South Africa has entered a critical phase of revamping its sole nuclear plant and needs it to run according to plan to avoid deepening power cuts that are already at a record and wreaking havoc on the economy. The first of two units at the 1 940-megawatt Koeberg plant was shut down last month for refueling and the replacement of its steam generators, work that’s expected to be completed in early June, state power utility Eskom said in an emailed response to questions. The overhaul of the second unit is due to begin a few months later.