Introduction

The proposed method aims to reformulate the load flow equations into an algebraic system composed of easily solvable linear equations and inequalities. A preprocessing method is proposed jointly to tighten the bounds on the variables in order to increase the quality of the solution.

Technical features

As a result of the change in the traditional electrical system, new methods and models need to be developed to optimize power flows in the grid. The mathematical model that accurately describes the power flows within an electrical system is defined by the load flow equations, which are nonlinear and non-convex. Therefore, it is necessary to find methods to make these equations convex. The proposed method aims to completely reformulate the load flow equations using the Cartesian representation of complex numbers, thus obtaining a non-convexity characteristic of the problem in bilinear terms. It is proposed to make the bilinear forms convex through McCormick envelopes by reformulating the load flow equations into an algebraic system composed of easily solvable linear equations and inequalities. To this end, a preprocessing method is jointly proposed to tighten the bounds on the current variables to increase the quality of the solution.

Possible Applications

• Dispatching of energy resources;
• Real-time energy market;
• Determination of ancillary services by generators and loads;
• Real-time control of micro-grids;
• Large-scale renewable generation plant design;
• Large-scale demand response.

Advantages

• Computational efficiency;
• Lower complexity;
• Less runtime compared to methods in the literature.