Distributed Energy Resources - Lectures 11-12: Modelling Summary & Optimization Overview

Other notes in this series from Kevin Kircher’s Distributed Energy Resources class are here.

Modelling Summary

Unsurprisingly, not much new in this review of previous modelling lectures. The one thing that jumped out was the combined flexible/deferrable loads represented by refrigerator/freezers and dishwashers. In the US, the first represents up to ~100GW (so about ~8% of US generation capacity) of flexible load thanks to their thermal capacity. The second is ~120GW of mostly deferrable load or ~10% of generation capacity. Those numbers are huge.

Optimization Overview

tl;dr - we want to reformulate optimisation problems as convex problems wherever possible because they are usually tractable, have polynomial (not exponential) runtime, and well supported by software solvers.

Notes

• Other DERs:
  • refrigerators and freezers
    • ∼200 million refrigerators and freezers in the US
      • all have some thermal mass and temperature flexibility
      • ∼500 W each, that’s ∼100 GW of flexible capacity (for comparison, total US generation capacity is ∼1.3 TW)
      • can model them as thermal circuits, just like buildings
  • Deferrable loads
    • some appliances just need to run before a deadline - eg: dishwasher
    • there are ∼80 million dishwashers in the US
    • at ∼1.5 kW each, that’s ∼120 GW of flexible capacity
    • clothes washers and dryers may have similar flexibility
• Optimisation
  • Most optimisation problems are intractable, but convex problems are (usually) tractable
    • for convex problems, all local optimizers are global optimizers
    • no analytical solution, but good algorithms
    • solve time is ∼proportional to max $\{n^3,n^{2}m\}$
    • includes least squares, linear programming, and much more
  • Example: choose solar array size (# of panels or rated power) and orientation
    • possible objectives:
      • initial cost (hardware, permitting, installation, … )
      • electricity revenues or cost savings
      • greenhouse gas emission reductions
    • possible constraints:
      • budget
      • usable rooftop or ground area
      • panel power output equations
  • Example: choose charging powers at each time over a planning horizon
    • possible objectives:
      • electricity costs
      • greenhouse gas emissions
      • peak electricity demand
    • possible constraints:
      • battery energy and power capacities
      • battery dynamics
      • charging deadline