Smart-Grid CalculusDan-Cristian Tomozei (joint work with J.-Y. Le Boudec)

DESL-LCA2 WorkshopOrsières-Verbier

26-27 March 2013

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

𝑹 𝑹∗

Output flow𝑆

What is Network Calculus?

• Guaranteed flow characteristics• Arrival curves, service curves, shaping, etc.

• Sizing (of buffers)Input flow

𝑹 𝑹∗

Output flow𝛽

What is Network Calculus?

• Performance bounds based on flow characteristics (e.g., arrival curves); hold for any flow satisfying them

• Allows concatenation of several network elements• System algebra [simpler than it sounds!]• Yields global properties

Smart-Grid Service Guarantees

• For consumers• Demand-response: guaranteed energy

• For producers• Generation-control: guaranteed income

• For the grid• Guaranteed voltage profile?

Demand-Response w/ Serv. Curves

• Demand • Service curve contract:

• Guaranteed energy delivery over interval

• Modulated demand s.t.

• E.g., guarantee maximum power for at least 20h/24h and for the rest of the time

• Decouples consumer problemand DSO problem!

What about the demand?

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]

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]

Battery Calculus

1h/24hServiceinterruption

+

=

𝛼

Conclusions

• Can be implemented in a SHC (Utkarsh did it!)• Decouples consumer and DSO problems

• Bémol: counters per consumer (verify that contract is satisfied)

• V1: Simplify to single counter per consumer• V2: Local check + broadcast. Probably works well with GECN!

Constraints: Demand Response: Perfect battery constraints:

Given (known) signals: The load

Allowed consumption

To be determined: Battery initial charge Max battery capacity Schedule (consumption from

grid)

Problem