## 3 Latest Applications in Distribution Systems
### State Estimation/Load Monitoring  
Distribution system state estimation (DSSE) is the backbone of modern distribution management systems (DMSs) to capture voltage phase angles and magnitudes at all buses, from available measurements, such as power injection/flow and voltage, for distribution system monitoring and control. Motivated by the increasing penetration level of DERs, it becomes vital to develop an accurate, efficient, and robust state estimation technique that addresses the complications that they generate [67]. Conventional DSSE methods that use measured data of the supervisory control and data acquisition (SCADA) system, such as the weighted least square (WLS) method, might be incapable of dealing with the system-wide unobservability, increased computational complexity, and topological variations emerging in modern distribution systems. Furthermore, these methods heavily rely on real-time measurements and fall short of clarifying important correlations hidden in historical DER data. Therefore, appropriate AI techniques, such as GNN, have been applied to address these shortcomings [68]. Moreover, this has also motivated the development of the wide area measurement system (WAMS) based on PMUs, and its integration with state-of-the-art AI techniques, which this section will explore in detail. To capture the spatial and temporal dependencies of power system measurements, a two-layer framework is adopted in [36], where a graph convolution layer that captures the spatial dependencies is followed by a gated recurrent unit (GRU) layer that captures thetemporal dependencies. Compared with support vector regression and Bayesian multivariate regression, ref. [36] shows improved accuracy, reduced latency, and computation time. Spatiotemporal correlations of historical measurement data are simultaneously captured in [37] by the proposed unrolled spatiotemporal GCN. This is accomplished by splicing spatial graphs of neighboring time steps which allows the capturing of the effects of adjacent nodes within current and adjacent time steps directly and simultaneously. Ref. [37] is also capable of capturing long-range dependencies by leveraging multi-module layers. DSSE often suffers from poor network observability as economic constraints limit the number of sensors installed in distribution systems. To address this issue, ref. [38] leverages the inter-dependencies of nodes learned by the GNN architecture to generate pseudo-measurements to achieve accurate estimations with lower computational times. Similarly, ref. [39] deals with the problem of poor network observability with sparse AMI measurements by utilizing the low pass property of voltage phasors of the buses. Then, graph signal processing (GSP) and [PERSON]'s sampling theorem are applied to reconstruct AMI measurements to enhance the robustness and scalability. Reference [43] develops an optimization strategy of PMU placement for NN design and then a physics-aware NN is proposed to utilize the PMU placement to determine the NN structure, which reduces the complexity of the NN architecture as well as enhances robustness against over-fitting. In the context of PGNN, ref. [44] incorporates line/shunt admittance and grid topology information into the NN architecture. Estimation accuracy is significantly improved when compared to the widely used WLS method, without specific PMU placement requirements. Rather than embedding physical information into the architecture, ref. [45] proposes a framework where the estimated states produced by the encoder-decoder architecture are evaluated against power flow equations governed by physical laws. Then, the loss function is shaped as the measurement weighted residual, which is back-propagated to adjust weights and biases in the NN for improved estimations. The accuracy and robustness of DSSE are greatly improved relative to conventionally used techniques such as WLS and long short-term memory (LSTM) networks.