PaperlayerView exact revision on arXiv

Source-linked AI summary

Proactive Demand Response for Data Centers: A Win-Win Solution

Hao Wang, Jianwei Huang, Xiaojun Lin, Hamed Mohsenian-Rad

arXiv:1511.00575v1eess.SYcs.DCcs.SY

TL;DR

The paper studies how data-center workload redistribution affects the power grid, a gap in research on active coordination between grids and data centers. It models utility pricing and data-center responses as a two-stage optimization problem; simulations report benefits for both power-load balancing and data-center energy costs.

  • Problem

    The paper examines how the power grid can use data-center load distribution for balancing, an interaction involving active decisions on both sides that had not been studied in this way.

    Source: §I · p. 2

  • Method

    The authors model utility-set dynamic prices and data-center energy responses as a two-stage problem, introduce benchmark problems, and develop a branch-and-bound method and a low-complexity heuristic.

    Source: §I · p. 2, §VIII · p. 12

  • Results

    The simulations show a win-win result: the proposed method can balance power load while reducing data centers’ total energy cost.

    Source: §I · p. 2, §VIII · p. 12

  • Takeaways & Limitations

    Dynamic pricing lets the utility company redistribute data-center energy consumption for load balancing while also reducing data-center energy costs.

    Source: §I · p. 2, B. Effectiveness of optimized dynamic… · p. 11

Abstract

from arXiv · show

In order to reduce the energy cost of data centers, recent studies suggest distributing computation workload among multiple geographically dispersed data centers, by exploiting the electricity price difference. However, the impact of data center load redistribution on the power grid is not well understood yet. This paper takes the first step towards tackling this important issue, by studying how the power grid can take advantage of the data centers' load distribution proactively for the purpose of power load balancing. We model the interactions between power grid and data centers as a two-stage problem, where the utility company chooses proper pricing mechanisms to balance the electric power load in the first stage, and the data centers seek to minimize their total energy cost by responding to the prices in the second stage. We show that the two-stage problem is a bilevel quadratic program, which is NP-hard and cannot be solved using standard convex optimization techniques. We introduce benchmark problems to derive upper and lower bounds for the solution of the two-stage problem. We further propose a branch and bound algorithm to attain the globally optimal solution, and propose a heuristic algorithm with low computational complexity to obtain an alternative close-to-optimal solution. We also study the impact of background load prediction error using the theoretical framework of robust optimization. The simulation results demonstrate that our proposed scheme can not only improve the power grid reliability but also reduce the energy cost of data centers.

I. INTRODUCTION

The introduction shifts distributed data-center energy management from cost minimization alone to coordinated grid and data-center decisions. It motivates dynamic pricing, benchmarks, and solution methods for balancing grid loads while reducing data-center energy costs.

I. INTRODUCTION

  • Dynamic utility pricing coordinates data-center energy use with grid load balancing, addressing the risk that cost-focused workload redistribution could harm grid stability.The framework lets the utility adjust prices while the cloud provider reallocates workload across data centers.Source: §I · p. 2
  • The paper frames active decisions by both the utility and data centers as a new interaction problem, and proposes benchmarks, a global branch-and-bound method, and a close-to-optimal heuristic.The authors report that the approach can balance grid loads while reducing data-center energy costs.Source: §I · p. 2

A. Literature Review

  • Prior data-center energy-management work largely targeted energy-cost reduction, while demand-response research often addressed time flexibility rather than load management across locations.The cited literature also leaves utility action and cross-location load fluctuations unaddressed in data-center workload management.Source: A. Literature Review · pp. 2–3

B. Motivation

  • Geographically dispersed data centers can shift workload across locations, motivating a dynamic-pricing mechanism for one utility and one cloud provider with multiple data centers.The cloud provider's workload distribution offers flexibility across locations, unlike residential demand in the discussion.Source: B. Motivation · p. 3

III. SYSTEM MODEL

The system models a cloud provider and utility coordinating across geographically dispersed data centers in two stages: the utility sets billing references, then the provider allocates workload and servers to minimize energy cost while meeting workload and delay requirements.

III. SYSTEM MODEL

  • The utility sets each data center’s billing reference first; the cloud provider then chooses workload allocation and active servers to minimize total energy cost.The model uses discrete time slots and assumes the data centers share one cloud provider and cooperate in their decisions.Source: §III · p. 3

1) Workload constraint:

  • Each time slot’s total incoming workload must be distributed across the data centers, with nonnegative allocation to each center.Source: 1) Workload constraint · p. 4

2) QoS (delay) constraint:

  • The QoS constraint accounts for transmission and queuing delays, requiring their total to remain within the delay bound.The queuing-delay model uses server service rates and active server counts; requests are assumed to share the same delay bound.Source: 2) QoS (delay) constraint · p. 4

3) Server constraint:

The provider’s energy-cost problem accounts for server operation and data-center power consumption. It chooses workload allocation and active server numbers subject to operational constraints to minimize total cost.

3) Server constraint:

  • Because each center has many servers, the model relaxes the integer constraint on active-server counts, which the authors say does not significantly affect the optimum.Source: 3) Server constraint · p. 4

4) Energy consumption constraint:

  • Data-center energy includes IT and ancillary consumption, with PUE used to relate total energy to IT energy.The resulting consumption model is affine in workload and active-server count, and power is bounded by available supply.Source: 4) Energy consumption constraint · p. 4
  • The Stage-2 problem minimizes total energy cost across locations and time slots by choosing workload allocations and active server counts.The operational constraints are decoupled across time slots.Source: 4) Energy consumption constraint · p. 5

B. Stage 1: Smart Grid’s Power Load Balancing Problem

The utility balances grid load by setting dynamic prices that shape data-center energy use, while price limits regulate the utility’s pricing discretion. The paper’s capacity-weighted load index targets equal load ratios in an unconstrained ideal case.

  • The utility sets billing references to balance load ratios across locations, with data-center consumption determined by the provider’s response.The model assumes the utility can forecast background loads before each time slot.Source: B. Stage 1: Smart Grid’s Power Load… · pp. 5–6
  • The Electric Load Index weights location load ratios by substation capacity; minimizing it yields equal load ratios in the ideal unconstrained case.The passage states that this ideal distribution avoids overloading and improves system reliability.Source: B. Stage 1: Smart Grid’s Power Load… · p. 5
  • Equal load distribution may be infeasible under workload and server constraints, and the utility cannot directly control data-center energy use because the provider operates the centers.Source: B. Stage 1: Smart Grid’s Power Load… · p. 5
  • Dynamic-price constraints bound regional prices and impose an average-price ceiling, so higher prices in some locations require lower prices elsewhere.The ceiling is specified by contract and is intended to prevent arbitrary increases in data-center energy costs.Source: B. Stage 1: Smart Grid’s Power Load… · p. 5

C. Two-stage Price Optimization Problem

The paper recasts the provider’s response as an energy-consumption distribution problem and links it to the utility’s price-setting stage. This coupling makes the two-stage optimization challenging and motivates benchmark bounds.

  • The provider’s Stage-2 problem can be rewritten as choosing data-center energy consumption directly, subject to equivalent energy bounds.The resulting formulation minimizes energy cost under the rewritten constraints.Source: C. Two-stage Price Optimization Problem · p. 6
  • In each time slot, the utility’s billing references determine prices for the provider, whose energy choices feed back into the utility’s load-balancing objective.Source: C. Two-stage Price Optimization Problem · p. 6
  • Because Stage 1 must account for the coupled Stage-2 response, the two-stage problem is challenging; the paper introduces benchmark problems to bound its optimum.Source: C. Two-stage Price Optimization Problem · p. 6

IV. PERFORMANCE BENCHMARKS

The integrated and restricted benchmarks bound the optimal ELI of the original two-stage problem from below and above. Their formulations trade direct utility control against more conservative pricing constraints.

A. The Integrated Problem

  • The integrated benchmark lets the utility directly choose workload assignments and active servers, yielding a convex quadratic program.It represents the ELI achievable under full cooperation between the utility and data centers.Source: A. The Integrated Problem · p. 6

IV. PERFORMANCE BENCHMARKS

A. The Integrated Problem

  • The lower-bound gap depends on pricing constraints (9) and (10); widening the allowed price range can bring optimal ELI closer to the bound.Source: A. The Integrated Problem · p. 7

B. The Restricted Problem

  • The restricted benchmark moves the energy-consumption bound (12) into Stage 1, shrinking the utility’s action set and producing an upper bound.Its estimation also depends on parameter configurations in constraints (9), (10), and (12).Source: B. The Restricted Problem · p. 7

V. SOLVING THE ORIGINAL TWO-STAGE PROBLEM

The paper solves the data centers’ response first, then uses it to formulate and solve the utility’s pricing problem. A customized branch-and-bound method finds the global optimum, though its worst-case complexity may limit large-scale use.

A. Solving the Stage-2 Problem

  • Given the utility’s charging reference, data centers choose workload allocations and active servers to minimize energy cost; the strictly convex response problem has a unique optimal solution.The response is derived using the Lagrangian dual method.Source: A. Solving the Stage-2 Problem · p. 8

B. Solving the Stage-1 Problem

  • With complete information, the utility company predicts data-center energy consumption from dynamic prices and incorporates PE2’s KKT conditions into PS1, transforming the two-stage problem into a single-level optimization problem.Because PE2 is strictly convex, its KKT conditions are necessary and sufficient for its optimum.Source: B. Solving the Stage-1 Problem · p. 8
  • Branch-and-bound splits binary variables in a relaxed problem, updates lower and upper bounds, and terminates at a global optimum when the bounds meet or all nodes are evaluated.The initial bounds come from the integrated and restricted benchmarks; the tree’s worst-case traversal is reported as 22N nodes.Source: B. Solving the Stage-1 Problem · p. 9, Figure 4 · p. 9

C. Heuristic Algorithm

A low-complexity descent heuristic offers a suboptimal alternative to branch-and-bound. It adjusts charging references to redistribute energy consumption and reduce ELI while retaining a feasible solution.

C. Heuristic Algorithm

  • Because branch-and-bound can have high worst-case complexity, the authors propose a descent heuristic that iteratively reduces ELI to obtain a suboptimal solution.Source: C. Heuristic Algorithm · p. 9
  • The heuristic lowers prices at high-consumption locations and raises them at low-consumption locations, using the response relation between charging references and energy consumption.The utility and data centers iterate over prices and consumption schedules; the stated convergence is to a feasible, possibly suboptimal solution.Source: C. Heuristic Algorithm · p. 9

VI. IMPACT OF BACKGROUND LOAD PREDICTION ERROR

The paper models background-load prediction errors within bounded uncertainty sets and optimizes worst-case ELI. The worst-case error occurs at the upper bounds of those sets.

VI. IMPACT OF BACKGROUND LOAD PREDICTION ERROR

  • The robust formulation represents actual background load as predicted load plus error and bounds prediction errors in known uncertainty sets.It seeks billing references that optimize worst-case load-balancing performance.Source: §VI · p. 10
  • The worst-case prediction error lies at the upper bounds of the uncertainty set, so those upper-bound errors are substituted into the worst-case optimization problem.Source: §VI · p. 10

VII. SIMULATION RESULTS

The evaluation compares electric load index and energy cost against benchmark solutions using realistic system parameters.

VII. SIMULATION RESULTS

  • The evaluation compares electric load index and energy cost from the proposed algorithms with benchmark solutions.The simulations use realistic system parameters.Source: §VII · p. 10
  • The case study models four data centers in New York, Maine, Rhode Island, and Boston, with 60,000–80,000 servers at each site.Each server consumes 200 watts at peak and 100 watts when idle; power usage effectiveness ranges from 1.2 to 1.5.Source: §VII · p. 10
  • Hourly locational marginal prices and demand from March 4, 2013, provide base prices and background loads; computing requests use a Google workload trace from December 20, 2013.The trace is normalized.Source: §VII · p. 10

A. Performance of the proposed algorithms

The two-stage solution’s electric load index is close to its lower bound, and the heuristic closely tracks the optimum. Optimized dynamic pricing reduces load imbalance and energy cost while redistributing consumption across locations.

A. Performance of the proposed algorithms

B. Effectiveness of optimized dynamic pricing

C. Impact of prediction errors

The robust optimization case study evaluates ELI under prediction errors, while the workload study finds that dynamic pricing lowers ELI across tested workloads. The conclusion reports a simulated win-win outcome and identifies renewable energy and incomplete information as future study areas.

C. Impact of prediction errors

D. Impact of computing workload

  • ELI reduction is 9.7% at 0.9 workload, versus 4.4% at 0.6 and 1.8% at 1.4 of the original workload.The improvement is relatively larger at intermediate workload than at light or heavy workload.Source: D. Impact of computing workload · p. 12
  • At light workload, low energy use limits overload risk; at heavy workload, data centers have little flexibility to shift workload while serving requests.Both conditions reduce the benefit of dynamic pricing.Source: D. Impact of computing workload · p. 12
  • Across workloads from 0.6 to 1.4 of the original value, dynamic pricing always achieves lower ELI than baseline pricing, while ELI rises with workload for both.The comparison uses one time slot and holds other simulation parameters unchanged.Source: Figure 13 · p. 12, D. Impact of computing workload · p. 12

VIII. CONCLUSIONS

  • The conclusion reports a simulated win-win solution for the utility company and data centers from the two-stage price optimization approach.The problem is reformulated as a mixed-integer quadratic program and addressed with a globally optimal branch-and-bound algorithm and a low-complexity heuristic descent algorithm.Source: §VIII · p. 12
  • Future work includes utility–data-center interaction with high renewable-energy penetration and incomplete information, including asymmetric information about data-center operations.The paper also identifies management of renewable-powered data centers as a topic for study.Source: §VIII · p. 12
Loading 1511.00575v1…