#### Document Type

Conference Paper

#### Subject Area

CPS Efficient Buildings, CPS Model-Based Design, CPS Embedded Control, CPS Real-Time

#### Date of this Version

10-2015

#### Publication Source

Proceedings of the 12th International Conference on Embedded Software (EMSOFT)

#### Start Page

137

#### Last Page

146

#### Abstract

Peak power consumption is a universal problem across energy control systems in electrical grids, buildings, and industrial automation where the uncoordinated operation of multiple controllers result in temporally correlated electricity demand surges (or peaks). While there exist several different approaches to balance power consumption by load shifting and load shedding, they operate on coarse grained time scales and do not help in de-correlating energy sinks. The Energy System Scheduling Problem is particularly hard due to its binary control variables. Its complexity grows exponentially with the scale of the system, making it impossible to handle systems with more than a few variables.

We developed a scalable approach for fine-grained scheduling of energy control systems that novelly combines techniques from control theory and computer science. The original system with binary control variables are *approximated by an averaged system* whose inputs are the *utilization values* of the binary inputs within a given period. The error between the two systems can be bounded, which allows us to derive a safety constraint for the averaged system so that the original system's safety is guaranteed. To further reduce the complexity of the scheduling problem, *we abstract the averaged system by a simple single-state single-input dynamical system* whose control input is the upper-bound of the total demand of the system. This model abstraction is achieved by extending the concept of simulation relations between transition systems to allow for input constraints between the systems. We developed conditions to test for simulation relations as well as algorithms to compute such a model abstraction. As a consequence, we only need to solve a small linear program to compute an optimal bound of the total demand. The total demand is then broken down, by solving a linear program much smaller than the original program, to individual utilization values of the subsystems, whose actual schedule is then obtained by a low-level scheduling algorithm. Numerical simulations in Matlab show the effectiveness and scalability of our approach.

#### Keywords

embedded control systems, peak power management, cyber-physical systems

#### Recommended Citation

Truong X. Nghiem and Rahul Mangharam, "Scalable Scheduling of Energy Control Systems", *Proceedings of the 12th International Conference on Embedded Software (EMSOFT)* , 137-146. October 2015.

#### Bib Tex

@inproceedings{nghiem2015scalable, title={Scalable scheduling of energy control systems}, author={Nghiem, Truong X and Mangharam, Rahul}, booktitle={Proceedings of the 12th International Conference on Embedded Software}, pages={137--146}, year={2015}, organization={IEEE Press} }

#### Included in

Computer Engineering Commons, Controls and Control Theory Commons, Energy Systems Commons, Power and Energy Commons

**Date Posted:** 15 January 2016

This document has been peer reviewed.

## Comments

Nghiem, Truong X., and Rahul Mangharam. "Scalable scheduling of energy control systems."

Proceedings of the 12th International Conference on Embedded Software. IEEE Press, 2015.