# Decentralized Coordination of DERs for Dynamic Economic Emission Dispatch
###### Abstract  
This paper focuses on the dynamic economic emission dispatch (DEED) problem, to coordinate the distributed energy resources (DERs) in a power system and achieve economical and environmental operation. Distributed energy storages (ESs) are introduced into problem formulation in which charging/discharging efficiency is taken into account. By relaxing the nonconvexity induced by the charging/discharging model of ESs and network losses, we convert the non-convex DEED problem into its convex equivalency. Then, through a Lagrangian duality reformulation, an equivalent unconstrained consensus optimization model is established--a novel consensus-based decentralized algorithm, where the incremental cost is chosen as the consensus variable. At each iteration, only one primal variable requires sub-optimization, and it is completely locally updated. This is different from the well-known alternating direction method of multiplier (ADMM)-based algorithms where more than one subproblem needs to be solved at each iteration. The results of the comparative experiments also reflect the algorithm's advantage in terms of computational efficiency. The simulation results validate the effectiveness of the proposed algorithm, achieving a balance between emissions and economic considerations.  
consensus-based methods; decentralized optimization; economic emission dispatch; energy storage; smart grid +
Footnote †: journal: Applied  
definition  
programming method [2], the Lambda-iteration method [3], the interior point method [4], computational intelligence methods [5], etc.  
As mentioned above, the objective of ED is to allocate power generation among generators to minimize the costs of power generation, but it neglects the gas produced by thermal generators. With the rising awareness of the global warming phenomenon, environmental concerns put forward requirements to reduce greenhouse gas emissions. Emission dispatching is an effective option to address this issue. However, more benefits of power generation and less emissions of greenhouse gases are mutually contradictory, which results in a sophisticated optimization problem, i.e., the combined economic emission dispatch (EED) problem. It has to achieve economical power generation and maintain a low emission level simultaneously [6].  
The reported work examining emissions in the SED/DED problem can be divided into three categories in accordance with the formulation of the EED problem. The first one is to optimize the power generation cost and convert the emission into a constraint with a pre-specified limit [7]. However, this formulation hampers the trade-off between cost and emission. The second one treats power generation cost and greenhouse gas emission as competitive objectives and minimizes both of them simultaneously [8; 9]. In the third one, through a linear combination of the two conflicting objectives based on the weight-sum method, a single structure of the optimization problem is formulated, where a user-defined weight factor is imposed on each objective function [10; 11; 12]. The weight factor can be used as a means of studying the trade-off between costs and emissions and usually refers to the importance of the objective. These methods receive meaningful results for the decision-maker by adjusting the value of the weight factor.