A new transient feature extraction method of power signatures for Nonintrusive Load Monitoring Systems

A new Transient Feature Extraction Method of Power Signatures for Nonintrusive Load Monitoring

Systems

Kun-Long Chen Center for Measurement Standards

Industrial Technology Research Institute

Taipei, Taiwan R. O. C. [email protected]

Hsueh-Hsien Chang Department of Electronic

Engineering Jinwen University of Science and

Technology Taipei, Taiwan R. O. C.

[email protected]

Nanming Chen Department of Electrical

Engineering National Taiwan University of

Science and Technology Taipei, Taiwan R. O. C.

[email protected]

Abstract—The traditional Nonintrusive Load Monitoring Systems (NILMs) often employ average power consumption ex. real power and reactive power to recognize electric loads ON/OFF status. However, aiming at variable loads owning variable property in their power, voltage, and frequency, the unsteady power signatures will increase the difficulty degree of load identification. A new extraction method of power signatures is proposed in this paper, convolution and wavelet multi-resolution analysis (WMRA) technique are employed to extract the new power signature from the raw instantaneous power waveforms. Parseval’s theorem is employed to obtain the power indices (PIs) from the new power signature. After inputting PIs of each electric load, inner product is used to identify the unknown loads.

Keywords—non-intrusive load monitoring; inner product; convolution; wavelet transform; Parseval’s Theorem

I. INTRODUCTION The traditional load monitoring method installs sensors in

each load which electrical operator would like to monitor, and these sensors need to be connected to the monitoring system [1]. When sensors detect the condition change, circuit breakers (CBs) or switches, belonging to loads, will act and then send a message to the load recorder through a connecting wire; subsequently, the message is sent back to the data collection center. Finally, the data is analyzed to know the operating interval of each load. There is only one set of voltage and current sensors are needed at electrical service entrance (ESE) for non-intrusive load monitoring systems (NILMs) to monitor the loads. In comparison, the NILM only integrates the monitoring device into the user’s meter, and then be installed in the ESE. Based on the analysis of voltage and current waveforms measured in the ESE, the operating condition and power consumption of each load can be known. The comparison of the two aforementioned load monitoring system can be seen clearly that the latter can monitor the operation condition of each load without many devices, so its cost also is lower than that of the former; moreover, the latter is relatively easy to install and remove. Furthermore, the latter can save a lot of maintenance costs since it does not have to install sensors

on each load.

In the past, the NILMs identify the electric loads mainly depend on average power consumption [2], [3]. Although the operation condition of each load could be recognized by the change of the average power consumption, the average power consumption cannot be able to correctly show the actual instantaneous states of loads on a bus, especially when the voltage disturbance or the voltage drop existing in the power cable causes the change of power consumption in each load, or when the electric load is a variable power load. In addition, the traditional power signatures, real power (P) and reactive power (Q), characterizes the additivity when multiple loads are used simultaneously. However, the difficulty of load identification will increase if loads include variable power loads or voltage disturbances occur [4]. Therefore, this research proposes a new transient extraction method for power signatures and a simpler recognition algorithm to identify the operation and load type for all electric loads.

In an innovative extraction method of power signature, convolution and the multi-resolution analysis (MRA) technique of discrete wavelet transform (DWT) are used to analyze the power signatures, instantaneous power waveforms (IPWs), of each load and combination of loads. In addition, the IPW, which is processed by the convolution operation, could immediately and accurately response to the transients of each turn-on/off load and a constant power of other loads that are operated in steady state before each turn-on/off load. The Parseval’s theorem is employed to quantify the IPW to become the power indices (PIs) for each turn-on/off load. The multi-resolution PIs in frequency domain represent the power signatures of each turn-on/off load. Regarding the load recognition algorithm, inner product (IP) is used to simplify the identification complexity, so its processing speed can be decreased. The IP between the PIs of the unknown turn-on/off load and the PIs of each known load stored in database is performed respectively. The greater values of IP represent the better similarity of two loads. Thus, in the proposed power signature extraction methods, the power signature of the individual event turn-on/off transient signal after using the convolution technique can accurately and immediately respond to turn-on/off transients of each load. Moreover, the IPW of

The authors would like to thank the financial support extended byIndustrial Technology Research Institute, Republic of China.

978-1-4673-5573-5/13/$31.00 ©2013 IEEE

filtering out the steady-state power, which exists after the unknown load is turned on, could represent the IPW of the unknown turn-on/off load. Therefore, the proposed method will facilitate the extraction and identification of power signature for the individual event turn-on/off transient load to save computation time. For this reason, the proposed methods are convenient and fast to extract the new power signatures and to identify the unknown turn-on/off loads.

II. PROPOSED METHODS A new method for performing the power signature

extraction is proposed; this method involves the use of series of signal processing, including convolution, DWT, and Parseval’s theorem, to extract the power signatures and PIs from the original instantaneous power waveforms.

A. Power Waveforms and Convolution Method A NILM system monitors the voltage and current

waveforms in a one-phase electrical service entrance powering representative loads in a house or a building. Another electric load is turned on in a certain phase of a power system after the loads operated in steady state. Assuming that the instantaneous voltage or current waveform is a linear combination for steady states and transients, this instantaneous voltage )(tv and instantaneous current )(ti can be computed by

)()cos()()()( tvtVtvtvtv TvmTS ++=+= θω (1)

)()cos()()()( titItititi TimTS ++=+= θω (2)

where the variables Sv and Si are the steady components

of voltage and current, respectively; the variables Tv and Ti are the transient components of voltage and current, respectively; mV and mI are the maximum value of voltage

and current, respectively, and the variables vθ and iθ are phase angles of voltage and current, respectively. The instantaneous power is the product of instantaneous voltage and instantaneous current, it can be computed by

)()()()()( titvtptptp TS =+= (3)

Conventionally, convolution theorem is used to filter the background-load value for performing signal and image filtering [5]. Therefore, this paper utilizes the convolution technique to perform the signal processing of instantaneous power.

ττττττ dtfpdtfptfp TS )()()()())(( −⋅+−⋅=⊗ ∫∫∞

∞−

∞

∞− (4)

where )t(f represents a rectangular pulse function, the magnitude of pulse function value is unit and the wide of it is one cycle. Thus, get (5).

τττθ dtfpIVtfp T )()(cos))(( −⋅+=⊗ ∫∞

∞− (5)

then,

θτττ cos))(()()( IVtfpdtfpT −⊗=−⋅∫∞

∞− (6)

Consequently, through the convolution method, the instantaneous power waveform of the individual event turn-on/off transient signal is shown in (6). The first term on the right side of (6) denotes the output waveform of convolution for the all load instantaneous power signals, while the second term denotes the average power of the loads which are operated in steady before the individual event turn-on/off transient signal. Thus, in the proposed power signature extraction method, the power signature of the individual event turn-on/off transient signal after using the convolution technique can accurately and immediately respond to turn-on/off transients of each load. Moreover, the IPW of filtering out the steady-state power, which exists after the unknown load is turned on, could represent the IPW of the unknown turn-on/off load. Therefore, the proposed method will facilitate the extraction and identification of power signature for the individual event turn-on/off transient load to save computation time.

The instantaneous power waveforms of the loads which are a hairdryer operated in steady and a light bulb turned on at the time of 0.1 s for 4 different trials are measured. Fig. 1 shows this instantaneous power waveforms processed by convolution method. Furthermore, the instantaneous average power of the hairdryer is quite constant; the instantaneous power waveform of the individual event turn-on transient signal for a light bulb can be filtered out from the constant power which exists before the unknown load is turned on. Moreover, the repeatability of the instantaneous turn-on power waveform is pretty higher from experiments. Fig. 2 shows the instantaneous power waveforms of the load which is only a light bulb turned on at the time of 0.1 s for 4 different trials.

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Fig. 1. Processed instantaneous power waveforms by the proposed methods for a NILM system.

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Fig. 2. Measured the instantaneous power waveforms of a light bulb for a NILM system.

B. Wavelet Multi-Resolution Analysis Technique When the discrete wavelet transform (DWT) is employed,

the problem that short-term Fourier transform (STFT) has a lack of accurate time information will be solved. J. Morlet and A. Grossman proposed the concept of wavelet transform, and the motivation is from a phenomenon they found; that is, the desired signal can be extracted by way of the proper process of function translation and function dilation. Also, the original fixed window (STFT) could be appropriately adjusted because of the processes of functions.

Discrete wavelet transform is to transfer continuous wavelet transform (CWT) into discrete counterpart, and the purpose of discretization is to analyze the digital signal. The discretization of CWT is derived as follows:

dtnbtatxDWT om

mnm )()(21

0),( −= −∞

∞−

∗∫ ψ (7)

where x(t) is the original signal; ψ(t) is the chosen mother wavelet.

Multi-resolution analysis (MRA) means that the complicated signal could be decomposed into the simple one by means of MRA. Therefore, some information hidden inside the complicated signal could be investigated [6]. The MRA technique of DWT is used to decompose a signal into multiple sets of signals using multiple sets of low-pass filters and high-pass filters. Fig. 3 shows the architecture of multi-resolution analysis of the first-order DWT [6]. It can be shown in Fig. 3, approximation value will be obtained when original signal pass through a low-pass filter; detail value will be obtained when original signal pass through a high-pass filter. The “first-order” in this architecture presents that original signal is only decomposed with a layer of a low-pass and a high-pass filter. Therefore, if multi-layer decomposition is needed, the approximation value obtained from upper low-pass filter is delivered to the next layer, and then regards as an input signal for the next layer, and so forth.

Fig. 3. Architecture of multi-resolution analysis for the first-order DWT.

A three-order DWT is shown in Fig. 4. Original signals are processed with three-layer decomposition, and an approximation value (A3) and three detail values (D1, D2 and D3) will be obtained. Therefore, if four-layer decomposition is selected, an approximation value and four detail values will be obtained. Consequently, no matter how many layers are chosen, only one approximation value will be obtained, but the number of detail values depends on how many layers chosen by the user. This architecture is called one-dimension multi-order DWT.

Fig. 4. Architecture of multi-resolution analysis for the multi-order DWT.

C. Parseval’s Theorem Parseval’s theorem is applied to in a situation of

trigonometric series, where the equal sign in Bessel’s inequalities is established; moreover, regarding the physical meaning, the signal energy in time-domain is permanent equal to the signal energy in frequency-domain [6]. Concerning the relationship of DWT and Parseval’s theorem, the MRA of DWT is actually applied to decompose the original signal into multiple signals which keep all information existing in the original signal, but too much data increase the difficulty of load recognition. For example, one-dimension N-order DWT will produce N detail values and one approximation value; namely, a total of N+1 time-domain signature waveforms are gotten,

resulting in taking a lot of time to identify loads. In this paper, the time-domain waveforms produced from DWT and MRA is converted into the frequency-domain power indices using Parseval’s theorem. The PIs are as a 1xN constant array, so they can be used to simplify the load recognition. The IPWs shown in Fig. 1 are further analyzed with the 20-order DWT of the proposed methods. The results are shown in Fig. 5. Moreover, Fig. 6 shows PIs which are resulted from waveforms in Fig. 2. To compare PIs of Fig. 5 with those of Fig. 6, whether the loads exist or not before the light bulb is turned on, the PIs characterize uniqueness and extreme repeatability.

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Level of Decomposition Fig. 5. Analyzed IPW of Fig. 1 by the proposed methods for 4 different trials.

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Fig. 6. Analyzed IPW of Fig. 2 by the proposed methods for 4 different trials.

With the technique of the proposed methods, PIs can be obtained. However, for accurately choosing the unique power signature to recognize the load, this research uses a number of different loads to compare the differences of their PIs. Finally, the low-frequency parts of PIs are deleted since they do not characterize the uniqueness, and the rest ports of PIs can stand for power signature of each load. Fig. 7 shows the comparison of three loads, ex. light bulb, fluorescent lamp, and fan which are processed with the proposed methods. It can be seen that 1-order to 8-order PIs own extreme difference for the high frequency, so these PIs are used for identifying loads. Moreover, this property can be explained according to the physical characteristics of loads, the IPWs of loads being turned on/off occur in the transient state; thus, the IPWs mainly consist of high-frequency components. And, the PIs distribution from the left to the right represents high-frequency signals to low–frequency signals; hence the left parts of PIs

characterize extremely high load recognition accuracy. Besides, the sampling rate of all instantaneous power waveforms is 3840 samples per second in this paper, hence the corresponding frequency of the 7-order PI is 60 Hz according to the MRA technique of DWT. Finally, this paper adopts the PIs of the first 8 orders to stand for power signature of each load.

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Fig. 7. PIs of three loads processed with the proposed methods.

III. RECOGNITION ALGORITHM Inner product (IP) proposed in this research is also called

dot product and is used as the load identification algorithm for NILM. Inner product can be expressed as follows:

θcosBABA =• (8)

where A and B represent two vectors; θ is the angle between the two vectors. When the two vectors are parallel to each other, the angle θ will be °0 ; moreover, when the two vectors are perpendicular to each other, the angle θ will be

°90 .

Therefore, it can be known from results that they will be same direction and nearly parallel to each other if the two vectors are similar to each other; Otherwise, they will be different from each other if the two vectors are not similar to each other,. In fact, the physical performance of IP is used to look for similar vectors; namely, similar waveforms. In the past, ANNs often applied to load identification algorithm in NILM. It should be trained through a network with the consideration of different parameter setups [7]. However, the IP is a simple mathematical operation, so network training is unnecessary. Under the condition of high recognition accuracy for both algorithms, the IP based load recognition can extremely reduce the whole time of identifying loads.

About the IP based load identification algorithm, the PIs of unknown load processed by the proposed methods are identified to carry out the IP operation with PIs of each known load which has been stored in database. Finally, the larger the result of the IP operation is, the more similar the two loads are. Regarding the actual database, the PIs of each known load is measured randomly for ten and five different trials, and then ten and five sets of PIs are stored to represent the power

signature of each load. To confirm the inferential PIs of the database, the PIs are created by two different scenarios, which are described as follows:

1. Scenario A: The load type recognized by the proposed features is recognized by the biggest value of results for inner product operation between the PIs of each known load in the database and the PIs of unknown load processed by the proposed methods.

2. Scenario B: The load type recognized by the proposed features is selected by the average value of two largest values among the results for inner product operation between the PIs of each known load in the database and the PIs of unknown load processed by the proposed methods.

Therefore, when identifying loads, the PIs of each unknown load is carried out the inner-product operation with the PIs for each load stored in database, respectively, and then the largest value among the results of the inner-product operations is used to represent the similarity between the unknown load and one of the known loads stored in database. Finally, after comparing all similarities of the unknown and each known load stored in database, the largest one represents the recognition result.

IV. EXPERIMENTAL RESULTS This research proposes a new transient extraction method

for power signatures in a NILM system. The PIs can be obtained by the proposed features to represent each turn-on unknown load and each known load. Then, the IP operation is employed to test the similarities of PIs between the measured turn-on unknown load and each known load in the database. In order to verify the recognition effect of the proposed features, two case studies, for example, constant power and variable power are tested in this paper. Moreover, the proposed features associated with the IP operation are compared with the conventional power signatures, real power (P) and reactive power (Q), associated with the ANNs.

A. Case Study 1-Constant Power Loads This research selects 5 kinds of constant power loads,

including fan, hairdryer, heater, light bulb, and fluorescent lamp, to test the recognition accuracy of the turn-on fan, light bulb, and fluorescent lamp after the heater or hairdryer operated in steady state, respectively. The recognition results for different kinds of power signatures are shown in Table I. The recognition results with the power signature (PQ) are better than those with the power signature (P), and can be up to 91.67 %. However, no matter Scenario A or Scenario B is used; the recognition result with the proposed features is even 100%.

Furthermore, the research carried out another experiment, where the quantity of PI sets for each load stored in database is decreased from 10 to 5, and the experiment results are shown in Table II. Recognition results of the proposed features with Scenario A and Scenario B are 98.33 % and 100 %, respectively.

TABLE I. EXPERIMENTAL RESULTS FOR 10 DIFFERENT TRIALS IN CASE STUDY 1

Power Signatures PQ P

Proposed Features

Scenario A

Proposed Features

Scenario B Recognition

Methods ANN ANN IP IP

Recognition Accuracy (%) 91.67 80 100 100

Note: ANN has been trained using light bulb, fluorescent lamp, and fan (10 trials for each load). 6 different kinds of experiments: (10 trials for each experiment)

(1) Background load: heater → light bulb is turned on

(2) Background load: heater → fluorescent lamp is turned on

(3) Background load: heater → fan is turned on

(4) Background load: hairdryer → light bulb is turned on

(5) Background load: hairdryer → fluorescent lamp is turned on

(6) Background load: hairdryer → fan is turned on

TABLE II. EXPERIMENTAL RESULTS FOR 5 DIFFERENT TRIALS IN CASE STUDY 1

Power Signatures Proposed Features Scenario A

Proposed Features Scenario B

Recognition Methods IP IP

Recognition Accuracy (%) 98.33 100

B. Case Study 2-Variable Power Loads Concerning the experiment of variable power loads,

computers, the most common variable loads in commercial offices and homes, combined with constant loads are tested. Three computers of different brands are selected, and their power signatures of turn-on transients change dramatically and have very different from each other, as shown in Fig. 8. In addition to these three computers, four kinds of constant power loads, including fan, hairdryer, light bulb, and fluorescent lamp, are operated simultaneously in steady state before turn-on each computer. The recognition results for different kinds of power signatures are shown in Table III. It can be seen in this table that the recognition results with the power signatures (PQ) merely achieve 73.33 % and is far below than 91.67 % which is the recognition result for features with PQ shown in Table I. In comparison, recognition results of the proposed features with Scenario A and Scenario B are 88.33% and 91.66%, respectively. Besides, Table IV shows recognition results of the proposed features with Scenario A and Scenario B are 86.66% and 88.33%, respectively.

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Computer (1) Computer (2) Computer (3) Fig. 8. Processed IPW of three computers with the proposed methods for 2 different trials.

TABLE III. EXPERIMENTAL RESULTS FOR 10 DIFFERENT TRIALS IN CASE STUDY 2

Power Signatures PQ Proposed Features

Scenario A Proposed Features

Scenario B Recognition

Methods ANN IP IP

Recognition

Accuracy (%)

73.33 88.33 91.66

Note: ANN has be trained using light bulb, fluorescent lamp, fan, hairdryer, computer (1), computer (2), and computer (3). (10 trials for each load). 6 different kinds of experiments: (10 trials for each experiment)

(1) Background load: computer(1) → computer(3) is turned on

(2) Background load: computer(3) → computer(1) is turned on

(3) Background load: fluorescent lamp → computer(3) is turned on (4) Background load: heater + fluorescent lamp + light bulb +

computer (3) → hairdryer is turned on (5) Background load: heater + fluorescent lamp + light bulb +

computer (3) → computer(1) is turned on (6) Background load: heater + fluorescent lamp + light bulb +

computer (1) → computer(3) is turned on

TABLE IV. EXPERIMENTAL RESULTS FOR 5 DIFFERENT TRIALS IN CASE STUDY 2

Power Signatures Proposed Features Scenario A

Proposed Features Scenario B

Recognition Methods IP IP

Recognition Accuracy (%) 86.66 `88.33

V. DISCUSSION AND CONCLUSION Aiming all kind of electric loads including constant power

loads and variable power loads, traditional NILM system based on the average power consumption cannot accurately determine the load type of electric loads, especially for variable power loads. A new transient extraction method for power signatures is proposed in this paper, convolution, DWT and Parseval’s theorem are employed to extract the new power signature from the raw IPWs. The experimental results shows that the new extracted power signature by the proposed method associated with the IP recognition algorithm will improve the recognition rate of unknown turn-on loads, which is above 86.66% with Scenario A. From the experimental results, even though the quantity of PI sets for each load stored in database is decreased from 10 to 5, the recognition results still can perform well. Furthermore, the recognition results with Scenario B are higher than those with Scenario A. The reason for these results is that adopting one value, the largest value, may own larger uncertainty and error for load identification compared with adopting the average of two largest values.

Besides, the proposed methods can not only save the computation time but also reduce the cost of database installation. Furthermore, the proposed features, PIs, are only a

1xN array, so its data quantity is far smaller than that of its original IPWs. Due to the small data quantity of the proposed features, NILM can be easily associated with the wireless communication, and then the electric information measured by future meters can be transmitted wirelessly to the cloud server for load identification.

REFERENCES [1] A. G. Bruce, “Reliability Analysis of Electric Utility SCADA Systems,”

IEEE Transactions on Power Systems, vol. 13, no. 3, pp. 844-849, 1998. [2] G. W. Hart, “Nonintrusive appliance load monitoring,” Proceedings of

the IEEE, vol. 80, no.12, pp. 1870-1891, 1992. [3] J. Lemmerhirt and R. Blevins, Nonintrusive Appliance Load Monitoring

System (NIALMS) Beta-Test Results, EPRI, TR-108419, 1997. [4] C. Langhman, K. Lee, R. Cox, S. Show, S. B. Leeb, L. Norford, and P.

Armstrong, “Power Signature Analysis” IEEE Power & Energy Analysis Magazine, pp.56-63, 2003.

[5] H. W. Park, Y. S. Park,and S. K. Oh, “L/M-fold image resizing in block-DCT domain using symmetric convolution,” IEEE Transactions on Image Processing, vol. 12, no. 9, pp. 1016 -1034, 2003.

[6] Y. C. Su, K. L. Lian, and H. H. Chang, “Feature Selection of Non-intrusive Load Monitoring System using STFT and Wavelet Transform,” IEEE 8th International Conference on e-Business and Engineering (ICEBE 2011), October 19-21, 2011, Tsinghua University, Beijing, China, pp. 293-298.

[7] H. H. Chang, “Genetic Algorithms and Non-intrusive Energy Management System Based Economic Dispatch for Cogeneration Units,” Energy, vol. 36, no. 1, pp. 181-190, Jan. 2011.