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Robust Economic Dispatch with Flexible Demand and Adjustable Uncertainty Set

Tian Liu, Su Wang, Danny H. K. Tsang

TL;DR

The paper tackles robust economic dispatch under wind uncertainty by co-optimizing an adjustable wind uncertainty set with multi-dimensional demand flexibility (MDF). It reformulates the CVaR-based losses for wind curtailment and deficiency into a linear program and applies a surrogate affine approximation to handle uncertainty in the constraints, yielding a convex and efficiently solvable formulation. A six-bus case demonstrates that MDF can reduce generation cost while maintaining CVaR-based risk within tunable bounds, with the wind uncertainty region expanding as risk priorities shift. This framework provides a scalable approach to integrating demand-side flexibility and probabilistic risk management into high-renewables dispatch.

Abstract

With more renewable energy sources (RES) integrated into the power system, the intermittency of RES places a heavy burden on the system. The uncertainty of RES is traditionally handled by controllable generators to balance the real time wind power deviation. As the demand side management develops, the flexibility of aggregate loads can be leveraged to mitigate the negative impact of the wind power. In view of this, we study the problem of how to exploit the multi-dimensional flexibility of elastic loads to balance the trade-off between a low generation cost and a low system risk related to the wind curtailment and the power deficiency. These risks are captured by the conditional value-at-risk. Also, unlike most of the existing studies, the uncertainty set of the wind power output in our model is not fixed. By contrast, it is undetermined and co-optimized based on the available load flexibility. We transform the original optimization problem into a convex one using surrogate affine approximation such that it can be solved efficiently. In case studies, we apply our model on a six-bus transmission network and demonstrate that how flexible load aggregators can help to determine the optimal admissible region for the wind power deviations.

Robust Economic Dispatch with Flexible Demand and Adjustable Uncertainty Set

TL;DR

The paper tackles robust economic dispatch under wind uncertainty by co-optimizing an adjustable wind uncertainty set with multi-dimensional demand flexibility (MDF). It reformulates the CVaR-based losses for wind curtailment and deficiency into a linear program and applies a surrogate affine approximation to handle uncertainty in the constraints, yielding a convex and efficiently solvable formulation. A six-bus case demonstrates that MDF can reduce generation cost while maintaining CVaR-based risk within tunable bounds, with the wind uncertainty region expanding as risk priorities shift. This framework provides a scalable approach to integrating demand-side flexibility and probabilistic risk management into high-renewables dispatch.

Abstract

With more renewable energy sources (RES) integrated into the power system, the intermittency of RES places a heavy burden on the system. The uncertainty of RES is traditionally handled by controllable generators to balance the real time wind power deviation. As the demand side management develops, the flexibility of aggregate loads can be leveraged to mitigate the negative impact of the wind power. In view of this, we study the problem of how to exploit the multi-dimensional flexibility of elastic loads to balance the trade-off between a low generation cost and a low system risk related to the wind curtailment and the power deficiency. These risks are captured by the conditional value-at-risk. Also, unlike most of the existing studies, the uncertainty set of the wind power output in our model is not fixed. By contrast, it is undetermined and co-optimized based on the available load flexibility. We transform the original optimization problem into a convex one using surrogate affine approximation such that it can be solved efficiently. In case studies, we apply our model on a six-bus transmission network and demonstrate that how flexible load aggregators can help to determine the optimal admissible region for the wind power deviations.
Paper Structure (12 sections, 30 equations, 6 figures, 4 tables)

This paper contains 12 sections, 30 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. System Modeling
  3. Controllable Generator and Fixed Load Model
  4. Load Aggregators with MDF
  5. Wind Power With Uncertainty
  6. Conditional Value-at-Risk
  7. Problem Formulation
  8. Multi-Period Economic Dispatch under Wind Uncertainty
  9. Transformation of CVaR
  10. Surrogate Affine Approximation
  11. Case Studies
  12. Conclusions

Figures (6)

  • Figure 1: Six-bus transmission network.
  • Figure 2: Fixed load, wind power output forecast and wind samples.
  • Figure 3: Flexibility region of load aggregators with MDF.
  • Figure 4: Hourly power consumption of flexible load aggregator at set-points.
  • Figure 5: Cumulative power consumption of flexible load aggregators at set points.
  • ...and 1 more figures