State Estimation applied to poorly observable Distribution networks: a case study in Milan

In the context of the ongoing energy transition and the rapid growth of distributed generation—mainly small-scale residential photovoltaic systems—along with the increasing electrification of consumption, the ability to control and manage distribution networks has become critical to ensuring reliability, stability, and service quality. This challenge is particularly evident in the medium-voltage distribution network of Milan, a highly energy-intensive city characterized by poor observability. This condition is not unique to Milan but reflects many distribution networks which were designed for centralized generation, unidirectional flows, and limited measurement capabilities. In such contexts, state estimation plays a key role by enabling a comprehensive reconstruction of the network’s operating state even when measurement devices are limited or sparse. This is achieved through the integration of pseudo-measurements, forecast data, and estimation techniques based on artificial intelligence. The objective of this thesis is to review the theoretical and mathematical foundations of the classical Weighted Least Squares (WLS) state estimation method and to evaluate its performance on Milan’s medium-voltage poorly observable distribution network under different scenarios, including both favorable and highly constrained measurement conditions. The methodology involved selecting a feeder with the highest available measurement coverage and performing state estimation across different periods and load levels. Additional scenarios were simulated with missing or incorrect measurements and with the integration of pseudo-measurements to test the algorithm’s robustness. The results demonstrate that, despite the limited number of real measurements, WLS state estimation can provide a coherent and sufficiently accurate representation of the network’s operating conditions. Pseudo-measurements proved essential for achieving observability, although their quality significantly affects the estimation accuracy. Furthermore, the algorithm showed intrinsic robustness by mitigating the impact of faulty measurements, preventing them from compromising the estimation results. From a strategic perspective, the findings indicate that while Milan’s current measurement infrastructure does not support advanced monitoring, combining a limited but strategically placed set of sensors with reliable pseudo-measurements can already deliver valuable operational visibility. Future improvements in measurement infrastructure together with AI-based forecasting and anomaly detection techniques, will further enhance estimation accuracy.