Accurate measurement-based convex model to estimate transmission loss coefficients in power systems

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This work proposes a convex methodology that uses power system measurements (power generation and total demand) to accurately estimate transmission loss coefficients (B-coefficients). The main contribution of this research is the possibility of incorporating the stochastic behavior of demand consumption in the final calculation of said coefficients. Power system simulations are considered, employing random variations in the active power injection of voltage-controlled nodes, in addition to power demands, using uniform or Gaussian distributions (for each variation, the power flow problem is solved using the classical Newton–Raphson approach). Based on the properties of the B-coefficients, a semi-definite programming model is proposed to obtain these parameters, considering that, for a power system with Ng generators, 0.5NgNg+3+1 measurements are required. The robustness of the proposed measurement-based optimization model is contrasted with a recent literature report using a linear solution method. Numerical results in the IEEE 14-, 39-, 57-, and 118- test feeders demonstrate the effectiveness of the proposed convex-based approach when using a different set of measurements (power system simulations) for cross variations, whose average estimation errors are between −0.1109% and 3.3967% for all the tested cases. All the numerical simulations were carried out using the MATLAB software and the MATPOWER 7.1 tool.