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The neutron's permanent electric dipole moment dn is constrained to below 3 × 10−26e cm (90% C.L.) [1, 2], by experiments using ultracold neutrons (UCN). We plan to improve this limit by an order of magnitude or more with PanEDM, the first experiment exploiting the ILL's new UCN source SuperSUN. SuperSUN is expected to provide a high density of UCN with energies below 80 neV, implying extended statistical reach with respect to existing sources, for experiments that rely on long storage or spin-precession times. Systematic errors in PanEDM are strongly suppressed by passive magnetic shielding, with magnetic field and gradient drifts at the single fT level. A holding-field homogeneity on the order of 10−4 is achieved in low residual fields, via a high static damping factor and built-in coil system. No comagnetometer is needed for the first order-of-magnitude improvement in dn, thanks to high magnetic stability and an assortment of sensors outside the UCN storage volumes. PanEDM will be commissioned and upgraded in parallel with SuperSUN, to take full advantage of the source's output in each phase. Commissioning is ongoing in 2019, and a new limit in the mid 10−27e cm range should be possible with two full reactor cycles of data in the commissioned apparatus.