TRV Lagrangian, de Vries [*et al.*]{} [@CM11] and also Bsaisou [*et al.*]{} [@JB13] derived the chiral potential up to next-to-next leading order (N2LO) including only nucleon-pion interaction and contact interactions. In both works also the electromagnetic currents which play a role at N2LO for the EDM were derived but only in Ref. [@JB13] they were used to evaluate the EDM of the deuteron. In Ref. [@JV11b] the calculation of the EDM of $\det$, $\tri$ and $\hel$ was performed using only the one-pion-exchange part of the TRV potential coupled with phenomenological potential for the parity conserving (PC) part of the interaction.

Subsequent works showed the presence in the TRV Lagrangian of a three-pion term [@JB150], which was included in the calculation for the first time by Bsaisou [*et al.*]{} [@JB151]. This term generates at next-to-leading order (NLO) also a TRV three body force, which contribution to the $\tri$ and $\hel$ EDM was found to be smaller than expected by the chiral counting. The calculation reported in Ref. [@JB151] was also the first to use a complete chiral approach including the TRV potential up to NLO and the PC potential up to N2LO.

The aim of this work is twofold: First, the 