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Stochastic Virtual Power Plant Dispatch via Temporally Aggregated Distributed Predictive Control with Performance Guarantees

Luca Santosuosso, Fei Teng, Sonja Wogrin

Abstract

This paper addresses the energy dispatch of a virtual power plant comprising renewable generation, energy storage, and thermal units under uncertainty in renewable output, energy prices, and energy demand. The nonlinear dynamics and multiple sources of uncertainty render traditional stochastic model predictive control (MPC) computationally intractable as the dispatch horizon, scenario set, and asset portfolio expand. To overcome this limitation, we propose a novel controller that seamlessly integrates MPC with time series aggregation and distributed optimization, simultaneously reducing the temporal, asset, and scenario dimensions of the problem. The resulting controller provides a rigorous performance guarantee through theoretically validated bounds on its approximation error, while leveraging dual information from previous MPC iterations to adaptively optimize the temporal aggregation. Numerical results show that the proposed controller reduces runtime by over 50% relative to traditional stochastic MPC and, crucially, restores tractability where the full-scale dispatch model proves intractable.

Stochastic Virtual Power Plant Dispatch via Temporally Aggregated Distributed Predictive Control with Performance Guarantees

Abstract

This paper addresses the energy dispatch of a virtual power plant comprising renewable generation, energy storage, and thermal units under uncertainty in renewable output, energy prices, and energy demand. The nonlinear dynamics and multiple sources of uncertainty render traditional stochastic model predictive control (MPC) computationally intractable as the dispatch horizon, scenario set, and asset portfolio expand. To overcome this limitation, we propose a novel controller that seamlessly integrates MPC with time series aggregation and distributed optimization, simultaneously reducing the temporal, asset, and scenario dimensions of the problem. The resulting controller provides a rigorous performance guarantee through theoretically validated bounds on its approximation error, while leveraging dual information from previous MPC iterations to adaptively optimize the temporal aggregation. Numerical results show that the proposed controller reduces runtime by over 50% relative to traditional stochastic MPC and, crucially, restores tractability where the full-scale dispatch model proves intractable.
Paper Structure (16 sections, 1 theorem, 26 equations, 8 figures, 2 tables, 1 algorithm)

This paper contains 16 sections, 1 theorem, 26 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Research Gaps and Contributions
  4. Methodology
  5. Overview of the Proposed Methodology
  6. Modeling
  7. Full-Scale Controller
  8. Temporally Aggregated Controller
  9. Closed-Loop A Posteriori Time Series Aggregation
  10. Temporally Aggregated and Distributed Controller
  11. Derivation of the Objective Function Bounds
  12. Simulation Results and Discussion
  13. Case Study Description
  14. Clustering Based on the Marginal Cost
  15. Performance Evaluation of the Proposed Controller
  16. ...and 1 more sections

Key Result

Proposition 1

Let $\boldsymbol{z}$ be a feasible solution to the full-scale model FS_SMPC. Let $\boldsymbol{\bar{z}}$ be derived from $\boldsymbol{z}$ as $\forall n, \forall g, \forall \omega, \forall r$. Then, $\boldsymbol{\bar{z}}$ is a feasible solution to the temporally aggregated model AGG_SMPC and it holds that $\bar{F}\left(\boldsymbol{\bar{z}}\right) \leq F\left(\boldsymbol{z}\right)$.

Figures (8)

  • Figure 1: Illustration of the proposed methodology for real-time energy dispatch of a VPP under uncertainty.
  • Figure 2: Illustration of the sliding window clustering technique.
  • Figure 3: Boxplots of the hourly uncertainty realization values. The box represents the interquartile range, the blue line indicates the median, and the whiskers extend to the minimum and maximum observations.
  • Figure 4: Clusters obtained using marginal costs as features for TSA in the dispatch of thermal and solar power units under varying emission limits.
  • Figure 5: Clusters obtained using different features (solar power, prices, or marginal costs) for TSA in the dispatch of storage and solar power units.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof