{"id":245,"date":"2016-02-28T12:41:14","date_gmt":"2016-02-28T17:41:14","guid":{"rendered":"https:\/\/engineering.jhu.edu\/gayme\/?page_id=245"},"modified":"2017-02-22T13:23:11","modified_gmt":"2017-02-22T18:23:11","slug":"networked-systems","status":"publish","type":"page","link":"https:\/\/engineering.jhu.edu\/gayme\/networked-systems\/","title":{"rendered":"Stability and Performance of Coupled Oscillator Networks"},"content":{"rendered":"

Many complex systems can be modeled as a network of interacting subsystems, each with simple dynamics. In this work we use oscillator networks as a model of power grids and vehicular platoons. By applying tools from control theory to this modeling framework we investigate the effect of network structure on the synchronization performance of such systems. We show that for a large class of performance measures, the performance is determined by effective resistances in the underlying graphs. These results show the strong connection between the synchronization performance of oscillator networks\u00a0and circuit theory. Applications include evaluating the transient resistive losses due to maintaining synchrony in power grids as well as quantifying the coherence of vehicular platoons with different control laws and communication structures.<\/p>\n

Nodes<\/p>\n

We can use oscillator networks to evaluate a network\u2019s synchronization performance.\u00a0 Synchrony exists when all subsystems, or agents in a system, reach a mutual goal.\u00a0 To improve the performance of a network, we can tune the dynamics at particular nodes, as shown in the diagram below.<\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

Example Network: Vehicular Platoons<\/p>\n

In the case of vehicular platoons, synchronization would occur if the vehicles reach nominal spacing and velocity.\u00a0 Here, tuning the dynamics at particular nodes involves reducing communication in a vehicle platoon by tuning the leader\u2019s dynamics.<\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

Example Network: Power Grid<\/p>\n

In the case of power grids, synchronization is reached when all generator phases reach nominal conditions with constant angular velocities.\u00a0 The cost associated with resynchronization, then, would be the transient losses of energy in a power grid.\u00a0 We can improve the performance by tuning a droop-controlled inverter and therefore reduce the resistive losses due to maintaining synchrony.\u00a0 The droop-control approximates the average power versus frequency properties of a synchronous generator, but has different dynamics.<\/p>\n

\"\"<\/a>

Power Grid<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

Many complex systems can be modeled as a network of interacting subsystems, each with simple dynamics. In this work we use oscillator networks as a model of power grids and vehicular platoons. By applying tools from control theory to this modeling framework we investigate the effect of network structure on the synchronization performance of such […]<\/p>\n","protected":false},"author":168,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"class_list":["post-245","page","type-page","status-publish","hentry"],"yoast_head":"\nStability and Performance of Coupled Oscillator Networks - Dennice F. Gayme<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/engineering.jhu.edu\/gayme\/networked-systems\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Stability and Performance of Coupled Oscillator Networks - Dennice F. Gayme\" \/>\n<meta property=\"og:description\" content=\"Many complex systems can be modeled as a network of interacting subsystems, each with simple dynamics. In this work we use oscillator networks as a model of power grids and vehicular platoons. 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