Hierarchical distributed ADMM for predictive control with applications in power networks

Abstract

Abstract-We present a variant of the alternating direction method of multipliers (ADMM) that can be implemented in a hierarchical distributed fashion for large-scale systems where the coupling between subsystems occurs in a structured way in the cost function. We show that this ADMM algorithm can be embedded in a model predictive control (MPC) implementation and subsequently apply this to three battery scheduling problems in the context of residential microgrid electricity networks.

Optimal power flow: an introduction to predictive, distributed and stochastic control challenges

“…maximal islanding time, black start, line switches, ...). With respect to the later issue elements of a convex reformulation of maximal-islanding-time constraints are presented in [12]. Finally, the fact that for k ∈ T the non-convex constraint set F(d(k)) depends on future (hence uncertain) values of d(k) underpins that uncertainty is always pivotal in opf Problems.…”

“…• Investigation of new decentralized and distributed control methods ensuring stable operation of distribution grids with a large share of volatile/uncertain renewables (which implies a large number of controllable devices such as storages and devices of sector coupling) and allowing for adaptive changes of grid topology (islanding of subsystems/microgrids) [8,12,61,81].…”

Toward economic NMPC for multistage AC optimal power flow

“…27 Economic mpc for multi-energy systems including storage can be found in the works of Arnold and Andersson 28 and Stoyanova et al 29 Furthermore, multistage opf can be used for cost-optimal energy management of microgrids based on price signals using a linearized dc model. 30 While Appino et al 31 discuss the effect of uncertain forecasts on storage scheduling, a distributed approach to scheduling is suggested in the work of Braun et al 32 The recent paper of Meyer-Hübner et al 33 considers mpc for storage scheduling in high-voltage grids. Stochastic economic nmpc of microgrids is proposed in the work of Vasilj et al 34 An approach to combined frequency regulation and economic dispatch via economic mpc, including stability analysis, with dc grid models is presented in the work of Köhler et al 35 With respect to the second branch, several works [36][37][38][39] consider voltage or frequency stabilization; frequency control and automatic generation control 40 as well as the use of quadratic stability constraints ensuring stability (which lead to state path constraints instead of terminal constraints) 41 have been investigated.…”

Constrained hierarchical networked optimization for energy markets

“…For example, in [18] an application to the energy market is considered, where a dynamic version of the sharing problem with a tracking profile system-level objective is decomposed using the Douglas-Rachford splitting. The same problem is solved in [19], where an adaptation of the ADMM algorithm for the sharing problem is used. This is the same solution approach proposed in [8], §7.3.…”

“…In [20] a high-level hierarchical control flow between the DSO, independent aggregators and prosumers is proposed, but no link is given between the different control signals. It is worth noting that some authors, as [16], [19], [15], use the term hierarchical to refer to a single level hierarchy, in which a the problem can be solve with a master-slave solution scheme. In this paper, we introduce a hierarchical market design that exploits the flexibility of prosumers located in different voltage levels of the distribution grid.…”