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Wireless sensor networks (WSNs) suffer not only from short lifetimes because of limited energy but also from an energy imbalance between the nodes close to the sink and the other nodes. To fundamentally resolve the issue of short lifetimes, recent studies have utilized environmental energy, such as solar power. Additionally, WSNs that employ energy-aware dynamic topology control are also being studied to address the energy imbalance. This paper proposes an improved collection tree protocol (CTP) scheme, called solar-CTP, that uses the two approaches of energy-harvesting and energy-aware topology control simultaneously. The proposed scheme is derived from the CTP scheme, which is a widely adopted data collection strategy designed for typical battery-based WSNs with a fixed sink. We tailor the CTP scheme for solar-powered WSNs operating with a mobile sink. Performance verification confirms that our scheme significantly reduces the number of blackout nodes compared to other CTP variants, thus increasing the amount of data collected by the sink.