Decentralized Multi-Area Economic Dispatch via Dynamic Multiplier-Based Lagrangian Relaxation

This paper introduces a dynamic multiplier-based Lagrangian relaxation approach for the solution to multi-area economic dispatch (MAED) in a fully decentralized manner. Dynamic multipliers refer to the multipliers associated with power balance equations at tie-line buses in each area. Dynamic multipliers can be approximated as linear functions of tie-line power exports via sensitivity analysis and can serve as the equivalent supply/demand functions to neighboring areas. In contrast to the conventional static point-wise multiplier, which is unable to reflect the marginal cost change that results from variations in the power exchange level, the proposed dynamic multiplier provides each area the look-ahead capability to foresee the range of the marginal cost for power export over a range of tie-line exchange variations. In turn, this allows for a significantly faster convergence to the global optimal solution. The algorithm is also shown to be early termination friendly, which is very desirable in practice for ultra-large systems such as the State Grid of China. Numerical examples in a 6-bus system, a 3-area 354-bus IEEE system, and large test systems illustrate the benefits of the proposed algorithm.