Asynchronous Distributed Control of Biogas Supply and Multienergy Demand

Abstract

In this paper we study the coordination between biogas producers who can either use the biogas themselves, exchange biogas with their neighbors, or deliver it to the various energy grids, such as the low pressure gas grid or the power grid. These producers are called prosumers. In this setting gas storage, fuel cells, micro combined heat power systems, and heat buffers are all part of the prosumers' node. We aim to optimize the imbalance, profit, and comfort levels per prosumer, while taking the constraints of the energy grids into account, and while allowing prosumers to exchange energy with each other. This results in a two-layer optimization problem formulation. In addition, in practice, communication between prosumers among each other and with grid operators is done in an asynchronous manner. In this paper we study the problem of two-layer optimization for biogas prosumers embedded in multiple energy grids, while the (bidirectional) communication between the various partners is done asynchronously. We prove the convergence of the asynchronous coordination algorithm that uses both the inputs and the states. We conduct simulations for the biogas prosumer setting, using realistic data to illustrate the convergence of the algorithm and to study its practical implementation. Note to Practitioners-This paper is motivated and supported by a smart gas grid project of the Energy Delta Gas Research (EDGaR) consortium in the Netherlands. The project deals with investigating the capacity of smart grid technologies to facilitate the introduction of new gases into the distribution grids, with diverse gas qualities and multiple injection points. The gas distribution grid will have to move from a passive to an active distribution system that dynamically control bidirectional flows between end-users and the grid operators. As the endusers may be equipped with energy converters, other energy distribution grids also need to transform to active distribution systems. Existing approaches are distributed, where each enduser and energy grid operator can locally solve their optimal control problem. In this paper, we consider the fact that both endusers and grid operators do not have access to a common clock when solving their problem and when sharing their information. The information includes some of their states and controllable inputs. The asynchronous information exchange problem was pointed out by DNV GL Netherlands, Gasunie, and Gasterra which are companies we collaborate with within the EDGaR consortium. It is highly relevant for practical implementation of our distributed algorithms. In future research, we will include practical control considerations due to on-off constraints of

Convergence Analysis of Dual Decomposition Algorithm in Distributed Optimization: Asynchrony and Inexactness

“…Moreover, we show that the asynchronous algorithm converges in O(1/k), which, to the best of our knowledge, has not been presented in the existing literature [6], [15]- [19].…”

“…By simply setting the inexactness or asynchrony parameter as zero, our result reduces to that given in [16] or [21], respectively. Our work also first gives the O(1/k) convergence rate for the asynchronous DD-DO algorithm, which, to the best of our knowledge, has not been presented in the existing literature [6], [16]- [18].…”

“…Dual decomposition is widely utilized in solving distributed optimization problems of multi-agent systems (MASs), such as communication networks [1]- [3], computer vision [4], [5], and power systems [6]- [8]. A dual decomposition algorithm usually involves two phases in each iteration: 1) a coordinator updates the dual variables (Lagrangian multipliers) and 2) individual agents solve their subproblems locally [9]- [11].…”

Distributed Optimal Control of Smart Electricity Grids With Congestion Management

“…At the level of the prosumers, the minimization of the prediction error in the operate phase is solved in a distributed manner, where each prosumer contributes to the optimization process based only on local information exchange with their neighbors. In [19], which considers a similar distributed MPC framework, although not in a market-based structure, it has been shown that the more information the prosumers share with each other, the less imbalance there is in the network. The role of the DSO is included in the model to avoid violation of the distribution network capacities.…”

Asynchronous Distributed Power Control of Multimicrogrid Systems

“…In practice, the communication channel is never perfect noting time delay, packet drops, congestion, and even failures [11]- [13]. In addition, nonidentical sampling/computation rates of different MGs also exist [14]. Then, asynchrony arises, which has a detrimental impact on the controller response speed, MG stability, and optimal operation [15]- [17].…”