertainty issues induced by the grid integration of large-scale renewable energy into new power systems, this paper proposes a new over-limit risk assessment method based on Probabilistic Interval Power Flow (PIPF). The method is implemented as follows: First, an affine operator is constructed using Chebyshev polynomials. Interpolation points are selected within the range of input interval variables to solve for affine coefficients, thereby establishing a Chebyshev affine model. The affine form of the variables to be solved is then substituted into the original power flow equations, which are reconstructed as an affine optimization model. Second, the output intervals of distributed energy resources are divided into multiple sub-intervals, each of which is assigned a corresponding probability to construct a focal element model. By leveraging the Chebyshev affine power flow, the PIPF model based on the focal element model is transformed into an interval optimization problem to obtain the solution. Finally, the probabilistic boundaries of the power flow solutions are derived via the combination rules of evidence theory. Voltage deviation and branch overload are adopted as indicators to classify the severity levels of over-limit risks, and the probability intervals corresponding to different risk levels are calculated. Simulations conducted on the IEEE 33-bus system verify that the proposed method can effectively narrow the probability interval of power flow solutions and improve the assessment accuracy, rendering it applicable to new power systems with a high penetration of new energy.