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Residential Household Non-Intrusive LoadMonitoring via Smart Event-based Optimization

Elnaz Azizi, Student Member, IEEE, Amin Mohammadpour Shotorbani, Member, IEEE,Mohhamd-Taghi Hamidi-Beheshti, Member, IEEE, Behnam Mohammadi-Ivatloo, Senior Member, IEEE and

Sadegh Bolouki, Member, IEEE,

Abstract—Home energy management requires accurate infor-mation about the appliances’ consumption pattern. This infor-mation can help consumers save energy, control their usageby shifting their usage to off-peak hours and reduce theirelectricity costs. Non-intrusive load monitoring (NILM) in whichthe power consumption profile of appliances are extracted fromthe aggregated signal of a household, provides this information.For the NILM problem, machine learning approaches as thetraining-based solutions require large training datasets for anaccurate disaggregation and the optimization-based approachesemploys prior information about the characteristics of appliances.This paper proposes a novel event-based optimization algo-rithm. In its first stage, the prior information about appliancesis extracted from the events of the consumption profiles ofappliances by means of clustering. Then, a new event-baseddown-sampling method and transition filtering are designed fordecreasing the computation time of optimization. At the laststage of the proposed algorithm, post-processing consideringON duration of appliances and varying states are proposed toincrease the accuracy of the power profile reconstruction. Theproposed approach was successfully tested for the low-frequencydataset of a house from the REDD. Numerical results showthe advantages of the proposed algorithm, marked improvementover classification-based NILM considering small training datasetand its applicability in disaggregating the power consumptionmeasured by the smart meter.

Index Terms—Demand-side management, load monitoring,event-detection, clustering.

I. INTRODUCTION

BECAUSE of low costs and financial risks, energy man-agement strategies have gotten lots of attention in dealing

with lack of fossil fuels, energy efficiency, global warming,and the ever-increasing energy consumption [1]. Providingfeedback to energy consumers, enables them to manage theirpower consumption using Demand-side management strategies[2]–[4]. Studies show that load monitoring can provide helpfulinformation about what and when certain appliances are beingused, which can decreases the energy consumption more than

E. Azizi, M.T. Hamidi Beheshti and S. Bolouki are with Depart-ment of Electrical and Computer Engineering, Tarbiat Modares Uni-versity, Tehran, Iran.e-mail:(e.azizi@modares.ac.ir, mbehesht@modares.ac.ir,bolouki@modares.ac.ir)

A. Mohammadpour Shotorbani is with the School of Engi-neering, University of British Columbia, Kelowna, BC, Canada.e-mail:(a.m.shotorbani@ubc.ca)

B. Mohammadi-Ivatloo is with Faculty of Electrical and Computer En-gineering, University of Tabriz, Tabriz, Iran and also with Institute ofResearch and Development, Duy Tan University, Da Nang, 550000, Vietnam.email:(mohammadi@ieee.org)

15% [5] through demand-side management. Moreover, loadmonitoring can help both electricity consumers and providersin detecting the devices with high consumption at peak hours,identifying the malfunctioning devices, forecasting the de-mand, etc. [6].

Generally, load monitoring methods can be categorized intotwo main approaches as: (I) intrusive load monitoring, inwhich a sensor is installed on the circuit of each appliance,and (II) non-intrusive load monitoring (NILM), in which thepower consumption profile of each appliance is extracted fromthe aggregated power signal using computational methods. Incomparison with intrusive load monitoring methods, the NILMrequires fewer sensors for measuring the consumption, but hasless accuracy and needs complex calculations for analyzing thedata [7]. Figure 1 illustrates the NILM schematic, in which,the power profile of each appliance is extracted from theaggregated power signal of a house in NILM.

Fig. 1. The schematic of disaggregating load profiles of appliancesfrom the total consumption power of a house.

More than 25 years ago, the original NILM was intro-duced by Hart [8]. Recently, NILM has attracted growingattention from researchers in the smart grid field, leadingto the development of various data-based analytic methods.These approaches are divided into machine learning andoptimization-based algorithms, with the latter being also ourfocus in this work. Some remarkable recent machine learning-based methods have utilized classification [9], multi-labelclassification [10], [11], clustering [12], deep learning [13],neural networks [14] and hidden Markov model (HMM) [15].The main drawback of the aforementioned algorithms is theneed for an enormous training dataset, which is in generalnot feasible to collect. Although, semi-supervised algorithmshave resolve this issue to some extent, they are not sufficientlyaccurate [16].

Despite machine learning-based NILM, optimization-basedapproaches do not generally require large training dataset.These algorithms rely on reducing the error between the real

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aggregated consumption power and the sum of disaggregatedones. Different optimization algorithms are used for solvingNILM problem which are discussed below.

Authors in [17] applied 6 different metaheuristic optimiza-tion algorithms on different datasets. NILM was formulatedas a convex quadratic programming problem based on HMMand the full dataset of time period was used for optimization.However, using time in the optimization-based NILM causeshigh computation complexity [18], and reduces its accuracy inapplying to a differnet house. In [19], the NILM was defined asa sparse optimization problem. The dictionary learning methodwith a fraction of the training dataset was employed to solvethe NILM problem. Other techniques to tackle this problemhave been used by integer programming [20], modified integerlinear programming (ILP) [21], and mixed integer nonlinearprogramming (MINLP) [22]. Formulating NILM as an integerprogramming help to detect simultaneous active devices anddevices with multiple operation modes [20]. In [22], authorsevaluated their proposed method by applying it to real data andalso comparing the results with the machine learning factorialHMM method. A modifications of integer linear programmingwas introduced in [21] by imposing new constraints such thatcertain appliances always draw some power, median filteringand linear programming-based refinement. Authors of [23] for-mulated the NILM as an MINLP problem, and used a window-based algorithm to enhance its computational performance.Authors in [24] proposed a hybrid method, merging integerlinear programming and clustering, to decrease the number ofappliances for detection in each iteration.

Generally, these optimization-based approaches requireprior information about the appliances such as the consump-tion power of their different operating modes, which are so-called the states of the appliance. In majority of the afore-mentioned researches, this information was obtained visuallyfrom the consumption profile [22] or based on characteristicsheet of each appliance [21]. Due to the presence of noise andpower fluctuations, these methods resulting in fixed states arenot accurate, and a systematic method to determine the satesof the appliances and the optimal number of states is needed.

Additionally,the states of appliances are assumed to be fixedin the above-mentioned studies. Nonetheless, the active powerof an appliance at each mode is not fixed in practice andvaries slightly depending on the supply voltage fluctuations,load impedance variations, etc. [25]. Moreover, there usuallyis an overshoot at the start point of each mode. Consequently,fixed state is an erroneous assumption and results in loweraccuracy.

Furthermore, the high computation time is the other mainchallenge of the optimization-based NILM methods. To ad-dress this issue, authors of [21] down-sampled the data witha fixed rate and authors in [22] divided the dataset to 4320subsets and applied the algorithm to each subset separately inorder to increase the speed of analysis. Nonetheless, determin-ing the optimal rate for down-sampling is a further challengeto avoid concealing the certain valuable data.

In order to solve the above-mentioned deficiencies andimprove the performance of the available optimization-basedNILM methods, a novel event-based optimization algorithm is

proposed in this paper. The main contributions of the proposedalgorithms in comparison with the previous works are shownin Fig. 2, which are summarized as:

• In our proposed method, the power states of the appli-ances are determined through clustering, which provides asystematical approach and increases the accuracy of thealgorithm in comparison to previous works with visualdetection of the states.

• An analytic method of down-sampling with a varying rateis proposed including the events and the states, whichsignificantly decreases the computation time and effort.

• A new transition filtering is proposed considering thetransitions with a low probability in addition to theprevious available methods assuming only 0% and 100%probabilities. It helps to reduce the computation effort ofsolving the NILM problem with the personal computers.

• A variable state reconstruction phase is proposed, whichassumes that the values of the states are not strictly con-stant, despite the previous studies. This proposed methodimproves the accuracy of signal reconstruction, whichmost importantly can be used to evaluate the efficiencyand safety of appliances and detecting the faulty ones.

• A novel post-optimization processing approach based onON duration of appliances, is designed for increasing thepower reconstruction accuracy.

• The proposed method can accurately extract the requiredinformation from a small training dataset measured bycurrently used energy meters, which makes it inexpensiveand practical.

The remainder of this paper is organized as follows; thepreliminaries of the optimization-based NILM and its formu-lation is described in Section II. In Section III, the proposedalgorithms including the event-based NILM are described indetail. Effectiveness of the proposed algorithms are evaluatedand compared to other methods, using the REDD [26] inSection IV. Finally, Section V concludes the paper.

Fig. 2. Main contributions of the proposed NILM method.

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II. PRELIMINARIES OF OPTIMIZATION-BASED NILM

A. Optimization-Based NILM definition

As described previously, the main objective of load dis-aggregation is to extract the appliances power consumptionprofiles from the aggregated signal, herein denoted by P (t),taken from a single point power meter of a house [22].Let N and {1, 2, . . . , N} be the number and the dataset ofappliances, respectively, and suppose appliance i, 1 ≤ i ≤ N ,has mi operating modes. Denoting the power consumption ofappliance i by Pi(t), the goal is to extract Pi(t), 1 ≤ i ≤ N ,from P (t) noting that

P (t) =

N∑i=1

Pi(t). (1)

However, the power consumption of the appliance i at theoperating mode j, 1 ≤ j ≤ mi is not fixed in practice, andincludes an overshoot at the start point of the mode in additionto slight fluctuations throughout. Ignoring these overshoots andfluctuations in current literature, Pi(t) is estimated by a piece-wise constant function. More specifically, defining xij , 1 ≤i ≤ N , 1 ≤ j ≤ mi, as the fixed and known power stateof appliance i at operating mode j, the estimated piece-wiseconstant power consumption of appliance i, denoted by Pi(t),can be formulated as [22]:

Pi(t) ' Pi(t) = ΘTi (t)Xi, (2)

where Xi = [x1, ..., xm] is a constant vector, that its elements(i.e. xi) are the power consumption states of each appliance,and Θi =

[θi1 . . . θimi

]Tis a binary-valued vector indi-

cating the operating mode of appliance i at time t, defined as:θij(t)=1 if i operates in mode j at time t, otherwise θij(t)=0.

The general purpose of NILM can be described as de-termining Pi(t), or equivalently Θi(t), which minimizes thefollowing error over some time period [0, T ].

e(t) = P (t)−N∑i=1

Pi(t) = P (t)−N∑i=1

ΘTi (t)Xi (3)

This leads to an optimization formulation of the problem basedon standard least-square minimization [22]:

Problem I:minθij(t)

T∑t=1

∥∥e(t)∥∥22

(4)

s.t.

∀t = 1, ..., T :

mi∑j=1

θij(t) = 1 (5)

where ‖ . ‖2 denotes the 2-norm. The constraint 5 ensures thatan appliance is operating in only one state at each time instant.

In order to overcome overparameterization in Problem 1 (i.e.(4)), the following piece-wise constancy of the power profilesof appliances is assumed [22] and added to (4) as:

Problem II:minθij(t)

T∑t=1

∥∥e(t)∥∥22

+ λFpc (6)

s.t.

∀t = 1, ..., T :

mi∑j=1

θij(t) = 1 (7)

where Fpc is the piece-wise constancy function defined as:

Fpc =

N∑i=1

T∑t=2

mi∑j=1

li∥∥θij(t)− θij(t− 1)

∥∥22

(8)

where λ ≥ 0 is a penalty factor that represents a trade-offbetween the fitting error e and piece-wise constancy of Θi’stuned through cross validation, and the weight li is defined as

li =nmt-train

ntrainntest, (9)

where nmt-train is the total number of mode transitions in thetraining dataset, whereas ntrain and ntest are, respectively, thetotal number of samples in the training dataset and the testdataset after down-sampling. We note that li can be viewedas the expected number of mode transitions in the test datasetgiven the training dataset.

B. K-means Clustering

The clustering segments the objects into optimally homoge-neous groups, whose members are similar in some way. Thegoal is to achieve high intra-cluster similarity and low inter-cluster similarity. There are numerous methods of clusteringn unlabeled data points in to K clusters C1, . . . , CK . Eachmethod follows a specific dataset of rules for defining thesimilarity among the data points [27]. K-means, as a commonmethod of clustering, segments the given samples z1, . . . , znbased on minimizing f1, defined as:

f1 =

K∑j=1

∑i:zi∈Cj

∥∥zi − zj∥∥22 , zj =1

|Cj |∑

i:zi∈Cj

zi. (10)

where zj represents the centroid of the cluster j as defined:

zj =1

|Cj |∑

i:zi∈Cj

zi. (11)

The pseudo code of this method is presented in algorithm1. This algorithm is fast in comparison with other clusteringmethods, but its main challenge is choosing K [28]. In order tofind the optimal number of clusters (i.e. K) in this paper, theelbow method is applied to the events dataset. This methodis based on minimizing f1 for each choice of K. The firstpoint at which increasing K would not significantly reducethe minimized error is considered as an optimal number ofclusters for that dataset. For instance, as depicted in Fig. 3,the optimal number of states of oven in REDD [26] is K = 3.

C. Accuracy metrics

In order to evaluate the accuracy of the proposed NILMmethod, the following two metrics are employed. The metric(12) shows the normalized absolute error between the actualand the estimated power consumption of each appliance.

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Algorithm 1 Pseudo-code of k-means for state detectionStep 0: Initialization:• Get the data: the dataset of n objects to cluster.• Consider K samples as the initial centroids of clusters.

Loop until the termination criteria is met (i.e. the change inthe objective function is less than the threshold):Step 1: Compute (10) and find the closest centroids to eachdata point.Step 2: Assign each data point to the closest cluster.Step 3: Update the centers of the clusters: Compute the meanof the members of each cluster and consider it as the centroid.

Error(%)

Fig. 3. The Optimal number of states via elbow method for the oven.

Equation (13) computes the square error of mean in relationto the variance of real dataset.

ACi = 1−

∑Tt=1

∣∣∣Pi(t)− Pi(t)∣∣∣2∑Tt=1 Pi(t)

. (12)

R2i = 1−

∑Tt=1

(Pi(t)− Pi(t)

)2∑Tt=1(Pi(t)− Pi)2

, Pi =

∑Tt=1 Pi(t)

T. (13)

III. METHODOLOGY OF THE PROPOSED PRE- ANDPOST-PROCESSING ALGORITHMS

This section proposes a novel pre- and post-optimizationprocessing algorithms considering a small training dataset.The schematic of the proposed algorithms is presented inFig. 4. As shown, the backbone of the proposed pre- andpost-optimization processing algorithms is as follows, theimproved three-point event detection method is introducedin subsection III-A; The proposed non-off state detection ofappliances including 3 steps, is presented in III-B; SubsectionIII-C proposes the novel event-based down-sampling method.Defining new constraints for transition filtering is presentedin subsection III-D; and finally, Section III-E proposes post-optimization approach in 2 steps, omitting devices with smallON duration time, and considering varying states.

A. Event Detection

Given the total power consumption over the time, an eventindicates a mode transition in an appliance. In the vast majorityof literature, an event is in general detected based on thedifference between two consecutive samples. More precisely,if the difference is greater than a certain threshold, an eventis said to have happened between two consequent samplingtimes. The main challenges of this method are determiningthe proper threshold not to miss any actual event or detect

Fig. 4. The architecture of the proposed NILM method with theproposed pre- and post-processing algorithms.

non-existing events and considering the overshoots of signalas a part of events. A new, elegant method of event-detection,called the three-point method, was proposed in [29], whichutilizes the local mean and deviation of the data and is free ofsaid threshold. This method proves to be robust in the presenceof noise and the high consumption peak at the point of anappliance mode transition. The main drawback of this methodis that it is unable to detect an event which lasts less thanthree samples. To overcome the issue of missing short-lastingevents, data are first up-sampled to a second, and then thedetection algorithm is applied. For simplicity, we also use P (t)for the up-sampled signal. Figure 5 demonstrates the flowchartof utilized event detection method, which is described in thefollowing. The proposed up-sampling at the initial stage of thealgorithm ensures detecting all the desired events.

Fig. 5. The flowchart of the three-point event detection algorithmusing the proposed up-sampling method for NILM.

An adapted description of the three-point method [29],

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comes in the following: First, any three consecutive samplesof the (up-sampled) signal P (t) are compared. To this aim, asignal is constructed as:

P (t) =1

3

3∑τ=1

P (t− τ) (14)

σ2P (t) =

1

3

3∑τ=1

(P (t− τ)− P (t)

)2(15)

If σP (t) is greater than the deviation of power grid noisesaid σg , P (t) is recorded (in the signal PS), otherwise it isdiscarded, i.e.,

if σP (t) < σg : PS(t) = P (t)if σP (t) ≥ σg : PS(t) = PS(t− 1)

(16)

We note that PS in (16) is designed in such a way that partsof P (t) corresponding to the overshoots at the mode transitionpoints of appliances are discarded. Finally, events are detectedbased on how PS changes over time, that is

∆PS(t) = PS(t)− PS(t− 1) (17)

if ∆PS(t) ≥ σg : T (q) = t (18)

where T (q) indicates the time of the q-th event.As an example, Fig. 6 illustrates the events detected for

the oven consumption profile in the REDD [26].

Power Profile

Positive EventNegative EventEvent

Fig. 6. Detection of events in power profile of the oven.

B. Proposed Event-based States DetectionIn this section a novel event-based non-off state detection

method is proposed in three steps: I) In order to get the events,three-point event detection method is applied on data, II) Thedataset of events is defined considering the positive/absoluteof negative events, in which the power consumption in-creases/decreases, III) K-means clustering method is applied tothe dataset of events and the optimal number of clusters, theircentroids as the states of appliances and the standard deviationof members in each clusters are extracted. The schematic ofproposed method is illustrated in Fig. 7 and Fig. 8 illustratesthe non-off state of refrigerator from the REDD [26].

C. Proposed Event-based Down-sampling MethodIn the following, a new event-based method for down-

sampling the data is proposed, in which the events are firstdetected and then data are sampled based on the events. Asshown in Fig. 9, the consumption power between two eventsis somewhat constant with small fluctuations. For extractingnew samples, the mean of the power consumption betweentwo sequential events is considered. As an example, there are400 samples and six events in the Fig. 9. By applying the newmethod of down-sampling, seven samples are obtained.

Up-sample the data

to a higher time

resolution (1 Second)

Calculate the optimal number of states

by applying the Elbow method on the

events set to

Use k-means clustering algorithm to

get the centroids and members of the

clusters

Define the set of events

{ Positive and Negative Events}

Input the power profile

of an appliance from

the training dataset

Apply three-point method

event detection on the up-

sampled dataset

Fig. 7. The flowchart of event based state detection.

Fig. 8. Calculating the non-off state of refrigerator using the proposedevent-based state-detection method.

Fig. 9. The down-sampled data points using the proposed event-baseddown-sampling method.

D. Proposed Transition Filtering Considering TransitionProbability

For devices with multi non-off states, it is implausible thatall transitions between states can happen. Therefore, comput-ing the probability of occurrence of transitions between statesin training dataset can help to filter out implausible transitions.Four different groups of transitions can be considered as: I)transitions which do not occur, II) transitions between non-offstates which occur in limited times, III) transitions from offstate to any non-off state which are most likely to happen, andIV) remaining in the same state.

In this work, in order to reduce the burden of computationalcomplexity and time, the first two types of transition are usedas the optimization constraints. Consequently, the ultimateoptimization problem is defined as:

Problem III:minθij(t)

T∑t=1

∥∥e(t)∥∥22

+ λFpc (19)

s.t.

∀t = 1, ..., T :

mi∑j=1

θij(t) = 1 (20)

∀t, ∃i, j, l : θij(t− 1) + θil(t) < 2 (21)

∀t,∃i, g, h : αmini <

T∑t=2

θig(t− 1) θih(t) < αmaxi (22)

6

where αmini and αmaxi indicate the minimum and maximumnumber of occurrence for the specific transition (from g to h)of appliance i extracted from the training dataset.

In order to ban a transition, θ for these states at sequentialsamples during a day should not be 1 at the same time which isdefined in (21). For limiting the number of transitions from onestate to the other one, the sum of multiple of θ for these statesat sequential samples during a day should be lower/higher thanan amount which is defined as (22).

As an example, consider the oven from REDD with threestates [26]. Figure 10 illustrates the state transition diagram ofthis appliance. For defining a constraint for transitions whichcannot happen (such as transition from state 3 to state 2) and aconstraint for transitions with limited time of occurrence (suchas transition from state 2 to state 3) equation (21) and (22)are used respectively.

Fig. 10. The state transition diagram of the oven

E. Applying the Proposed Varying States

In practice, the consumption of appliances in ON mode isnot constant and has deviations from the assumed constantpower states. Furthermore, there is an overshoot at the startpoint of each mode of an appliance [25]. Sometimes, theamount of the overshoot of an appliance equals the nominalpower consumption of the other one, which results in inaccu-rate appliance ON/OFF mode detection. In order to improvethe accuracy, the event-based post-processing algorithm isproposed. This method works based on minimum period ofON mode for each appliance in training dataset (durON ). ThedurON of each appliance is computed as algorithm 2.

Algorithm 2 The proposed algorithm for computing theminimum period of ON mode (i.e. durON ) of each appliance.Step 0: Load the training dataset and get the consumptionprofile of the appliances.Step 1: Apply three-point event detection method to theconsumption profile of appliances.Step 2: Determine the occurrence time of positive andnegative events (i.e. TP i and TNi, respectively).Step 3: durON = min (TNi − TP i), i = 1, ...,Ne

After optimization, if the ON period of an appliance is lessthan durON , we change its mode to OFF. Then the followingerror is measured for each sample:

e(t) = P (t)−N∑i=1

Pi(t), t = 1, ..., Ns (23)

where P (t) is average of the total power consumption at t andPi(t) is the estimated power of each appliance at t and Nsis the total number of samples after down-sampling. For eachsample, this error is separated between the ON appliances inthat sample based on their standard deviation extracted fromthe training dataset.

IV. SIMULATION RESULTS

NILM on a low-frequency dataset is more beneficial in realworld applications. Therefore, we evaluate our proposed event-based NILM on the low-frequency dataset of house 1 in theREDD [26]. In this study, 5 devices are considered in orderto discuss the proposed algorithm in detail. These devicesincludes oven, microwave, kitchen outlets and dishwasher,having a high consumption state; and a refrigerator with highon/off frequency.A. Detecting the States of Appliances Using the ProposedEvent-based Algorithm

In order to get the optimal number of states of appliancesand their power consumption in each mode, 14 days of theirconsumption profiles are used as the training dataset. Proposednon-off state detection method is applied on these profilesseparately in 3 phases: 1) detecting events, 2) applying elbowmethod to events to get the optimal number of modes, and3) using K-means clustering to get the consumption amountof each mode. Figure 11 and Table I show the non-off statesof each appliance and their standard deviation. As shown, theovershoots at the profiles are ignored using the proposed event-based non-off state detection method. Furthermore, the non-off states of the appliances are detected precisely from thetraining data of two weeks. This shows the effectiveness ofthe proposed method in analyzing a small training dataset.

Fig. 11. Detected non-off states of appliances using the proposedmethod.

TABLE ITHE DETECTED STATES OF THE APPLIANCES AND THEIR STANDARD

DEVIATION IN EACH STATE USING THE PROPOSED METHOD.

Appliance Calculated optimalnumber of states

Detectedstates (W)

Standarddeviation (W)

Oven 3 0, 40, 4137 0, 3.8, 121Microwave 3 0, 90, 1490 0, 11, 178

Kitchen-outlets 2 0, 1070 0, 120Dishwasher 2 0, 2730 0, 201Refrigerator 2 6, 200 0, 23

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B. Proposed method of Down-Sampling and Computing liIn two days of our training dataset we have non-off modes

for all five appliances (5-th and 10-th day of dataset). Thesedays considered as a training dataset to compute li. Figure 12shows the usage pattern of the test day. The proposed down-sampling approach is applied to total power of each day oftraining dataset and the test power signal. Number of samplesbefore down-sampling is 28800. Table II shows the number ofdown-sampled samples and mode changes for each appliancefor training and test days.

0 6 12 18 24

Time (h)

0

2000

4000

6000

Active

Pow

er(W

)

Fig. 12. Total consumption power of the test day.

C. Proposed Transition filteringIn this study, there are two appliances with more than one

non-off state, i.e., oven and microwave.Transitions betweentheir non-off modes in the training dataset are analyzed. Inboth appliances’ consumption profiles no transition from thehigher non-off mode to the lower non-off mode is observed.Therefore, a constraint can be applied to avoid them fromhappening. Moreover, the transitions from lower mode to thehigher mode are in limited number. Therefore, a constraint isconsidered to limit the number of their occurrence. Based onthe cross validation in training dataset αmin and αmax in (21)and (22) are considered 4 and 10 for the oven and 5 and 15for the microwave respectively.

D. Evaluation and Comparison with MLKNN methodMINLP is applied to 163 new samples considering different

constraints in GAMS utilizing Lindoglobal solver. Based onthe cross validation λ = 3000. Then, the proposed post-optimization processing is applied to the results. Figure 13demonstrates the disaggregated power profile of appliancesbased on the proposed method. Then, the proposed post-processing method is applied on the disaggregated powerprofiles of appliances. Figure 14 shows a part of consumptionprofile of each appliance considering the fixed and non-fixedpower consumption at each state.

Fig. 13. Disaggregated power consumption profiles of the appliancesusing the proposed method.

The performance of the proposed algorithms are evaluatedfrom two different points of view: the compilation time and

the accuracy metrics. Table III illustrates the compilationtime of the optimization-based NILM, considering differentconstraints. As shown, applying the proposed constraint ontransition filtering has a significant impact on reducing thecomputation time in comparison with the common approachand power comparison constraint. It is noted that powercomparison constraint deactivates the states that are higherthan the total power consumption in each time sample [22].

In order to illustrate the efficiency of our proposed algorithmin dealing with small training dataset, the multi-label KNN(MLKNN) a common method of multi-label classificationapplied to the data, considering consumption profile of 14days as the training dataset. Table IV shows the accuracymetrics of MLKNN. The results indicate that when the NILMis resolved by MLKNN considering small training dataset, theaccuracy is lower in comparison with our proposed method. Inother words, there is no need for huge training dataset in ourproposed algorithms, which can be considered as an advantageof the proposed method over the MLKNN method.

100 150 200 250 300 350 400 450 500

Sample

180

190

200

210

220

230

Active P

ow

er

(W)

Real consumption

Fixed state

Varying state

Fig. 14. Reconstructed consumption of the refrigerator in one sample.Using the proposed varying-states, considering 197W at each state,decreases the error more than considering fixed state (200W).

V. CONCLUSION

This work proposed a novel event-based technique forthe NILM, framed as an MINLP optimization problem. Theproposed algorithm involves two main new phases: 1) pre-optimization processing including, a novel event-based down-sampling and transition filtering for decreasing computationtime and extraction of prior information about appliances, and2) post-optimization processing, i.e. applying the proposedvarying states method in order to increase the accuracy ofpower reconstruction of appliances. The proposed methodsenhanced the performance of the optimization-based NILMin different ways. This method not only extract the requiredprior information from a small training dataset, but also enrichthe capability of increasing the accuracy of reconstructingthe power profile. Performance of the proposed algorithmis compared to conventional optimization-based NILM andclassification-based NILM considering low-frequency dataset.Results show that the proposed method decreases the com-putation time and increases the reconstruction accuracy. Highreconstruction accuracy of the proposed method helps examinethe efficiency and safety of appliances. As a result, there isno need for special equipment to be installed on appliancesto detect the faulty ones. The low computation burden of thismethod, makes it suitable and inexpensive for practical caseswith small training datasets measured by the currently usedenergy meters.

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TABLE IINUMBER OF SAMPLES AND MODE CHANGES IN THE TRAINING AND TEST DATASET USING THE PROPOSED ALGORITHM.

DatasetNumber of mode changes using the proposed approach Number of down-sampled data

in the proposed approachOven Microwave Kitchen-outlets Washer dryer Refrigerator

Training day 1 34 44 4 64 38 232

Training day 2 14 34 6 90 48 194

Test day 15 39 5 74 42 163

TABLE IIICOMPUTATION TIME CONSIDERING DIFFERENT CONDITIONS.

Proposed down-sampling 3 3 3

Power comparison constraint [22] 3 3

Proposed transitions constraints 3 3

Computation time 9’19” 2’06” 2’05”

TABLE IVPERFORMANCE OF THE PROPOSED APPROACH COMPARED TO

CONVENTIONAL OPTIMIZATION-BASED AND MLKNN-BASED NILM.

ApplianceAccuracy metrics

ProposedOptimization-based NILM

Proposedpre-and post-optimization

MLKNN

ACi R2i ACi R2

i ACi R2i

Oven 0.86 0.75 0.91 0.86 0.79 0.68

Microwave 0.77 0.83 0.80 0.84 0.79 0.81

Kitchen outlets 0.85 0.96 0.86 0.96 0.73 0.84

Washer dryer 0.94 0.91 0.96 0.92 0.93 0.91

Refrigerator 0.94 0.83 0.94 0.83 0.94 0.82

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