A recuperated solar-dish Brayton cycle with an off-the-shelf turbocharger as micro-turbine is investigated for potential low-cost power generation. Integrated phase-change thermal storage in the solar receiver can be used to improve the power stability and performance of the cycle; however, the phase-change temperature affects the solar conversion efficiency. In this paper, three different off-the-shelf turbochargers and various recuperator geometries are considered so that the maximum thermal efficiency of the cycle can be found for a fixed receiver geometry at different solar receiver temperatures. Metallic phase-change material of high conductivity is proposed as thermal storage material which is placed around a coiled tube in an open-cavity tubular solar receiver. An analytical model is presented to determine the thermal efficiency of the cycle for different solar receiver temperatures. Results show that maximum thermal efficiencies of 20.2–34.2% can be achieved at receiver temperatures of between 900 K and 1200 K, and that solar conversion efficiencies of 13.5–21% (11–17% when dish reflectivity and intercept factor are both assumed 90%) can be achieved. High solar conversion efficiencies require a large solar input power which would require a more expensive solar dish. A map is therefore provided for each turbocharger which shows the expected solar input power for the shaft power generated at different solar receiver temperatures. Overall, the results show that an open-cavity tubular solar receiver with metallic phase-change thermal storage material can be used together with an off-the-shelf turbocharger for power generation in a solar-dish Brayton cycle.