An operator splitting approach for distributed generalized Nash equilibria computation

Asynchrony widely exists in microgrids (MGs), such as non-identical sampling rates and communication delays, which challenges the MG control. This paper addresses the asynchronous distributed power control problem of hybrid microgrids, considering different kinds of asynchrony, such as non-identical sampling rates and random time delays. To this end, we first formulate the economic dispatch problem of MGs and devise a synchronous algorithm. Then, we analyze the impact of asynchrony and propose an asynchronous iteration algorithm based on the synchronous version. By introducing a random clock at each iteration, different types of asynchrony are fitted into a unified framework, where the asynchronous algorithm is converted into a fixed-point iteration problem with a nonexpansive operator, leading to a convergence proof. We further provide an upper bound estimation of the time delay of the communication. Moreover, the real-time implementation of the proposed algorithm in both AC and DC MGs is introduced. By measuring the frequency/voltage, the controller is simplified by reducing one order and adapt to the fast varying load demand. Finally, simulations on a benchmark MG and experiments are utilized to verify the effectiveness and advantages of the proposed algorithm. Index Terms-Asynchronous control, distributed control, multi-agent system, multi-microgrid networks, time delay. I. INTRODUCTION Multi-Microgrid systems or Microgrids (MGs) are clusters of distributed generators (DGs), energy storage systems and loads, which are generally categorized into three types: AC, DC and hybrid AC/DC MGs [1], [2]. A hybrid AC/DC MG has the advantage of reducing processes of multiple inverse conversions in the involved individual AC or DC grid [3]. Recently, the distributed power control for MGs has attracted more and more attention due to its fast response speed, privacy

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“…Next, we show that (7a)−(7f) can be converted into a fixedpoint iteration problem with an averaged operator [26], [33].…”

Section: B Algorithm Reformulationmentioning

confidence: 99%

“…N Ω (x) also serves as an operator, whose inputs are a nonempty closed convex set Ω and a point x, and the output is the points v satisfying {v| v, y − x ≤ 0, ∀y ∈ Ω}. We have P Ω (x) = (Id + N Ω ) −1 (x) [26], [27,Chapter 23.1]. For a single-valued operator T :…”

Section: A Notations and Preliminariesmentioning

confidence: 99%

Asynchronous Distributed Power Control of Multimicrogrid Systems

Wang

Chen

Liu

et al. 2020

IEEE Trans. Control Netw. Syst.

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“…Several algorithms are available in the literature to find a solution of the aggregative game in (15), e.g. [7]- [10]. Among these methods, the algorithm proposed in [9] for the special class of generalized games with linearly coupled cost functions is shown to be particularly efficient in terms of convergence speed.…”

Section: A a Distributed Algorithm For Gne Seekingmentioning

confidence: 99%

Energy Management and Peer-to-peer Trading in Future Smart Grids: A Distributed Game-Theoretic Approach

Belgioioso¹,

Ananduta

Grammatico

et al. 2020

2020 European Control Conference (ECC)

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We consider the economic dispatch problem for a day-ahead, peer-to-peer (P2P) electricity market of prosumers (i.e., energy consumers who can also produce electricity) in a distribution network. In our model, each prosumer has the capability of producing power through its dispatchable or nondispatchable generation units and/or has a storage energy unit. Furthermore, we consider a hybrid main grid & P2P market in which each prosumer can trade power both with the main grid and with (some of) the other prosumers. First, we cast the economic dispatch problem as a noncooperative game with coupling constraints. Then, we design a fully-scalable algorithm to steer the system to a generalized Nash equilibrium (GNE). Finally, we show through numerical studies that the proposed methodology has the potential to ensure safe and efficient operation of the power grid.

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“…We refer to [148], [149] for the explicit derivation of the algorithm in (32) via operator splitting, for aggregative and network games, respectively. Under the postulated technical assumptions, for small-enough step size ✏ > 0, the algorithm converges to some zero of T in (30), (u ⇤ , µ ⇤ ), where u ⇤ is the unique v-GNE of the game in (24), indeed.…”

Section: Coordination Algorithms For Asymptotic Balancingmentioning

confidence: 99%