smart-grid calculus dan-cristian tomozei (joint work with j.-y. le boudec) desl-lca2 workshop...
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Smart-Grid CalculusDan-Cristian Tomozei (joint work with J.-Y. Le Boudec)
DESL-LCA2 WorkshopOrsières-Verbier
26-27 March 2013
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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
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What is Network Calculus?
• Guaranteed flow characteristics• Arrival curves, service curves, shaping, etc.
• Sizing (of buffers)Input flow
𝑹 𝑹∗
Output flow𝛽
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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
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Smart-Grid Service Guarantees
• For consumers• Demand-response: guaranteed energy
• For producers• Generation-control: guaranteed income
• For the grid• Guaranteed voltage profile?
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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?
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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]
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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]
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Battery Calculus
1h/24hServiceinterruption
+
=
𝛼
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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!
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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