Directional relays without voltage sensors for distribution networks: Use of symmetrical components and effect of the distributed generation

Fortescue´s theory introduced in 1918 [1] allows to study a 3-phase coupled electrical network as 3 independent uncoupled circuits. It supposes the electrical network is symmetric and linear: self and mutual impedances of each phase are equal. The decomposition gives 3 independent sequences: zero (o), positive (1) and negative (2) sequences (symmetrical base). Real (A, B, C) and symmetrical (0, 1, 2) signals are linked by: