Global synchronization analysis of droop-controlled microgrids—A multivariable cell structure approach

Abstract

The microgrid concept represents a promising approach to facilitate the large-scale integration of renewable energy sources. Motivated by this, the problem of global synchronization in droop-controlled microgrids with radial topology is considered. To this end, at rst a necessary and sucient condition for existence of equilibria is established in terms of the droop gains and the network parameters. Then, the local stability properties of the equilibria are characterized. Subsequently, sucient conditions for almost global synchronization are derived by means of the multivariable cell structure approach recently proposed in [1]. The latter is an extension of the powerful cell structure principle developed by Leonov and Noldus to nonlinear systems that are periodic with respect to several state variables and possess multiple invariant solutions. The analysis is illustrated via numerical examples.

Steady state characterization and frequency synchronization of a multi-converter power system on high-order manifolds

“…. In fact, we can establish a formal link between the linear subspace span{v(z * )} and the steady state set [z * ] in (7) as follows: for all θ ∈ S 1 , (10) which follows from (7). In fact, v(z * ) is the tangent vector of [z * ] in the θ -direction and lies on the tangent space T z * M. Hence, [z * ] is the angle integral curve of span{v(z * )}.…”

“…Under Condition III.2, the trajectories initialized on C ε in (28) are contracting, and any solution to (3) converges towards [z * s,i ] for some i, see [39,Theorem 4]. It is common to project into the orthogonal complement of the consensus subspace, using the angle transformation ξ = B θ , which can be interpreted as a quotient map (see [10]) or also ground a node [12] in low-order power system models. Due to non-direct dependency of (3) on angle differences as in typical Swing equation models [3], [21], and the dependence of the subspace span{v(z * )} on the steady state z * under consideration, (as opposed to the fixed direction given by 1 n 0 for Swing equations or Droop-like control), and the steady state manifold [z * ] is its angle integral curve, the conventional quotient map cannot be adopted.…”

A Hamiltonian control approach for electric microgrids with dynamic power flow solution

“…With respect to this structure, it is possible to find results, see e.g. Schiffer, Efimov, and Ortega (2019) and Simpson-Porco, Dörfler, and Bullo (2013), where the model is simplified by omitting the converters' dynamic, other which focuses on finding a solution to the nonlinear algebraic equations (Molzahn & Hiskens, 2019) leaving aside the dynamical variables, and some results where even that the dynamical variables are included (Tucci & Ferrari-Trecate, 2020) the network is represented after a Kron's reduction process. This paper's main objective is to address the MGs' voltage regulation and power balance control problems by explicitly including in the controller design both a dynamical model for the network (and the associated converters) and the constraints imposed by the power balance equations.…”

Fully decentralized conditions for local convergence of DC/AC converter network based on matching control

“…In particular, the rotational invariance indicates the absence of a reference frame or absolute angle in power system and presents a fundamental obstacle for defining suitable error coordinates. A common approach in power system literature is to eliminate this continuum of equilibria, e.g., by performing transformations either resulting from grounding a node [8], or projecting into the orthogonal complement [9], if the equilibrium manifold is a linear subspace, where classical stability tools such as Lyapunov direct method, can be deployed. Nonetheless, this type of transformations are not possible for high-order systems, where the dynamics do not have a direct coupling term or if the Laplacian matrix cannot be expressed explicitly.…”