## Wide Area Control of IEEE 39 New England Power Grid Model
## Problem descriptionThe IEEE New England Power Grid Model consists of buses and generators. Generator is an equivalent aggregated model for the part of the network that we do not have control over; generators to are equipped with Power System Stabilizers (PSSs), which provide good damping of local modes and stabilize otherwise unstable open-loop system. We use a sparsity-promoting optimal control strategy to design a supplementary wide area control signal aimed at achieving a desirable trade-off between damping of the inter-area oscillations and communication requirements in the distributed controller. Inter-area oscillations are associated with the dynamics of power transfers and they are characterized by groups of coherent machines that swing relative to each other. These oscillations are caused by weakly damped modes of the linearized swing equations and they physically correspond to active power transfer between different generator groups. In the absence of higher-order generator dynamics, for purely inductive lines and constant-current loads, the dynamics of each generator can be represented by the electromechanical swing equations where denotes the number of generators, is the generator power injection in the network-reduced model, and is the Kron-reduced admittance matrix describing the interactions among generators. After linearization at an operating point the swing equations reduce to
Let the state of the power network be partitioned as where and are the rotor angles and frequencies of synchronous generators and are the state variables which correspond to fast electrical dynamics. The sparsity-promoting minimum-variance optimal control problem can then be formulated as: where we use the weighted norm to induce sparsity in the state feedback gain matrix . ## Computational resultsWe next present computations resulting from the use of the sparsity-promoting framework with logarithmically-spaced points for . In the objective function we choose , , and set in order to penalize deviation from synchrony. This choice of is inspired by slow coherency theory with denoting a small regularization parameter and denoting the vector of all ones. Download Matlab code ## Performance vs Sparsity
## Signal exchange networkThe sparsity pattern of the optimal feedback gain illustrates interactions between different generators. In the figures below, nine rows correspond to nine control inputs to controlled generators; the columns correspond to different states variables. Blue dots in each block represent local interactions within each generator, and red dots represent interactions between different generators.
## Dominant inter-area modes
## Presentations**Slow coherency and sparsity-promoting optimal wide-area control**
*Los Alamos National Lab* Los Alamos, NM; July 2013**Sparsity-promoting wide-area control of power systems**
*2013 American Control Conference* Washington, DC; June 2013
## Publications**Sparsity-promoting optimal wide-area control of power networks** F. Dorfler, M. R. Jovanovic, M. Chertkov, and F. Bullo
*IEEE Trans. Power Syst.*, 2014; in press; also arXiv:1307.4342.**Sparse and optimal wide-area damping control in power networks** F. Dorfler, M. R. Jovanovic, M. Chertkov, and F. Bullo
*2013 American Control Conference*, Washington DC, June 2013.
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@article{dorjovchebulTPS14, author = {F. D\"orfler and M. R. Jovanovi\'c and M. Chertkov and F. Bullo}, title = {Sparsity-promoting optimal wide-area control of power networks}, journal = {IEEE Trans. Power Syst.}, year = {2014}, note = {in press; also arXiv:1307.4342} } @inproceedings{dorjovchebulACC13, author = {F. D\"orfler and M. R. Jovanovi\'c and M. Chertkov and F. Bullo}, booktitle = {Proceedings of the 2013 American Control Conference}, title = {Sparse and optimal wide-area damping control in power networks}, year = {2013}, address = {Washington, DC}, pages = {4295-4300} } @article{linfarjovADMM13, author = {F. Lin and M. Fardad and M. R. Jovanovi\'c}, title = {Design of optimal sparse feedback gains via the alternating direction method of multipliers}, journal = {IEEE Trans. Automat. Control}, volume = {58}, number = {9}, pages = {2426-2431}, year = {2013} } |