I'm starting to take a closer look at your calculation here, and I believe your values are completely meaningless. I remember going through this exercise about 2 years ago and found that the papers you are referencing. They aren't applicable, unfortunately. There are far too many input value assumptions that are wrong.
One of the biggest problems in your input assumption is that the production energy requirements are on a per kg basis, not per kWh. The specific energy of the cells used in the studies are a mismatch. Ellingsen's assumption is 27% lower than the Tesla/Panasonic original 18650 cell from 2012. That alone throws off a tremendous amount. Majeau-Bettez's assumption is 42% too low. And Tesla/Panasonic is currently using an even denser cell. Just from that, the energy required on a per kWh basis drops by 42% to 274 MJ/kWh. I haven't gone back through all their various erroneous assumptions, but likely your energy requirements are high by about an order of magnitude, if not more.
BTW, you need to address the paper by Dunn. She critiques the approaches used by predecessors like Majeau-Bettez and also compares against EPA's data. Unfortunately she is modeling LMO chemistry, but the critique still applies. She's modeling a cell with 148 Wh/kg specific energy and has 10.7 MJ/kWh of energy. Notter has 143 Wh/kg and 3.1 MJ/kWh. Majeau-Bettez's approach is 40 to 105 times higher. It's far higher than EPA's estimate too of around 28 MJ/kWh for 167 Wh/kg. Using the EPA figures, at 260 Wh/kg, that's 18 MJ/kWh, or 5 kWh to make 1 kWh of cells.
That's 525 GWh per year of electricity usage using EPA's data and only correcting for specific energy. Add in process improvements, and we're talking about far less than even that. Your calculations are likely around 10x, if not 15x too high.
In the supplemental material of Dunn et al (2014, p.10,
http://www.rsc.org/suppdata/ee/c4/c4ee03029j/c4ee03029j1.pdf) they estimate that a pioneer battery assembly plant will consume 780 MJ per kg of NMC battery and the Nth plant operating at full capacity will consume 4.5 MJ / kg. Certainly Dunn is right about the Nth plant using less energy, but I wasn't convinced by Dunn et al's estimate of 4.5 MJ / kg, because the GREET group at Argonne Nat. Lab. simply contacted the manufacturer of dry room equipment in 2011 and asked for an estimate of how much energy would be consumed per tonne of battery material (p. 32,
https://greet.es.anl.gov/files/lib-lca), whereas Ellingsen et al (2014) used real plant data and arrived at 100 - 400 MJ / kg of battery cell. I also tend to distrust Dunn et al, because some of their estimates for other battery components are 1/10 of the estimates found in other LCA studies and the process-sum methodology often underestimates, whereas top-down is better at captured all associated processes to make a good.
I explained in my article why I think that all the existing LCA studies are underestimating the energy to produce lithium, nickel and cobalt (and probably copper as well), since they are based on brine operations with high lithium content in Chile and sulfide ores (that are often processed with cleaner energy in North America). The energy to produce these raw materials will likely increase in the future. However, the more I think about it, you are probably right that the Gigafactory will use much less than 100MJ / kg of battery in assembly. I doubt that it is as low as 4.5 MJ / kg, but 10 - 30 MJ / kg does seem possible if the Gigafactory is able to achieve an 80% energy reduction in the drying rooms and those drying rooms represent 60% of the total energy usage in the Gigafactory. The other thing is that I reread Ellingsen et al and they say that pack assembly has very low energy usage, so my guesstimate of 25 MJ / kg for pack assembly is wrong.
Based on that, let's redo the estimates as 10 - 30 MJ per kg in cell assembly and 1 - 2 MJ per kg in pack assembly, so you need 333 - 958 GWh per year (or 38 - 109 MW on average) at the Gigafactory. That would mean a solar array of 137 - 395 MW in nameplate capacity costing $137 - $395 million and battery storage of 0.9 - 2.6 GWh costing $137 - $394 million. Those totals would be doubled if wanting to operate at 100% renewable energy in the winter with onsite solar.
That level of energy consumption will be challenging with 100% onsite solar, but not impossible, especially if you are talking about net 100% renewable energy, so the Gigafactory sells solar energy during the summer and buys outside energy during the winter. Tesla still has to build the largest solar farm outside the prime solar radiation zones in the US and its panels will cost more than the CdTe panels used by almost all the large solar farms in the US. There is a reason why almost every US solar farm over 100 MW in size is located in southern California, Arizona and the southwest tip of Nevada where there is the best sun and they almost all use First Solar panels. The Panasonic/Tesla panels are not a good choice for $ per kW.
I understand your point about increasing energy density in batteries, but I don't understand your argument why MJ / kWh would be better than using MJ / kg for making estimates. We aren't sure about the rate of change for either of them. It is currently very hard to estimate anything based on either MJ / kWh or MJ / kg because of the dramatic improvements in the energy efficiency of drying rooms and using multiple production lines, so that equipment is always operating at maximum efficiency. We are also getting dramatic energy efficiency improvements by shipping materials directly from the refiners and recyclers so there is less transportation and less reprocessing of materials. However, these are one-time improvements in efficiency and they will not keep increasing in the future. In theory, the MJ / kg should be relatively stable in the future once all battery manufacturing moves to Gigafactory-style production whereas MJ / kWh will keep changing.
One of my frustrations is that EV advocates aren't demanding that Panasonic/Tesla, LG, Samsung and BYD share data about their battery factories. We can't resolve this debate about energy usage without hard data. If these companies want to claim that they are helping the environment, then they need to provide the data. Consumers and governments should demand more transparency from the battery industry. Whether you believe in EVs or not, it seems to me that it is in everyone's best interest to have good assessments of their environmental impact.
This debate about the MJ / kg of batteries and energy usage in the Gigafactory is ignoring the more fundamental questions which I raised in my article about whether we have the metal reserves to make 95 million BEVs every year and whether can we sustain the rising environmental costs per kg of mining so much lithium, nickel, cobalt and copper. Can we reduce the number of vehicles down to a sustainable level so that we avoid those rising environmental costs in metal mining? Can BEVs truly reduce the GHG emissions for the transportation sector by 90% or do we need to be focusing on other policies? It seems to me that these are the fundamental questions to be addressed if lithium-ion batteries are to be a fundamental part of Musk's vision for "sustainable transport".
