To address the problem of solving affine coefficients in existing Taylor expansion-based affine power flow methods

a Chebyshev affine power flow calculation method for distribution networks considering correlation is proposed. First

Chebyshev polynomials are used to construct affine operators

and several interpolation points are extracted within the interval ranges of the input variables to solve for the affine coefficients

thereby establishing a Chebyshev affine model. Based on this model

the affine form of the variables to be solved is constructed and substituted into the original power flow equations to reconstruct the equations

obtaining an affine optimization model with respect to the noise elements of the target variables. The correlation of the distributed wind power output is described using the hybrid box-ellipsoid set

and through coordinate transformation

the hybrid box-ellipsoid set is converted into new affine constraints and embedded into the affine optimization model for simultaneous solution. Simulation results on two distribution network examples show that

compared with the Taylor expansion affine model

the proposed model has higher calculation accuracy and efficiency

and is more suitable for interval power flow analysis scenarios under larger fluctuation ranges. Meanwhile

the hybrid box-ellipsoid set effectively reflects the impact of different correlation levels on the calculation results.