Relativistic electrons can penetrate spacecraft shielding and can damage satellite components. Spacecraft in medium Earth orbit pass through the heart of the outer radiation belt and may be exposed to large fluxes of relativistic electrons, particularly during extreme space weather events. In this study we perform an extreme value analysis of the daily average internal charging currents at three different shielding depths in medium Earth orbit as a function of L∗ and along the orbit path. We use data from the SURF instrument on board the European Space Agency’s Giove-A spacecraft from December 2005 to January 2016. The top, middle, and bottom plates of this instrument respond to electrons with energies >500 keV, >700 keV, and >1.1 MeV, respectively. The 1 in 10 year daily average top plate current decreases with increasing L∗ ranging from 1.0 pA cm−2 at L∗=4.75 to 0.03 pA cm−2 at L∗=7.0. The 1 in 100 year daily average top plate current is a factor of 1.2 to 1.8 larger than the corresponding 1 in 10 year current. The 1 in 10 year daily average middle and bottom plate currents also decrease with increasing L∗ ranging from 0.4 pA cm−2 at L∗=4.75 to 0.01 pA cm−2 at L∗=7.0. The 1 in 100 year daily average middle and bottom plate currents are a factor of 1.2 to 2.7 larger than the corresponding 1 in 10 year currents. Averaged along the orbit path the 1 in 10 year daily average top, middle, and bottom plate currents are 0.22, 0.094, and 0.094 pA cm−2, respectively.