1. Smart-Grid Calculus Dan-Cristian Tomozei (joint work with J.-Y. Le Boudec) DESL-LCA2 Workshop Orsières-Verbier 26-27 March 2013

2. What is Network Calculus? "a set of mathematical results which give insights into man-made systems such as concurrent programs, digital circuits and communication networks." Deterministic queuing system theory Input flow Output flow

3. What is Network Calculus? Guaranteed flow characteristics Arrival curves, service curves, shaping, etc. Sizing (of buffers) Input flow Output flow

4. What is Network Calculus?

5. Smart-Grid Service Guarantees For consumers Demand-response: guaranteed energy For producers Generation-control: guaranteed income For the grid Guaranteed voltage profile?

6. Demand-Response w/ Serv. Curves What about the demand?

7. Flexible Demand: Peak Shaving Electric vehicles Arrive with a random (depleted) battery level Need to be charged by a given deadline [Le Boudec, T. 2011]

8. Inflexible Demand:Battery Calculus E.g., datacenter that wants a lower electricity bill Goal: find the smallest battery size that guarantees no interruptions Load sees no constraints Grid Actual consumption (constrained!) “Energy buffer” [Le Boudec, T. 2012]

9. Battery Calculus 1h/24h Service interruption + =

10. Conclusions

11. Problem