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

Online pricing for demand‐side management in a low‐voltage resistive micro‐grid via a Stackelberg game with incentive strategies

It has been demonstrated that online pricing mechanisms are a viable solution for demand side management in power systems. This study deals with the analysis and design of a droop-controlled low-voltage resistive AC micro-grid network system. Such a system is subjected to a dynamic demand obtained from an online pricing mechanism, which is proposed as a novelty in the study of micro-grids. This mechanism is derived from a variation of the Stackelberg game, which includes the use of incentive strategies. First, a configuration in which a supplier announces an incentive function and (Formula presented.) -consumers’ reaction to the resulting personalised price is presented. Then, a detailed stability analysis of the micro-grid is presented as a result of the interaction with the aforementioned online pricing mechanism. The units of the micro-grid (generators as the supplier and loads as the consumers) operate under either conventional or bounded droop control. The novelty of the approach is that it bridges the gap between the physical and the market layers of the problem. The ways in which the existence of multiple equilibrium points is guaranteed for both the consumer's load and the supplier's announced incentive are shown. A detailed design process for the profit functions of the players is shown in conjunction with the parameter selection for their implementation. Finally, simulations that demonstrate the system stability and its convergence to different equilibria are implemented under scenarios with one and multiple consumers