Dimension reduction for NILM classification based on principle component analysis
Introduction
In the last decades smart grid technologies attract worldwide attention [1]. A recent advancement is the use of monitoring systems that are based on smart meters which may help consumers manage their energy expenses by estimating the power consumption of each device in the system. Open access to such information can encourage energy saving behavior, improved fault detection, better demand forecast, energy incentives, and more [2].
A trivial method for measuring the power consumption of individual devices in a system is to use smart appliances that are capable of reporting their power consumption. However, this method is complex and expensive. A more efficient method for estimating the consumption of individual devices is Non-Intrusive Load Monitoring (NILM). NILM methods use a single meter which measures the total power consumption of a system, in order to estimate the power consumption of individual appliances. Since it was first introduced by Hart [3], many NILM techniques have been explored. Several of those are based on factorial hidden Markov models [4], machine learning algorithms [5], deep neural networks [6], [7], cross-entropy method [8], time series distance [9] and optimal classifier [10]. Additional approaches for NILM can be found in the following surveys [11], [12], [13]. A recent development is the increasing availability of public data sets that can be accessed as a reference for NILM algorithms such as REDD [14], AMPds [15] and PLAID [16].
Several NILM algorithms use active power as the only feature. However, many smart meters measure additional features such as reactive power, power factor (PF), total harmonic distortion (THD) and apparent power. These signals may be used for improved classification. One popular feature is the active-reactive power signal, which was also used in the first NILM technique suggested by Hart [3]. This signal is used for classification based on several approaches, such as finite-state-machine based on transients [17], Mixed-Integer Linear Programming [18], wavelet transform [19], ZIP modeling [20] and additive factorial hidden Markov models [21]. If more features are used the classification of individual appliances can be improved. For example, classification based on current harmonics features is presented in [22], [23]. Other power features include active-reactive power and THD [24], active-reactive power and harmonics [25], active-reactive power, THD and harmonics [26], active-reactive-apparent power, PF and THD [27], and more [28]. Another important feature is the V-I trajectory that uses voltage and current waveforms. Some works utilizing this feature are [29], [30], [31].
While additional features might improve the accuracy of NILM algorithms, adding features is not always the best approach due to increased time complexity. Moreover, there is no guaranty that additional features improve the classification accuracy, since too many features might lead to over-fitting. To overcome the mentioned problems some works suggest to use a feature selection approach, in which the goal is to find a simple model with a minimal number of features [32]. The earliest work for feature selection in NILM is [33], which uses a neural network. Later, [34] uses the short-time Fourier transform and the wavelet transform to select the features. More recent research works which studied feature selection are [35] and [36]. In [35] a recursive feature elimination process is used to identify the most effective feature set based on the PLAID dataset [16]. This approach is based on elimination of features based on heuristic methods, and have relatively high complexity. Work [36] implements a forward selection algorithm which is used to select features by analyzing fast transients, based on four different datasets. In addition, [37], [38] convert correlated features into non-correlated ones, in order to simplify the classification process. The data conversation is based on the principle component analysis (PCA) transform, which is used in this works for new data representation.
Feature selection methods will always lose information since, by definition, several features are removed from the dataset. Therefore, in this work we propose to use the PCA method for efficient dimension reduction for NILM classification. The main idea is to use PCA to reduce the dimension of the power feature vector, while preserving information. This leads to reduced time complexity, which is critical for real-time operation. Note that in comparison to [37], [38] which used PCA for new data representation, we use it for dimension reduction. Additional advantages of the proposed approach is that the PCA is applied to raw data and operates independently of the NILM classification algorithm and the dataset. The sampling rate is irrelevant to the PCA, so this method can be used with smart meters with various sampling rates, ranging from milliseconds to minutes. The proposed method is tested on two classification algorithms using the public dataset AMPds [15], and a private dataset that was collected in a typical kitchen using the SATEC PM135 smart meter.
The paper is organized as follows. Section 2 outlines properties of NILM features. Section 3 explains how PCA can be used for dimension reduction in NILM. Section 4 presents simulation results based on the AMPds public dataset. Section 5 shows experimental and simulation results based on a private dataset collected by the SATEC PM135 smart meter. Finally, Section 6 concludes the paper.
Section snippets
One state and multi-state formulation
Consider a house or facility with m appliances (), each with d power features . The aggregated power features, Ψ, measured during sample time n at the entry point of the facility iswhere xi[n] denotes the On/Off [0,1] status of appliance i, and ϵ[n] represents background noise due to low-power appliances. It is also assumed that for at least one power feature ψi, v ≠ ψb, v, for i ≠ b. The purpose of
Principal component analysis - background
Principal Component Analysis (PCA), also known as the Karhunen-Loeve transform, is a widely used technique in applications such as feature selection, lossy data compression and dimension reduction [43], [44], [45]. PCA simplifies the complexity of high-dimensional data while retaining trends and patterns, by transforming the data into a lower dimension. PCA may be considered an unsupervised feature transformation method, which requires no label data, and is completely non-parametric. There are
Settings and test scenario
AMPds is an open data set proposed by SFU [15]. The data are collected from a house in Canada over 1 year. AMPds contains low sample-rate recordings of 60 s for 21 sub-meters, and includes active, reactive and apparent powers, in addition to current and power factor signals. In this simulations 7 sub-meters were classified, six of them containing a single load, and one sub-meter that contains multiple loads. The selected power features are active power, reactive power, apparent power and
Settings and test scenario
This experiment is done in a private house during two days. The first day is used for the training process and the second day is used for the inference stage. The private dataset was collected in a typical kitchen using the SATEC PM135 smart meter which is presented in Fig. 9. The data is sampled in a low sample-rate of 10 s from 7:00 to 19:00. The SATEC PM135 smart meter measures active power, reactive power, apparent power, current, power factor, harmonics and THD signals. In this experiment
Conclusions
This paper suggests to use PCA as an efficient dimension reduction method for NILM. The suggested method can be used with any NILM classification technique, and with various datasets and sample-rates. The training stage calculates the principal components based on past recorded data, and the inference stage uses the principal components for reducing the dimension of new samples. The proposed modified PCA procedure is tested using the public dataset AMPds and a private dataset that was collected
Declaration of Competing Interest
The authors whose names are listed immediately below certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in
Acknowledgment
Y. Levron was partly supported by Israel Science Foundation grant No. 2//7221. Y. Beck was partly supported by the Israeli Innovation Authority under Grant 60689. The authors also want to thank SATEC Ltd. for contributing their power quality monitors.
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