A distributed normalized Nash equilibrium seeking algorithm for power allocation among micro-grids

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https://doi.org/10.1007/s11431-019-1538-6

A distributed normalized Nash equilibrium seeking algorithm for power allocation among micro-grids ¨ JinHu3, YAO YiYang4 & MEI Feng4 FU Zao1, YU WenWu1,2* , LU 1 School

of Cyber Science and Engineering, Southeast University, Nanjing 210096, China; 2 School of Mathematics, Southeast University, Nanjing 210096, China; 3 School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China; 4 State Grid Zhejiang Electric Power Company Information & Telecommunication Branch, Hangzhou 310007, China Received November 4, 2019; accepted February 11, 2020; published online October 19, 2020

In this paper, a power allocation problem based on the Cournot game and generalized Nash game is proposed. After integrating dynamic average consensus algorithm and distributed projection neural network through singular perturbation systems, a normalized Nash equilibrium seeking algorithm is presented to solve the proposed power allocation problem in a distributed way. Combine Lyapunov stability with the singular perturbation analysis, the convergence of the proposed algorithm is analyzed. A simulation on IEEE 118-bus confirms that the proposed distributed algorithm can adjust the power allocation according to different situations, while keeping the optimal solution within the feasible set. generalized Nash game, normalized nash equilibrium points, distributed nash equilibrium seeking algorithm Citation:

Fu Z, Yu W W, L¨u J H, et al. A distributed normalized Nash equilibrium seeking algorithm for power allocation among micro-grids. Sci China Tech Sci, 2020, 63, https://doi.org/10.1007/s11431-019-1538-6

1 Introduction Nowadays, with constantly emerging of the distributed electrical equipment (such as distributed generators, loads, energy storage systems, electric vehicles), the power grid is required to be compatible with a wider variety of environments [1–4]. Although, new types of electric energy technologies possess numerous advantages than traditional technologies, but it is impossible to make new technologies instead of traditional technologies within a short time [5]. Within such a hybrid environment of the power grid, how to aggregate their respective advantages and balance the weight of each part becomes a great challenge. For example, in a micro-grid group, one of these challenges is how to make each microgrid reach a balance between the main grid supply and local distributed generator supply under the circumstance that each *Corresponding author (email: [email protected])

micro-grid only aims to minimize its own power cost. With the emergence of the micro-grids, vast power grids have to face similar situations. In addition, the increasing of distributed electrical equipment not only brings an enormous impact on power grid construction, structure planning, supply plan, but also empowers users can be more involved in power allocation, which means the majority of conventional control strategies and scheduling methods are no longer