Compressive Non-Intrusive Load Monitoring Shikha Singh Indraprastha Institute of Information Technology, Delhi, India shikhas@iiitd.ac.in Angshul Majumdar Indraprastha Institute of Information Technology, Delhi, India angshul@iiitd.ac.in Stephen Makonin Simon Fraser University Vancouver, BC, Canada smakonin@sfu.ca ABSTRACT In non-intrusive load monitoring (NILM), an increase in sampling frequency translates to capturing unique signal features during tran- sient states, which, in turn, can improve disaggregation accuracy. Smart meters are capable of sampling at a high frequency (typi- cally 20kHz). However, transmitting signals continuously would choke the network bandwidth. Given the deployment of millions of smart meters which communicate over a wireless wide-area net- work (WAN), utilities can only collect power signals at very low frequencies. We propose a compressive sampling (CS) approach. Af- ter measuring the high-frequency power signal from a smart meter will be encoded (by a random matrix) to very few samples making the signal suitable for WAN transmission without choking network bandwidth. CS guarantees the recovery of the high-frequency sig- nal from the few transmitted samples under certain conditions. This work shows how to simultaneously recover the signal and disaggregate it; hence, the name Compressive NILM. CCS CONCEPTS · Information systems → Information retrieval. KEYWORDS non-intrusive load monitoring, NILM, energy disaggregation, com- pressed sensing, compressive sampling, sparse coding ACM Reference Format: Shikha Singh, Angshul Majumdar, and Stephen Makonin. 2020. Compressive Non-Intrusive Load Monitoring. In The 7th ACM International Conference on Systems for Energy-Efcient Buildings, Cities, and Transportation (BuildSys ’20), November 18ś20, 2020, Virtual Event, Japan. ACM, New York, NY, USA, 4 pages. https://doi.org/10.1145/3408308.3427613 1 INTRODUCTION Energy disaggregation is the task of estimating the energy consump- tion of individual electrical appliances given the total consumption recorded by the smart-meter. It is a single channel (smart-meter) blind source (appliances) separation problem. This makes the prob- lem highly underdetermined in nature ś one equation (smart-meter consumption) and many variable (appliance consumption). There- fore the problem has infnitely many solutions. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for proft or commercial advantage and that copies bear this notice and the full citation on the frst page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specifc permission and/or a fee. Request permissions from permissions@acm.org. BuildSys ’20, November 18ś20, 2020, Virtual Event, Japan © 2020 Association for Computing Machinery. ACM ISBN 978-1-4503-8061-4/20/11. . . $15.00 https://doi.org/10.1145/3408308.3427613 When the power signal is of sufciently high frequency, integer programming based approaches provide a feasible solution [2, 20]. Similarly factorial hidden Markov model (FHMM) is used to dis- aggregate appliance loads from high frequency samples [12, 16]. The performance of such techniques degrades when the sampling frequency is reduced. Sparse coding approaches yield somewhat better results at low-frequencies [9, 11]; however, even with sparse coding, higher frequencies translate to better results. Smart-meters can sample at high frequencies, but higher frequen- cies mean generation of more data. Transmitting this data from the building smart-meter to the cloud at the utilities consumes some bandwidth; higher the sampling frequency higher is the bandwidth consumed. Note that, it is not only one building that would be trans- mitting this data, all the buildings would be transmitting it; in such a scenario it is likely the entire network bandwidth will be consumed for only transmitting power signals! To keep the network usage at check, the smart-meter transmits the signal at low-frequencies (even though it is capable of sampling at high frequencies). Typically it is expected that energy disaggregation would be ofered as a service by the utilities. However, since the utilities will have access to only low-frequency information, the disaggrega- tion accuracy is likely to sufer. To bridge the gap between high- frequency sampling and low-frequency transmission we propose a compressed sensing / compressive sampling (CS) approach [4, 5, 7]. We project the high frequency signal to a lower dimension em- bedding by a random projection matrix. The lower dimensional signal will emulate a low frequency signal which can be then trans- mitted. The random projection can be easily integrated into hard- ware [6, 21]. Under certain conditions, such a lower dimensional embedding approximately preserves the information of the high frequency signal and can be recovered using sparsity promoting techniques like ℓ 1-minimization [10] or matching pursuits like al- gorithms [18]. This work extends the traditional compressed sensing dictates (e.i., recovering the signal) by adding simultaneous disaggregation as part of the recovery process. Our formulation is based on the dictionary learning approach [19] (the same technique used in sparse coding [9, 11]). The paper will be organized into several sections. We will discuss the basics of CS in the following section. In Section 3, we describe our proposed formulation. The results will be detailed in Section 4. Finally, the conclusions of this work will be discussed in Section 5. 2 COMPRESSIVE SAMPLING Compressed Sensing (CS) studies the problem of solving an under- determined linear system of equations where the solution is known to be sparse. In practical scenarios, the system is corrupted by noise as well.