Chapter 3 - Power-flow analysis of microgrids

Abstract

This chapter presents a novel approach for robust, balanced, and unbalanced power-flow analysis of microgrids, including wind/solar, droop-controlled, and electronically-coupled distributed energy resources. This method uses radial basis function neural networks (RBFNNs) that can be applied to a wide range of non-linear equation sets. Unlike conventional Newton-Raphson, the presented method does not need to calculate partial derivatives and inverse Jacobian matrix and so, has less computation time, can solve all the equation sets for the power grid and distributed energy resources exactly and simultaneously, and has enough robustness concerning the R/X ratio and load changes. Also, because the power electronic interface provides some degrees of freedom in the steady-state and dynamic models, a new approach is required to solve the nonlinear set of the power grid and distributed energy resource equations even with unequal numbers of equations and variables. The proposed method is a general method applicable to all power networks, including radial, meshed, and open-loop. It includes all types of buses, i.e., PQ, PV, and slack buses. This method is tested on different microgrid test systems, and the comparative results validate its efficiency and accuracy. Next, we extend the proposed method for probabilistic and harmonic power-flow. This chapter also presents a new method based on fuzzy unscented transform and RBFNNs for possibilistic-probabilistic power-flow in the microgrids, including uncertain loads, correlated wind and solar distributed energy resources, and plug-in hybrid electric vehicles. When sufficient historical data of the system variables are not available, a probability density function might not be defined, while they must be represented in another way, namely, possibilistically. When some uncertain system variables are probabilistic, and some are possibilistic, neither the conventional pure probabilistic nor pure possibilistic methods can be implemented. Hence, a combined solution methodology is needed. The proposed method exploits RBFNNs and unscented transform in nonlinear mapping with an acceptable level of accuracy, robustness, and reliability. Simulation results for the proposed probabilistic power-flow algorithm and its comparison with the reported methods for different test power systems reveal its efficiency, accuracy, robustness, and authenticity. Finally, Also, a harmonic power-flow calculation is presented.