# Decentralized Coordination of DERs for Dynamic Economic Emission Dispatch
### Motivations
#### 1.2.2 Technical Level Motivation  
Note that all of the above-mentioned works for ED or EED problems are centralized methods, where all committed generators are regulated by the central coordinator. The future power system will be integrated with a great number of DERs, advanced communication, and control technologies [13]. Centralized methods have to confront the following challenges:  
1. Increasing computational and communicational costs of the central coordinator. 2. Scalable and flexible coordination of DERs. 3. Privacy and prerogative concerns raised by different DER owners. Hence, the pattern of dispatch methods needs to endow control systems with high flexibility, efficiency, security, and low computation and communication costs. To overcome the limitations and meet the requirements, an alternative decentralized scheme has become a well-studied methodology for dealing with dispatch problems in power systems. The key is to decentralize the complex task of the central coordinator into coordinators embedded in each committed generating unit, achieving an optimal schedule through local communications and computations. We would like to emphasize that the decentralized paradigm does not mean the complete elimination of the central coordinator but a useful complement of localized manipulations to realize scalable and flexible management of distributed generators. The majority of research on decentralized methods for ED problems is consensus-based protocols, conducted on various situations, including fixed networks [14; 15], dynamic networks [16; 17], information losses [18; 19], etc. Due to the importance of ES devices in improving the reliability of power supply, [PERSON] et al. [20] propose a leader following a consensus algorithm for the DED problem, where the ES is considered the leader. Then, [PERSON] et al. [21] removed the requirement of a leader and developed a fully decentralized DED algorithm over time-varying directed networks. Furthermore, the ADMM [22] and Quasi-Newton methods [23] show their effectiveness in DED. The research on decentralized algorithms for the EED problem is relatively scarce. Recently, the push-sum method [24] has been employed to address the EED problem involving energy storage devices without the consideration of charging/discharging efficiency [25]. In [26], the authors present a decentralized algorithm for the EED problem over dynamic networks, where two consensus protocols run in parallel in each generator. Nevertheless, both [24; 26] are only applicable to a static case where ramp constraints are neglected. In recent years, ADMM received popularity in decentralized optimization, due to its high adaptability, easy implementation, and fast convergence. In [27], a decentralized algorithm is developed on the basis of ADMM for DEED. The updates of primal and dual variables are decomposed into separate steps, and each of them is executed in a decentralized manner. Two primal variables are updated by solving sub-optimization problems, one uses the consensus theory, the other is further decomposed into independent sub-problems. Ref. [28] takes into account environmental cost with an E-exponential term; the formulated DEED problem is solved by an ADMM-based algorithm. By using the consensus theory and a parallel projection approach in the primal updates, the algorithm achieves decentralized implementation. In [29], a dual consensus ADMM is proposed for dynamic optimal power flow with the carbon emission trading problem. By applying ADMM to the dual problem, it reduces public information at each iteration. Communication uncertainties, including packet drops and delays, are considered in [30] for ED problems. Similar with [28], a consensus-based ADMM is proposed where the primal updates use the consensus theory and a projection operator. It is worth noting that most current distributed ADMM approaches model the optimization problem in the form of two- or multi-block joint optimization, see [27; 28; 30] and the references therein.