SMART-Invest is designed as a streamlined version of SMART-ISO to allow it to find optimal mixes of wind, solar and storage. It models the entire year (in hourly increments), capturing wind, solar storage, as well as fast and slow fossil generation.

Slow and fast fossil generation is planned (at an aggregate level) using a rolling 36-hour horizon (optimized every hour). Slow generation is fixed 24 hours in advance; fast fossil generation is fixed 1 hour in advance. Slow and fast generation may be tuned (within ramp rates) in real time, responding to actual wind and solar. Storage is used as needed.

The model optimizes across the mix of investments using a descent vector computed using numerical derivatives. Each evaluation of the objective function involves optimizing over all 8,760 hours (52 weeks are run in parallel to improve speed).

Major features of the model include:

o Careful modeling of the variability and uncertainty of renewables over the entire year, at the one-hour level.

o We assume that fast and slow fossil generation will be part of any energy portfolio involving wind, solar and storage, which means that we have to handle the need to make advance commitments (we commit to slow fossil 24 hours in advance, while fast fossil is committed 1 hour in advance).

o Modeling of the full energy stack, but not the grid, and not individual generators.

o Investment decisions take into consideration the marginal value of investments in wind, solar and storage.

o SMART-Invest is sensitive to the cost of fossils, as well as carbon taxes and SREC prices.

The graphic below illustrates the logic.

A complete summary of the model along with a series of simulations is given in the following working paper (under review). We have run a series of illustrative policy studies, but we do not intend this as a policy paper, since the results are quite sensitive to assumptions about costs. We do offer this paper as an illustration of proper modeling of the variability and uncertainty of wind and solar, acknowledging the many simplifications required for this type of policy study.

J. Khazaei, W. B. Powell, “SMART-Invest -A stochastic, dynamic planning for optimizing investments in wind, solar, and storage in the presence of fossil fuels: The Case of the PJM Electricity Market,” Working paper, Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08540, April, 2015.