State Estimation for Water Distribution Networks in the Presence of Control Devices with Switching Behavior
In process monitoring and control, state estimation is the fundamental tool for processing redundant and noise-corrupted measurements in order to provide reliable estimates of the state of a system. In the context of water distribution networks (WDNs), state estimation has been proposed as the core technology which can enable various applications ranging from real-time monitoring and control to anomaly diagnosis, such as leak detection and localization. Measurements are typically available from sparse and often scarce telemetry sensors, such as flow at the inlet of a district metered area (DMA) and pressure at some nodes, or from utility estimates, for example prior estimates of the nodal demands. The problem consists of using the available measurements to reconstruct an estimate of the state variables and is solved iteratively by minimizing the weighted least squares (WLS) of the differences between the measurements and model predictions, typically with gradient methods. WDN state estimation in the presence of control devices, such as pressure reducing valves, remains an open problem due to the complexity in modeling efficiently their switching behavior. Control elements prevent from obtaining an explicit function of the measurements with respect to the state variables for all possible switching statuses. In this paper, an extension to traditional state estimation methods is proposed, which only requires a minor modification of existing WLS solvers based on gradient methods. Based on residual analysis, conditions are given in order to verify correct convergence at the end of a state estimation or to identify changes in connectivity due to opening/closing of control elements before proceeding to a new run. The method does not require including explicit binary variables to model the state of control elements, which would require complex heuristic-based solvers and would present scalability challenges for large networks with many such elements. Results on a real-world test case with two PRVs are reported to demonstrate the effectiveness and of the proposed method.