In view of the large scale and distributed characteristics of transformers, which lead to inconvenient manual inspection and state monitoring, and the limited energy of batteries restricting the development of wireless sensor nodes (WSNs), WSNs powered by solar energy are a promising approach. We propose a power management circuit for dual energy storage and dual-channel charging of a supercapacitor and a lithium battery with four modes to deal with the different charging currents of photovoltaic power generation under strong and weak light illumination, as well as the time mismatch between the energy harvesting power and WSN consumption power. We designed a low-power WSN with temperature, humidity, vibration, and illumination sensors in a low-duty-cycle operation mode with an average current consumption of 4.96 mA. Our solar power management circuit with undervoltage lockout (UVLO), maximum power point tracking (MPPT), quick charging, and a sustainable output characteristic is designed by LTspice simulation and verified by experiment in alternating light outdoors. The experiment demonstrates sustainable autonomous wireless sensing by dual charging and the feasibility of our storage design for solar energy harvesting, indicating its potential application in grid transformers.