Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators

This paper examines the dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of Van der Pol oscillators. The general strategy of controlling inverters to emulate the behavior of nonlinear oscillators presents a compelling time-domain alternative to ubiquitous droop control methods which presume the existence of a quasi-stationary sinusoidal steady state and operate on phasor quantities. We present two main results in this work. First, by leveraging the method of periodic averaging, we demonstrate that droop laws are intrinsically embedded within a slower time scale in the nonlinear dynamics of Van der Pol oscillators. Second, we establish the global convergence of amplitude and phase dynamics in a resistive network interconnecting inverters controlled as Van der Pol oscillators. Furthermore, under a set of non-restrictive decoupling approximations, we derive sufficient conditions for local exponential stability of desirable equilibria of the linearized amplitude and phase dynamics

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

Automatic power sharing modification of P/V droop controllers in low-voltage resistive microgrids

Microgrids are receiving an increasing interest to integrate the growing share of distributed generation (DG) units in the electrical network. For the islanded operation of the microgrid, several control strategies for the primary control have been developed to ensure a stable microgrid operation. In lowvoltage microgrids, active power/voltage (P/V ) droop controllers are gaining attention as they take into account the resistive nature of the network lines and the lack of directly-coupled rotating inertia. However, a problem often cited with these droop controllers is that the grid voltage is not a global parameter. This can influence the power sharing between different units. In this paper, it is investigated whether this is actually a disadvantage of the control strategy. It is shown that with P/V droop control, the DG units that are located electrically far from the load centres automatically deliver a lower share of the power. This automatic power sharing modification can lead to decreased line losses, thus, an overall better efficiency compared to the methods that focus on perfect power sharing. In this paper, the P/V and P/f droop control strategies are compared with respect to this power sharing modification and the line losses

Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs

A third-order three-stage explicit Two-step Runge-Kutta-Nystr¨om (TSRKN) method embedded into fourth-order three-stage TSRKN method is developed to solve special second-order initial value problems (IVPs) directly. The stability of the method is investigated. Numerical results are obtained by solving a standard set of test problems, which then reduced to first-order system when solved using Runge-Kutta (RK) method and comparison are made with existing RK method with same order using variable step-size. The results clearly showed the advantage and the efficiency of the new method

Advanced Control Architectures for Intelligent MicroGrids, Part I:Decentralized and Hierarchical Control

This paper presents a review of advanced control techniques for microgrids. This paper covers decentralized, distributed, and hierarchical control of grid-connected and islanded microgrids. At first, decentralized control techniques for microgrids are reviewed. Then, the recent developments in the stability analysis of decentralized controlled microgrids are discussed. Finally, hierarchical control for microgrids that mimic the behavior of the mains grid is reviewed

Inter-Microgrid Operation: Power Sharing, Frequency Restoration, Seamless Reconnection and Stability Analysis

Electrification in the rural areas sometimes become very challenging due to area accessibility and economic concern. Standalone Microgrids (MGs) play a very crucial role in these kinds of a rural area where a large power grid is not available. The intermittent nature of distributed energy sources and the load uncertainties can create a power mismatch and can lead to frequency and voltage drop in rural isolated community MG. In order to avoid this, various intelligent load shedding techniques, installation of micro storage systems and coupling of neighbouring MGs can be adopted. Among these, the coupling of neighbouring MGs is the most feasible in the rural area where large grid power is not available. The interconnection of neighbouring MGs has raised concerns about the safety of operation, protection of critical infrastructure, the efficiency of power-sharing and most importantly, stable mode of operation. Many advanced control techniques have been proposed to enhance the load sharing and stability of the microgrid. Droop control is the most commonly used control technique for parallel operation of converters in order to share the load among the MGs. But most of them are in the presence of large grid power, where system voltage and frequency are controlled by the stiff grid. In a rural area, where grid power is not available, the frequency and voltage control become a fundamental issue to be addressed. Moreover, for accurate load sharing a high value of droop gain should be chosen as the R/X ratio of the rural network is very high, which makes the system unstable. Therefore, the choice of droop gains is often a trade-off between power-sharing and stability. In the context, the main focus of this PhD thesis is the fundamental investigations into control techniques of inverter-based standalone neighbouring microgrids for available power sharing. It aims to develop new and improved control techniques to enhance performance and power-sharing reliability of remote standalone Microgrids. In this thesis, a power management-based droop control is proposed for accurate power sharing according to the power availability in a particular MG. Inverters can have different power setpoints during the grid-connected mode, but in the standalone mode, they all need their power setpoints to be adjusted according to their power ratings. On the basis of this, a power management-based droop control strategy is developed to achieve the power-sharing among the neighbouring microgrids. The proposed method helps the MG inverters to share the power according to its ratings and availability, which does not restrict the inverters for equal power-sharing. The paralleled inverters in coupled MGs need to work in both interconnected mode and standalone mode and should be able to transfer between modes seamlessly. An enhanced droop control is proposed to maintain the frequency and voltage of the MGs to their nominal value, which also helps the neighbouring MGs for seamless (de)coupling. This thesis also presents a mathematical model of the interconnected neighbouring microgrid for stability and robustness analysis. Finally, a laboratory prototype model of two MGs is developed to test the effectiveness of the proposed control strategies