On Stability of a Distributed Averaging PI Frequency and Active Power Controlled Differential-Algebraic Power System Model

We consider the problems of stability, frequency restoration and optimal steady-state resource allocation in a heterogeneous and structure-preserving differential-algebraic equation (DAE) power system model. Thereby, we include constant-power-controlled loads (CPCLs) and constant-power-controlled sources (CPCSs) explicitly in the analysis and network control design. This results in a power system model with mixed algebraic as well as first- and second-order differential dynamics. We show that the abovementioned control objectives can be achieved via a distributed averaging proportional integral (DAPI) control and, in particular, extend the stability proof in [1] to the resulting closed-loop DAE system

A power consensus algorithm for DC microgrids

A novel power consensus algorithm for DC microgrids is proposed and analyzed. DC microgrids are networks composed of DC sources, loads, and interconnecting lines. They are represented by differential-algebraic equations connected over an undirected weighted graph that models the electrical circuit. A second graph represents the communication network over which the source nodes exchange information about the instantaneous powers, which is used to adjust the injected current accordingly. This give rise to a nonlinear consensus-like system of differential-algebraic equations that is analyzed via Lyapunov functions inspired by the physics of the system. We establish convergence to the set of equilibria consisting of weighted consensus power vectors as well as preservation of the weighted geometric mean of the source voltages. The results apply to networks with constant impedance, constant current and constant power loads.Comment: Abridged version submitted to the 20th IFAC World Congress, Toulouse, Franc

Gather-and-broadcast frequency control in power systems

We propose a novel frequency control approach in between centralized and distributed architectures, that is a continuous-time feedback control version of the dual decomposition optimization method. Specifically, a convex combination of the frequency measurements is centrally aggregated, followed by an integral control and a broadcast signal, which is then optimally allocated at local generation units. We show that our gather-and-broadcast control architecture comprises many previously proposed strategies as special cases. We prove local asymptotic stability of the closed-loop equilibria of the considered power system model, which is a nonlinear differential-algebraic system that includes traditional generators, frequency-responsive devices, as well as passive loads, where the sources are already equipped with primary droop control. Our feedback control is designed such that the closed-loop equilibria of the power system solve the optimal economic dispatch problem

Voltage Stabilization in Microgrids via Quadratic Droop Control

We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters ("microgrids"). A droop-like voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic load models. Controller optimality is characterized as follows: we show a one-to-one correspondence between the high-voltage equilibrium of the microgrid under quadratic droop control, and the solution of an optimization problem which minimizes a trade-off between reactive power dissipation and voltage deviations. Power sharing performance of the controller is characterized as a function of the controller gains, network topology, and parameters. Perhaps surprisingly, proportional sharing of the total load between inverters is achieved in the low-gain limit, independent of the circuit topology or reactances. All results hold for arbitrary grid topologies, with arbitrary numbers of inverters and loads. Numerical results confirm the robustness of the controller to unmodeled dynamics.Comment: 14 pages, 8 figure

Analysis of the effect of clock drifts on frequency regulation and power sharing in inverter-based islanded microgrids

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Local hardware clocks in physically distributed computation devices hardly ever agree because clocks drift apart and the drift can be different for each device. This paper analyses the effect that local clock drifts have in the parallel operation of voltage source inverters (VSIs) in islanded microgrids (MG). The state-of-the-art control policies for frequency regulation and active power sharing in VSIs-based MGs are reviewed and selected prototype policies are then re-formulated in terms of clock drifts. Next, steady-state properties for these policies are analyzed. For each of the policies, analytical expressions are developed to provide an exact quantification of the impact that drifts have on frequency and active power equilibrium points. In addition, a closed-loop model that accommodates all the policies is derived, and the stability of the equilibrium points is characterized in terms of the clock drifts. Finally, the implementation of the analyzed policies in a laboratory MG provides experimental results that confirm the theoretical analysis.Peer ReviewedPostprint (author's final draft

A Lyapunov Approach to Control of Microgrids with a Network-Preserved Differential-Algebraic Model

We provide sufficient conditions for asymptotic stability and optimal resource allocation for a networkpreserved microgrid model with active and reactive power loads. The model considers explicitly the presence of constantpower loads as well as the coupling between the phase angle and voltage dynamics. The analysis of the resulting nonlinear differential algebraic equation (DAE) system is conducted by leveraging incremental Lyapunov functions, definiteness of the load flow Jacobian and the implicit function theorem