# Economic power dispatch in smart grids: a framework for distributed optimization and consensus dynamics

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## Abstract

By using the distributed consensus theory in multi-agent systems, the strategy of economic power dispatch is studied in a smart grid, where many generation units work cooperatively to achieve an optimal solution in a local area. The relationship between the distributed optimization solution and consensus in multi-agent systems is first revealed in this paper, which can serve as a general framework for future studies of this topic. First, without the constraints of capacity limitations, it is found that the total cost for all the generators in a smart grid can achieve the minimal value if the consensus can be reached for the incremental cost of all the generation units and the balance between the supply and demand of powers is kept. Then, by designing a distributed consensus control protocol in multi-agent systems with appropriate initial conditions, incremental cost consensus can be realized and the balance for the powers can also be satisfied. Furthermore, the difficult problem for distributed optimization of the total cost function with bounded capacity limitations is also discussed. A reformulated barrier function is proposed to simplify the analysis, under which the total cost can reach the minimal value if consensus can be achieved for the modified incremental cost with some appropriate initial values. Thus, the distributed optimization problems for the cost function of all generation units with and without bounded capacity limitations can both be solved by using the idea of consensus in multi-agent systems, whose theoretical analysis is still lacking nowadays. Finally, some simulation examples are given to verify the effectiveness of the results in this paper.

## Keywords

power dispatch strategy consensus incremental cost capacity limitations distributed protocol multi-agent systems## Notes

### Acknowledgements

This work was supported by National Key Research and Development Program of China (Grant No. 2016YFB0800401), National Natural Science Foundation of China (Grant Nos. 61673107, 61673104, 61621003, 61532020), National Ten Thousand Talent Program for Young Top-notch Talents, Cheung Kong Scholars Programme of China for Young Scholars, Six Talent Peaks of Jiangsu Province of China (Grant No. 2014-DZXX-004), and Fundamental Research Funds for the Central Universities of China (Grant No. 2242016K41058).

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