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Quadratic Performance of Primal-Dual Methods with Application to Secondary Frequency Control of Power Systems


John W. Simpson-Porco, B.K. Poolla, Nima Monshizadeh, F. Dörfler

IEEE Conference on Decision and Control, pp. 1840-1845

Primal-dual gradient methods have recently attracted interest as a set of systematic techniques for distributed and online optimization. One of the proposed applications has been optimal frequency regulation in power systems, where the primal-dual algorithm is implemented online as a dynamic controller. In this context, however, disturbances arise from fluctuating load and renewable generation, and input/output performance becomes important to quantify. Here we use the H2 system norm to quantify how effectively these distributed algorithms reject disturbances. For the linear primal-dual algorithms arising from quadratic programs, we provide an explicit expression for the H2 norm, and examine the performance gain achieved by augmenting the Lagrangian. Our results suggest that the primal-dual method may perform poorly when applied to large-scale systems and that Lagrangian augmentation can partially (or completely) alleviate these scaling issues. We illustrate our results with an application to power system frequency control by means of distributed primal-dual controllers.


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% Autogenerated BibTeX entry
@InProceedings { SimEtal:2016:IFA_5398,
    author={John W. Simpson-Porco and B.K. Poolla and Nima Monshizadeh and F.
    title={{Quadratic Performance of Primal-Dual Methods with
	  Application to Secondary Frequency Control of Power Systems}},
    booktitle={IEEE Conference on Decision and Control},
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