Demand Response of Data Centers: A Real-time Pricing Game between Utilities in Smart Grid

1 / 18 Demand Response of Data Centers: A Real-time Pricing Game between Utilities in Smart Grid Nguyen H. Tran (nguyenth@khu.ac.kr) Kyung Hee University Usenix Feedback Computing 2014

2 / 18 1 Introduction Motivation Challenges Approaches 2 Two-stage Stackelberg Game Stage II: DCs Cost Minimization Stage I: Non-Cooperative Pricing Game 3 Equilibrium and Algorithm Backward Induction: Optimal Solutions at Stage II Backward Induction: Nash equilibrium at Stage I Distributed Algorithm 4 Trace-based Simulations 5 Conclusions 6 Q&A

3 / 18 Motivation 1 DCs consumed 1.5% of the worldwide electricity supply in 2011 and this fraction is expected to grow to 8% by 2020 2 DC operators paid more than $10M (Qureshi 2009) 3 DC operators can save 5% 45% cost by leveraging time and location diversities of prices The electricity price applying on DC does not change with demand Demand Response of Data Centers: receiving consideration Pricing for DR: a right price not only at the right time but also on the right amount of demand

Vertical Dependence 4 / 18 Challenges Location 1 Location 2 Location Utility Utility Utility Set price (require Demand) Give Demand (require Price) Data Center Set price (require Demand) Give Demand (require Price) Data Center Set price (require Demand) Give Demand (require Price) Data Center Horizontal Dependence Workload Distribution

5 / 18 Approaches DemandPResponseP ofpdatapcenterspusing SmartPGrid Utility Two-stageP Stackelberg Game Stage I: UtilityPprofitP maximization Real-timeP PricingP GameP betweenp UtilitiesP Distributed Algorithm Smart Meters DataPCenter Stage II: DataPCenters PcostP minimization WorkloadP Distribution DynamicP Server Provisioning 17

6 / 18 Stage II: DCs Cost Minimization Optimization Problem DC : minimize subject to T t=1 i=1 I e i (t)p i (t) + ωd i λ 2 i (t) (1) 1 s i (t)µ i λ i (t) + d i D i, i (2) I i=1 λ i (t) = Λ(t), t, (3) 0 s i (t) S i, i, t, (4) 0 λ i (t) s i (t)µ i, i, t, (5) variables s i (t), λ i (t), i, t. (6)

7 / 18 Stage I: Utility Revenue and Cost Revenue R i (p(t)) = ( e i (p(t)) + B i (p i (t)) ) p i (t) Cost ( ) ei (p(t)) + B C i (p(t)) = γeli = γ i (p i (t)) 2 C i (t), C i (t)

8 / 18 Stage-I: A Non-Cooperative Pricing Game Formulation Players: the utilities in the set I; Strategy: p l i p i (t) p u i, i I, t T ; Payoff function: T t=1 u i(p i (t), p i (t)), i I. u i (p i (t), p i (t)) = R i (p(t)) C i (p(t)),

9 / 18 Backward Induction: Optimal Solutions at Stage II Observe that the QoS constraint must be active [ 1 ( s i (λ i ) = λ i + µ D 1 )] S i i, i 0 Optimization Problem DC : min. λ I I i=1 f i(λ i ) (7) s.t. λ i = Λ, i=1 (8) λ i 0, i, (9) ) ) f i (λ i ) := ωd i λ 2 i + p i (a i + b i µ i λ i + p i (e b + b 1 i D i µ i

Vertical Dependence 10 / 18 Backward Induction: Optimal Solutions at Stage II Location 1 Location 2 Location Utility Utility Utility Set price (require Demand) Give Demand (require Price) Data Center Set price (require Demand) Give Demand (require Price) Data Center Set price (require Demand) Give Demand (require Price) Data Center Horizontal Dependence Workload Distribution e i (p) = A2 i p i 2ωd i ( 1 ˆdd i 1) + A i 2ωˆdd i j i A j p j d j + A iλ + b i + ei ˆdd b. i µ i Di

11 / 18 Backward Induction: Nash equilibrium at Stage I Existence: concave game (Rosen 1965) Best response updates p (k+1) i = BR i ( p (k) i ( h 1 γn i /C i ) = 1/2 γn i/c i p (k) i ( N i ) ) Pi, i Uniqueness: pi e Condition ω max i = BR i (p i e ), i { Ai j i A j/d j A 2 i } ˆd(1 1/(d i ˆd)), 2β i ˆddi

Distributed Algorithm Location 2 Location 1 Utility 2 DC 2 Location I 2 2 ( ) Utility 1 DC 1 1 ( ) DC I Utility I 1 Internet ( ) ( 1,, ) 1 ( ),, ( ) Front-end Server ( ) 12 / 18

13 / 18 Trace-based Simulations Workload Workload eb(t) (MW) 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 MSR 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0 100 200 300 400 500 600 700 FIU Google

14 / 18 Dynamic Prices Prices ($/MW) 200 150 100 50 0 200 150 100 50 0 The Dalles, OR Mayes County, OK 200 Berkeley County, SC 150 100 50 0 0 100 200 300 400 500 600 700 Hour (a) FIU trace Council Bluffs, IA Lenoir, NC Douglas County, GA Baseline 1 Baseline 2 Alg. 1 0 100 200 300 400 500 600 700 Hour

15 / 18 DC s cost and utilities profit DCs cost ($) Utilities profit ($) 50000 40000 30000 20000 10000 0 50000 40000 30000 20000 10000 Baseline 1 Alg. 1 0 0 100 200 300 400 500 600 700 Hour (a) FIU trace

PAR PAR 3.5 3.0 2.5 2.0 1.5 3.58 Baseline 1 Baseline 2 3.13 3.03 Alg 1 2.80 2.61 2.40 2.37 2.23 2.22 2.28 2.18 2.13 2.06 1.97 1.62 1.48 1.46 1.51 PAR 3.5 3.0 2.5 2.0 1.5 3.58 Baseline 1 Baseline 2 3.13 3.03 Alg 1 2.80 2.63 2.40 2.37 2.23 2.22 2.28 2.19 2.13 2.06 1.97 1.63 1.47 1.45 1.49 1.0 1.0 0.5 0.5 0.0 The Dalles, OR Council Bluffs, IA Mayes County, OK Lenoir, NC Berkeley County, SC Douglas County, GA 0.0 The Dalles, OR Council Bluffs, IA (a) γ = 1, (b) γ = 4 Mayes County, OK Lenoir, NC Berkeley County, SC Douglas County, GA 16 / 18

17 / 18 Summary and Future Work Summary DR of DCs: interactions between DCs and utilities via pricing Two-stage Stackelberg game: utilities are leaders, DCs are follows Flatten the demand over time and space Future Work Deadline constraint Workload estimation errors Risk consideration

/ 18 Q&A? 18