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

## TL;DR

This paper introduces a non-iterative coordinated optimization framework for hierarchical power systems using equivalent projection, ensuring optimality while avoiding iterative communication and enhancing privacy and practicality.

## Contribution

It develops the theory of equivalent projection for subsystem models and constructs a non-iterative coordination framework that guarantees optimality in hierarchical power dispatch.

## Key findings

- Guarantees same optimality as joint optimization.
- Avoids iterative information exchange among subsystems.
- Compatible with practical multi-level dispatch schemes.

## 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.