Real-time water quality (WQ) sensors in water distribution networks (WDN) have the potential to enable network-wide observability of water quality indicators, contamination event detection, and closed-loop feedback control of WQ dynamics. To that end, prior research has investigated a wide range of methods that guide the geographic placement of WQ sensors. These methods assign a metric for fixed sensor placement (SP) followed by \textit{metric-optimization} to obtain optimal SP. These metrics include minimizing intrusion detection time, minimizing the expected population and amount of contaminated water affected by an intrusion event. In contrast to the literature, the objective of this paper is to provide a computational method that considers the overlooked metric of state estimation and network-wide observability of the WQ dynamics. This metric finds the optimal WQ sensor placement that minimizes the state estimation error via the Kalman filter for noisy WQ dynamics -- a metric that quantifies WDN observability. To that end, the state-space dynamics of WQ states for an entire WDN are given and the observability-driven sensor placement algorithm is presented. The algorithm takes into account the time-varying nature of WQ dynamics due to changes in the hydraulic profile -- a collection of hydraulic states including heads (pressures) at nodes and flow rates in links which are caused by a demand profile over a certain period of time. Thorough case studies are given, highlighting key findings, observations, and recommendations for WDN operators. Github codes are included for reproducibility.
PMU Placement Optimization for Smart Grid Obvervability and State Estimation
University of Technology Sydney（悉尼科技大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）；Queen’s University Belfast（贝尔法斯特女王大学）；Princeton University（普林斯顿大学）
In this paper, we study the structural state and input observability of continuous-time switched linear time-invariant systems and unknown inputs. First, we provide necessary and sufficient conditions for their structural state and input observability that can be efficiently verified in $O((m(n+p))^2)$, where $n$ is the number of state variables, $p$ is the number of unknown inputs, and $m$ is the number of modes. Moreover, we address the minimum sensor placement problem for these systems by adopting a feed-forward analysis and by providing an algorithm with a computational complexity of $ O((…
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Optimal sensor placement is an important yet unsolved problem in control theory. In biological organisms, genetic activity is often highly nonlinear, making it difficult to design libraries of promoters to act as reporters of the cell state. We make use of the Koopman observability gramian to develop an algorithm for optimal sensor (or reporter) placement for discrete time nonlinear dynamical systems to ease the difficulty of design of the promoter library. This ease is enabled due to the fact that the Koopman operator represents the evolution of a nonlinear system linearly by lifting the stat…
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The lack of measurements in distribution grids poses a severe challenge for their monitoring: since there may not be enough sensors to achieve numerical observability, load forecasts (pseudo-measurements) are typically used, and thus an accurate state estimation is not guaranteed. However, an estimation is required to control distribution grids given the increasing amount of distributed generation. Therefore, we consider the problem of optimal sensor placement to improve the state estimation accuracy in large-scale, 3-phase coupled, unbalanced distribution grids. This is a combinatorial optimi…
Sensor selection is critical for state estimation, control and monitoring of nonlinear processes. However, evaluating the performance of each possible combination of $m$ out of $n$ sensors is impractical unless $m$ and $n$ are small. In this paper, we propose a sensitivity-based approach to determine the minimum number of sensors and their optimal locations for state estimation. The local sensitivity matrix of the measured outputs to initial states is used as a measure of the observability. The minimum number of sensors is determined in a way such that the local sensitivity matrix is full colu…
With the increasing penetration of converter-based renewable resources, different types of dynamics have been introduced to the power system. Due to the complexity and high order of the modern power system, mathematical model-based inertia estimation method becomes more difficult. This paper proposes two novel machine learning assisted inertia estimation methods based on long-recurrent convolutional neural (LRCN) network and graph convolutional neural (GCN) network respectively. Informative features are extracted from ambient measurements collected through phasor measurement units (PMU). Spati…
State estimation is crucial for the monitoring and control of post-combustion CO2 capture plants (PCCPs). The performance of state estimation is highly reliant on the configuration of sensors. In this work, we consider the problem of sensor selection for PCCPs and propose a computationally efficient method to determine an appropriate number of sensors and the corresponding placement of the sensors. The objective is to find the (near-)optimal set of sensors that provides the maximum degree of observability for state estimation while satisfying the budget constraint. Specifically, we resort to t…
