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Smart- Grid Calculus. Dan-Cristian Tomozei (joint work with J.-Y. Le Boudec) DESL-LCA2 Workshop Orsières-Verbier 26-27 March 2013. What is Network Calculus ?.
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Smart-GridCalculus Dan-Cristian Tomozei (joint workwith J.-Y. Le Boudec) DESL-LCA2 Workshop Orsières-Verbier 26-27 March 2013
Whatis Network Calculus? "a set of mathematical results which give insights into man-made systems such as concurrent programs, digital circuits and communication networks." • Deterministicqueuing system theory Output flow Input flow
Whatis Network Calculus? • Guaranteed flow characteristics • Arrivalcurves, service curves, shaping, etc. • Sizing (of buffers) Output flow Input flow
Whatis Network Calculus? • Performance boundsbased on flow characteristics (e.g., arrivalcurves); hold for any flow satisfyingthem • Allowsconcatenation of several network elements • System algebra [simpler than it sounds!] • Yields global properties
Smart-GridService Guarantees • For consumers • Demand-response: guaranteedenergy • For producers • Generation-control: guaranteedincome • For the grid • Guaranteed voltage profile?
Demand-Response w/ Serv. Curves • Demand • Service curvecontract: • Guaranteedenergydelivery over interval • Modulateddemand 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) batterylevel • Need to becharged by a given deadline [Le Boudec, T. 2011]
Inflexible Demand:BatteryCalculus • E.g., datacenterthatwants a lowerelectricity bill • Goal: find the smallestbattery size thatguarantees no interruptions [Le Boudec, T. 2012] Actual consumption (constrained!) Grid Loadsees no constraints “Energy buffer”
BatteryCalculus + 1h/24h Service interruption =
Conclusions • Can beimplemented in a SHC (Utkarsh didit!) • 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!
Problem Given (known) signals: • The load • Allowed consumption To be determined: • Battery initial charge • Max battery capacity • Schedule (consumption from grid) Constraints: • Demand Response: • Perfect battery constraints: