Identifying Parameter Space for Robust Stability in Nonlinear Networks: A Microgrid Application

Abstract

As modern engineering systems grow in complexity, attitudes toward a modular design approach become increasingly more favorable. A key challenge to a modular design approach is the certification of robust stability under uncertainties in the rest of the network. In this paper, we consider the problem of identifying the parametric region, which guarantees stability of the connected module in the robust sense under uncertainties. We derive the conditions under which the robust stability of the connected module is guaranteed for some values of the design parameters, and present a sum-of-squares (SOS) optimizationbased algorithm to identify such a parametric region for polynomial systems. Using the example of an inverter-based microgrid, we show how this parametric region changes with variations in the level of uncertainties in the network.

Impact of the Interaction of Synchronous Machines and Virtual Inertia Provisions on the Small Signal Stability of Microgrids

“…Recently, conditions on the droop parameter has been derived for the lossless microgrid assumption using a Port-Hamiltonian representation [9]. In [10], a barrier function approach is taken to provide the safety conditions of the parameters in the microgrid. Recently, the small signal model of DERs with virtual inertia control has been derived in [11].…”

Distributed Small-Signal Stability Conditions for Inverter-Based Unbalanced Microgrids

“…A sum-of-squares optimization method was used in [12] to compute robust distributed stability certificates on the inverter droop gains, under bounded and time-varying uncertainties. A computational method using the dissipativity approach was proposed in [14] to estimate stability certificates in different frequency regions.…”

“…Moreover, it is assumed that Π34 0 0 0; (recall that G + G 0 0 0 by definition, while G is signindefinite). Applying the inequality (12) to Π, we obtain…”

Distributed Transient Safety Verification via Robust Control Invariant Sets: A Microgrid Application

“…Many recent efforts have addressed this need via, for example, stability and security-constrained optimization [3], [5], [7], identification of local and distributed parametric stability conditions [6], [8], [9], etc. The distributed identification of stability conditions are particularly interesting since these fit well into a multi-ownership models of microgrid resources, and facilitate hierarchical and plug-andplay operations [10].…”