Smoothing the Energy Consumption: Peak Demand Reduction in Smart Grid Shaojie Tangy, Qiuyuan Huangz, Xiang-Yang Liy∗, Dapeng Wuz yDepartment of Computer Science, Illinois Institute of Technology, USA ∗School of Software, TNLIST, Tsinghua University zDepartment of Electrical & Computer Engineering, University of Florida Abstract—Assume that a set of Demand Response Switch In this work, we study two energy consumption schedule (DRS) devices are deployed in smart meters for autonomous problems. The first problem is Peak Demand Minimization demand side management within one house. The DRS devices problem. For this problem, we assume that all appliances or are able to sense and control the activity of each appliance. We propose a set of appliance scheduling algorithms to 1) minimize jobs must be scheduled within a given finite time duration. Our the peak power consumption under a fixed delay requirement, goal is to find an appliance scheduling strategy that will mini- and 2) minimize the delay under a fixed peak demand constraint. mize the peak demand while not violating the delay constraint. For both problems, we first prove that they are NP-Hard. Then Here the peak demand is defined as the largest power demand we propose a set of approximation algorithms with constant at any time instant. The other problem studied in this work is approximation ratios. We conduct extensive simulations using both real-life appliance energy consumption data trace and called Delay Minimization problem, which is a dual problem synthetic data to evaluate the performance of our algorithms. to the first one. Essentially, we assume that there is a pre- Extensive evaluations verify that the schedules obtained by our defined maximum peak demand constraint, and the objective is methods significantly reduce the peak demand or delay compared to design an appliance scheduling strategy that will minimize with naive greedy algorithm or randomized algorithm. the delay while not violating the peak demand constraint. We first prove that both problems are NP Hard. We further I. INTRODUCTION propose several approximation algorithms (MP algorithm for It was reported by U.S. Department of Energy in 2008 minimizing the peak demand, and MD1 and MD2 algorithms [25] that energy consumptions from buildings account for ap- for minimizing the delay) which can achieve constant approx- proximately 74% of the nation’s total electricity consumption. imation ratios on the performances. We then briefly discuss Unfortunately, due to inefficient energy consumption pattern in the online setting of energy consumption scheduling problem. most buildings, billions of dollars were wasted. To improve en- Under online setting, a simple yet efficient greedy algorithm ergy usage efficiency, two different approaches could be used: is proposed. This algorithm has a constant competitive ratio reducing consumption and shifting consumption [18]. Notice for online delay minimization problem. We conduct extensive that reducing consumption could be achieved through either evaluations to study the performances of our methods using more careful consumption behaviors or constructing more both real-life appliance energy consumption data trace and energy-efficient appliances. For example, we could encourage synthetic data. Extensive evaluations verify that the schedules people to use less energy consuming appliances. In this work, obtained by our methods significantly reduce the peak demand we are particularly interested at the second approach. As or delay compared with naive greedy algorithm or randomized a complimentary approach to the first one, we stress the algorithm. For example, MP algorithm achieves an average of importance of reducing peak demand through shifting heavy- more than 30% savings on peak power consumption compared load appliances to off-peak hours, which makes it easy for to the Greedy algorithm, both in small-scale and large-scale e- power generation to match the demand. valuations. MD1 and MD2 algorithms outperform the Greedy Energy consumption or load scheduling have been well algorithm by more than 50% and 40% savings on execution studied since thirty years ago [5], [9] [28]. However, recent time respectively. advancements in smart metering and smart grid infrastructure allow us to adopt fine-grained energy consumption scheduling. In this work, we aim at optimally scheduling the household or The paper is organized as follows. Section II and Sec- industry energy consumption in each appliance in order to re- tion III introduce the system model, motivation and problem duce the peak energy consumption or demand. We assume that formulation. Section IV and Section V describe our scheduling several appliances within one building access to one energy schemes for both peak demand minimization problem and resource. Each appliance is equipped with a Demand Response delay minimization problem. We investigate online setting Switch (DRS) device. The DRS devices are connected to the of both problems in Section VI. Extensive evaluation results power line and are able to communicate with each other. based on real data trace are reported in Section VII. We review The DRS devices will follow the optimal energy consumption related work in Section VIII and conclude the paper with some schedule to coordinate each appliance. future work directions in Section IX. II. SYSTEM MODEL III. PROBLEM FORMULATION We consider a discrete time system and a time period In this paper, we first study the Peak Demand Minimiza- [0;T ] during which n electrical jobs or appliance, J = tion Problem for peak demand reduction. We assume that fJ1;J2; ··· ;Jng, should be scheduled. Here T typically is time horizon is finite with duration T since users do not want 24 hours. We adopt similar notations used in [6] in the to delay their jobs forever. rest of this paper: the i-th job J has a demand profile D i i Problem 1 (Peak Demand Minimization Problem). Compute parameterized by (d ; τ ), where d denotes J ’s instantaneous i i i i starting time s for each job J to minimize the peak demand power consumption and τ represents its duration. When the i i n D . Then the optimization problem for minimizing peak job J is scheduled to start at time s , it specifies a power P eak i i demand during a finite horizon T > 0, is formulated as: consumption function: Problem: Peak Demand Minimization Scheduling Di(t) = di · I[si;si+τi](t); Objective: Minimize DP eak subject to: 8 where I[a;b](t) is a step function that has value 1 at the interval (1) D (t) = d I (t) > i i [si;si+τi] [a; b] 0 > n and elsewhere. We assume that the job cannot be <>(2) D(t) P D (t) = P d I (t) s , i i i=1 i [si;si+τi] interrupted once it starts. In general, the starting time i should (3) 0 ≤ s ≤ T − τ s d s d > i i satisfy ti ≤ si ≤ ti , where ti and ti represent the earliest > :(3) DP eak = max D(t) and latest starting time of the job. In this work, we aim at t2[0;T ] assigning each job Ji a starting time 0 ≤ si ≤ T − τi under We first show that even when all durations τn are equal, various constraints to reduce the peak demand. Consequently, finding an optimal schedule is still an NP-hard problem (i.e., under a given schedule, the total load on the network at time can be reduced to the Subset-Sum problem). instance t is Lemma 1. The Peak Demand Minimization Problem is NP- n n X X Hard. D(t) , Di(t) = di · I[si;si+τi](t): i=1 i=1 Proof: We will reduce our problem from the Subset-Sum Problem: Given a set of integers A = fI1; ··· ;Ing, determine We next reveal the motivations of this study by introducing whether there exists a subset Ac of numbers from A such that two widely adopted utility cost model. For each of those the sum of those numbers models, in order to reduce the utility cost, it is essential to find X X an energy consumption scheduling with small peak demand. Ii = Ii=2 I 2Ac I 2A Utility Cost Model I: Let C represent the utility cost from a i i group of appliances. In a demand based tariff for commercial Then given an input as listed above, we construct a peak energy customers [21], the utility cost is calculated by demand minimization problem as follows: In the constructed case, there are n jobs J1; ··· ;Jn each of which has identical C = pu · DT ot + pd · DP eak duration T=2. We assume the demand of each job di = Ii. We want to decide if there is a schedule with peak demand where D = max D(t) is the peak aggregate de- P P eak t2[0;T ] Ii=2, which clearly is the minimum. P Ii2A mand and DT ot = t2[0;T ] D(t) represents the total energy Clearly if there exists a subset of numbers from A such that consumption, pu the usage price, and pd the demand price. P P the sum of those numbers c I = I =2, we are Ii2A i Ii2A i Usually, pd is significantly higher than pu, e.g., in Pennsyl- able to find a scheduling with minimum height P I =2 Ii2A i vania, pd is 240 times pu [21]. The penalty for high peak by scheduling all jobs in Ac at time 0, and scheduling all power consumption is particularly significant, which motivates remained jobs at time T=2. On the other hand, if there exists research on reduction of peak power consumption. Clearly, a scheduling with height P I =2, we can pick those jobs Ii2A i given a fixed amount of total demands, the utility bill is that start from time 0 and the union of their demands must be minimized when the peak power consumption is minimized a feasible Ac.