Design of grounding systems in substations using a mixed-integer linear programming formulation

The main purpose of this paper is the development of an optimization model to design grounding grids in electrical substations. The design of a grounding grid in a substation is formulated as a mixed-integer linear programming problem. The developed optimization model incorporates the constructive characteristics, as well as the technical and security requirements inherent to the construction, installation and operation of these grids.The model includes variables defining the grid characteristics according to the configurations admitted by the designer, which are selected amongst a set of pre-selected grounding designs. The definition of these configurations includes the geometry of the grid, the depth at which the conductors will be installed and the radius of the conductor. A finite number of configurations can be generated before running the optimization process by considering all the variables in accordance with the IEEE Std 80-2000. The optimization problem also includes safety constraints related with the maximum allowed touching and step voltages, which are defined according to the fibrillation discharge limits. These fibrillation discharge limits are defined by IEEE Std 80-2000 for low frequencies (for high frequencies, the limits are not the same as in 50 Hz). The model also includes the equivalent impedance of the transmission line supplying the substation where it will be located the grounding grid to be designed. As a result, the problem outputs define the most adequate grounding grid among the possible pre-selected configurations. This selection is driven by the total investment and installation costs, corresponding to the objective of the optimization model. To illustrate the interest of this research, the paper includes a case study based on a real situation, as an example of a potential application of this approach for engineering grounding design.Finally, it should also be referred that the scope of application of this methodology is potentially very wide given that it is in accordance with the specifications defined by the IEEE Std 80-2000.