  We study the energy-momentum characteristics of the plane ``+''-polarised
gravitational wave solution of general relativity in the Teleparallel
Equivalent of General Relativity (TEGR) and the Symmetric Teleparallel
Equivalent of General Relativity (STEGR) using the previously constructed
Noether currents. The current components describe locally measured by observer
energy-momentum if the displacement vector $\xi$ is equal to the observer's
4-velocity. To determine the non-dynamical connection in these theories we use
the unified ``turning of'' gravity principle. For a constructive analysis of
the values of Noether currents and superpotentials in TEGR and STEGR, we use
the concept of ``gauges''. The gauge changing can affect the Noether current
values. We study under what conditions the Noether current for the freely
falling observer is zero. When they are established, zero result can be
interpreted as a correspondence to the equivalence principle, and it is a
novelty for gravitational waves in TEGR and STEGR. We highlight two important
cases with positive and zero energy, which reproduce the results of previous
works with a different approach to determine gravitational energy-momentum in
TEGR, and give their interpretation.
