I'm predicting that the Gigafactory will consume between 3,229 and 4,688 GWh of electricity per year (or between 367 and 535 MJ on average).I don't know I think when you say
"We will be using 100% sustainable energy through a combination of a 70 MW solar rooftop array and solar ground installations. "
it's pretty reasonable. Especially since that comment allows for an unlimited number of solar ground installations.
The average capacity factor of utility scale PV solar in the US in 2016 was 0.2769. Looking through the EIA data for solar farms around Reno, Nevada, they seem to have capacity factors pretty close to the national average. There are places in Southern California that do much better, but the Gigafactory won't get that kind of sun.
With a capacity factor of 0.2769 the Gigafactory will need a solar array of between 1331 MW and 1932 MW in nameplate capacity. If Tesla wants a solar array that generates between 367 and 535 MJ in December when the average CF is 0.1550, then it will need an array between 2378 and 3452 MW in nameplate capacity. Because of the reduced solar irradiance in the winter, it is highly likely that the Gigafactory will be using a lot of dirty grid electricity from Nevada during the winter, which mostly comes from burning natural gas.
Telsa simply can't generate that much solar energy on the current acreage of the Gigafactory. Taking the average of the 6 largest solar farms in the US (which all get better sun than the Gigafactory), we get 0.333 GWh per acre per year. If we use that average on the 2864 acres of the Gigafactory we get 953 GWh per year, which is far less than the 3,229 to 4,688 GWh that will be needed. Also remember that the Gigafactory is located on hilly terrain which will block the sun in some parts and it will have parking lots and roads, so all 2864 acres will not be suitable for solar panels.
Of course Tesla can easily buy more land and better land for a solar farm in the region. The problem is the cost. Currently utility-scale PV solar costs roughly $1.1 million per MW of nameplate capacity, so Tesla will have to spend between $1464 and $2126 million to build a solar farm which is double the size of the biggest solar farm in the world. If the Gigafactory will have all its energy in December coming from onsite solar, then those costs balloon to between $2616 and $3798 million.
Another problem is the size and cost of the battery array to store the solar energy. Currently, Telsa charges $250 per kWh for the PowerPack. Let's guesstimate that the installation of a battery storage system will cost Tesla $150 per kWh. Since Tesla claims that it will be using 100% renewable energy, presumably it will need a full day's worth of electricity in its battery storage, so it will need between 8.8 and 12.8 GWh of battery storage. That means that Tesla will spend between $1327 and $1926 million on battery storage.
It is highly unlikely that Tesla will be spending this sort of money, so it won't be using 100% renewable energy. It is far more likely that it will have a 200 to 300 MW solar farm on the site of the Gigafactory and a small battery to smooth the solar output, but it will be buying power from the dirty Nevada grid for the rest of its needs.