WO2016141978A1 - Improved non-intrusive appliance load monitoring method and device - Google Patents

Improved non-intrusive appliance load monitoring method and device Download PDF

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Publication number
WO2016141978A1
WO2016141978A1 PCT/EP2015/054994 EP2015054994W WO2016141978A1 WO 2016141978 A1 WO2016141978 A1 WO 2016141978A1 EP 2015054994 W EP2015054994 W EP 2015054994W WO 2016141978 A1 WO2016141978 A1 WO 2016141978A1
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events
branch
nialm
event
aggregate
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PCT/EP2015/054994
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French (fr)
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Marc DE MEY
Frédéric KLOPFERT
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You Know Watt
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Priority to PCT/EP2015/054994 priority Critical patent/WO2016141978A1/en
Publication of WO2016141978A1 publication Critical patent/WO2016141978A1/en

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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R21/00Arrangements for measuring electric power or power factor
    • G01R21/133Arrangements for measuring electric power or power factor by using digital technique
    • G01R21/1331Measuring real or reactive component, measuring apparent energy
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R19/00Arrangements for measuring currents or voltages or for indicating presence or sign thereof
    • G01R19/25Arrangements for measuring currents or voltages or for indicating presence or sign thereof using digital measurement techniques
    • G01R19/2513Arrangements for monitoring electric power systems, e.g. power lines or loads; Logging
    • G01D2204/24

Abstract

The present invention concerns a non-intrusive appliance load monitoring method for monitoring components of appliances in a system (268) comprising a set of branched circuits (256, 257, 258, 259), comprising the steps of: (a) detecting system events in an aggregate electrical signal comprising aggregate power consumption information of said system (268), said system events representing state transitions of the appliances in the system (268), and said system (268) events comprising on-events and off-events; (b) for at least one and preferably each of said branch circuits (256, 257, 258, 259): separately detecting branch events in a branch electrical signal comprising branch power consumption information of said branch circuit (256, 257, 258, 259) of said system (268), said branch events representing state transitions of the appliances connected to said branch circuit (256, 257, 258, 259); (c) pairing on-events and off-events, thereby obtaining a set of paired events; and (d) detecting and/or identifying components on the basis of said set of paired events, characterized in that an on-event and an off-event are identified as a paired event only if both the on-event and the off-event are detected as branch events of the same branch circuit (256, 257, 258, 259).

Description

Improved non-intrusive appliance load monitoring method and
device
Technical field
The invention pertains to the technical field of automatic appliance detection, in particular Non-Intrusive Appliance Load Monitoring (NIALM), which refers to the automated detection of the state of appliances, e.g. household appliances, industrial appliances, a company's appliances, etc., from a total energy consumption signal. More in particular, the present invention relates to obtaining information at the component level of electrical appliances in a system, e.g. a household or a company, from a measurement of the total electricity consumption of said system. This information at the component level may include but is not limited to: the presence, the state and/or the energy consumption. The system may also be comprised of a single or a few appliances, whereby the methods, devices and/or systems of the present invention can be used for condition monitoring of one or more appliances. Background
WO 2012/160062 Al discloses a method for detecting transitions in a measured signal e.g. a discrete time signal and current waveform, which is induced by elements i.e. components of appliances, of a physical system i.e. a house. The method involves generating a residual signal, i.e. transition likelihood signal, from a measured signal, i.e. a discrete time signal, where the residual signal is provided with a high amplitude when transitions occur and with low amplitude in other cases. Rules concluding that transitions occur when the residual signal is larger than a threshold stable value, are provided, where the stable value is automatically defined from local values of the residual signal and defined as a function of local background noise. The measured signal is filtered before generating residual signal. The method enables defining a time index corresponding to end of transient state to maximize a distance between transient states and a straight line passing through the transient state, thus improving separation between transient and steady states, and hence detecting transitions in the measured signal, and monitoring automatic-setup non-intrusive appliance load for identifying appliances energy consumption in a reliable manner. This document also discloses an automatic-setup non-intrusive appliance load monitoring method (50) for identifying appliances energy consumption and comprising the steps of:
• detecting transitions in a measured signal;
• characterizing differences between steady states before and after these transitions; • characterizing transient states located between steady states;
• identifying components;
• identifying appliances from the components identified in the previous step;
• providing appliances energy consumption. The step of identifying components is hereby performed by selecting spectral features or features describing a current waveform for the steady states, with the possibility of the chosen features being grouped together in well-separated clusters for different components.
Hereby, a first step of component identification consists in clustering and classifying the components according to their nature (motor, resistor, heater, television are examples of different natures). A second step classifies the components within their nature cluster; this is the component classification itself.
Identifying a nature of a component is a classification problem with a predefined number of classes. Therefore, a K-means algorithm is preferably chosen. A K- means method is a clustering technique that partitions n observations into K clusters, where K is a predefined value. It classifies the components according to their nature; there will be as much classes as defined component natures. Three examples of different natures are resistors, motors and electronic devices. Not all features are relevant when looking only at a component nature. Preferably, when searching a nature of a component, one can consider THD (total harmonic distortion), or ratio Q/P (Q = reactive power and P = active power).
The second classification step is far different because the number of clusters to identify is generally large and unknown; no prior information is generally available about a number of appliances contained in a house, so no prior information is available concerning the identification of components within their nature. Hence, a DBScan (Density Based Spatial Clustering for Applications with Noise) classification algorithm is preferably used. Looking at the steady states, the components will differ for instance by a magnitude of their consumption from others within a component nature cluster. As far as the transient state features are concerned, two nearly identical but different components could have different transient shapes. Note hereby, that although the number of clusters does not have to be specified up front when using the DBSCAN algorithm, the number of clusters which is found by the DBSCAN algorithm has been observed not always to correspond with the actual number of electrical components in the system. Although the above methodology, in particular regarding the second step above, may work in a controlled set-up, it has been found that large problems remain occurring in real-life application of the above clustering and component identification methods. More in particular, the fact that the number of clusters to identify is unknown for any household, company, industry or other environment, poses severe problems for present state of the art clustering techniques within the field of NIALM.
WO2009/103998 discloses a method of inference of appliance usage from a point measurement on a supply line, said supply line being common to multiple appliances and/or components of appliances comprising the steps of: · obtaining data from said measurement point;
• sampling power and reactive power at intervals substantially throughout periods of operation of said appliances or components of appliances corresponding to appliances or components of appliances being in ON and/or OFF modes of use;
· identifying characteristics of events by assessing power and reactive power change during an event; and by
• assessing one or more additional characteristics derivable from said power and reactive power to characterize an appliance;
• grouping events and/or cycles of events into clusters of similar characteristics; and
• inferring appliance usage based on said grouping.
This document does not seem to disclose how to separate clusters of events in an automated method, independent of the system is being monitored. This document discloses the possibility of using a look-up table in which ranges of clusters' properties are provided that correspond to particular appliances and appliance components. Obviously, such a look-up table technique will depend highly on the quality and continuous updating of the look-up table, and will allow identification of a limited number of electrical components only. Furthermore, this document discloses a stepwise cluster identification on the basis of the distance of events, whereby events within a pre-set distance are assumed to belong to the same cluster, after which the events belonging to the cluster with the greatest number of events are removed from the data, and the next cluster is identified.
Note that methods such as the one described in WO2009/103998, use a pre-set maximal inter-event distance, on the basis of which events are assigned to a cluster, whereby clusters identification is made at least partially on the basis of a minimal number of events assigned to that cluster. Both steps introduce a certain degree of arbitrariness into the method which results both in uncertainties with respect to the correctness, as well as in errors for the resulting identified clusters as well.
Prior art techniques for identifying electrical components within a system from a measured electrical power consumption signal, have been noticed to require extra input with respect to the appliances comprised in the system, either by simply providing the method with characteristic signals of each single appliance up front, or by providing an extensive look-up table of characteristic signals of appliances. Such techniques could be deemed impractical for systems in which the number or type of appliances changes over time, such as a common household or a company, and could be deemed unworkable as it requires constant updating of a look-up table with characteristic signals from all possible appliances.
Prior art techniques for identifying electrical components within a system from a measured electrical power consumption signal, have been seen to be not completely reliable with respect to the grouping of events extracted from the measured signal into clusters. Furthermore, prior art techniques do not seem to allow to fully compute or estimate the uncertainty or error which arises from the clustering the events.
The present invention provides a NIALM method which allows an improved component detection, in particular in the case no prior information on the components or appliances in the system is known. In such a case, the number of components (N) is a priori unknown and an automated determination of this number of components is required. Hereby, each correctly detected event can be associated to one of the N components. The present invention hereto provides an improved clustering technique for events, which in cooperation with the other steps of the method, allows to better identify electrical components. More in particular, techniques proposed in the literature use prior information about parametric finite state machine (FSM) models, parameters being automatically tuned to fit to the observations. As reported by Johnson and Willsky, "Bayesian Nonparametric Hidden Semi-Markov Models", arXiv preprint, 2012, this information should be learned from the data. Since information can be extracted from the aggregate consumption as e.g. detailed in this document, one could wonder if this information can be straightforwardly computed to obtain component state sequences. Given the assumption that appliances are either on/off loads or systems of such loads, the ideal case for the evaluation of the state sequence is as follows: first, events correspond to on/off switching of components and there are no fictitious events and, second, for a given component, signatures of both on and off transitions belong to one single cluster. Further, no events related to other components share that cluster. In this ideal case, components are directly represented by clusters, their operations correspond to time intervals between on and off events and the evaluation of their state sequence simply consists to pair successive on and off events that are within identical clusters. The aggregate consumption is then modeled by combining the individual sequences.
Actual situations differ from this ideal case in several ways:
SI :
Some on/off switching are missing from the event sequence and there are fictitious events.
- Why: Because there are false (positive and negative) detections in the segmentation step, or because there is noise or non-linearities.
So what: Neither complementary events to missing ones nor fictitious detections should be paired with other events.
S2 : - Events of a single component are classified into different clusters.
Why: On and off event signatures might differ because of nonideal segmentation of turn-on transients or variable consumption of loads during their operations, because of noise or because of non-linearities.
So what: On and off events of different clusters should be paired to obtain component state sequences.
S3 :
Events corresponding to different components belong to a single cluster.
Why: There are components with similar properties w.r.t. the clustering parameters (or completely similar components).
- So what: Events of that single cluster must be distributed into different component state sequences.
S4:
There are events whose signatures are combinations of others
Why: Some on/off switching are simultaneous switch events.
- So what: These events should be paired to several events distributed in different clusters. The problem consists to find the underlying electrical components responsible for the observed aggregate consumption. Only then could states sequences be correctly evaluated and cope with the deviations from the ideal case (SI to S4).
Ideally, one cluster corresponds to one electric component and inversely. In practice, several clusters might correspond to a single component, e.g. if turn-on and turn-off features differ, and several components might correspond to a single cluster, e.g. a household or a company which own many similar electrical components. Therefore, prior art methods using clustering do not automatically lead to component detection.
The present invention provides a NIALM method which allows an improved component detection, in particular in case a system comprises one or more components having different turn-on and turn-off features and thus giving rise to separate clusters, or in case of a system comprising many similar electrical components which gives rise to events which are attributed to one cluster, or in any of the above four cases SI to S4. The present invention hereto provides an improved component detection technique, which in cooperation with the other steps of the NIALM method, allows to better identify electrical components on the basis of clusters of events.
Summary of the invention
The present invention provides for a non-intrusive appliance load monitoring (NIALM) method for monitoring components of appliances in a system. Preferably said components are electrical components and/or said appliances are electrical appliances. The NIALM method comprises the steps of: detecting events in an electrical signal, preferably a measured electrical signal, comprising power consumption information of said system, said events representing state transitions of the appliances in the system;
- characterizing said events by an event signature, taking into account differences between steady states before and after the event and/or taking into account transient states located between steady states before and after the event;
clustering events into a set of clusters on the basis of their signatures;
- identifying components on the basis of said set of clusters;
optionally identifying appliances from the components identified in the previous step;
optionally providing appliances' energy consumption or providing the components' energy consumption. In an alternatively preferred embodiment, said electrical signal is a simulated electrical signal.
Hereby, said clustering comprises an initial clustering of said events into an initial set of clusters on the basis of a first clustering criterion, and a subsequent reclustering of at least one of said initial clusters on the basis of a second clustering criterion different from the first clustering criterion. Preferably said first clustering criterion is computed taking into account event signatures from substantially all events detected in said electrical signal, and whereby said second clustering criterion is computed taking into account signatures of substantially only events in said one initial cluster which is to be reclustered.
The NIALM method can be used to identify electrical components in a system on the basis of an electrical signal, preferably a measured electrical signal, comprising power consumption information of said system. The identification of the electrical components allow for a further identification of electrical appliances, which is particularly useful in systems where the number and/or nature of appliances is not known a priori, or can change in time. Therefore, in a preferred embodiment, the method comprises the step of identifying appliances from the components ion the basis of the identified electrical components.
The NIALM method can also be used for condition monitoring of an appliance. Typically, but not in a limitative way, condition monitoring of an appliance can be performed to check if or when the appliance is functioning normally or abnormally, and/or to give an alarm if a malfunction is observed. The appliance which is being monitored using the NIALM method of the present invention, can be identified using a method as described in this document, or by another method. In a preferred embodiment, the method comprises providing appliances' energy consumption or providing the components' energy consumption. The energy consumption of the appliances or the components can be given in the form of a report to the user of the appliance or of the system, or to the electricity provider to detect malfunctions or to optimize energy efficiency either for a single system or for a number of systems.
The present invention further provides for a recursive clustering method for clustering events obtained from an electrical signal, preferably a measured electrical signal, comprising power consumption information of a system, said events at least partially characterized by an event signature, said recursive clustering method comprising : an initial step of clustering events of an initial event set into a set of clusters using a clustering criterion for deciding whether two events belong to the same cluster and/or whether an event belongs to an existing cluster, said criterion computed on the basis of signatures from substantially all events from said initial event set; and
a recursive step of reclustering events belonging to a cluster into a set of sub- clusters using an updated clustering criterion for deciding whether two events belong to the same cluster and/or whether an event belongs to an existing cluster, said updated criterion computed on the basis of signatures substantially only of events from said cluster, thereby obtaining one, two or more sub-clusters, preferably whereby if two or more sub-clusters are obtained, these two or more sub-clusters are reclustered using the present recursive step.
The present invention also provides for a method for clustering events detected in an electrical signal, preferably a measured electrical signal, comprising power consumption information of a system, preferably comprising electrical power consumption information of a system, said events at least partially characterized by a signature comprising a set of event features, the method comprising the steps of: defining principal components of said event features for said events;
computing a clustering criterion on the basis of the principal components of substantially all of said events;
clustering said events into a set of clusters; characterized in that it comprises the steps of: sub-clustering at least one cluster of said set of clusters by:
(i) redefining principal components of the event features for events belonging to said one cluster, thereby substantially excluding event features for events not belonging to said one cluster;
(ii) recomputing the clustering criterion for said one cluster on the basis of the redefined principal components of substantially all of the events belonging to said one cluster;
(iii) clustering said events belonging to said one cluster in one, two or more sub-clusters;
optionally, if two or more sub-clusters are obtained after step (d)(iii), performing step (d) taking at least one of said sub-clusters from step (d)(iii) as a cluster to be sub-clustered. Hereby, step (d) is preferably performed recursively for each cluster of said set of clusters and/or for all sub-clusters obtained by performing step (d) until no further sub-clustering in two or more sub-clusters is obtained.
Typically, the events relate to on-off switching of components of appliances in the system. Events can be classified by their signatures, which refer to a set of properties or features which characterize transitions in the electrical signal. These properties or features can be computed from a current waveform extracted from the electrical signal, and preferably from a delta waveform extracted from the electrical signal. More preferably, features are computed on the basis of a frequency spectrum of the delta waveform, for example features could relate to harmonic magnitudes or phases. Preferred features which are computed to characterize events are: active power (P), reactive power (Q), fundamental frequency (H i), odd harmonics preferably of order 3 to 13 and preferably normalized to the amplitude of the fundamental frequency component of the current, continuous component and/or second order harmonics which are preferably normalized to the amplitude of the fundamental frequency component of the current, total harmonic distortion (THD), ratio |Q/P| , maximal IM and minimal Im values of the current.
As a non-limiting, but preferred example, a signature of an event k, preferably a steady-state event, could be written as Xss(k) = [P, Q, H i, H0/i, H2/i, Hodd(3→i3)/i, THD, I Q/P I , IM, Im], wherein Hn/i refers to the n'th Harmonic normalized to the magnitude of the fundamental frequency component of the current.
In a preferred embodiment, and most preferably for transient state events, a signature of an event comprises a time series of a quantity derivable from the electrical signal, preferably the quantity being the active power and/or the current. Typically said time series of said quantity comprises a set of values for said number ordered chronologically.
When clustering events, a decision criterion, or clustering criterion, needs to be applied to decide whether or not an event belongs to a cluster, or two events belong to the same cluster. Such a criterion preferably comprises computing an inter-event distance to compare events, said inter-event distance being compared to one or more delimiting values, which are parameters of the clustering algorithm.
In the present invention it should be noted that in the reclustering or recursive step, whereby a parent cluster is being reclustered or sub-clustered into child clusters or sub-clusters, the clustering criterion is updated substantially only on the basis of the events which have been identified previously as being part of the parent cluster, i.e. events which could have been part of the initial event set, but were not identified as being part of the parent cluster, are not taken into account when updating the clustering criterion for reclustering or subclustering the parent cluster. This allows a reclustering of the parent cluster which is specifically adapted for that parent cluster, which allows to zoom in on the parent cluster and use a clustering criterion which is especially selective for events in that parent cluster. This concept makes the clustering method more robust, and more applicable for all types of measured signals coming from all types of systems, and in particular for systems comprising appliances which are not frequently or regularly used, or for systems in which new appliances are added or old ones are removed. Furthermore, it has been observed that methods of the present invention provide an improved clustering for systems comprising small and/or similar loads.
Therefore, in an embodiment, events are compared by computing an inter-event distance. This distance could preferably, and in particular for comparing events characterized by steady-state features, be a Euclidean distance or a Mahalanobis distance, or any combination thereof. This distance could preferably, and in particular for comparing events characterized by transient-state features, be a Minkowski distance, a Dynamic Time Warping (DTW) distance, a Longest Common Subsequence (LCSS) distance, or any combination thereof. Also preferred are distances which are at least partly in a one-to-one correspondence with the above-mentioned distances or any combination thereof.
In a preferred embodiment of the methods for clustering events as disclosed herein, events are characterized by steady-state features or transient-state events. In the method for clustering wherein the clustering criterion is computed on the basis of the principal components of events, preferably events which are characterized by steady- state features are clustered as these events have been noticed to comprise principal components which can be identified unambiguously in a principal component analysis, e.g. by means of looking at those linear functions of the event features which maximize the variance, e.g. as further explained in I. T. Jolliffe, "Principal Component Analysis", Vol. 30, Springer Series in Statistics, Springer, 2nd ed., 2002.
In a preferred embodiment, said clustering and/or reclustering and/or subclustering is performed using a density-based algorithm, such as a DBSCAN algorithm, an OPTICS algorithm and/or a DBCLASD algorithm, said algorithm based on a density defined by the amount of events which can be found in an e-neighborhood of a point of the cluster, said e-neighborhood of a point p defined as
Ne(p) = {q e X\d(p, q)≤e}, where X is the signature space, preferably a feature space, d() represents a distance function between points and/or events, and e is an inter-event distance delimiting the neighborhood, whereby two kinds of points are defined : core points which have a density \Ne(p)\≥ MinPts, MinPts being a number higher than 1, and preferably lower than 20, and border points which belong to an e-neighborhood of a core point without being a core point itself, whereby two points are defined as density-reachable if there exists a sequence of points such that each one belongs to the an e-neighborhood of its predecessor, the latter being a core point, whereby two points are defined as density- connected if they are density-reachable from a common point, whereby said clustering criterion comprises evaluating if an event is density-connected to a point and/or an event in a cluster.
The applicant would like to note that descriptions of neighborhoods which are in correspondence, in particular in a bijectional correspondence, with the description given here above can also be used. In a more preferred embodiment, said clustering criterion is computed and/or recomputed by computing and/or recomputing e and/or MinPts, preferably e.
Preferably, said events are characterized by steady-state features and/or transient- state features.
The inventors have found that prior art techniques seem to rely on external input, e.g. maximal inter-event distance or minimal number of events, in order to determine which event belongs to which cluster or which cluster can be deemed complete. Although such prior art techniques allow identification of relatively simple components at a reasonable level, the techniques seem to fail when applied to more intricate systems, such as households or companies, which comprise electrical appliances with complicated electrical components.
This is at least partly due to a degree of arbitrariness which is introduced in the method, in particular in a step related to clustering of events, prior to identification of components on the basis of the computed clusters. Although the results for the component identification can be improved on a case-by-case basis, i.e. largely depending on the type of system which is being monitored, it is clear that the prior art does not disclose a method which can be applied to any type of system, or the systems which change over time, e.g. a household or a factory.
The inventors have also found that the current invention results in a clustering of events which is clearly better than prior art techniques, and thus leads to better component identification and appliance load monitoring. The present invention further allows to quantify or objectivate any error which is made during the clustering. The information on the error allows to improve the techniques further or to identify irregularities in the system.
In a further aspect, the present invention also provides a component detection method comprising the steps of: obtaining clusters of events obtained from a, preferably measured, electrical signal comprising power consumption information of a system, said events comprising on-events and off-events, whereby each of said events comprises a cluster ID which allows to identify the cluster to which the event belongs, preferably whereby said clusters of events are obtained using a method according to the present invention;
pairing on-events and off-events from said electrical signal, thereby obtaining a set of paired events, each paired event comprising paired cluster ID information representing the cluster ID of the on-event and the cluster ID of the off-event in said paired event;
detecting components, preferably electrical components, by identifying recurrent paired cluster ID information within said set of paired events.
In a preferred embodiment, whereby said step of pairing on-events and off-events comprises extremizing, i.e. minimizing or maximizing, a cost function which depends on variations in energy, in power, in current, in energy fit errors, in power fit errors, in current fit errors or in any combination thereof, preferably in a linear combination of at least two of said variations, more preferably variations in power and in power fit errors.
The present invention further concerns the use of any of the clustering methods and/or the component detection method in a non-intrusive appliance load monitoring method and/or for condition monitoring of an appliance.
The component detection method of the present invention is particularly suited for a system wherein electrical appliances are on/off components, or consist of such on/off components, and, their consumption can be modeled by constant power segments during steady states. For these systems, any on-event should be followed by an off- event with similar power step (with opposite sign). "Explained power steps" are the ones for which complementary power steps can be identified following the idea that: if a component has been turned on at time ton, it should be turned off at a time toff > ton. Further, constant power draw is assumed and we search for the pair (ton, toff) minimizing fit-errors. Note that the component detection method of the present invention allows not to rely on prior models of the system and/or its appliances and is robust to clustering errors.
The present invention also concerns a processing unit arranged for performing a NIALM method, any clustering method and/or a component dtetction method according to the present invention. Preferably said processing unit is arranged for performing a recursive clustering method or a method for clustering according to the present invention, and a component detection method according to the present invention.
The present invention further concerns a device, preferably a computer-mountable and/or meter-mountable device, comprising instructions for executing a NIALM method, any clustering method and/or a component detection method according to the present invention. Herein, 'meter-mountable' device refers to a device which can be linked to an electrical meter, such as an electrical meter which can be found in a residence, a business or any system comprising an electrically powered device, and which measures the consumption, and/or optionally the generation, of electrical energy. Preferably said processing unit is arranged for performing a recursive clustering method or a method for clustering according to the present invention, and a component detection method according to the present invention.
In a preferred method, said device is a separate device, i.e. which can be releasably linked to a computer or a meter or a system comprising electrical appliances. In another preferred method, said device is integrated in a meter, such as a smart meter, or in a circuit breaker of said system.
The present invention further concerns a NIALM system comprising a client device and a server device, whereby said client device and server device are linkable, and optionally are linked, and whereby said client device and server device are configured to together execute a NIALM method according to the present invention, a recursive clustering method according to the present invention, a method according to the present invention, and/or a component detection method according to the present invention. This system allows to perform the separate steps of the methods according to the present invention on the client device or on the server device or on both. In particular certain steps of the methods of the present invention can be performed on the client device while the remaining steps of the methods can be performed on the server device, i.e. the client device can be configured to perform a first subset of the steps of the methods of the present invention, while the server device can be configure to perform a second subset of the remaining steps of the methods of the present invention. In a preferred embodiment, said client device is configured to obtain a measured electrical signal comprising power consumption information of a system.
In an embodiment, the client device is configured to perform the following steps: detecting events in a, preferably measured, electrical signal comprising power consumption information of said system, said events representing state transitions of the appliances in the system;
transferring information representing said detected events to said server device; and the server device is configured to perform the following steps: - obtaining said information representing said detected events from said client device;
characterizing said events by an event signature, taking into account differences between steady states before and after the event and/or taking into account transient states located between steady states before and after the event;
clustering events into a set of clusters on the basis of their signatures;
identifying components on the basis of said set of clusters;
optionally identifying appliances from the components identified in the previous step;
- optionally providing appliances' energy consumption or providing the components' energy consumption.
In an embodiment, the client device is configured to perform the following steps: detecting events in an electrical signal, preferably a measured electrical signal, comprising power consumption information of said system, said events representing state transitions of the appliances in the system;
characterizing said events by an event signature, taking into account differences between steady states before and after the event and/or taking into account transient states located between steady states before and after the event;
- transferring information representing said event signatures to said server device; and the server device is configured to perform the following steps: obtaining said information representing said event sigantures from said client device; clustering events into a set of clusters on the basis of their signatures;
identifying components on the basis of said set of clusters;
optionally identifying appliances from the components identified in the previous step;
- optionally providing appliances' energy consumption or providing the components' energy consumption.
In an embodiment, the client device is configured to perform the following steps: detecting events in an electrical signal, preferably a measured electrical signal, comprising power consumption information of said system, said events representing state transitions of the appliances in the system;
characterizing said events by an event signature, taking into account differences between steady states before and after the event and/or taking into account transient states located between steady states before and after the event;
- clustering events into a set of clusters on the basis of their signatures;
transferring information representing said set of clusters to said server device; and the server device is configured to perform the following steps: obtaining said information representing said set of clusters from said client device;
- identifying components on the basis of said set of clusters;
optionally identifying appliances from the components identified in the previous step;
optionally providing appliances' energy consumption or providing the components' energy consumption. In the NIALM system's embodiments given above, said clustering comprises an initial clustering of said events into an initial set of clusters on the basis of a first clustering criterion, and a subsequent reclustering of at least one of said initial clusters on the basis of a second clustering criterion different from the first clustering criterion.
The use of a NIALM system with a client device and a server device provides a number of advantages, including, but not limited to:
- the possibility to optimize and update the algorithms in an easy way, in particular for the algorithms of the server device, and in particular the clustering algorithm, - the possibility to collect data centrally in order to assess and improve the efficiency of the used algorithms,
the possibility to perform an analysis of the aggregate energy or power consumption of a number of systems. Therefore, the present invention also concerns a database comprising information representing identified components in a system, preferably of a multitude of systems, said information obtained using a NIALM method according to a method disclosed in this document. Preferably the database also comprises information representing identified appliances and/or information representing energy consumption of the appliances and/or components in said system or said multitude of systems.
The present invention also concerns a NIALM method for monitoring components of appliances in a system, by detecting events in an electrical signal comprising power consumption information of said system, said events representing state transitions of the appliances in the system, and by identifying components on the basis of the detected events, characterized in that the events are detected in a multi-step approach comprising at least two of the following steps and preferably all of the following steps:
(1) detecting high variations in the electrical signal by taking into account local derivative information of the electrical signal, preferably by computing a derivative of the electrical signal and/or by applying a derivative filter to the electrical signal; preferably the detection is performed by comparing the computed derivative or the results of the applied derivative filter to a threshold; more preferably a derivative filtering algorithm based on the first derivative of Gaussian (FDOG) is used;
(2) detecting stable steps in the electrical signal by comparing the electrical signal with a modeled sliding step signal within a sliding frame;
(3) detecting significant changes in the electrical signal by comparing statistical parameters of the electrical signal for different, preferably subsequent or partly overlapping, time frames. Preferably a cumulative sum (CUSUM) algorithm is used.
In an embodiment of the above NIALM method, the components are identified on the basis of the detected events by:
- characterizing said events by an event signature, taking into account differences between steady states before and after the event and/or taking into account transient states located between steady states before and after the event;
- clustering events into a set of clusters on the basis of their signatures; - identifying components on the basis of said set of clusters.
In an embodiment of the above NIALM method, the electrical signal comprises, and preferably consists of, an electrical current signal.
In an embodiment of the above NIALM method, the electrical signal comprises, and preferably consists of, a fifth harmonics of an electrical current signal.
The present invention further concerns a NIALM method for monitoring components of appliances in a system, by detecting events in an electrical signal comprising power consumption information of said system, said events representing state transitions of the appliances in the system, and by identifying components on the basis of the detected events, characterized in that said electrical signal comprises an electrical current signal and said events are detected on the basis of a fifth harmonic of said electrical current signal.
In order to detect changes or steps in an electrical signal, odd harmonics are in general preferred over even harmonics. The first and/or third harmonics in a signal are preferably used as they are expected to be the most dominant harmonics. However, the inventors have found that the fifth harmonics of the electrical signal, and more in particular of the current waveform extracted from the electrical signal, may comprises valuable additional information, which allows to significantly and unexpectedly improve upon the detection of events. Without wishing to be bound by a theoretical explanation, the increasing use of three-phase electric power in household, industrial, commercial and other systems, could make the fifth harmonics of the electrical signal, and more particularly of the current waveform, the most important harmonics to collect information from.
Furthermore, active power consumed by some electric components appears to be low whereas their global current consumption is not negligible. This high current consumption relates to distorted current. The distorted current is not visible in power consumption since voltage is approximately a perfect 50Hz waveform. As a result, information in current harmonics is lost. In order to extract remaining information in the current, event detection can be improved by at least partly basing the process on the current waveform extracted from the electrical signal, and preferably on the fifth harmonic in the current.
In a related aspect, the present invention concerns a multi-step event detection method for detecting events in an electrical signal comprising power consumption information of a system, comprising at least two of the following steps and preferably all of the following steps: (1) detecting high variations in the electrical signal by taking into account local derivative information of the electrical signal, preferably by computing a derivative of the electrical signal and/or by applying a derivative filter to the electrical signal; preferably the detection is performed by comparing the computed derivative or the results of the applied derivative filter to a threshold; more preferably a derivative filtering algorithm based on the first derivative of Gaussian (FDOG) is used;
(2) detecting stable steps in the electrical signal by comparing the electrical signal with a modeled sliding step signal within a sliding frame;
(3) detecting significant changes in the electrical signal by comparing statistical parameters of the electrical signal for different, preferably subsequent or partly overlapping, time frames. Preferably a cumulative sum (CUSUM) algorithm is used.
In another related aspect, the present invention concerns an event detection method for detecting events in an electrical signal comprising power consumption information of a system, characterized in that the electrical signal comprises an electrical current signal and said events are detected on the basis of a fifth harmonic of said electrical current signal.
The present invention also concerns a processing unit arranged for performing a NIALM method as disclosed in this document, a multi-step event detection method as disclosed in this document, and/or an event detection method as disclosed in this document; and a device, preferably a computer-mountable or meter-mountable device, comprising instructions for executing a NIALM method as disclosed in this document, a multi-step event detection method as disclosed in this document, and/or an event detection method as disclosed in this document.
In yet another aspect, the present invention concerns a non-intrusive appliance load monitoring (NIALM) method for monitoring components of appliances in a system comprising a set of branched circuits. With reference to figures 25a and 25b which show exemplary embodiments of this method and the related system, the method comprises the steps of:
(a) detecting system events in an aggregate electrical signal comprising aggregate power consumption information of said system (268), said system events representing state transitions of the appliances in the system, and said system events comprising on-events and off-events;
(b) for at least one and preferably each of said branch circuits (256, 257, 258, 259) : separately detecting branch events in a branch electrical signal comprising branch power consumption information of said branch circuit (256, 257, 258, 259) of said system, said branch events representing state transitions of the appliances connected to said branch circuit;
(c) pairing on-events and off-events, thereby obtaining a set of paired events; and (d) detecting and/or identifying components on the basis of said set of paired events, whereby an on-event and an off-event are excluded from being paired if the on-event and the off-event are detected as branch events of different branch circuits, and whereby preferably an on-event and an off-event are identified as a paired event only if both the on-event and the off-event are detected as branch events of the same branch circuit. One difficulty which arises in performing a NIALM method on the basis of paired on- and off-events, as e.g. amply disclosed in the present document, is ensuring a correct pairing of events, in particular if similar electrical components are present in the system (e.g. similar light bulbs). In the majority of systems, an electrical component and also an electrical appliance is electrically connected to a single branch circuit (256, 257, 258 or 259) in a system (268), which remains typically the same branch circuit for a while. More importantly, if an electrical component is connected to a certain branch circuit (e.g. 256) and switched on, this will trigger an on-event on that branch circuit (256). If the electrical component is then switched off or disconnected from the branch circuit (256), this will trigger an off- event on the same branch. By checking if the on-event and the off-event are detected in the same branch, extra information is provided for correctly pairing on- and off- events detected in the aggregate signal. This allows distinguishing of similar electrical components which are connected to different branch circuits and hence allows a separate monitoring of those components.
In an embodiment, more than one branch circuits are present in the system, e.g. 2, 3, 4, 5, 6, 7, 8, 9, 10 or more branch circuits.
In an embodiment, the aggregate electrical signal is obtained at an aggregate sampling frequency and said branch electrical signal is obtained at or resampled to a branch sampling frequency, characterized in that the aggregate sampling frequency is different than, preferably larger than, the branch sampling frequency, preferably by a factor which is at least the number of branch circuits in said system, and more preferably by a factor which at least 10 times the number of branch circuits in the system. In a preferred embodiment wherein more than one branch circuits are present in the system, preferably the branch electrical signal of each branch circuit is obtained or resampled at a branch sampling frequency which is optimized for said branch circuit and which is optionally different from the branch sampling frequencies used for the other branch circuits.
In an embodiment, the aggregate sampling frequency is at least 100 Hz, preferably at least 500 Hz, more preferably at least 800 Hz, most preferably at least 1600 Hz, and/or whereby said branch sampling frequency is at least 0.001Hz, preferably at least 0.01 Hz, more preferably at least 0.1 Hz, most preferably at least 0.5 Hz.
Both the aggregate electrical signal as the branch electrical signals can be used as input for any of the NIALM methods described in the present document which allow the monitoring, detection and/or identification of electrical components of appliances in the system or, mutatis mutandis, in a branch of the system. However, in a preferred embodiment, one of the NIALM methods which are disclosed in the present document, is executed using the aggregate electrical signal as electrical signal for the detection of events in the system, with the additional feature whereby an on-event and an off-event are excluded from being paired if the on-event and the off-event are detected as branch events of different branch circuits, and whereby preferably an on- event and an off-event are identified as a paired event only if both the on-event and the off-event are detected as branch events of the same branch circuit. In this case, the event detection algorithm used on the aggregate electrical signal can be different than the event detection algorithm or algorithms used on each of the branch electrical signals, allowing to optimize the event detection per branch circuit and for the aggregate signal. Note that in the present embodiment, it is not necessary to perform a full NIALM method for each branch circuit, but that only event detection needs to be performed on the branch electrical signal. Accordingly, the frequency at which the aggregate electrical signal is being sampled, needs to be high enough to perform a NIALM methods, e.g. 1600 Hz, whereas the sampling frequency at which the branch electrical signal is being sampled needs to be high enough to perform event detection, which can be lower than the frequencies necessary for performing the NIALM method, e.g. around 0.5 Hz. Additionally, by keeping the branch sampling frequency low, the data transfer between a branch device which obtains and samples the branch electrical signal and optionally detects branch events, and an aggregate device which receives the data for further processing, can be kept low. As a result, the minimal requirements of the data transfer means can also be kept low. Hence, transfer via wireless means, via the electrical wiring of the system itself, or via a dedicated set of wiring, are achievable. In an embodiment, the system events are clustered into clusters of system events. Hereby, preferably each of said system events comprises a cluster ID which allows to identify the cluster to which the event belongs and each paired event comprises paired cluster ID information representing the cluster ID of the on-event and the cluster ID of the off-event in said paired event. The components are then detected and/or identified by identifying recurrent paired cluster ID information within said set of paired events.
In some embodiments, components or appliances are connected to the same branch circuit during execution of the method, i.e. they are not moved or connected to a different branch circuit during the period over which the aggregate electrical signal and the branch electrical signals are obtained. In such cases and in a preferred embodiment, system events which correspond to branch events of different branch circuits are excluded to be clustered in the same cluster of system events.
In a related aspect, the present invention concerns a NIALM system for monitoring components of appliances in a system comprising a set of branched circuits, comprising :
(i) an aggregate NIALM device which is mountable on one or more main electrical power line of the system for obtaining the aggregate electrical signal comprising aggregate power consumption information of said system;
(ii) one or more branch NIALM devices, each of which is mountable on a branch circuit of the system for obtaining the branch electrical signal comprising branch power consumption information of said branch circuit, and
(iii) connection means for connecting said one or more branch NIALM devices to said aggregate NIALM device and allowing information exchange between each of said branch NIALM devices and said aggregate NIALM device, whereby said NIALM system comprises instructions for executing a NIALM method for monitoring components of appliances in a system comprising a set of branched circuits as disclosed in this document.
In an embodiment, said aggregate NIALM device comprises instructions for executing steps (a), (c) and (d) of the NIALM method for monitoring components of appliances in a system comprising a set of branched circuits, and said one or more branch NIALM devices comprise instructions for executing step (b) of the method for monitoring components of appliances in a system comprising a set of branched circuits.
In an alternative method, said aggregate NIALM device comprises instructions for executing steps (a), (b), (c) and (d) of the NIALM method for monitoring components of appliances in a system comprising a set of branched circuits, and said one or more branch NIALM devices comprise instructions for obtaining a branch electrical signal comprising branch power consumption information of a branch circuit and for transmitting said branch electrical signal to the aggregate NIALM device. In an embodiment, the aggregate NIALM device comprises an aggregate sampler, arranged for sampling an aggregate electrical signal of the system at an aggregate sampling frequency, said one or more branch NIALM devices each comprise a branch sampler, arranged for sampling a branch electrical signal of a branch circuit at an branch sampling frequency, whereby said aggregate sampling frequency is higher than said branch sampling frequency.
In a preferred embodiment, at least one and preferable each NIALM device is a circuit breaker, is mounted on a circuit breaker, comprises a circuit breaker, or any combination thereof.
In an embodiment, the connection means are wireless means, and/or comprise electrical wiring of the system, and/or comprise a dedicated set of wiring.
Exemplary embodiments of this method and the related system are illustrated in figs. 25a and 25b.
Description of figures
Figure 1 shows three methods to evaluate similarities between time series: the Minkowski distance, the dynamic time warping (DTW) and the least common subsequence (LCSS).
Figure 2 shows how the amount of outliers mainly decreases with k, the amount of nearest neighbors in the k-dist criterion.
Figure 3 shows that when increasing k, the decrease of outlier points is mainly located in the origin of the P-Q plane but small clusters are then considered as outliers.
Figure 4 illustrates substructures which are better emphasized if principal components are evaluated for specific data subsets.
Figure 5 shows a modeled aggregate power based on paired events. The evaluation is independent from the classification results.
Figure 6 shows that, once pairs have been assigned to components, the considered power steps derive from the clusters. Figure 7 shows sequences of on-off cycles which are generated for nine appliances such that their aggregate consumption is not cyclic over the three-hour period.
Figure 8 shows nine appliances which draw specific current waveforms.
Figure 9 shows that the microwave is not a two state-device. Moreover, it exhibits cycling operations depending on the average power asked by the user.
Figure 10 shows events and their features - events corresponding to: the kettle, the vacuum cleaner and the microwave oven.
Figure 11 shows events and their features, zooming in at the origin of the P-Q plane.
Figure 12 shows that some turn-on transients systematically lead to several detections.
Figure 13 shows power variations of the ventilator which are significant compared to the power it consumes. Outliers risk to be associated with clusters of such a variable and low power device.
Figure 14 shows that clusters which are obtained after a first clustering iteration do not correctly reveal the complete data structure.
Figure 15 shows that an iterative clustering procedure according to the present invention efficiently captures the data substructure.
Figure 16 shows a classification according to the highest membership value based on the Mahalanobis distance. Figure 17 shows that there is almost no confusion between clusters of transient patterns. However, no clusters are discovered for the kettle, the ventilator and the vacuum cleaner.
Figure 18 shows that component ID are assigned to recurrent pairs of nonoutliers. As a result, equivalent component ID are assigned to on and off event clusters. Figure 19 shows first, the modeled aggregate power is evaluated with all paired events; and second, electrical components are discovered from recurrent pairs of nonoutliers. Finally, state sequences are evaluated based on classified event pairs.
Figure 20 shows paired events are assigned to components according to their cluster identifiers. Figure 21 shows state sequences evaluated from the event pairs assigned to pure component. Results from the state sequence evaluation are given in the top plots and the measurement in the bottom ones.
Figure 22 illustrates an event detection algorithm structure according to the present invention.
Figure 23 illustrates how temporary results can be managed in an event detection method according to the present invention.
Figure 24 illustrates the usefulness of current harmonics in an event detection method according to the present invention. Figures 25a and 25b illustrate exemplary embodiments of a non-intrusive appliance load monitoring (NIALM) method for monitoring components of appliances in a system comprising a set of branched circuits and a related system according to the present invention.
Detailed description of the invention NIALM techniques are either pattern recognition-based or optimization-based approaches, also referred to as event-based or non event-based. In the former case, samples correspond to state changes of appliances, referred to as 'events'. These methods are also referred to as event-based NIALM. Signatures are used to associate events to appliances. State sequences of appliances then result from classification algorithms. In supervised approaches, changes of appliance states are matched one- by-one to known signatures. Where learning is unsupervised, the recurrence of signatures is exploited to recognize appliances.
The present invention concerns an unsupervised, event-based NIALM method according to claim 1. The present invention also concerns methods which optimize the NIALM method, including a recursive clustering method for recursively clustering similar events according to claim 5, a method for clustering similar events taking into account principal components of the event's signature according to claim 9, a component detection method according to claim 13, as well as the use of any of these methods or their combination in a NIALM method or for condition monitoring of an appliance. The present invention also concerns a processing unit arranged for executing any of these methods and a device comprising instructions for carrying out these methods, as well as a NIALM system comprising a client device and a server device as specified in claims 19 and 20 and a database according to claim 21. Unless otherwise defined, all terms used in disclosing the invention, including technical and scientific terms, have the meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. By means of further guidance, term definitions are included to better appreciate the teaching of the present invention. As used herein, the following terms have the following meanings:
"A", "an", and "the" as used herein refers to both singular and plural referents unless the context clearly dictates otherwise. By way of example, "a compartment" refers to one or more than one compartment.
"About" as used herein referring to a measurable value such as a parameter, an amount, a temporal duration, and the like, is meant to encompass variations of +/- 20% or less, preferably +/-10% or less, more preferably +/-5% or less, even more preferably +/-1% or less, and still more preferably +/-0.1% or less of and from the specified value, in so far such variations are appropriate to perform in the disclosed invention. However, it is to be understood that the value to which the modifier "about" refers is itself also specifically disclosed.
"Comprise", "comprising", and "comprises" and "comprised of" as used herein are synonymous with "include", "including", "includes" or "contain", "containing", "contains" and are inclusive or open-ended terms that specifies the presence of what follows e.g. component and do not exclude or preclude the presence of additional, non-recited components, features, element, members, steps, known in the art or disclosed therein.
The recitation of numerical ranges by endpoints includes all numbers and fractions subsumed within that range, as well as the recited endpoints.
The expression "% by weight", "weight percent", "%wt" or "wt%", here and throughout the description unless otherwise defined, refers to the relative weight of the respective component based on the overall weight of the formulation.
As used herein, the DBSCAN algorithm refers to density-based spatial clustering of applications with noise. In DBSCAN, a distance parameter, i.e. an inter-event distance parameter, defines the neighborhood of a point, i.e. an event. A zone is considered as dense if a sufficiently large number of points, i.e. events, is found within the given neighborhood. DBSCAN hereby requires only two parameters and no range of values must be specified for the number of clusters to investigate. Instead, the number of clusters is an output of the algorithm. We refer to M. Ester, H .-P. Kriegel, J. Sander and X. Xu, "A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise", Knowledge Discovery and Data Mining 96: 226-231, 1996 for more detailed information about this algorithm.
As used herein, the OPTICS algorithm refers to an algorithm for ordering points to identify the clustering structure. We refer to M. Ankerst, M. M. Breunig, h-P Kriegel and J. Sander, "OPTICS: ordering points to identify the clustering structure", ACM SIGMOD Record 28 :49-60, 1999, for more information.
As used herein, the DBCLASD algorithm refers to a distribution-based clustering algorithm for mining in large spatial databases. We refer to X. Xu, M. Ester, H . P. Kriegel and J. Sander, "A distribution-based clustering algorithm for mining in large spatial databases", International Conference on Data Engineering, Vol. 1, pp. 324-331, 1998, for further information.
When clustering events, a decision criterion needs to be applied on whether or not an event belongs to a cluster, or two events belong to the same cluster. Such a criterion preferably comprises computing an inter-event distance to compare events. Therefore, in an embodiment, events are compared by computing an inter-event distance. This distance could preferably, and in particular for comparing events characterized by steady-state features, be a Euclidean distance or a Mahalanobis distance, or any combination thereof. This distance could preferably, and in particular for comparing events characterized by transient-state features, be a Minkowski distance, a Dynamic Time Warping (DTW) distance, a Longest Common Subsequence (LCSS) distance, or any combination thereof. Also preferred are distances which are at least partly in a one-to-one correspondence with the above-mentioned distances or any combination thereof.
As used herein, the term "Euclidean distance", "Mahalanobis distance", "Minkowski distance", "Dynamic Time Warping (DTW) distance" and "Longest Common Subsequence (LCSS) distance" refer to specific types of distances between events, which are discussed in what follows.
Euclidean and Minkowski distance
Figure imgf000027_0001
wherein p=2 for the Euclidean distance, and p= l, 3, 4 or more for a Minkowski distance. Herein, X and Y refer to event signatures characterized by a set of N features Xi and y resp. Preferably, these features are normalized, e.g . with respect to the minimum and maximum values of the features from the events which are taken into account to define or compute the clustering criterion, according to
Figure imgf000028_0001
wherein x, refers to the i'th feature in the signature, and xijn refers to the normalized feature value.
Mahalanobis distance :
Let Xc (nc x p) be a set of nc p-feature signatures grouped within a cluster. The variance-covariance matrix of cluster Xc is
Let further x be a signature whose distance w. r.t. Xc is to be evaluated and Xc the vector of mean feature values of Xc. The Mahalanobis distance is defined as follows:
Figure imgf000028_0002
This distance is evaluated in the original feature space, i.e. in the features described in Chapter 6. The membership value is simply expressed as the inverse of the point-to- cluster distance.
The Mahalanobis distance better deals with the dispersion of clusters along different directions than e.g . the Euclidean. Therefore, the Mahalanobis distance is better suited to identify the cluster to which outlier events belong . Outliers are isolated points in the feature space. They do not systematically exhibit extreme feature values. Instead, the distance to their nearest neighbors is high compared to the one of non outlier points. Consequently, the d istance of a point to its k nearest neighbors is an image of its likelihood to be an outlier. We refer to such a distance as k-dist. Outliers are then points with the highest k-dist values. As an example for deciding which events are outlier events, a threshold on k-dist values could be defined to decide whether or not points are outliers. In an embodiment, a maximum nonoutlier (MNO) value of the k-dist distribution could be used : it is defined as the highest observed value below the upper quartile increased by 1.5 times the interquartile range. Following this definition, the threshold value on the k-dist is obtained with the following formula :
£ outliers max [k— dist (p) < Q75 + L75(Q7S — Q25) where Q75 and Q25 are the upper and lower quartiles of the k-dist distribution. Herein, k can preferably take any value between 1 and 20, preferably between 4 and 15, more preferably 10.
Dynamic time warping (DTW) distance and least common subsequence (LC55) distance:
The principle of the dynamic time warping (DTW) and the least common subsequence (LCSS) are illustrated in figure 1, which shows three methods to evaluate distances, in particular distances between time series: the Minkowski distance, the dynamic time warping (DTW) and the least common subsequence (LCSS).
DTW allows to deal with sequences with different lengths and different localization in the window. LCSS further allows to skip samples considered as outliers in the pattern. When sequences that we compare are isolated patterns, the globally optimal alignment obtained with DTW is a suitable way to measure the similarity. Considering that different transients have been separated by the segmentation and that turn-on transients follow a continuous process on the time axis (no step in time), the DTW is chosen over the LCSS method. Further, the DTW has the advantage that the entire sequences must be matched which avoids that spurious transient states be matched to subparts of true transients. In other words, DTW performs matching with time shift analysis robust to positive false detections. The average distortion is used instead of the total distortion in order to normalize for different segment lengths.
The objective of DTW is to compare two sequences X = (xi, .., xN) and Y = (yi, .., yM) of length N and M. A warping path is a sequence p = (pi, .., pL) with pi = (ri|,mi) satisfying the three conditions:
Boundary condition : pi = (1, 1) and pL = (N,M)
Monotonicity condition : ni < n2 < ... < nL and mi < m2 < ... < mL
- Step size condition : p,+1 - p, e {(1, 0), (0, 0), (0, 1)} for I e [1,L - 1] Provided a distance metric d(x,, y,) between two elements x, and y, (e.g. Euclidean distance), the total cost of a warping path p is L
Figure imgf000030_0001
and the optimal warping path p* is the one minimizing the total cost among all possible paths. The distance DTW(X, Y) is defined as the total cost associated to the optimal path p* : DTW(X, Y) = cp*(X, Y)
= min {cp(X, Y) | p is a warping path}
Finally, the average DTW distance is DTW(X,Y)/L where L is the length of the optimal path p*.
The present invention will be now described in more details, referring to examples that are not limitative.
Examples
Example 1 : Feature extraction on the basis of principal components
Electric signatures have been evaluated because they characterize the electric consumption of components, not because they allow to classify components. Features might be correlated and less features could then be used to represent the data structure. Also, some features might be better than others to reveal similarities and differences between signatures. Considering non relevant features would add similarities between events.
In this example, we present the principal component analysis (PCA) as a tool to extract relevant features for clustering purpose. Because PCA is based on data scattering analysis, outliers might severely impact the results. They should consequently be removed from the data before that PCA be performed. Their detection is the subject of Section 2. Then, in Section 3, we expose how the features are extracted from the steady state signatures in our NIALM procedure. 1. Principal component analysis
We propose a concise description of the principal component analysis based on the work by I. T. Jolliffe, "Principal Component Analysis", Vol. 30, Springer Series in Statistics, Springer, 2nd ed., 2002. "The central idea of principal component analysis (PCA) is to reduce the dimensionality of a data set consisting of a large number of interrelated variables, while retaining as much as possible of the variation present in the data set. This is achieved by transforming to a new set of variables, the principal components (PCs), which are uncorrelated, and which are ordered so that the first few retain most of the variation present in all of the original variables".
Suppose that x is a vector of p random variables, and that the variances of the p random variables. The first step is to look for a linear function αΊ x of the elements of x having maximum variance, where O i is a vector of p constants an, o12, O iP, and ' denotes transpose, so that
Figure imgf000031_0001
Next, look for a linear function a'2x, uncorrelated with αΊχ and having maximum variance. The procedure is repeated so that at the k'th stage a linear function a x is found that has maximum variance subject to being uncorrelated with αΊχ, α'2χ, ..., a'k-ix. The k'th derived variable, a x is the k'th PC. Detailed equations for the principal component analysis can be found in the work by Jolliffe.
The number of features will be smaller if the initial ones are not independent. Jolliffe suggested that a subset of the principal components be chosen such that their cumulative percentage of total variation be between 70% and 90%. Let o2 j be the variance of the data along principal component PC,, the cumulative percentage of total variation corresponding to the PC k is: , .; 1 (-'
We set that value to 85% in our implementation. The principal components (PC) taken into account are then the set of first PCs covering 85% of the variance. In addition to adding relevant variations, considering more PCs will, on the one hand, add distinctions between points of a same cluster and, on the other hand, add similarities between points of different clusters.
2. Detection of outlier points
Outliers might impact the result of the principal component analysis. They are mainly related to errors from the underlying data generation, e.g. they can be related to errors insignal segmentation leading to outliers. Herein, the errors can be due to noise or non-linearities, or due to transients which can be very long and hence could be seen as two or more different events. They are also rare events resulting from simultaneous on/off switching of components. They should be removed from the data set before searching for the principal components.
Outliers are isolated points in the feature space. They do not systematically exhibit extreme feature values. Instead, the distance to their nearest neighbors is high compared to the one of non outlier points. Consequently, the distance of a point to its k nearest neighbors is an image of its likelihood to be an outlier. We refer to such a distance as k-dist. Outliers are then points with the highest k-dist values.
Signatures consist of features, with very different magnitudes. In order to give similar impact to each feature in the k-dist evaluation, data are normalized. The min-max normalization can be appropriate to detect the outliers and the reduced data are then :
Figure imgf000032_0001
max Xj— null a¾
Each feature xijn ranges between 0 and 1 and the k-dist of events is the Euclidean distance between their normalized feature vectors and the one of their kth nearest neighbor.
A threshold on k-dist values must be defined to decide whether or not points are outliers. X. M. Lopez et al., "Clustering methods applied in the detection of Ki67 hot- spots in whole tumor slide images: an efficient way to characterize heterogeneous tissue-baked biomarkers", Cytometry, Part A: the journal of the International Society for Analytical Cytology, Vol. 81(9) : 765-775, September 2012, reported on the use of the maximum nonoutlier (MNO) value of the k-dist distribution : it is defined as the highest observed value below the upper quartile increased by 1.5 times the interquartile range. Following this definition, the threshold value on the k-dist is obtained with the following formula :
^outliers max [k— dist(p) < Q75 + 1.75(QJS— Q2' ) where Q75 and Q25 are the upper and lower quartiles of the k-dist distribution. Another approach to detect outliers is proposed by Jolliffe. It consists to look at the extreme values of the last PCs. A value must be chosen for k, the number of neighbors taken into account in the kdist. Figure 2 illustrates the relative evolution of the number of outliers according to the value of k for five different data subsets. We see that increasing the number of neighbors considered in the k-dist decreases the number of outliers. Variations are mainly located in the origin of the P - Q plane which corresponds to false positive detections and small loads whose signature evaluation is impacted by fluctuations of the mixture. However, increasing k also leads to considering points of small clusters as outliers. These two aspects are illustrated in figure 3.
Detecting loads consuming low power compared to the aggregate consumption is the biggest challenge of NIALM . Consequently, it is desired that the false positive detections be correctly identified as outliers. This will facilitate the detection of points which cluster around the origin of the P - Q plane and are related to signatures of small loads. Taking this reasoning into account and the choice of DBSCAN parameters presented below, k is set to 10. 3. Non outlier PCA
Outliers add non relevant scattering of the data. Obviously, that impacts the evaluation of the principal components which are based on variance-covariance evaluation. The principal component analysis should consequently be evaluated solely with the non outlier points. Furthermore, because PCA selects features in order to maximize the variance of the data, variables with higher amplitudes will be given higher weight and will be systematically considered in the first PCs. For instance, the active power ranges from some dozens of watts up to some kilowatts whereas normalized harmonic amplitudes range between 0 and 1. Data should then be reduced before the PCA be applied in order to give the same weight to the different features.
Our non outlier PCA works as follows :
Ignore outliers and,
a. Normalize the data
Outliers have been identified . It is then possible to reduce their impact on data normalization . The min-max normalization defined above is applied to the data, but the outliers are ignored from the search for the minimum and maximum values. This avoids that data be compressed because of extreme feature values of outliers. n xf — ιηϊιι .τί ' ,
¾ = L- v7i . vn , Vl €E l , p]
l mas a¾» o _ mill ¾Λ ϋ ■ 1 ' J J where the exponent NO stands for non outliers. X n = (x i,n , x p,n) b. Evaluate the principal component transformation a = PCA(XNO n) where PCA() refers to the calculations of the linear combinations C to ap explained in Section 1.
Then, for the entire data set
c. normalize with the transformation of step a,
Figure imgf000034_0001
project the data into the new features with the transformation matrix obtained in b.
Xpc = d Xn
PCA has been applied to the normalized dataset whose normalized active and reactive power are shown in the upper plot of figure 4. The two first PC are plotted in the leftmost below plot. The PCA is also applied to the same data set limited to events with active power first higher and then lower than 500W (respectively in the middle and right-most plots). For each of these three cases, the weights assigned to the features in the first PC are given in Table 1 and the percentage of total variance of the three first PCs in Table 2.
Figure imgf000034_0002
THD on Hzn Hm H7n Hon Hi In
all •: i :so 1 1.1 15 ( ', 02 \ A\J ' 1 L'S 0.2 1 ' 1 23 I I .2 ] i i. 1 7
< 500W 0.42 0.06 0.01 0.43 0.42 0.36 0.36· 0.33 0..23
> 500W 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.01 0.01 Table 1 : Weights of the features in the PCI for the data in figure 4
Figure imgf000035_0001
Table 2 : Cumulative percentage of total variance
Different comment can be formulated based on this illustrative example. - In the three cases, three features are given quasi null weight |Q/P| , H0n, H2n.
This means either that they are heavily correlated with other features ( |Q/P| ) or that there is no variations along these features (H0n and H2n).
When the entire data set is considered, the first PC is the combination of most features. But for both data subsets, only some features have relatively high weights: the PCI of the λ> 500W' subset involves the fundamental components whereas the one of the λ< 500W' subset is mainly limited the harmonic content and the reactive power. This could have been expected.
Whereas for the λ> 500W' data subset the PCI is sufficient to explain the variance of the data, PC2 is needed in the case of the entire data set to satisfy the 85% criterion. For the λ< 500W' subset, the three first PCs must be used.
It follows that adapting the extracted features to the considered data subset will improve the clustering.
Example 2: Component discovery
The method to discover instances of electrical components from clusters and the event time sequence can be illustrated by the following example.
First, on and off events are paired such that the fit-error is minimized. Second, cluster identifiers of paired events yield links between clusters which reflect electrical components. Third, assign event pairs to components to derive state sequences.
1. Pairing events by minimizing energy errors and error variations Considering two-state devices, if a component is turned off, it has previously been turned on. Following this, off-events should be paired to on-events to represent occurrences of unknown components. Constant power loads being assumed, the aggregate power is straightforwardly obtained for any sample k as the power of all pairs with kon < k < koff . If yk is the power measured at sample k and APk is a vector whose nonzero entries correspond to the signed power step values of paired events, the modeled aggregate power at sample k, yk, can be written as fc
§k = I/O + ^ Λ/ ' .
i=l y0 stands to account for loads that would have been switched on before the first sample of the observation window.
The ideal set of event pairs is the one for which the modeled aggregate power is the closest to the measured one. At each time, the power of the unknown components considered as active should sum up to the measured aggregate power. However, segmentation errors or simultaneous switch events lead to impossibility to truly fit the measured power simply by pairing events. Their impact on subsequent decisions should be minimized. This can be achieved by penalizing the bestfit solution with the total variation of the fit-error. We formalize this in the next paragraphs.
In the ideal case, all on/off switching have been detected and all events are correctly paired. In that case, differences between the modeled power ( ) and the measured one (y) derive from non constant power consumptions. Among different pairing possibilities, the optimal one is the one which minimizes the difference between y and y. But to deal with missed events, a gap should be allowed and its variations should then be minimized. The fit-error and the variations of this error are respectively defined as:
Figure imgf000036_0001
e,k = ek— efc- i . where yk is the median value of the power samples within steady state k. Note that also energy fit-errors and variations of energy fit-errors can be defined analogously for different time periods. This corresponds to modeling the observed aggregate power as constant segments. The use of median values instead of mean values allows the method to be more robust to segmentation errors: if there is a non detected power step within a steady state (i.e. there are actually two steady states), the longer one determines the constant power segment.
Pairing on-events and off-events can be done by extremizing a cost function which depends on variations in energy, in power, in current, in energy fit errors, in power fit errors, in current fit errors or in any combination thereof, preferably in a linear combination of at least two of said variations, more preferably variations in power and in power fit errors. preferred embodiment, the cost function is given by
Figure imgf000037_0001
wherein preferably λ= 1 and β= 1.
For the remainder of this example, we define the cost function :
Figure imgf000037_0002
where k varies on a considered window as explained in the next subsection. The optimal set of event pairs is the one minimizing this cost function. Summation limits are not explicited since no optimization window needs to be defined yet at this stage in the procedure. The use of the energy error instead of the power error (first term of cost function equation) could be investigated. But variations of power fit errors (second term) should be kept since variations in modeled energy are not relevant. If the first term were to be replaced by energy errors, weights between both terms should be carefully studied. 1.1. Searching for locally optimal pairs
An approach to find the optimal solution consists to test all combinations of event pairs. Of course, this is neither possible nor judicious. We propose a windowed approach to find locally optimal solutions. The use of optimization programming techniques is discussed in the next section. A local window is considered, the length of which is a parameter (we set the initial value to W = 10 minutes). If events candidate to be paired to an on-event are investigated, the window starts right before the studied on-event. Similarly, it ends right after studied off-events. In this local window, each candidate k' is tested as follows in three steps: a. the amplitude of the turn-off power step is assigned to APk and APk<, with appropriate signs,
b. the modeled aggregate power is evaluated with the equation given above where y0 is the power of the first sample in the window,
c. the cost function l~ k< is evaluated with summations limited to the local window.
Since off-event signatures are not impacted by turn-on transients, they are more reliable. This is why they are considered instead of on-event signatures in Step a. Step b allows to hide deviations from ideal fit due to previous erroneous pairing since y is systematically initialized to the first sample in the local window. In step c, the minimum cost rk< obtained with the different candidates in the window is compared to the costs of two other cases:
• 'no pair with event k' (ΓΝΡ) : APk is kept equal to zero, considering that event k is a fictitious transition
· 'candidate for event k is out of window' (Γ0νν) : ΔΡ|< is set to the observed power step at event k without assigning any complementary power step.
The next step is conditioned by the case that minimized the cost function :
• rk< is minimum
Events k and k' are paired. If the candidate k' was previously paired to another event, the previous pair is canceled. The entries of ΔΡ are updated accordingly.
• rNP is minimum
The event is not paired. It probably results from a false positive detection or its partner has not been detected.
• Tow is minimum
If the 'candidate out of window' solution minimizes the cost function, the local window size is enlarged and new candidates are investigated in the new time interval.
This process is repeated for all events in a global window. An example of modeled aggregate power is shown in figure 5. 2. From clusters to electrical components
Events have been paired and each event has been assigned to a cluster. We extract pairs which are constituted by non-outlier points, since these points are likely to be true events. If events associated to different clusters are often paired, these two clusters are considered to contain events from a single component. In such a case, an instance of electrical component is recorded and its electrical properties derive from the electric signatures of the clusters. Pairs of nonoutlier events with identical cluster ID lead to a direct association of a cluster to a component.
To summarize, a component can be defined as a recurrent link between clusters required to appropriately model the aggregate power.
3. Evaluation of component state sequences
Instances of electrical components have been learned from pairs of nonoutlier points. Since all events have been assigned to a cluster owing to the point-to-cluster Mahalanobis distances, a first approximation for state sequences of the discovered components consists of pairs of events assigned to the corresponding clusters. An example is given in figure 6.
However, the discovered components could also be used as input for NIALM methods with prior information.
Example 3 : Results of laboratory testing
Algorithms were developed considering both laboratory and field data. However, to evaluate performances at the different stages of the NIALM procedure, a reliable ground truth is required. The latter is only available with laboratory data. Algorithms have been developed with the aim of providing parameter settings which are not tuned to specific data. Consequently, a new data set was generated in the laboratory (ELDA) specifically for this performance evaluation.
In Section 1 below, the data set is presented. The results are given in Section 2 and discussed in Section 3. 1. Data set
Measurements have been performed in the laboratory developed for this research (ELDA). In addition to measuring the voltage and the aggregate current, each appliance is individually monitored. The appliance level consumption is consequently known. To obtain the ground truth about times of appliance state changes, the power consumed in each outlet is thresholded. However, this works only for two-state appliances since, with multi component appliances, once a device is in operation additional state changes cannot be detected by simply thresholding the power draw. For example, if the heating resistor of a washing machine is in operation, state changes of the drum cannot be detected by thresholding the power since the latter varies between e.g . 2000W and 2200W. Consequently, mainly two-state devices were considered.
Nine devices were cyclically turned on and off during a 3-hour period : a kitchen mixer, a hair dryer in low power mode, a kettle, a 50W incandescent light bulb, a ventilator, a vacuum cleaner, a 200W halogen light bulb, a 10W economic light and a microwave oven. All these devices but the microwave are two-state appliances. The power they consume during one on-off cycle is shown in figure 7 and their current waveforms are shown in figure 8.
Cycles have been generated such that repetitive simultaneous state changes are avoided. However, simultaneous on/off switching might still occur. Cyclic behavior of appliances has no impact on the results since times and durations of use are not taken into account. Furthermore, even if appliances are cyclically operated, the aggregate consumption is not cyclic and various load combinations are obtained.
Some occurrences of the microwave oven are shown in figure 9. This appliance has more than two states: it consists of a light bulb, a motor and a magnetron. Furthermore, it can be noticed that, according to the average power asked by the user, the magnetron is turned on and off during its operations. Consequently events were manually added to the ground truth to account for these state changes.
2. Performance evaluation
In this section, results obtained at the different stages of the consumption analysis procedure are assessed and illustrated. Results will also be analyzed with the aim to identify suggestions for future work.
2.1. Event detection
The power trace was median filtered with LM = 50 and the cusum detector parameters were set to vm = 20 and Nd = 50. The rate of correct detections and the amount of missed detections can be evaluated for each individual load. The figures are reported in Table 3. We observe a global rate of 91%. Load True detection rate Detected / Total
Mixer 93 % l . i s , " . ] >
Hair dryer 97 % H i:; . I H ;
100% 108/108
SOW light bulb 96 % I -i . ΐ ·;
Ventilator 88 % 105/120
Vacuum cleaner 99 % I l lf i J 7
200W light bulb 97 % 1 " 7 2
Microwave oven 94 % 183/195
Eco light 76 % 212/279
T< )t al f i r 1.195/1,310
Table 3 : Detection rate obtained with vm = 20 and Nd = 50. Most missed detections comes from low power loads.
2.2. Feature evaluation
The detected events are plotted in the ΔΡ-AQ plan in figure 10 and figure 11. Each couple color-symbol represents one appliance, as indicated by the ground truth. In the following paragraphs, we comment on what can be observed from these plots.
Turn-on events with slow time decay lead to several detections. In the studied data set, this impacts the segmentation of turn-on transients corresponding to the mixer and the vacuum cleaner, as shown in figure 12. This leads to different steady state feature values for turn-on and turn-off events. This can be seen with the green point cluster in figure 10 for the vacuum cleaner and with the red point cluster in figure 11 for the mixer. The events corresponding to both these loads form substructures. Furthermore, fictitious second events limit the search for the knee in the power trace which prevent from properly capturing the transient dynamics.
Events corresponding to the microwave exhibit a more complex scattering. Based on the power cycles shown in figure 9, two observations can be made. First, events corresponding to its light lead to points in the cluster around the origin of the P-Q plane (see figure 10). Second, turn-on transients result systematically in two detected events, as illustrated in figure 12. The second ones form the cluster right under 1000W in figure 10. They are not labeled in the ground truth and are then considered as false positive detections.
It can be observed in figure 11 that most fictitious detections lead to points located between clusters of low power loads. Some also lie in clusters formed by events of these loads (in the P-Q plan). Moreover, the relative impact of variations in the mixture on the feature evaluation is more important for these low power loads. In addition, the ventilator shows relatively important power variations with respect to the power it consumes. This is illustrated in figure 13. This will probably harden the identification task.
Note finally that, when transients states are defined such that they contain two switch events, the assigned ground truth label is the one of the firstly actuated appliance. This explains why red crosses indicating events of the economic light lie with events of the 200W light bulb in figure 11.
2.3. Clustering the signatures
Clusters obtained with a first run of DBSCAN are shown in figure 14 and the ones resulting from the iterative procedure are shown in figure 15. Note that these classification results are only based on steady-state features since no mean to obtain a single data partitioning from SS and TS clusters has been implemented. Clusters of transient patterns are however shown at the end of this section. Three observations should be done: · Low power loads are well identified thanks to the adaptive feature extraction and definition of the o-neighborhood in the iterative clustering procedure. This is observed by comparing figure 14 and figure 15.
• Second events of microwave turn-on transients are also divided in two clusters.
This is not desired but could be expected since these events clearly form two clusters in the P-Q plot.
• However, it can be observed that the cluster of on-events of the vacuum cleaner is not divided although distinct clusters appear in the P-Q plot. This means that they are close enough thanks to other features.
The link between clusters and monitored appliances is given in Table 4. All figures but the ones in the first row are numbers of events. The table is structured as follows:
• Each column corresponds to one cluster: the first row gives the cluster identifier (ciD) corresponding to figure 15 and events are distributed in rows according to the ground truth. Outliers are reported in the last column along with nondetected events.
· Rows correspond to appliances as defined by the ground truth. The last row corresponds to events for which no identifier has been assigned in the ground truth. They are mostly false positive detections, but second events of microwave turn-on transients also lie in this category.
Figure imgf000043_0001
Table 4: There is almost no confusion between clusters resulting from the iterative clustering procedure.
Differences in the total number of events in Table 4 (and following) compared to Table 3 are due to simultaneous switch events. Since, in these cases, one event appears in the result instead of two, it is only counted once and is considered to belong to the appliance firstly turned on.
We analyze further the results given in Table 4.
• Single clusters are identified for the hair dryer (ciD = 3), the kettle (ciD = 1), the 50W light bulb (ciD = 14), the 200W light bulb (ciD = 10) and the economic light (do = 11). The low confusion between events of the economic light and the ventilator observed at this stage is an interesting result. This would probably not be achievable if only P and Q were considered.
• Two clusters are identified for events corresponding to the mixer: one for on- events (ciD = 9) and one for off-events (ciD = 12). The situation is similar for the vacuum cleaner (ciD = 4 and CiD = 5). It is expected that the time sequence analysis reveal that these clusters belong to a single component.
• The power consumed by the ventilator is low and shows variation of the order of 20%. This is illustrated in figure 13. Consequently, outliers are associated to its cluster (ciD = 2).
• The situation is more complex for the microwave. Its turn-off events form a single cluster (ciD = 8). On the contrary, its turn-on transients are systematically segmented in two events: the first ones form one cluster (ciD = 6) while the second ones are grouped in two clusters (ciD = 7 and CiD = 15). · Except for clusters 2 and 13, all events appearing in entries others than the main one result from simultaneous switch events. In these cases, only the appliance firstly turned on was reported in the ground truth. These results show that clusters are appropriate to learn electrical component signatures since there is little confusion between components: columns contain manly one single entry.
Membership values are evaluated with the Mahalanobis distance in the initial feature space. The classification corresponding to the minimum distance is shown in figure 16 and the corresponding figures are given in Table 5. In this table, figures in the rightmost column correspond to non detected events. The most important observation is that outliers are mostly assigned to one cluster, the one constituted by events of the ventilator (ciD = 2). This suggest that a method to limit the impact of outliers be investigated in future research. For instance, it could be useful that a 'bin' cluster be defined or that a threshold on membership values be used not to associate spurious events to clusters.
Figure imgf000044_0001
Table 5 : Outliers are associated to clusters with the Mahalanobis distance evaluated in the initial feature space. Spurious events are mostly assigned to the cluster
corresponding to the ventilator.
Note that microwave oven events assigned to clusters 2 and 14 correspond to the light bulb belonging to this appliance.
Regarding transient states, patterns corresponding to the identified clusters are given in figure 17. No cluster are found for the kettle, the vacuum cleaner and the ventilator. This could be expected for the kettle and the ventilator since their turn-on transients are only step-ups. This is however surprising for the vacuum cleaner; this means its transient patterns are too scattered to be clustered. There are two clusters for the microwave oven corresponding to the two parts of its turn-on transients. Transients of the mixer are divided into two distinct clusters.
Again, the discovered clusters are appropriate to learn component signatures since there is almost no confusion between components. 2.4. Discovering the components
Events are paired following the local window approach of the best-fit technique exposed earlier in this document. The modeled aggregate power resulting from paired events is shown in figure 19. Components are defined as recurrent associations of cluster IDs within nonoutiier event pairs. The resulting component identifiers (compiD) are shown in figure 18 and given in Table 6.
Figure imgf000045_0001
Table 6 : All appliances have a pure or quasi pure group of event pairs that can be used to learn component signatures. The following observations can be formulated :
• All appliances have a pure or quasi pure group of event pairs that can be used to learn component signatures.
• There is one component (compiD = 5) composed of events from the hair dryer and the 200Wlight bulb, whereas these two components are not confused regarding the signature classification (Table 5). This suggests that the membership values be used in some ways in the pairing procedure. On the contrary, the confusion between the ventilator and the economic light (compiD = 3) was already present in the classification.
• Since second events of microwave turn-on transients were divided in two clusters, pairs remain divided in two component identifier. Future works could address the analysis of their time sequences to detect that they belong to one single electrical component. Actually, they should not exhibit simultaneous on states and should have similar duration of use distribution.
• First events of microwave turn-on transients are successfully rejected. In future works, additional analysis could detect that such a rejected cluster derive from the segmentation of single transients. For instance, this could be based on the following considerations: events of CiD = 6 (figure 15) are always followed by events of CiD = 7/15 and the sum of their linear features lies in cluster CiD = 8 which exhibits subsequent off-events.
2.5. Energy disaggregation
Although the proposed tool focuses on discovering the set of components, it is interesting to look at how component state sequences are evaluated and how aggregated energy can be segmented into the one of individual components. Since a membership value has been assigned to all events. The method simply consists to assign component identifier to event pairs according to their cluster identifiers, the resulting classification is given in figure 20 and Table 8.
The state sequence of each pure component is evaluated and shown in figure 21. The state sequence of the ventilator is based on compiD = 2 although it is not a pure component. Furthermore, both compiD = 7 and compiD = 8 are manually associated to the microwave oven. Regarding the economic light, it can be seen in figure 21 that, although paired events correspond to events of this light, pairs do not properly link successive on and off events. This also occurs in a lesser way for the ventilator.
The energy corresponding to the state sequences is contrasted with the one obtained from the submetering in Table 7. The low percentages of energy recovery suggest that more robust techniques be implemented to exploit the discovered component signatures and better evaluate the state sequences.
Figure imgf000046_0001
Table 7 : Energy assigned to individual components (in Wh). The link between the components and the devices is manually defined. T (True) stands for energy consumed by the appliance and properly assigned to a component state sequence. F (False) stands for energy assigned to a state sequence whereas the corresponding appliance exhibits no consumption.
Figure imgf000047_0001
Table 8 : Paired events are assigned to components according to their cluster identifiers.
3. Discussion The results presented in this example showed that it is possible to discover the electrical components responsible for the aggregate consumption, and this, without prior information. Component state sequences have been evaluated with the present algorithm, mainly for illustrative purpose.
Example 4: Event detection In the following example, event detection algorithms in the context of a NIALM method are further discussed and specific implementation and results are explained in detail. References within this example are made to the following documents:
[1] G. W. Hart, "Nonintrusive Appliance Load Monitoring," Proc. IEEE, vol. 80, no. 12, pp. 1870-1891, 1992. [2] M. Zeifman and K. Roth, "Nonintrusive Appliance Load Monitoring : Review and Outlook," IEEE Trans. Consum. Electron., vol. 57, no. 1, pp. 76-84, 2011.
[3] H . Najmeddine, "Methode d'identification et de classification de la consommation d'energie par usages en vue de I'integration dans un compteur d'energie electrique," UNIVERSITE BLAISE PASCAL - CLERMONT II, 2009. [4] M. Basseville and I. V Nikiforov, Detection of Abrupt Changes : Theory and Application. 1993. [5] Q. Jossen, "Unsupervised learning procedure for nonintrusive appliance load monitoring," Universite libre de Bruxelles, 2013.
[6] M. Basseville, "Detecting changes in signals and systems— A survey," Automatica, vol. 24, no. 3, pp. 309-326, May 1988. [7] M. Basseville and A. Benveniste, "Design and Comparative Study of Some Sequential Jump Detection Algorithms for Digital Signals," IEEE Trans. Acoust., vol. assp-31, no. 3, pp. 521-535, 1983.
[8] D. Luo, L. K. Norford, S. R. Shaw, S. B. Leeb, R. Danks, and G. Wichenko, "Monitoring HVAC equipment electrical loads from a centralized location - Methods and field test results," in ASHRAE Transactions, 2002, vol. 108 PART 1, pp. 841-857.
[9] M. Berges, E. Goldman, H . S. Matthews, L. Soibelman, and K. Anderson, "User- Centered Nonintrusive Electricity Load Monitoring for Residential Buildings," J. Comput. Civ. Eng., vol. November/D, 2011.
[10] L. Farinaccio and R. Zmeureanu, "Using a pattern recognition approach to disaggregate the total electricity consumption in a house into the major end-uses," Energy Build., vol. 30, no. 3, pp. 245-259, 1999.
1. Introduction
In a domestic context, NIALM applications (Non-Intrusive Appliance Load Monitoring) are more and more used. It allows the consumer knowing his electrical consumption without having to install lots of sensors in his house. There are several ways to obtain information from an aggregated signal of electrical consumption. In each case, the first step consists in detecting ONs and OFFs of electrical appliances connected in the house. This is called "Event Detection".
This example attends to present a global event detection algorithm with high robustness against noise in the active power signal. The example will present a preferred detection approach, based on 3 different detection steps, that decreases the complexity of each step.
In the framework of NIALM applications, several different methods are possible.
The analysis can be based only on active and reactive power measured at the meter location for example. The sampling frequency is generally low in this case (0.001Hz to lHz typically). No information on the current waveform is used in this approach, only macroscopic information is kept. That was the first approach proposed by Hart [1] . The transient in the power itself can also be lost with this logic (depending on the exact sampling frequency and the kind of transient).
Today, researchers agree that, in order to increase quality of disaggregation, the current waveform should be taken into account. For example, information can be obtained looking at the third harmonics of the current or the waveform in the current- versus-voltage plane (I-V plane). This approach requires a higher sampling frequency depending on the needed current information (Typically in the range from a few hundred to a couple of thousands Hertz). The transient in the active power is kept with this sampling frequency [2] [3] . Another possibility is to base the process on electromagnetic transients. When an electrical component is connected to the grid, there is a generation of an electromagnetic wave in the range of some Megahertz. If the sampling frequency is high enough, it can be detected and used to characterize the load that has been connected [3] . This paper does not discuss this aspect. All approaches will have the same first analysis step: detection of events i.e. detection of ONs and OFFs of electrical components. In this example, this stage is named "Event Detection". We will detail our approach for Event Detection in what follows.
Section 2 of this example will give the literature review for Event Detection. The general structure of the Event Detection algorithm will be given in Section 3. Next, in Section 4, the detailed algorithm will be presented. Finally, Sections 5 and 6 will be dedicated respectively to results on real measurements and conclusions.
2. Literature review
We would like to cite a good reference for general literature review on the NIALM topic. This reference is [2] . 2.1. Event Detection
The global process of Event Detection can be seen as a global filter with a chosen signal X(k) in input and a detection signal D(k) in output defined by:
D(k)= 1 if an event occurs in X(k), and 0 otherwise
X is "as close as possible" to a piecewise constant signal. The problem of determining D becomes a well-known problem : the change detection problem. This problem has been addressed in several research works. The interested reader can refer to [4] for a good summary on the topic. The change detection problem can be described as a 3-stages process:
Choosing X and perhaps filtering it to cancel partly the noise
Creating a residual signal which has a high value during events and a low value otherwise Thresholding the residual signal to obtain D
In this section, only stage 2 will be discussed. For this stage, one can basically distinguish 2 different approaches. First possible approach is based on the discrete derivative of the studied signal. The second method consists in statistical tests.
2.1.1. Methods based on discrete derivative
A very simple approach to extract moment of events can be based on the derivative of the signal X. Indeed, X is piecewise constant: in theory, its derivative is non-zero when an event occurs and zero otherwise. Using a specific threshold applied on the derivative of X could then be a good idea. This approach is often used in image processing to find edges in an image. [4] and [5] introduce basic concepts of using such a principle. Main drawback of this principle is the poor robustness related to noise. However, the main advantage is the local vision of such a filter. Indeed, the derivative is local information concerning the slope of X.
The discrete derivative of a signal is defined simply as: Y(k)=X(k)-X(k-l)
Unfortunately, directly thresholding γ would lead to very poor performances because of the unavoidable noise present in X. To solve this problem, other calculations for this derivative can be operated thanks to derivative filters. Among those derivative filters, we can mention an interesting one: the filter based on the first derivative of Gaussian (FDOG). We will detail our approach of using this filter in Section 4.
2.1.2. Methods based on statistical tests
Main drawback of the previous method (based on the discrete derivative) is the poor robustness to noise. An idea to increase this robustness is to observe a larger window in the signal and divide this window in 2 different parts. The time of this division is let undefined. The idea is to study the first part of the signal as a random variable Xi and the second part as a second random variable X2. If parameters related to the variable Xi (typically the mean μ or perhaps the standard deviation σ) are "significantly" different from parameters extracted from X2, it means that there was an event in the signal between the situation in Xi and the one in X2.
This method can be generalized by searching for N events in the defined window but this increases quickly the computational complexity. Lots of different algorithms are based on this principle. There are some of them more dedicated to online processes whereas others are more used in offline configurations. Parameters of defined distribution Xi and X2 can be known or unknown, the processed window length and thresholds can be fixed or variable. The summary given here will not mention all of them but only the 2 most interesting approaches according to us. The interested reader can refer to [4], [6], [7] and [8] .
CUSUM algorithm for "Cumulative SUM" is an algorithm based on the integration of the difference between the mean value of the signal X(k) (or an estimate for this value) and the signal itself. This algorithm is well-known and has been addressed in plenty of publications. A good summary on the different versions of this algorithm can be found in [4] . A specific formulation of this algorithm will be used and described in this example in Section 4. Our approach is similar to the one proposed by [5] with some additional changes for improving robustness against false detection.
GLR algorithm for "Generalized Likelihood Ratio" is an interesting approach of the Event Detection problem. A good example of a work using this principle is [9] . They propose to use the generalized likelihood ratio computed along a sliding window. The point with the highest test statistic (consisting in a summation of likelihood ratios) in the sliding window is assigned a vote. The process allows a point to receive several votes, each for one position of the sliding window and, as a result, a point with a high number of votes is a good candidate for an event time. According to authors, this process is powerful when only one event fits in the sliding window entirely but fails if transients in power related to events are longer than the window or if more than one event takes place in the window.
2.1.3. Intrusive Methods
Our goal is to establish the literature review for methods detecting automatically changes in signal without a priori knowledge on the signal itself. If a database for events is built, one can compare this database with the signal and decide if an event occurred. This approach was proposed by [10] . However, this approach needs a supervised learning procedure which is out of our scope up to now and as a result will not be investigated in this paper. 3. Global Algorithm Structure
3.1. 3 steps approach for Event Detection
The choice of a multi-step approach is based on the fact that some events are easily detected while other events are not. The detection of an event can be influenced by the signal around this event. If there are 2 significant events close to each other, it is probable that one detection algorithm will merge both. The idea is the following : first detect the easily detected events and then the more complicated ones. With this approach, the stage operating on complicated events will be less influenced by the easy detections and will work better. The detection process is based on the active power averaged on one fundamental period (one sample for each 50Hz period). A detection is considered when a "significant" change occurs in the active power signal P(k). P(k) is assumed to be piecewise constant. Of course, this is an ideal case but P(k) must be as close as possible to this perfect case. To cancel partly the noise, the signal P(k) is median filtered with a window size of 11 fundamental periods and afterwards mean filtered with a window size of 5 fundamental periods. Notation "P(k)" will now refer to this filtered signal.
P(k) is processed in 3 steps. The global detection logic is shown in Fig 22.
The first step of the analysis is the detection of big events i.e. high derivatives. This step is based on a derivative filter: the "first derivative of gaussian" filter (FDOG).
The second step is based on the recognition of stable steps. The idea is that, if an event is really stable in time, it can be detected even if the level of noise is in the order of magnitude of the event itself because there is a clear change of mean.
The third and final step is based on the CUSUM algorithm which is a change of mean detector.
Next session will illustrate how all those detection techniques were implemented.
3.2. Interfacing the different Event Detection stages
Because we introduce a multi-step approach, we introduce interfaces to manage between different steps. In this example, we will not detail the way used to handle the different temporary results. To illustrate the general principle of interfacing, the reader can refer to Fig. 23. 4. Detailed Algorithm
This section will describe in detail the whole logic contained in each detection step. As a reminder, a 3 step approach is adopted for Event Detection.
4.1. Detection of high variations based on derivative
The first step ensures to find the biggest variations of the signal P(k). In order to do so, a derivative filter is used. The filter is based on FDOG. This consists in thresholding the signal P(k) convoluted with a filter based on the first derivative of the Gaussian function. The filter used is given in (1).
Figure imgf000053_0001
N represents the length of the convolution window in samples. σ2(Ι) represents the variance of the signal P(k) in the convolution window. This is not conventional and allows to have detectability depending on the signal itself: very good detectability when the signal is highly varying (potential high event present in the window) and a lower detectability in case the signal is less variant. This means that higher events are privileged for detection in this stage of Event Detection.
A specific threshold is then applied to this result. The threshold depends on the level of events to detect ΔΡ during this stage.
For this step, the only parameters to be defined are the length of the window N and ΔΡ. To detect strong variations, i.e. big events, even in case of short durations of those variations, ΔΡ should be high and N small.
4.2. Detection of stable steps
In the previous detection method, the idea was to detect strong variations of the power (ΔΡ high enough) even with short durations (N low enough).
The idea behind this detection step is to detect events in the power which are really stable. The level of variation could be low (the level of noise for example) because there is a strong stability in the event.
In a preferred embodiment, the general principle of this part of the Event Detection is to compute the distance between a perfect active power step and the active power signal P(k). The step is sliding on the whole observation frame and this distance is computed for each point (in principle even if, for computational complexity reasons, it is computed uniquely when need be).
In a preferred embodiment, the sliding step can be defined with the following logic:
Figure imgf000054_0001
The Euclidean distance between the step and the signal is then computed. A threshold is applied to the computed distance. If the computed distance is lower than the threshold, there is detection. This threshold depends on the noise of the signal P(k).
The only parameter to define is the length of the sliding window n. This length should be large to follow the logic of stability in the event.
4.3. Detection thanks to CUSUM
At this level of the analysis, high events and low and stable events are normally detected. It remains the low and less stable events.
This detection technique is, in a preferred embodiment, based on the CUSUM algorithm. We will not present in detail the well-known CUSUM algorithm.
We will here just remind the general principle and give specific changes that we made to the original algorithm.
General principle is to compute the following detectors:
U(k) = U(k-l)-(P(k)- )+v (5)
T(k)=T(k-l)-(P(k)- )-v (6)
The maximum/minimum of the detectors U/T is memorized in Umax/Tmin . A threshold δ is then applied on the differences below to trigger the detection :
Umax-U(k)>6 (7)
T(k)-Tmin>6 (8)
Equations (5) to (8) contain 2 undefined parameters v and δ. Moreover, the estimated mean μ is not defined accurately. In our implementation, the mean μ is computed periodically with a user-defined period max. This calculation is done uniquely if no detection is in process i.e. detectors T/U are decreasing and increasing respectively. The 2 parameters v and δ are defined thanks to 2 parameters: the minimum detectable power step Pmin and the period of computation for μ : Kmax. In fact, Pmin is computed thanks to the evaluated noise in the signal.
4.4. Use of Current 5th harmonics
The whole process described here before is based on the filtered active power P(k). Active power consumed by some electric components appears to be low whereas their global current consumption is not negligible. This high current consumption relates to distorted current. The distorted current is not visible in power consumption since voltage is approximately a perfect 50Hz waveform. As a result, information in current harmonics is lost. In order to extract remaining information in the current, the process described before is applied to the computed fifth harmonic in the current. The different thresholds defined in the previous subsections are adapted to match the current range.
The fifth harmonic of the current can be computed, in a preferred embodiment, thanks to a Fourier analysis thanks to a sliding window on the current. The sliding window slides with a 50Hz period (one computed value for each 50Hz period, as in the case of the power). For computational reason, only the 250Hz component is computed.
/5 (fc) = (9)
Figure imgf000055_0001
I5 is the fifth harmonics in the current signal i(k). N is the size of the sliding window. I corresponds to the index of 250Hz component in the frequency spectrum of the signal (I is not necessarily an integer).
Fig. 24 illustrates the usefulness of the current harmonics in Event Detection. The above signal is the 5th harmonics signal whereas the signal below corresponds to the power. The events in the power signal are lost in the noise (especially the OFFs transitions) whereas those events are obvious in the 5th current harmonics signal.
The general algorithm analyzes the events present in the current fifth harmonics and then the events present in the active power signal. We adopted this logic because of the density of events in the signal : there are less events in I5 (linear components do not consume distorted current). As a consequence, the analysis is simpler in the case of the I5 signal. Management of temporary results is carried out as explained in Fig 23.
5. Experimental Results
We implemented the algorithm described in section 3 and 4. The data set used is composed of different appliances: hotplates, an air extractor, a dishwasher, a washing machine, a dryer, a fridge, a refrigerator, an oven, a microwave oven, a boiler, a coffee maker, a television, a decoder, a heat pump and light devices. Unfortunately, this data set is not supervised automatically: a manual supervision was constructed visually inspecting the power signal P(k). As a consequence, only events recognized by an expert are considered. Moreover, no label is attached to events; only ON/OFF information is available. The algorithm was tested on the data set with measurements corresponding to 1 day.
Quantification of results is operated thanks to 2 different indicators: The first indicator Indi is the ratio between the number of detected events which were marked as events in the manual supervision and the total number of marked events. This indicator is called detection rate. For good performances, this indicator must be close to 100%.
The second indicator Ind2 is the ratio between the number of detected events considered as wrong (with a second visual inspection) and the total number of detected events. This indicator is called overdetection rate. For good performances, this indicator must be close to 0%.
Jj^^ ^ detected_and_marked (10)
^marked tected
The number of marked events after visual inspection is 4597 (= Nmarkeci). The total number of events detected thanks to the algorithm is 4480 (= Ndetected)- The indicators Indi and Ind2 equal to: lnd1 = 91.26 % , Ind2 = 4.21%
Using only the active power P(k) as an input for the algorithm, the indicators equal to : lnd1 = 88.17 % , Ind2 = 2.11 %
Those results are encouraging. We can conclude on the validity of using current 5th harmonics for Event Detection because this increases the detection rate. The cost of using the 5th harmonics is an increase in the overdetection rate but we expect this effect to be reduced with future improvements.
6. Conclusions
We implemented an algorithm for Event Detection for NIALM applications. The algorithm is based on the active power signal and on the fifth harmonics present in the current. The method used for this algorithm is a multi-step approach. The multi-step approach allows to decrease the complexity of each step in the analysis.
The first results are very promising. A detection rate of 91% was obtained. According to us, the use of current harmonics, and in particular of the fifth harmonics, for Event Detection increases the detection capabilities of the algorithm.
Example 5: System with branch circuits
Figures 25a and 25b illustrate exemplary embodiments of a non-intrusive appliance load monitoring (NIALM) method for monitoring components of appliances in a system comprising a set of branched circuits and a related system according to the present invention.
Four branch circuits (256, 257, 258, 259) are connected to an external power grid (251), which provides power (252) to a system (268) e.g. via a distribution box (253). Each branch circuit has a circuit breaker (260, 261, 262, 263) onto which a branch device (264, 265, 266, 267) is mounted, the branch device being arranged to obtain a branch electrical signal and preferably each branch device being provided with instructions to at least detect branch events. The information about detected branch events can be sent to a NIALM device (254), e.g . via the branch circuit wiring and the distribution box (253) in fig. 25a or via a bus wiring (269) in fig . 25b. The NIALM device is provided with instructions to detect system events on the aggregate electrical signal, which it can obtain from the power input (252) and/or via the distribution box (253), and to pair system on- and off-events, taking into account the information it receives from the branch devices. The results of the pairing can be sent directly, or after further processing to an external device or user, e.g. via wireless communication means (255) as in fig. 25a or via the power line and external power grid (251, 252) as in fig. 25b.

Claims

Claims
1. Non-intrusive appliance load monitoring (NIALM) method for monitoring components of appliances in a system comprising a set of branched circuits, comprising the steps of: (a) detecting system events in an aggregate electrical signal comprising aggregate power consumption information of said system, said system events representing state transitions of the appliances in the system, and said system events comprising on-events and off-events;
(b) for at least one and preferably each of said branch circuits: separately detecting branch events in a branch electrical signal comprising branch power consumption information of said branch circuit of said system, said branch events representing state transitions of the appliances connected to said branch circuit;
(c) pairing on-events and off-events, thereby obtaining a set of paired events; and
(d) detecting and/or identifying components on the basis of said set of paired events,
characterized in that an on-event and an off-event are identified as a paired event only if both the on-event and the off-event are detected as branch events of the same branch circuit.
2. NIALM method according to claim 1, whereby said aggregate electrical signal is obtained at an aggregate sampling frequency and said branch electrical signal is obtained at or resampled to a branch sampling frequency, characterized in that the aggregate sampling frequency is different from the branch sampling frequency.
3. NIALM method according to claim 2, whereby the aggregate sampling frequency is higher than the branch sampling frequency, preferably by a factor which is at least the number of branch circuits in said system.
4. NIALM method according to any of the previous claims, whereby said aggregate sampling frequency is at least 100 Hz, preferably at least 500 Hz, more preferably at least 800 Hz, most preferably at least 1600 Hz, and/or whereby said branch sampling frequency is at least 0.001Hz, preferably at least 0.01 Hz, more preferably at least 0.1 Hz, most preferably at least 0.5 Hz.
5. NIALM method according to any of the previous claims, whereby system events are clustered into clusters of system events.
6. NIALM method according to claim 5, whereby: each of said system events comprises a cluster ID which allows to identify the cluster to which the event belongs;
each paired event comprises paired cluster ID information representing the cluster ID of the on-event and the cluster ID of the off-event in said paired event, and
components are detected and/or identified by identifying recurrent paired cluster ID information within said set of paired events.
7. Non-intrusive appliance load monitoring (NIALM) system for monitoring components of appliances in a system comprising a set of branched circuits, comprising :
(i) an aggregate NIALM device which is mountable on one or more main electrical power line of the system for obtaining the aggregate electrical signal comprising aggregate power consumption information of said system;
(ii) one or more branch NIALM devices, each of which is mountable on a branch circuit of the system for obtaining the branch electrical signal comprising branch power consumption information of said branch circuit, and
(iii) connection means for connecting said one or more branch NIALM devices to said aggregate NIALM device and allowing information exchange between each of said branch NIALM devices and said aggregate NIALM device, whereby said NIALM system comprises instructions for executing a NIALM method according to any of the claims 1 to 6.
8. NIALM system according to claim 7, whereby said aggregate NIALM device comprises instructions for executing steps (a), (c) and (d) of the method according to any of the claims 1 to 6, and said one or more branch NIALM devices comprise instructions for executing step (b) of the method according to any of the claims 1 to 6, or
said aggregate NIALM device comprises instructions for executing steps (a), (b), (c) and (d) of the method according to any of the claims 1 to 6, and said one or more branch NIALM devices comprise instructions for obtaining a branch electrical signal comprising branch power consumption information of a branch circuit and for transmitting said branch electrical signal to the aggregate NIALM device.
9. NIALM system according to any of the claims 7 to 8, whereby said aggregate NIALM device comprises an aggregate sampler, arranged for sampling an aggregate electrical signal of the system at an aggregate sampling frequency;
said one or more branch NIALM devices each comprise a branch sampler, arranged for sampling or resampling a branch electrical signal of a branch circuit at a branch sampling frequency, whereby said aggregate sampling frequency is different than said branch sampling frequency.
10. NIALM system according to claim 9, whereby said aggregate sampling frequency is higher than said branch sampling frequency.
11. NIALM system according to any of the claims 7 to 10, whereby at least one and preferable each NIALM device is a circuit breaker, is mounted on a circuit breaker, comprises a circuit breaker, or any combination thereof.
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