Scalable and Interactive Electricity Grid Expansion Planning

Abstract

Large scale grid expansion planning studies are essential to rapidly and efficiently decarbonizing the electricity sector. These studies help policy makers and grid participants understand which renewable generation, storage, and transmission assets should be built and where they will be most cost effective or have the highest emissions impact. However, these studies are often either too computationally expensive to run repeatedly or too coarsely modeled to give actionable decision information. In this study, we present an implicit gradient descent algorithm to solve expansion planning studies at scale, i.e., problems with many scenarios and large network models. Our algorithm is also interactive: given a base plan, planners can modify assumptions and data then quickly receive an updated plan. This allows the planner to study expansion outcomes for a wide variety of technology cost, weather, and electrification assumptions. We demonstrate the scalability of our tool, solving a case with over a hundred million variables. Then, we show that using warm starts can speed up subsequent runs by as much as 100x. We highlight how this can be used to quickly conduct storage cost uncertainty analysis.

Figures (4)

• Figure 1: Workflow for interactive planning studies. The planner first establishes an initial plan on a large scale, high-fidelity grid model. Based on initial results, the planner interactively updates assumptions (e.g., an emissions target or the cost of transmission upgrades) and quickly receives a new plan, iteratively repeating this process.
• Figure 2: Objective values (evaluated on 360 days of data) for stochastic gradient descent solved on 16 days of data (blue curve) and 360 days of data (orange curve). Both runs use a batch size $B=8$, take the same time to complete, and are evaluated on the full 360 days. Sampling from the full dataset leads to 11.3% reduction in objective value.
• Figure 3: Warm starts significantly speedup solve times for large planning problems. (Top) Convergence plots for 500 iterations of stochastic gradient descent applied to a emissions-aware planning problem with a $150.0 / ton CO$_2$ carbon weight. Blue curve: loss when initialized from "no-expansion", which converges in 235 iterations. Orange curve: loss when warm started from the solution to a similar problem with carbon weight $200.0 / ton CO$_2$, which converges in just 21 iterations. (Bottom) Speedup achieved by warm starting as a function of the size of the perturbation to the carbon weight. For small perturbations, warm starting leads to upwards of a 100x speedup.
• Figure 4: Warm starting enables rapid exploration of potential expansions under different battery cost assumptions. (Blue bars) Initial capacity of each asset before expansion. (Orange, green, and red bars) Expanded capacity of each asset battery capital costs are 50%, 100%, and 200%, respectively, of NREL ATB National-Renewable-Energy-Laboratory2022-ma forecasts. Optimal investment in transmission and generation capacity are stable across different battery cost assumptions; optimal investment in battery storage depends on assumed technology costs.