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Chance Constrained Economic Dispatch Considering the Capability of Network Flexibility Against Renewable Uncertainties

Yue Song, Tao Liu, David J. Hill

TL;DR

This work extends chance-constrained economic dispatch (CCED) by incorporating continuous network flexibility through adjustable line susceptances. It reveals, under Gaussian uncertainty, that renewable variability reduces usable line capacities while network flexibility can re-route base-case flows to mitigate congestion, enabling cost savings. The authors develop an efficient two-part solver: a master SOCP for generation dispatch with fixed susceptances and a linear subproblem for susceptance adjustments derived from dual sensitivities, implemented via an alternating iteration; they further extend the framework to non-Gaussian uncertainty using Gaussian mixture models (GMM) with Iterative Risk Allocation (IRA). Case studies on IEEE 14-bus and 118-bus systems show significant generation-cost reductions and improved security under uncertainty, with continuous flexibility outperforming discrete alternatives. The approach provides a practical, principled way to exploit transmission flexibility to enhance economic efficiency in high-renewable grids.

Abstract

This paper incorporates a continuous-type network flexibility into chance constrained economic dispatch (CCED). In the proposed model, both power generations and line susceptances are continuous variables to minimize the expected generation cost and guarantee a low probability of constraint violation in terms of generations and line flows under renewable uncertainties. From the analytical form of CCED, we figure out the mechanism of network flexibility against uncertainties -- while renewable uncertainties shrink the usable line capacities and aggravate transmission congestion, network flexibility mitigates congestion by re-routing the base-case line flows and reducing the line capacity shrinkage caused by uncertainties. Further, we propose an alternate iteration solver for this problem. By duality theory, we set up a master problem in the form of second-order cone programming to optimize generation dispatch scheme and a subproblem in the form of linear programming to optimize line susceptances. A satisfactory solution can be obtained efficiently by alternately solving these two problems. The proposed method applies to both Gaussian uncertainty and non-Gaussian uncertainty by means of Gaussian mixture model. The case studies on the IEEE 14-bus system and IEEE 118-bus system suggest that network flexibility can significantly improve operational economy while ensuring security under uncertainties.

Chance Constrained Economic Dispatch Considering the Capability of Network Flexibility Against Renewable Uncertainties

TL;DR

This work extends chance-constrained economic dispatch (CCED) by incorporating continuous network flexibility through adjustable line susceptances. It reveals, under Gaussian uncertainty, that renewable variability reduces usable line capacities while network flexibility can re-route base-case flows to mitigate congestion, enabling cost savings. The authors develop an efficient two-part solver: a master SOCP for generation dispatch with fixed susceptances and a linear subproblem for susceptance adjustments derived from dual sensitivities, implemented via an alternating iteration; they further extend the framework to non-Gaussian uncertainty using Gaussian mixture models (GMM) with Iterative Risk Allocation (IRA). Case studies on IEEE 14-bus and 118-bus systems show significant generation-cost reductions and improved security under uncertainty, with continuous flexibility outperforming discrete alternatives. The approach provides a practical, principled way to exploit transmission flexibility to enhance economic efficiency in high-renewable grids.

Abstract

This paper incorporates a continuous-type network flexibility into chance constrained economic dispatch (CCED). In the proposed model, both power generations and line susceptances are continuous variables to minimize the expected generation cost and guarantee a low probability of constraint violation in terms of generations and line flows under renewable uncertainties. From the analytical form of CCED, we figure out the mechanism of network flexibility against uncertainties -- while renewable uncertainties shrink the usable line capacities and aggravate transmission congestion, network flexibility mitigates congestion by re-routing the base-case line flows and reducing the line capacity shrinkage caused by uncertainties. Further, we propose an alternate iteration solver for this problem. By duality theory, we set up a master problem in the form of second-order cone programming to optimize generation dispatch scheme and a subproblem in the form of linear programming to optimize line susceptances. A satisfactory solution can be obtained efficiently by alternately solving these two problems. The proposed method applies to both Gaussian uncertainty and non-Gaussian uncertainty by means of Gaussian mixture model. The case studies on the IEEE 14-bus system and IEEE 118-bus system suggest that network flexibility can significantly improve operational economy while ensuring security under uncertainties.

Paper Structure

This paper contains 20 sections, 31 equations, 8 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Formulating CCED with network flexibility
  3. The original problem formulation
  4. Analytical form of CCED
  5. Role of decision variables in transmission congestion
  6. Solution methodology
  7. Master problem to optimize generation dispatch
  8. Subproblem to optimize line susceptances
  9. Alternate iteration algorithm
  10. Extension to non-Gaussian uncertainty
  11. Case study
  12. IEEE 14-bus system: congestion fully eliminated after optimization
  13. IEEE 118-bus system: congestion mitigated after optimization
  14. Further discussion on CCED parameters
  15. Degree of network flexibility
  16. ...and 5 more sections

Figures (8)

  • Figure 1: A possible realization of flexible line susceptance via transformers.
  • Figure 2: The algorithm flow chart.
  • Figure 3: Diagram of the IEEE 14-bus system with renewables and flexible susceptance lines.
  • Figure 4: IEEE 14-bus system: Generation costs and dual variables of flow constraints during the iteration.
  • Figure 5: IEEE 118-bus system: Generation costs and dual variables of flow constraints during the iteration.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4