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Non-Iterative Solution for Coordinated Optimal Dispatch via Equivalent Projection-Part I: Theory

Zhenfei Tan, Zheng Yan, Haiwang Zhong, Qing Xia

TL;DR

This work tackles coordinated optimal dispatch in hierarchically structured power systems by overcoming the drawbacks of iterative coordination, such as slow convergence and information exchange. It introduces Equivalent Projection (EP), a theory that externalizes a subsystem's optimization model through a polyhedral projection of its feasible region onto coordination variables, with costs embedded via epigraph reformulation. The EP framework enables a non-iterative, privacy-preserving coordination scheme that preserves optimality relative to the joint optimization and scales to multi-level systems. The approach shifts computational burden to lower-level subsystems and requires only a single round of information exchange, promising practical benefits for real-world dispatch and planning. Part II will detail the projection algorithm and demonstrate broader applications.

Abstract

Coordinated optimal dispatch is of utmost importance for the efficient and secure operation of hierarchically structured power systems. Conventional coordinated optimization methods, such as the Lagrangian relaxation and Benders decomposition, require iterative information exchange among subsystems. Iterative coordination methods have drawbacks including slow convergence, risk of oscillation and divergence, and incapability of multi-level optimization problems. To this end, this paper aims at the non-iterative coordinated optimization method for hierarchical power systems. The theory of the equivalent projection (EP) is proposed, which makes external equivalence of the optimal dispatch model of the subsystem. Based on the EP theory, a coordinated optimization framework is developed, where each subsystem submits the EP model as a substitute for its original model to participate in the cross-system coordination. The proposed coordination framework is proven to guarantee the same optimality as the joint optimization, with additional benefits of avoiding iterative information exchange, protecting privacy, compatibility with practical dispatch scheme, and capability of multi-level problems.

Non-Iterative Solution for Coordinated Optimal Dispatch via Equivalent Projection-Part I: Theory

TL;DR

This work tackles coordinated optimal dispatch in hierarchically structured power systems by overcoming the drawbacks of iterative coordination, such as slow convergence and information exchange. It introduces Equivalent Projection (EP), a theory that externalizes a subsystem's optimization model through a polyhedral projection of its feasible region onto coordination variables, with costs embedded via epigraph reformulation. The EP framework enables a non-iterative, privacy-preserving coordination scheme that preserves optimality relative to the joint optimization and scales to multi-level systems. The approach shifts computational burden to lower-level subsystems and requires only a single round of information exchange, promising practical benefits for real-world dispatch and planning. Part II will detail the projection algorithm and demonstrate broader applications.

Abstract

Coordinated optimal dispatch is of utmost importance for the efficient and secure operation of hierarchically structured power systems. Conventional coordinated optimization methods, such as the Lagrangian relaxation and Benders decomposition, require iterative information exchange among subsystems. Iterative coordination methods have drawbacks including slow convergence, risk of oscillation and divergence, and incapability of multi-level optimization problems. To this end, this paper aims at the non-iterative coordinated optimization method for hierarchical power systems. The theory of the equivalent projection (EP) is proposed, which makes external equivalence of the optimal dispatch model of the subsystem. Based on the EP theory, a coordinated optimization framework is developed, where each subsystem submits the EP model as a substitute for its original model to participate in the cross-system coordination. The proposed coordination framework is proven to guarantee the same optimality as the joint optimization, with additional benefits of avoiding iterative information exchange, protecting privacy, compatibility with practical dispatch scheme, and capability of multi-level problems.
Paper Structure (26 sections, 3 theorems, 15 equations, 4 figures, 2 tables)

This paper contains 26 sections, 3 theorems, 15 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Literature Review
  4. Coordinated dispatch
  5. System reduction
  6. Contributions and Paper Organization
  7. Problem Formulation
  8. Basic Notation
  9. Joint Optimal Dispatch
  10. Primal Decomposition
  11. Equivalent Projection Theory
  12. Reformulation of Objective Function
  13. Equivalent Projection
  14. Discussions
  15. Privacy protection
  16. ...and 11 more sections

Key Result

Theorem 1

The reformulated JOD model jed2 is equivalent to the original JOD model jed.

Figures (4)

  • Figure 1: System structure of two adjacent levels.
  • Figure 2: Procedure of the EP-based coordinated optimization.
  • Figure 3: Coordination scheme for the multi-level system.
  • Figure 4: Illustrative example results. (a) and (b) are OFRs of lower-level system 1 and system 2. (c) and (d) are EP models of lower-level systems in the coordination space. (e) exhibits the upper-level optimization results.

Theorems & Definitions (8)

  • Theorem 1
  • proof
  • Definition 1: OFR
  • Definition 2: EP
  • Theorem 2
  • proof
  • Theorem 3
  • proof