A Port-Hamiltonian Approach to Plug-and-Play Voltage and Frequency Control in Islanded Inverter-Based AC Microgrids

Abstract

One of the major challenges of voltage stabilization in converter-based DC microgrids are the multiple interacting units displaying intermittent supply behavior. In this paper, we address this by a decentralized scalable, plug-and-play voltage controller for voltage-source converters (VSCs) at primary level. In contrast to existing approaches, we follow a systematic and constructive design based on port-Hamiltonian systems (PHSs) which does neither require the heuristic proposition of a Lyapunov function nor the computation of auxilliary variables such as time-derivatives. By employing the Hamiltonian naturally obtained from the PHS approach as Lyapunov function and using the modularity of passive systems, we provide sufficient conditions under which the designed VSC controllers achieve microgrid-wide asymptotic voltage stability. Integral action (IA), which preserves the passive PHS structure, robustifies the design against unknown disturbances and ensures zero voltage errors in the steady-state. Numerical simulations illustrate the functionality of the proposed voltage controller. arXiv:2002.05050v1 [eess.SY]

A Distributed Scheme for Voltage and Frequency Control and Power Sharing in Inverter Based Microgrids

“…Constant power loads can be nonpassive due to their negative incremental resistance [22]. In the latter case, the network is guaranteed to be passive under an appropriate condition as derived in [17], that is satisfied when a sufficient number of constant impedance loads is present.…”

“…Remark 7: The upper bound in (17) can easily be computed as L and M(0) are known matrices. It should also be noted that in the example given in section V, this condition is only slightly conservative and is easily satisfied (with considerable margin) for all realistic values of δ * .…”

“…Both L and LM(0) have exactly one zero eigenvalue, as already shown above. Suppose the second smallest eigenvalue of Ĥ, λ n−1 ( Ĥ), satisfies condition (17). Then the the second smallest eigenvalue of LM(δ * ) is strictly positive and hence all other eigenvalues of LM(δ * ) are strictly positive.…”

“…The necessity to have flexible and resizeable microgrids, where the DG units and loads can be connected/disconnected over time requires the design of control architectures that are scalable, i.e. they provide a plug-and-play capability [12], [14], [17]. The work in [12] proposes controllers with a plug-andplay capability based on a restricted coupling that depends on the line dynamics, whereas passivity based techniques can lead to scalable designs for general line parameters [17].…”

“…they provide a plug-and-play capability [12], [14], [17]. The work in [12] proposes controllers with a plug-andplay capability based on a restricted coupling that depends on the line dynamics, whereas passivity based techniques can lead to scalable designs for general line parameters [17]. In [14] a dynamic controller that satisfies mixed passivity and H ∞ criteria is also proposed.…”