The digital simulation of goaf line is of great significance to study the characteristics of the line and analyze the influence of tower inclination on the continuous transmission line status in collapsed areas. Considering that the tensile deformation of the wire mainly comes from the self weight of the wire

taking the length of the wire after the completion of the stringing and regarding the self weight as a fixed value

we construct a contour two node parabolic model that can reflect the stress characteristics of the transmission line in the collapsed area. The horizontal displacement of the span endpoint is used to represent the changes in the horizontal tension and sag of the wire. Then

based on the node force balance condition

the element stiffness matrix is integrated to obtain the overall statics balance equation of continuous span overhead conductor transmission line. Finally

taking isolated span as an example

we verify the accuracy of the model by comparing the calculation results of the catenary model and two commonly used ANSYS suspension cable form finding methods. Based on the two node parabolic model

we simulate and calculate the continuous span transmission line in the goaf

and analyze the influence of gear distance change caused by different factors on the sag and tension of conductor

as well as on the tension of suspension insulator string. The results show that this model has good accuracy and it can conveniently simulate the initial shape of the wire with fewer sensors. The wire state is sensitive to the increment of span

and a small change in span can cause a significant change of tension. The algorithm designed based on this parabolic model can effectively simulate and analyze state of transmission lines in the goaf collapse area.