We currently make around 1 TW of photovoltaic cells per year, globally. The proposal here is to launch that much to space every 9 hours, complete with attached computers, continuously, from the moon.
edit: Also, this would capture a very trivial percentage of the Sun's power. A few trillionths per year.
Doubling every three years; at that rate it would take about 30 years for 1TW to become 1000TW. Whether on not the trend continues largely depends on demand, but as of right now humanity seems to have an insatiable demand for power.