Complex systems such as power networks exhibit instabilities that can be addressed either through the addition of active control or redesign. Often, these networks’ control authority is limited to hybrid components like switches, fuses and transformers which have a finite number of operating modes.

With proper hybrid control—like the systematic approaches in Iterative Methods in Switched System Optimal Control—a power network can recover from large disturbances due to transients and network failures.

The graphic to the right is a representation of the IEEE Case 118 power network test case. The green circles are generators, the blue square is a reference generator, the red lines are power lines, and switched capacitors (in grey) are placed in series on a subset of the power lines. The goal is to control the capacitor switches in order to drive the system toward a neighborhood of stability.

We show that this goal can be reached through simultaneous switching of all capacitors—i.e. with a single bit of control.  This result demonstrates that minimal control authority given by systematic hybrid optimal control algorithms is a viable option for controlling complex networks.

This project has three main components:

1. Control synthesis through mode scheduling,
2. Design for effective mode scheduling, and
3. Power network results.

Please see the following videos for more information.

Relevant Videos:

The following videos show animations of a simple power network, providing evidence that proper capacitor switching control will improve network performance. This example has a single capacitor that can be switched in series on the line shown. This connecting and disconnecting of the capacitor is the only control.

Power generators fail when they are sufficiently out of phase with the rest of the network. The amount each generator is in phase is depicted by the color scale from green to red.  Therefore, the network is performing well when all of the generators are “green”. Additionally, each generator’s phase is shown in the phase ring at the top right.

Disturbance and No Control A large disturbance from steady state occurs and the system goes unstable without capacitor switching control.	Disturbance and Switching Control The same large disturbance occurs but is mitigated by active capacitor switching control.

Relevant Papers:

[1]

T.M. Caldwell. Iterative methods in switched system optimal control, 2013. (Doctoral Dissertation) [link]

[2]

T.M. Caldwell and T.D. Murphey. Sufficient descent and backtracking for optimal mode scheduling. (Submitted to IEEE Transactions on Automatic Control)