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Capacity Expansion Planning under Uncertainty subject to Expected Energy Not Served Constraints

Marilena Zampara, Daniel Ávila, Anthony Papavasiliou

TL;DR

The work develops a scalable solution for stochastic capacity expansion planning with explicit reliability constraints expressed as EENS limits. It introduces a Lagrange-relaxation framework and a subgradient-based decomposition to solve large-scale CEP-EENS problems in parallel, plus a feasibility-recovery step to derive upper bounds. Applied to a pan-European ERAA-like case, the method achieves a 1.3% optimality gap and shows up to 1.6% total-cost savings compared with implicit reliability treatments, while quantifying the costs and investments associated with different EENS limits. The approach also yields zone-specific load-shedding multipliers that offer policy insights for balancing reliability targets and expansion investments in interconnected systems.

Abstract

We present a method for solving a large-scale stochastic capacity expansion problem which explicitly considers reliability constraints, in particular constraints on expected energy not served. Our method tackles this problem by a Lagrange relaxation of the expected energy not served constraints. We solve the relaxed formulation in an iterative manner, using a subgradient-based method. Each iteration requires the solution of a stochastic capacity expansion problem, for which we implement a subgradient decomposition scheme in a high-performance computing infrastructure. We apply the proposed methodology on the Economic Viability Assessment model that is used by ENTSO-E in the annual European Resource Adequacy Assessment, extended to include explicit reliability constraints. The approach is able to solve this model achieving a 1.3% optimality gap. We compare our approach against accounting for reliability through penalizing load shedding at VOLL, and find that the former results in 1.6% savings in total cost. We are also able to quantify the cost savings from allowing some load curtailment in the capacity planning process, which ranges from 1.6 to 6% in the cases analyzed.

Capacity Expansion Planning under Uncertainty subject to Expected Energy Not Served Constraints

TL;DR

The work develops a scalable solution for stochastic capacity expansion planning with explicit reliability constraints expressed as EENS limits. It introduces a Lagrange-relaxation framework and a subgradient-based decomposition to solve large-scale CEP-EENS problems in parallel, plus a feasibility-recovery step to derive upper bounds. Applied to a pan-European ERAA-like case, the method achieves a 1.3% optimality gap and shows up to 1.6% total-cost savings compared with implicit reliability treatments, while quantifying the costs and investments associated with different EENS limits. The approach also yields zone-specific load-shedding multipliers that offer policy insights for balancing reliability targets and expansion investments in interconnected systems.

Abstract

We present a method for solving a large-scale stochastic capacity expansion problem which explicitly considers reliability constraints, in particular constraints on expected energy not served. Our method tackles this problem by a Lagrange relaxation of the expected energy not served constraints. We solve the relaxed formulation in an iterative manner, using a subgradient-based method. Each iteration requires the solution of a stochastic capacity expansion problem, for which we implement a subgradient decomposition scheme in a high-performance computing infrastructure. We apply the proposed methodology on the Economic Viability Assessment model that is used by ENTSO-E in the annual European Resource Adequacy Assessment, extended to include explicit reliability constraints. The approach is able to solve this model achieving a 1.3% optimality gap. We compare our approach against accounting for reliability through penalizing load shedding at VOLL, and find that the former results in 1.6% savings in total cost. We are also able to quantify the cost savings from allowing some load curtailment in the capacity planning process, which ranges from 1.6 to 6% in the cases analyzed.

Paper Structure

This paper contains 23 sections, 21 equations, 3 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. The European Resource Adequacy Assessment
  3. Methodology
  4. Challenges
  5. Stochastic CEP with Reliability Constraints in the Literature
  6. Contribution of the Present Work
  7. Paper Structure
  8. Stochastic CEP Model Formulation
  9. Proposed Solution
  10. Lagrange Relaxation Scheme
  11. Estimating an Upper Bound
  12. Decomposition Scheme for Computing the Lagrange Dual Function
  13. Parallelization Strategy
  14. Case Study
  15. Case Study Description
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Evolution of the main algorithm for the ERAA21 case, starting from an unfavourable initial point and utilizing 1 CPU per task. The optimality gap shown in the dashed line is the best gap obtained so far.
  • Figure 2: Investments results for the case with ERAA21 limits. The case of explicit reliability constraints corresponds to the results of the proposed algorithm, while the implicit case corresponds to results obtained from a single run of the algorithm for a uniform $\lambda$ of 15 000 EUR/MWh for all bidding zones. Final investments and retirements are the ones obtained from the feasibility recovery (feas. rec.) procedure of section \ref{['Estimate UB']}.
  • Figure 3: The shadow price of EENS constraints ($\lambda$) for the ERAA21 case. Blue is used for values below the benchmark of 15 000 EUR/MWh, and red for values above the benchmark.