*Article* **Multi-Agent Cooperation Based Reduced-Dimension Q(** λ**) Learning for Optimal Carbon-Energy Combined-Flow**

#### **Huazhen Cao 1, Chong Gao 1, Xuan He 1, Yang Li 1 and Tao Yu 2,\***


Received: 17 June 2020; Accepted: 31 August 2020; Published: 14 September 2020

**Abstract:** This paper builds an optimal carbon-energy combined-flow (OCECF) model to optimize the carbon emission and energy losses of power grids simultaneously. A novel multi-agent cooperative reduced-dimension Q(λ) (MCR-Q(λ)) is proposed for solving the model. Firstly, on the basis of the traditional single-objective Q(λ) algorithm, the solution space is reduced e ffectively to shrink the size of *Q*-value matrices. Then, based on the concept of ant cooperative cooperation, multi-agents are used to update the *Q*-value matrices iteratively, which can significantly improve the updating rate. The simulation in the IEEE 118-bus system indicates that the proposed technique can decrease the convergence speed by hundreds of times as compared with conventional Q(λ), keeping high global stability, which is very suitable for dynamic OCECF in a large and complex power grid compared with other algorithms.

**Keywords:** multi-agent cooperation; reduced-dimension Q(λ); optimal carbon-energy combined-flow
