# Power Profiling of Smart Grid Users Using Dynamic Time Warping +
## 2 Related Work  
User consumption data are analyzed for various purposes, including modeling energy consumption trends, anomaly detection [20], predictive modeling, and visualization. In this section, we provide an overview of existing research in power consumption forecasting, anomaly detection, and user profiling as they relate to our work. Time-series analysis techniques are widely used to model and forecast energy consumption trends [21]. For instance, in [22], regression models were developed using load data time series to predict consumption. [PERSON] proposed a short-term load forecasting method to extract load patterns from consumption data [23]. Clustering consumption time series is commonly employed to monitor power consumption in smart grid applications for purposes such as demand forecasting and anomaly detection. [PERSON] et al. [24] applied forecasting models to predict electricity demand for industrial consumers using time-series clustering. [PERSON] et al. [25] introduced an enhanced version of the D-Stream clustering algorithm to monitor power demands in smart grids. The resulting clusters were used to detect abnormalities in users' consumption, such as defective appliances. Additionally, in [26], smart grid users were classified by clustering their consumption data obtained from smart meters, and this classification was leveraged to forecast power consumption.  
Measuring the distance between power consumption time series has been widely used to detect anomalies in operation or malicious activities, such as energy theft [27; 28; 29; 30; 31; 32]. [PERSON] et al. [27] identified anomalies in smart meter devices by analyzing correlation patterns in power consumption data. A combination of DTW and k-nearest neighbors (KNN) was employed in [28] to detect malicious activities such as data tampering and manipulation. In this work, DTW measured the similarity between usage time series, while KNN ranked anomalous behavior. [PERSON] et al. [29] detected users' behavioral changes by measuring the DTW distance in usage data, identifying anomalies caused by malfunctions or fraudulent activities. Similarly, [PERSON] et al. [30] used a combination of a convolutional neural network (CNN) and a long short-term memory (LSTM) model to detect electricity theft by analyzing power consumption time series. In [31], the authors introduced a photovoltaic power prediction model based on FastDTW, which is a computationally efficient approximation of DTW with linear time and space complexity [32]. This model predicted users' power consumption by identifying consumption similarities over different time durations.  
Profiling users in smart grids has been studied for various purposes, such as optimizing energy usage, detecting anomalies, and providing personalized services [33; 34; 35]. In [34], [PERSON] et al. proposed a clustering model to profile smart grid consumers with or without solar panels (e.g., rooftop photovoltaic (PV) systems) for demand prediction. This load profiling allowed for the distinction of PV users and facilitated their inclusion in dedicated demand response programs. The results also provided insights into the relationship between socio-demographic factors and PV installations. [PERSON] et al. [35] discussed two data-driven schemes, at the smart meter level and at an aggregate level, to profile users' consumption and detect potential power theft. [PERSON] et al. [36] proposed an electric vehicle (EV) charging schedule algorithm aimed at minimizing power fluctuations. EV users were profiled based on their power loading behavior, such as connection times, battery residuals, and expected state-of-charge levels. Smart grid user profiling was further explored in [37] to monitor individuals suffering from self-limiting conditions (e.g., Alzheimer's, Parkinson's disease, and clinical depression). Changes in a consumer's power usage behavior were used to assess their well-being or state of mind.