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High-Resolution PTDF-Based Planning of Storage and Transmission Under High Renewables

Kevin Wu, Rabab Haider, Pascal Van Hentenryck

TL;DR

This work tackles Transmission Expansion Planning (TEP) in high-renewables settings with large-scale distributed storage. It develops a multiperiod, two-stage PTDF-based DCOPF that co-optimizes transmission upgrades and storage siting/sizing, and introduces a trust-region, multicut Benders scheme warm-started from per-representative-day optima to tackle scale and degeneracy. Applied to a 2,000-bus synthetic Texas system under high-renewables projections, the approach achieves final optimality gaps of at most $\leq 1\%$, deploying storage at roughly 179–180 nodes, amounting to about $32\%$ of peak renewable capacity. The results demonstrate scalable, high-fidelity planning that supports large distributed storage fleets and robust congestion relief in high-renewables grids, with practical implications for long-horizon infrastructure investment decisions.

Abstract

Transmission Expansion Planning (TEP) optimizes power grid upgrades and investments to ensure reliable, efficient, and cost-effective electricity delivery while addressing grid constraints. To support growing demand and renewable energy integration, energy storage is emerging as a pivotal asset that provides temporal flexibility and alleviates congestion. This paper develops a multiperiod, two-stage PTDF formulation that co-optimizes transmission upgrades and storage siting/sizing. To ensure scalability, a trust-region, multicut Benders scheme warm-started from per-representative-day optima is proposed. Applied to a 2,000-bus synthetic Texas system under high-renewable projections, the method attains final optimality gaps below 1% and yields a plan with storage at about 180 nodes (32% of peak renewable capacity). These results demonstrate that the proposed PTDF-based methodology efficiently handles large distributed storage fleets, demonstrating scalability at high spatial resolution

High-Resolution PTDF-Based Planning of Storage and Transmission Under High Renewables

TL;DR

This work tackles Transmission Expansion Planning (TEP) in high-renewables settings with large-scale distributed storage. It develops a multiperiod, two-stage PTDF-based DCOPF that co-optimizes transmission upgrades and storage siting/sizing, and introduces a trust-region, multicut Benders scheme warm-started from per-representative-day optima to tackle scale and degeneracy. Applied to a 2,000-bus synthetic Texas system under high-renewables projections, the approach achieves final optimality gaps of at most , deploying storage at roughly 179–180 nodes, amounting to about of peak renewable capacity. The results demonstrate scalable, high-fidelity planning that supports large distributed storage fleets and robust congestion relief in high-renewables grids, with practical implications for long-horizon infrastructure investment decisions.

Abstract

Transmission Expansion Planning (TEP) optimizes power grid upgrades and investments to ensure reliable, efficient, and cost-effective electricity delivery while addressing grid constraints. To support growing demand and renewable energy integration, energy storage is emerging as a pivotal asset that provides temporal flexibility and alleviates congestion. This paper develops a multiperiod, two-stage PTDF formulation that co-optimizes transmission upgrades and storage siting/sizing. To ensure scalability, a trust-region, multicut Benders scheme warm-started from per-representative-day optima is proposed. Applied to a 2,000-bus synthetic Texas system under high-renewable projections, the method attains final optimality gaps below 1% and yields a plan with storage at about 180 nodes (32% of peak renewable capacity). These results demonstrate that the proposed PTDF-based methodology efficiently handles large distributed storage fleets, demonstrating scalability at high spatial resolution
Paper Structure (35 sections, 2 theorems, 20 equations, 7 figures, 4 tables)

This paper contains 35 sections, 2 theorems, 20 equations, 7 figures, 4 tables.

Table of Contents

  1. Sets
  2. Parameters
  3. Variables
  4. Introduction
  5. Related Work
  6. Contributions
  7. Formulation
  8. The Two-Stage TEP+Storage PTDF Formulation
  9. Investment decisions and variables
  10. Objective
  11. Constraints
  12. Scalable PTDF Reformulation
  13. Methodology
  14. Multicut Benders for TEP+Storage
  15. Benders MP
  16. ...and 20 more sections

Key Result

Theorem 1

For each $s\in\mathcal{S}$, define the day-$s$ feasible set and the all-scenarios feasible set: Given the feasible sets, define the corresponding minimum first stage costs for feasible day-s and all-scenarios: and first-stage optimal investments for scenario $s$: Let $\hat{s} \in \arg\max_{s\in\mathcal{S}} c^{\mathrm{feas}}_s$. Then In particular, $f(\gamma^{\hat{s}}_{\mathrm{feas}},\sigma^{\h

Figures (7)

  • Figure 1: Benders Schematic Flow Diagram.
  • Figure 2: Workflow of the proposed methodology.
  • Figure 3: Generator sites of the system. Black circles indicate nonrenewable, blue circles indicate wind, and red circles indicate solar generators.
  • Figure 4: Representative days by average demand vs. wind in 2022. Red circles indicate selected representative days. Transparent blue circles indicate non-selected days.
  • Figure 5: WS computation times by representative day for each 5-year investment period.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof