optimization

[nickolasclarke]

Basic Costs / Inputs:

• Base Bus (w/out batteries):$550k
• Battery Kwh: $100 (current), $50 (future)
• DCFC Charger (opportunistic, probably quite low density)
  • Rate: 500kw
  • Cost: ~$600k NREL, pg 5
• In Depot Charger:
  • Rate: 125kw
  • Cost: ~$50k
  • note: we don't have logic to decide how many chargers are needed per depot
• Bus Efficiency: 1.1 kwh/km

Archived Version

Modeling Objective: Minimize the cost of an EV bus deployment

Optimization

min $\sum^{n}_{i=1}x_i$ subject to $g_i(x)$ and $h_j(x)$

Decision Variables

The decisions the model is making, in order to minimize our costs.

• # of Buses
  • $550,000 w/out batteries (proterra CEO 2019)
• Kwh of battery per bus
  • ~$100 - $150 BNEF
  • could be fun to model with lower prices as well.
• # of chargers
  • this is dependent on the discussion about charging rate. see below.
• # of depots
  • This is also dependent on discussion of charging rate. Also this may simply be a equality constraint

These are all discrete integers, but I think that they could be treated as continous and simply round up to the nearest int value.

Inequality Constraints (a ranged constraint) $g(x)$

note: I think all of these could be set as equality constraints instead, and addressed through scenarios

• min/max of kwh per battery
  • $E_{bat} \ge 0 \le 660$
  • BYD: ~450 kwh
  • Proterra: ~660 kwh
  • could be interesting to raise this for future projected energy densities?
  • alternative min could be the lowest commercially available bus battery size. This would make the cost of a bus vs kwh easier to estimate based off of public data.
• density of chargers across termini
  • $\rho_{term}$
  • this is highly subjective. Right now, we site chargers based on "popularity" of the route at an arbitrary level of >= 100 discrete bus trips through the termini at a time. There are two main options in my mind now:
    • 1. Continue with some subjective level, either absolute (>=100 trips at a termini), or a percentage of total system trips threshold (5%? 10%?)
    • 2. make this the decision variable instead of # of chargers, could likely be unbounded. Would require a spatial optimization as well though. Also would have to be done before running the model? This seems complicated and somewhat convoluted, though perhaps more accurate.
    • Perhaps instead this becomes an equality constraint at a fixed level and we include different levels in the various scenarios described further below.

Equality Constraints (fixed constraint) $h(x)$

• charging rate @ termini chargers
  • possible range: $P_{term} \ge ~100 \le ~240$
  • Further discussion needed. We could make the argument for having low density but high power capacity chargers, while depots have slower chargers. (this probably matches closer to how fleets would actually be operated, I think)
• charging rate @ depot
  • possible range: $P_{dep} \ge 100 \le 500$
  • Proterra bus ranges
  • Proterra charger ranges
• must serve all trips
• all trips must be served at the exact time
• Bus energy >=0 (is this needed?)
• $E_{bus}$
• drivetrain efficiency (see proterra specs sheets)
  • $\eta_{dt} \ge 1.5 \le 2.3$
  • We could simply fix this with no high/med/low. Probably most prudent.

Scenario runs

For each feed, the model should be run with a minimum of high/medium/low values for the relevant equality constraints. This would result in a combinations table of all possible scenarios. We can add more nuance to this 3

cite

[r-barnes]

The kWh range on these is pretty big! Do you know why?

[r-barnes]

Do you know what "Power" means in the context of the buses?

[nickolasclarke]

@r-barnes Re kwh: I think its simply different bus models and perhaps more importantly the year of development. I think some of those listed are pretty old, mostly novelty models. BYD and Proterra have a significant portion of the market I believe, so they should serve as a good baseline for what would be expected in the field.

Re Power: I believe on that graphic it is the rate of charge it can accept. It seems unlikely from the context that it is the motor output. Forgot to cite that image, I'll see if I can track it down.

[nickolasclarke]

@r-barnes sorry, I forgot gh doesnt render latex in markdown.

[r-barnes]

I think it would be reasonable to transform the bus data into a YAML file, which we can later parse with YAML.jl.

[r-barnes]

Maybe CSV is better: the table format makes things easier to read and manipulate.