Initial applications of complex artificial neural networks to load-flow analysis

Artificial neural networks (ANNs) have been widely used in the power industry for applications such as fault classification, protection, fault diagnosis, relaying schemes, load forecasting, power generation and optimal power flow etc. At the time of writing this paper, most ANNs are built upon the environment of real numbers. However, it is well known that in computations related to electric power systems, such as load-flow analysis and fault-level estimation etc., complex numbers are extensively involved. The reactive power drawn from a substation, the impedance, busbar voltages and currents are all expressed in complex numbers. Hence, ANNs in the complex domain must be adopted for these applications, although it is possible to use ANNs in the conventional way by dividing a complex number into two real numbers, representing both the real and imaginary parts. It is shown, by illustration with a simple complex equation, that the behaviour of a real ANN simulating complex numbers is inferior to that of an ANN which is intrinsically complex by design. The structure of the complex ANN and the numerical approach in handling back propagation for online training under the complex environment are described. The application of this newly developed ANN on load flow analysis in a simple 6-busbar electric power system is used as an illustrative example to show the merits of incorporating complex ANNs in power-system analysis