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The NASA Solar Probe Plus (SPP) mission will fly into and study the Sun's corona, reaching as close as 8.5 solar radii from the surface of the Sun. Power generation for the spacecraft will be provided by two solar array wings, which are being designed and built by Johns Hopkins University Applied Physics Laboratory and Emcore Photovoltaics. SPP will get closer to the Sun than any previous mission, and the solar array will therefore need to operate reliably under unusually high irradiances, temperatures, and angles of incidence, a situation that introduces intriguing challenges for the array design. This paper presents an overview of the array-geometry optimization method we have developed, the goal of which is to allow for the most benign nominal operating conditions possible, given the mission requirements for minimum power generation and maximum heat dissipation. We also outline the engineering trade-offs associated with the available options for cell lay-down onto the panel, including the non-standard material choices necessary for optimal thermal, mechanical, optical and electrical performance and robustness of the array. We conclude by presenting the near-term test plan included in the SPP array-development program, and summarize the data from preliminary measurements performed to date.