# A Two-Stage Household Electricity Demand Estimation Approach Based on Edge Deep Sparse Coding
## 1 Introduction  
Countries worldwide have committed to promoting and enhancing the efficiency and sustainability of power grids in recent years. Meanwhile, the widespread popularity of advanced metering infrastructure (AMI) enables the collection of an immense amount of fine-grained, real-time consumption data [1]. The effective management and analysis of AMI data can facilitate a bidirectional information flow and friendly interaction between customers and grids [2]. They also play a nontrivial role in accurate demand response (DR) [3], power reliability and efficiency improvement [4], electricity price design [5], and other personalized services [6, 7]. The core of realizing these new services is to develop a highly accurate residential load forecast [8]. Two basic issues are associated with meter-level electricity consumption estimation. The first issue is the challenge of data transmission, numeration, and storage. Most power supply companies currently alleviate the tremendous pressure exerted on communication links and data storage computing powerby simply reducing sampling frequency [9]. However, this method may result in the loss of effective information and cannot satisfy precision and rapid interaction requirements. Therefore, alleviating the communication and storage burden under the premise of ensuring the availability of effective information is a prerequisite for the effective analysis of energy consumption data [10]. The second issue is that high-resolution load data can no longer be limited to simple consumer segmentation (i.e., industrial, commercial, and residential) [11; 12], but should further utilize hidden value or useful information to extract the electricity consumption behavior and lifestyle of consumers. The data compression algorithm can be divided into lossless compression and lossy compression, depending on whether the original data can be restored after reconstruction. The reconstruction data are entirely the same as the raw data in lossless compression algorithms. By contrast, lossy compression is focused on similarity search and information extraction [13] and plays a nontrivial role in power load curve analysis [14]. Common lossy compression algorithms include discrete fourier transform (DFT) [15], discrete wavelet transform (DWT) [16], principal component analysis (PCA) [17], singular value decomposition (SVD) [18], and a combination of these methods. A load data compression method was proposed in [13], wherein the load status and other load characteristics were first introduced to process the data. The recoverable linear-time complexity data compression algorithm proposed in [19] is suitable for an error-prone transmission line. Focusing on smart meter data lossy compression, a non-negative k-means-singular value decomposition (K-SVD) algorithm was analyzed in [20], and the extracted behavioral patterns were used only to classify consumers into residents and small and medium-sized enterprises. The electricity consumption behavior at the household or building levels has become a popular research topic in recent years. Compared with load profiles aggregated at high voltage levels, load profiles at the household level are frequently more volatile and sensitive to customer behavior or environmental variables, such as temperature, relative humidity, and their higher-order terms and interactions [21; 22]. The load status of electrical appliances was first introduced to load forecasting in [23]. However, the sparsity of load data was not considered to pretreat the immense amount of original load data. Sparsity is a key characteristic in household-level load forecasting. Sparse coding was proposed to model usage patterns in [24]. The case study indicated that including sparse coding features led to a 10% improvement in forecast accuracy. A neural network prediction model with k-means clustering, which is a type of sparse coding algorithm, was used for load estimation in [25]. The K-SVD algorithm is a more flexible load curve coding method than k-means clustering.