Formulation of problem

The main purpose of TEP in competitive environment is to provide a competitive, unprejudiced and sure environment for all the market actors and in minimum cost. The prerequisite for providing such an environment is to consider some indices in designing and development of transmission network. Considered indexes in the paper are the level of competition, dependability, and investment cost which are presented in the following.

Investment cost index

Economic justifying is important in competitive environment. Thus, development costs have to be considered in TEP to minimize investment budgets and transmission tariffs. Thus, the present value of total investment cost is formulated during the planning period as follows: \[ic^k=\sum_{p-1}^{np}\frac{IC^P}{(1+r)^{p-1}}\ \ \ p=1,2,\dots,np\ \ \ \ \ \ \ \ \ \ \ \ \left(6\right)\]
While \(IC^P\)  is the investment cost for the new lines installed in year p ($) and \(ic^k\)  is the present pure value of investment cost during programming horizon. Also, k is programming horizon.

Lines density cost index  

Density cost is a function of density level and its duration in a network. Here, density cost is calculated according to load peak over time and it is going to be minimized as a goal of TEP. Line density cost (as shown in Figure 1 ) is formulated as follows: