In this work we presented an Expert System built with Paraconsistent Logic applied in a transmission electrical power system operation support in real time. The computational program forms a Paraconsistent Expert System PES capable to offer a risk analyses, diagnosis and the optimal restorative strategy proposition to the electrical power transmission system after an outage. The logic used for the PES to make decisions is the Annotated Paraconsistent Logic (APL) that belongs to a class of the Non-classic Logical denominated of Paraconsistent Logic-PL. This Paraconsistent Expert System PES uses a type of the Annotated Paraconsistent logic denominated Annotated Paraconsistent logic with annotation of two values APL2v to produce diagnosis suggesting the restorative strategy based in the analysis of occurrence information (electric Switches, Circuit breakers, protections, etc…). The use of APL brings certain advantages in comparison with the classic logic because allow to manipulate contradictory signals, and like this presenting a faster and reliable action for make decision in case of the reception of vague, ambiguous and inconsistent information. The results demonstrate that the Paraconsistent Logic, with their algorithms extracted of APL2v methodology, also opens a wide field for researches and developments and can be used with promising results for implementations of applied Expert Systems in Electric Power Systems re-establishment at different topologies.