Electrification of end-use sectors is widely seen as a central decarbonisation strategy. However, the process of electrification is rarely discussed beyond electric end-use technologies such as electric vehicles or heat pumps. While electrification of end-use sectors is about new types of consumption, it also requires new technological interfaces with the electricity system. The paper provides a first conceptualisation of electrification as a multi-system interaction process, involving changes in both end-use sectors and in the electricity system. Electrification is thought to involve two core processes: (1) transitions in systems where electric niches challenge fossil energy regimes, and (2) reconfiguring patterns of multi-system interactions across production, distribution, and use of electricity. Through a case study design, we compare three sectoral cases that differ substantially in degrees and speed of electrification: ferries, construction sites and ammonia production. We explain these differences by analysing how the actors, technologies and institutions in each system shaped both the diffusion of electric end-use technologies and the interactions with the electricity distribution system. We find that the speed and ease of electrification depend on varying mixes of technological, actor, and institutional change processes. The severity and pervasiveness of grid connection challenges are arguably the most important finding. Grid connection challenges were significant in all three cases and continue to hamper electrification in two cases. Based on those findings, we conclude that grid capacity is increasingly problematic. Electricity system actors are overwhelmed with new demand, resulting in long lead times. And, they are further constrained by institutions that were designed to optimise for the efficient operation of existing assets rather than to innovate and transform electricity grids.