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Distributionally Robust Frequency-Constrained Microgrid Scheduling Towards Seamless Islanding

Lun Yang, Haoxiang Yang, Xiaoyu Cao, Xiaohong Guan

TL;DR

This paper tackles frequency security in microgrids during unscheduled islanding by introducing a distributionally robust frequency-constrained microgrid scheduling (DR-FCMS) framework. It jointly optimizes unit commitments, dispatch, PFR reserves, virtual inertia from RESs, RES deloading ratios, and BESS operations under RES forecast uncertainty modeled with a Wasserstein ambiguity set, and enforces frequency constraints as distributionally robust quadratic/chance constraints that are reformulated into tractable SOC programs. The key contributions include (i) a comprehensive affinely adaptive uncertainty framework, (ii) tight conic reformulations of DR linear and quadratic chance constraints, (iii) a tight rotated-conic relaxation for nadir constraints, and (iv) extensive case studies showing that co-optimizing power exchange, PFR reserves, and frequency constraints yields secure, cost-efficient operation with favorable EVP trade-offs compared to Gaussian or moment-based DRCC methods. The work demonstrates that EW-DRCC and optimized deloading ratios can substantially improve robustness and economic performance, enabling seamless islanding with realistic RES contributions in microgrids.

Abstract

Unscheduled islanding events of microgrids result in the transition between grid-connected and islanded modes and induce a sudden and unknown power imbalance, posing a threat to frequency security. To achieve seamless islanding, we propose a distributionally robust frequency-constrained microgrid scheduling model considering unscheduled islanding events. This model co-optimizes unit commitments, power dispatch, upward/downward primary frequency response reserves, virtual inertia provisions from renewable energy sources (RESs), deloading ratios of RESs, and battery operations, while ensuring the system frequency security during unscheduled islanding. We establish an affine relationship between the actual power exchange and RES uncertainty in grid-connected mode, describe RES uncertainty with a Wasserstein-metric ambiguity set, and formulate frequency constraints under uncertain post-islanding power imbalance as distributionally robust quadratic chance constraints, which are further transformed by a tight conic relaxation. We solve the proposed mixed-integer convex program and demonstrate its effectiveness through case studies.

Distributionally Robust Frequency-Constrained Microgrid Scheduling Towards Seamless Islanding

TL;DR

This paper tackles frequency security in microgrids during unscheduled islanding by introducing a distributionally robust frequency-constrained microgrid scheduling (DR-FCMS) framework. It jointly optimizes unit commitments, dispatch, PFR reserves, virtual inertia from RESs, RES deloading ratios, and BESS operations under RES forecast uncertainty modeled with a Wasserstein ambiguity set, and enforces frequency constraints as distributionally robust quadratic/chance constraints that are reformulated into tractable SOC programs. The key contributions include (i) a comprehensive affinely adaptive uncertainty framework, (ii) tight conic reformulations of DR linear and quadratic chance constraints, (iii) a tight rotated-conic relaxation for nadir constraints, and (iv) extensive case studies showing that co-optimizing power exchange, PFR reserves, and frequency constraints yields secure, cost-efficient operation with favorable EVP trade-offs compared to Gaussian or moment-based DRCC methods. The work demonstrates that EW-DRCC and optimized deloading ratios can substantially improve robustness and economic performance, enabling seamless islanding with realistic RES contributions in microgrids.

Abstract

Unscheduled islanding events of microgrids result in the transition between grid-connected and islanded modes and induce a sudden and unknown power imbalance, posing a threat to frequency security. To achieve seamless islanding, we propose a distributionally robust frequency-constrained microgrid scheduling model considering unscheduled islanding events. This model co-optimizes unit commitments, power dispatch, upward/downward primary frequency response reserves, virtual inertia provisions from renewable energy sources (RESs), deloading ratios of RESs, and battery operations, while ensuring the system frequency security during unscheduled islanding. We establish an affine relationship between the actual power exchange and RES uncertainty in grid-connected mode, describe RES uncertainty with a Wasserstein-metric ambiguity set, and formulate frequency constraints under uncertain post-islanding power imbalance as distributionally robust quadratic chance constraints, which are further transformed by a tight conic relaxation. We solve the proposed mixed-integer convex program and demonstrate its effectiveness through case studies.
Paper Structure (39 sections, 3 theorems, 40 equations, 7 figures, 4 tables)

This paper contains 39 sections, 3 theorems, 40 equations, 7 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Formulation of Frequency Constraints
  3. Constraints on RoCoF
  4. Constraints on Maximum Frequency Deviation
  5. Constraints on Quasi-Steady State
  6. DR-FCMS Formulation
  7. Network Representation
  8. Modeling of System Responses under Uncertainty
  9. RES Uncertainty
  10. DGs
  11. BESSs
  12. Power Exchanges
  13. Line Power Flows
  14. Voltage Magnitudes
  15. Objective Function
  16. ...and 24 more sections

Key Result

Proposition 1

$\sup_{\mathbb{P}\in \mathcal{P}_t}\mathbb{E}_\mathbb{P}\left [c(x_t)^{\text{T}}\xi_t\right]$ with the ambiguity set in (Wassambiguityset) and an elliptical reference distribution $\hat{\mathbb{P}}=\mathbb{P}_{(\mu_t,\Sigma_t,g)}$ is equivalent to: where $\hat{\mathbb{P}}=\mathbb{P}_{(\mu_t,\Sigma_t,g)}$ and $||c(x_t)||_{\Sigma_t^{-1}}$ is the Mahalanobis norm associated with inverse matrix $\Sig

Figures (7)

  • Figure 1: Microgrid frequency excursion after an unscheduled islanding event: (a) frequency falls when $p_t^{imb}>0$ or (b) frequency rises when $p_t^{imb}<0$.
  • Figure 2: Profiles of RES active power forecast values and total load: RESs (left plot) and total load (right plot).
  • Figure 3: Results of power exchange realizations and total PFR reserve: M1 (top), M2 (middle), and M3 (bottom).
  • Figure 4: The distributions of post-islanding RoCoF (top) and MFD (bottom) in M1 under 100 post-islanding realizations.
  • Figure 5: The distributions of post-islanding RoCoF (top) and MFD (bottom) in M2 under 100 post-islanding realizations.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • proof