Linearly constrained programming with integer variables for conductor size selection in electrical distribution grids considering the impact of electricity price

Abstract

One major subproblem in planning distribution grids is optimally choosing conductor sizes. This subproblem often employs nonlinearly
constrained optimization with integer variables as its modeling approach. Attaining optimality on a global scale is not always guaranteed by
the nonlinear optimization formulation. As a means of determining the area of the wire’s section in the distribution grid in the most efficient
manner possible, this study suggests a model that is based on linearly constrained optimization with integer variables. While adhering to load
flow equations, maximum loading restrictions on branches, voltage magnitude bounds, and investment budget constraints, the goal function
is minimizing the cost across the lifetime of the distribution system. Piecewise linearization methods and accurately linearized expressions
of multiplying a binary variable by a continuous variable are deployed in order to convert the initially nonlinear model into the suggested
optimization model. A programming environment called GAMS and an optimizer called CPLEX are used to evaluate the recommended
optimization formulation on a 33-node test distribution network. The evaluation is implemented using diverse scenarios about the price of
electricity. The calculation outcomes indicate that the size of conductors is significantly influenced by the electricity price. Furthermore, the
conductor size based on the suggested methodology is more cost-effective than the one obtained using the method currently utilized in
Vietnam