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Non-Iterative Solution for Coordinated Optimal Dispatch via Equivalent Projection-Part II: Method and Applications

Zhenfei Tan, Zheng Yan, Haiwang Zhong, Qing Xia

Abstract

This two-part paper develops a non-iterative coordinated optimal dispatch framework, i.e., free of iterative information exchange, via the innovation of the equivalent projection (EP) theory. The EP eliminates internal variables from technical and economic operation constraints of the subsystem and obtains an equivalent model with reduced scale, which is the key to the non-iterative coordinated optimization. In Part II of this paper, a novel projection algorithm with the explicit error guarantee measured by the Hausdorff distance is proposed, which characterizes the EP model by the convex hull of its vertices. This algorithm is proven to yield a conservative approximation within the prespecified error tolerance and can obtain the exact EP model if the error tolerance is set to zero, which provides flexibility to balance the computation accuracy and effort. Applications of the EP-based coordinated dispatch are demonstrated based on the multi-area coordination and transmission-distribution coordination. Case studies with a wide range of system scales verify the superiority of the proposed projection algorithm in terms of computational efficiency and scalability, and validate the effectiveness of the EP-based coordinated dispatch in comparison with the joint optimization.

Non-Iterative Solution for Coordinated Optimal Dispatch via Equivalent Projection-Part II: Method and Applications

Abstract

This two-part paper develops a non-iterative coordinated optimal dispatch framework, i.e., free of iterative information exchange, via the innovation of the equivalent projection (EP) theory. The EP eliminates internal variables from technical and economic operation constraints of the subsystem and obtains an equivalent model with reduced scale, which is the key to the non-iterative coordinated optimization. In Part II of this paper, a novel projection algorithm with the explicit error guarantee measured by the Hausdorff distance is proposed, which characterizes the EP model by the convex hull of its vertices. This algorithm is proven to yield a conservative approximation within the prespecified error tolerance and can obtain the exact EP model if the error tolerance is set to zero, which provides flexibility to balance the computation accuracy and effort. Applications of the EP-based coordinated dispatch are demonstrated based on the multi-area coordination and transmission-distribution coordination. Case studies with a wide range of system scales verify the superiority of the proposed projection algorithm in terms of computational efficiency and scalability, and validate the effectiveness of the EP-based coordinated dispatch in comparison with the joint optimization.
Paper Structure (30 sections, 1 theorem, 16 equations, 3 figures, 4 tables, 1 algorithm)

This paper contains 30 sections, 1 theorem, 16 equations, 3 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Literature Review
  3. Contributions and Paper Organization
  4. Calculation Method for EP
  5. Problem Setup
  6. Representations of the EP model
  7. PVE Algorithm
  8. Vertex identification problem
  9. Initialization
  10. Inner loop
  11. Outer loop and termination criterion
  12. Discussions
  13. Properties of the PVE algorithm
  14. Accelerating strategies
  15. Analysis of adaptability
  16. ...and 15 more sections

Key Result

Theorem 1

If error tolerance $\varepsilon>0$, the output of the PVE algorithm is a conservative approximation of the exact projection. If $\varepsilon=0$, the exact projection can be obtained via the PVE algorithm within finite calculations.

Figures (3)

  • Figure 1: Illustrative example of the PVE algorithm. (a) Vertex identification in outer loop 1. (b) Number of new vertices and the error metric of each outer loop.
  • Figure 2: EP models of the IEEE-24 system at (a) valley hour and (b) peak hour.
  • Figure 3: EP models of the IEEE-13 distribution network at (a) valley load and (b) peak load.

Theorems & Definitions (2)

  • Theorem 1
  • proof