Unsupervised Disaggregation of Low Frequency Power Measurements Hyungsul Kim∗ Manish Marwahy Martin Arlitty Geoff Lyony Jiawei Han∗ Abstract electricity and/or gas use could be reduced by up to Fear of increasing prices and concern about climate change 50% [14], although typical savings were in the 9%-20% are motivating residential power conservation efforts. We range [42, 20, 45, 1, 47]. Improved feedback can also investigate the effectiveness of several unsupervised disag- gregation methods on low frequency power measurements help curtail peak use by up to 50% [27, 44]. collected in real homes. Specifically, we consider variants Much of this research occurred decades ago, in re- of the factorial hidden Markov model. Our results indi- sponse to the oil crisis in the 1970s [39]. At that time, cate that a conditional factorial hidden semi-Markov model, which integrates additional features related to when and computer hardware technology was not as advanced, so how appliances are used in the home and more accurately providing frequent feedback to home owners cost effec- represents the power use of individual appliances, outper- tively seemed infeasible [19]. As the crisis subsided forms the other unsupervised disaggregation methods. Our results show that unsupervised techniques can provide per- (and prices dropped), the financial incentive to con- appliance power usage information in a non-invasive manner, serve diminished [45]. The growing concern over climate which is ideal for enabling power conservation efforts. change has revived the importance of conservation. To- day, computer hardware technology is more advanced, 1 Introduction so frequent feedback is now feasible. In particular, as Concern over global climate change has motivated ef- old power meters are replaced with smart meters, more forts to reduce the emissions of CO2 and other GHGs information will be available to consumers [38]. (greenhouse gases). Energy use in the residential sector An open issue is how to provide an appliance- is a significant contributor of GHGs [49]. For example, specific breakdown of energy use in a cost-effective the residential sector is responsible for over one third of manner. Without this, residential energy conservation all electricity use in the United States [2]. While infor- efforts are unlikely to achieve widespread success. This mation is available on the typical use of electricity in paper investigates how to obtain this information via homes (e.g., space heating, space cooling, water heat- power load disaggregation. While this topic has received ing and lighting account for about 50% of all residential attention since the early 1990s [18], our work has three electricity use [3]), it has not enabled most home owners distinguishing characteristics. First, we assume only low to reduce their electricity consumption. frequency measurements are available. This makes our Two typical approaches to conserving energy are ef- techniques more widely applicable since smart meters ficiency and curtailment [1]. The former involves one- typically provide samples no more than once per second. time actions (e.g., upgrading to more energy-efficient Second, we use an unsupervised disaggregation approach, appliances) that have a higher cost. The latter re- as this does not require the data to be labeled, which can quires continuous participation (e.g., using less heat- be laborious and intrusive. Third, we use empirical data ing/cooling on a daily basis), with a smaller incremen- collected from seven homes over a six month period. tal cost. There are two general issues that inhibit con- The specific problem we address is as follows. Given sumers from applying these techniques. First, energy the aggregate power consumption for T time periods, use is a very abstract concept to most consumers [24, 8]. Y = hy1; y2; : : : ; yT i, and the number of appliances, Second, consumers are often mistaken about how en- M, we want to infer the power load of each of the M ergy is used in the home, and thus which actions would appliances, that is, be most beneficial for conserving energy [15, 4, 38]. (1) (1) (1) (1) Numerous studies have identified the attributes of a Q = hq1 ; q2 ; : : : ; qT i (2) (2) (2) (2) solution to these issues: personalized, frequent, con- Q = hq1 ; q2 ; : : : ; qT i tinuous, credible, clear and concise feedback that pro- . vides an appliance-specific breakdown of how energy is . (M) (M) (M) (M) used in the home [5, 19, 7, 1, 11, 13, 15, 38]. Field Q = hq1 ; q2 ; : : : ; qT i studies showed that with proper feedback, residential PM (i) (i) such that yt = i=1 qt , where qt is the power load ∗University of Illinois, Urbana-Champaign, IL of appliance i at time t. yHP Labs, Palo Alto, CA We achieve this using energy disaggregation meth- 747 Copyright © SIAM. Unauthorized reproduction of this article is prohibited. ods based on extensions of a hidden Markov model P(d1=2) (HMM). We use four HMM variants to model the data. q1 OFF ON ON OFF ON Factorial HMM (FHMM) models the hidden states of all the appliances. Conditional FHMM (CFHMM) ex- q2 OFF ON ON ON OFF tends FHMM to incorporate additional features, such as time of day, other sensor measurements, and depen- q3 ON ON ON OFF OFF dency between appliances. A third variant, factorial hidden semi-Markov model (FHSMM) extends FHMM y y y y y to better fit the probability distributions of the state oc- y t-2 t-1 t t+1 t+2 cupancy durations of the appliances. The fourth variant composes FHSMM and CFHMM, to consider the addi- Figure 1: Graphical representation of factorial HMM. tional features together with the more accurate proba- bility distributions of the state occupancy durations of the appliances. We refer to this variant as conditional { the emission matrix B = fb(ojSj)g, indicating the factorial hidden semi-Markov model (CFHSMM). probability of emission of symbol o 2 V when Our paper makes two key contributions. First, we system state is Sj; V can be a discrete or a explore four unsupervised techniques for disaggregating continuous set, in which case b(ojSj) is a probability low frequency power load data. Second, we provide a density function. performance evaluation of the techniques using power { π = fπig, the initial state probability distribution, load data from real homes. We find that CFHSMM outperforms the other variants, and demonstrate that πi = P (q1 = Si); 1 ≤ i ≤ N unsupervised disaggregation techniques are feasible. PN The remainder of the paper is organized as follows. with πi ≥ 0 and i=1 πi = 1. Section 2 provides background information and related work. Section 3 discusses features that can be used for Suppose we have sequential data y = disaggregation of low frequency power measurements. fy1; y2; : : : ; yt; : : : ; yT g. Every yt is generated Section 4 describes the four models we use to identify by a hidden state, qt. The underlying states the stable-state signatures of household appliances. Sec- q = fq1; q2; ··· ; qt; : : : ; qT g form a Markov chain. tion 5 presents our results, using power load data from Given the current state, the next state is independent actual homes. Section 6 summarizes our work. of the past (Markov property). 2 Background and Related Work P (qt+1jqt; qt−1; : : : ; q1) = P (qt+1jqt) 2.1 Background Hidden Markov Models (HMM) As an extension of HMMs, Ghahramani and Jor- are used for probabilistically modeling sequential data. dan [17] introduced factorial HMMs to model multiple HMMs are known to perform well at tasks such as independent hidden state sequences, as shown in Figure speech recognition [37], problems in computational bi- 1. In a FHMM, if we consider Y = hy1; y2; : : : ; yT i to be ology [28], etc. the observed sequence then q = fq(1); q(2);:::; q(M)g A discrete-time hidden Markov model can be viewed represents the set of underlying state sequences, where as a Markov model whose states are not directly ob- (i) (i) (i) q(i) = (q ; q ; : : : ; q ) is the hidden state sequence of served: instead, each state is characterized by a prob- 1 2 T the chain i. In general, factorial learning algorithms are ability distribution function, modeling the observations used to discover multiple independent causes or factors corresponding to that state. More formally, an HMM is underlying the data. FHMMs are preferred to HMMs defined by the following: for modeling time series generated by the interaction of several independent processes because using HMMs to { S = fS ;S ; ··· ;S g the finite set of hidden states. 1 2 N model such processes requires exponentially many pa- { the transition matrix A = faij; 1 ≤ i; j ≤ Ng rameters to represent all the states. representing the probability of moving from state Si to state Sj, 2.2 Related Work The initial solution for disaggre- gating residential power load information was proposed aij = P (qt+1 = Sjjqt = Si); 1 ≤ i; j ≤ N; by Hart [18]. Hart demonstrated how different electrical appliances generated distinct power consumption signa- PN with aij ≥ 0; j=1 aij = 1, and where qt denotes tures, which often could be seen in the aggregated power the state occupied by the system at time t. load. He showed how on-off events were sufficient to 748 Copyright © SIAM. Unauthorized reproduction of this article is prohibited. characterize the use of some appliances. For other ap- sensor to detect electrical events within a home. They pliances, Hart considered using Finite State Machines leverage the fact that mechanical switches produce elec- to develop signatures. Hart called this approach \Non- trical noise [21], and that the noise characteristics can intrusive Appliance Load Monitoring"(NALM). vary dramatically by appliance [48]. They apply ma- Other research efforts have attempted to improve chine learning techniques to recognize specific devices NALM, often by proposing alternative signature identi- being turned on or off.