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Optimal Virtual Power Plant Investment Planning via Time Series Aggregation with Bounded Error

Luca Santosuosso, Sonja Wogrin

TL;DR

The paper addresses VPP investment planning by formulating it as a MILP and applying time series aggregation (TSA) to reduce temporal resolution while enforcing bounded error on the objective. It develops an iterative TSA framework that yields a provable lower bound from the aggregated problem and a corresponding feasible upper-bound refinement of the full-scale problem, with bounds shown to hold at every iteration. The main theoretical contribution is a formal proof that the aggregated objective matches the full-scale objective for corresponding solutions ($J(z) = \hat{J}(\hat{z})$), ensuring $\hat{J}^\star \le J^\star$ and guaranteeing feasibility throughout. Numerical experiments demonstrate substantial computational savings over solving the full-scale MILP, with performance dependent on the clustering technique but robust bounds, making the approach scalable for large VPP investment problems.

Abstract

This study addresses the investment planning problem of a virtual power plant (VPP), formulated as a mixed-integer linear programming (MILP) model. As the number of binary variables increases and the investment time horizon extends, the problem can become computationally intractable. To mitigate this issue, time series aggregation (TSA) methods are commonly employed. However, since TSA typically results in a loss of accuracy, it is standard practice to derive bounds to control the associated error. Existing methods validate these bounds only in the linear case, and when applied to MILP models, they often yield heuristics that may even produce infeasible solutions. To bridge this gap, we propose an iterative TSA method for solving the VPP investment planning problem formulated as a MILP model, while ensuring a bounded error in the objective function. Our main theoretical contribution is to formally demonstrate that the derived bounds remain valid at each iteration. Notably, the proposed method consistently guarantees feasible solutions throughout the iterative process. Numerical results show that the proposed TSA method achieves superior computational efficiency compared to standard full-scale optimization.

Optimal Virtual Power Plant Investment Planning via Time Series Aggregation with Bounded Error

TL;DR

The paper addresses VPP investment planning by formulating it as a MILP and applying time series aggregation (TSA) to reduce temporal resolution while enforcing bounded error on the objective. It develops an iterative TSA framework that yields a provable lower bound from the aggregated problem and a corresponding feasible upper-bound refinement of the full-scale problem, with bounds shown to hold at every iteration. The main theoretical contribution is a formal proof that the aggregated objective matches the full-scale objective for corresponding solutions (), ensuring and guaranteeing feasibility throughout. Numerical experiments demonstrate substantial computational savings over solving the full-scale MILP, with performance dependent on the clustering technique but robust bounds, making the approach scalable for large VPP investment problems.

Abstract

This study addresses the investment planning problem of a virtual power plant (VPP), formulated as a mixed-integer linear programming (MILP) model. As the number of binary variables increases and the investment time horizon extends, the problem can become computationally intractable. To mitigate this issue, time series aggregation (TSA) methods are commonly employed. However, since TSA typically results in a loss of accuracy, it is standard practice to derive bounds to control the associated error. Existing methods validate these bounds only in the linear case, and when applied to MILP models, they often yield heuristics that may even produce infeasible solutions. To bridge this gap, we propose an iterative TSA method for solving the VPP investment planning problem formulated as a MILP model, while ensuring a bounded error in the objective function. Our main theoretical contribution is to formally demonstrate that the derived bounds remain valid at each iteration. Notably, the proposed method consistently guarantees feasible solutions throughout the iterative process. Numerical results show that the proposed TSA method achieves superior computational efficiency compared to standard full-scale optimization.
Paper Structure (12 sections, 1 theorem, 12 equations, 1 figure, 1 table, 1 algorithm)

This paper contains 12 sections, 1 theorem, 12 equations, 1 figure, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem Statement
  4. The Full-Scale Optimization Model
  5. The Aggregated Optimization Model
  6. Main Theoretical Result
  7. A Time Series Aggregation Method with Bounded Error
  8. Numerical Results
  9. Performance Evaluation of the Proposed Time Series Aggregation Method with Various Clustering Techniques
  10. Comparison with Standard Full-Scale Optimization
  11. Conclusion and Future Work
  12. Acknowledgment

Key Result

Proposition 1

Let $\boldsymbol{z}$ be a feasible solution to the full-scale model full_scale_investment_model. Let $\boldsymbol{\hat{z}}$ be derived from $\boldsymbol{z}$ accordingly to full_aggregated_variables_relationship1--full_aggregated_variables_relationship4. Then, $\boldsymbol{\hat{z}}$ is a feasible sol

Figures (1)

  • Figure 1: Upper and lower bounds computed for different clustering techniques using the proposed TSA with bounded error in the objective function.

Theorems & Definitions (2)

  • Proposition 1
  • proof