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A Distributionally Robust Model Predictive Control for Static and Dynamic Uncertainties in Smart Grids

Qi Li, Ye Shi, Yuning Jiang, Yuanming Shi, Haoyu Wang, H. Vincent Poor

TL;DR

This work addresses the challenge of uncertainties in smart grids by distinguishing static uncertainties that affect current states from dynamic uncertainties that propagate through dynamics. It introduces a two stage Wasserstein based Distributionally Robust MPC (WDR-MPC) that converts the stochastic MPC problem into a nominal one by constructing ambiguity tubes for dynamic uncertainties and applying a convex reformulation of CVaR based bounds for static uncertainties. A scalable acceleration method is developed to keep the computation tractable as the sample size grows, and the approach is validated on IEEE 38-bus and 94-bus networks, showing improvements in reliability and stability. The results indicate that WDR-MPC can robustly manage both RES forecasting errors and random PEV charging patterns, with promising implications for grid reliability and scalability to larger networks.

Abstract

The integration of various power sources, including renewables and electric vehicles, into smart grids is expanding, introducing uncertainties that can result in issues like voltage imbalances, load fluctuations, and power losses. These challenges negatively impact the reliability and stability of online scheduling in smart grids. Existing research often addresses uncertainties affecting current states but overlooks those that impact future states, such as the unpredictable charging patterns of electric vehicles. To distinguish between these, we term them static uncertainties and dynamic uncertainties, respectively. This paper introduces WDR-MPC, a novel approach that stands for two-stage Wasserstein-based Distributionally Robust (WDR) optimization within a Model Predictive Control (MPC) framework, aimed at effectively managing both types of uncertainties in smart grids. The dynamic uncertainties are first reformulated into ambiguity tubes and then the distributionally robust bounds of both dynamic and static uncertainties can be established using WDR optimization. By employing ambiguity tubes and WDR optimization, the stochastic MPC system is converted into a nominal one. Moreover, we develop a convex reformulation method to speed up WDR computation during the two-stage optimization. The distinctive contribution of this paper lies in its holistic approach to both static and dynamic uncertainties in smart grids. Comprehensive experiment results on IEEE 38-bus and 94-bus systems reveal the method's superior performance and the potential to enhance grid stability and reliability.

A Distributionally Robust Model Predictive Control for Static and Dynamic Uncertainties in Smart Grids

TL;DR

This work addresses the challenge of uncertainties in smart grids by distinguishing static uncertainties that affect current states from dynamic uncertainties that propagate through dynamics. It introduces a two stage Wasserstein based Distributionally Robust MPC (WDR-MPC) that converts the stochastic MPC problem into a nominal one by constructing ambiguity tubes for dynamic uncertainties and applying a convex reformulation of CVaR based bounds for static uncertainties. A scalable acceleration method is developed to keep the computation tractable as the sample size grows, and the approach is validated on IEEE 38-bus and 94-bus networks, showing improvements in reliability and stability. The results indicate that WDR-MPC can robustly manage both RES forecasting errors and random PEV charging patterns, with promising implications for grid reliability and scalability to larger networks.

Abstract

The integration of various power sources, including renewables and electric vehicles, into smart grids is expanding, introducing uncertainties that can result in issues like voltage imbalances, load fluctuations, and power losses. These challenges negatively impact the reliability and stability of online scheduling in smart grids. Existing research often addresses uncertainties affecting current states but overlooks those that impact future states, such as the unpredictable charging patterns of electric vehicles. To distinguish between these, we term them static uncertainties and dynamic uncertainties, respectively. This paper introduces WDR-MPC, a novel approach that stands for two-stage Wasserstein-based Distributionally Robust (WDR) optimization within a Model Predictive Control (MPC) framework, aimed at effectively managing both types of uncertainties in smart grids. The dynamic uncertainties are first reformulated into ambiguity tubes and then the distributionally robust bounds of both dynamic and static uncertainties can be established using WDR optimization. By employing ambiguity tubes and WDR optimization, the stochastic MPC system is converted into a nominal one. Moreover, we develop a convex reformulation method to speed up WDR computation during the two-stage optimization. The distinctive contribution of this paper lies in its holistic approach to both static and dynamic uncertainties in smart grids. Comprehensive experiment results on IEEE 38-bus and 94-bus systems reveal the method's superior performance and the potential to enhance grid stability and reliability.
Paper Structure (20 sections, 2 theorems, 48 equations, 7 figures, 4 tables, 1 algorithm)

This paper contains 20 sections, 2 theorems, 48 equations, 7 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Wasserstein Metric
  4. Stochastic Model Predictive Control
  5. Problem formulation
  6. Distribution Networks with Static Uncertainties
  7. Charging Stations with Dynamic Uncertainties
  8. Overall Optimization Formulation
  9. Solution Approach
  10. Static Uncertainty Formulation
  11. Stochastic MPC formulation of dynamic uncertainties
  12. WDR optimization reformulation and acceleration
  13. Summary of WDR-MPC
  14. Numerical results
  15. IEEE 38-bus system
  16. ...and 5 more sections

Key Result

Proposition 1

The risk function $\bm{J}_{risk}^G$ and $\bm{J}_{risk}^V$ for dGuG and dVuV are respectively,

Figures (7)

  • Figure 1: The framework of WDR-MPC in smart grid
  • Figure 2: Comparison of WDR-MPC and accelerated WDR-MPC
  • Figure 3: Reliability comparison of random disturbances in WDR-MPC
  • Figure 4: Comparisons between Static method, Normal MPC, SAA-MPC, and WDR-MPC for dynamic uncertainties
  • Figure 5: The power demands, power generation, and the RES generation of IEEE 38-bus system
  • ...and 2 more figures

Theorems & Definitions (3)

  • Definition 1
  • Proposition 1
  • Proposition 2