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On Resistive Networks of Constant Power Devices


J. Simpson-Porco, F. Dörfler, F. Bullo

IEEE Trans. on Circuits and Systems-I, vol. 62, no. 8, pp. 811-815, Note: Available at

We consider the problem of voltage stability and reactive power balancing in 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. We find that the operating points of the quadratic droop-controlled microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide detailed 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 both 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.


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% Autogenerated BibTeX entry
@Article { SimD_r:2015:IFA_5269,
    author={J. Simpson-Porco and F. D{\"o}rfler and F. Bullo},
    title={{On Resistive Networks of Constant Power Devices}},
    journal={IEEE Trans. on Circuits and Systems-I},
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