We propose a data-based method to solve a multi-stage stochastic optimal power flow (OPF) problem based on limited information about forecast error distributions. The framework explicitly combines multi-stage feedback policies with any forecasting method and historical forecast error data. The objective is to determine power scheduling policies for controllable devices in a power network to balance operational cost and conditional value-at-risk of device and network constraint violations. These decisions include both nominal power schedules and reserve policies, which specify planned reactions to forecast errors in order to accommodate fluctuating renewable energy sources. Instead of assuming that the uncertainties across the networks follow prescribed probability distributions, we consider ambiguity sets of distributions centered around a finite training dataset. By utilizing the Wasserstein metric to quantify differences between the empirical data-based distribution and the real unknown data-generating distribution, we formulate a multi-stage distributionally robust OPF problem to compute control policies that are robust to both forecast errors and sampling errors inherent in the dataset. Two specific data-based distributionally robust stochastic OPF problems are proposed for distribution networks and transmission systems.

The increasing distributed and renewable energy resources and controllable devices in distribution systems make fast distribution system state estimation (DSSE) crucial in system monitoring and control. We consider a large multi-phase distribution system and formulate DSSE as a weighted least squares (WLS) problem. We divide the large distribution system into smaller areas of subtree structure, and by jointly exploring the linearized power flow model and the network topology, we propose a gradient-based multi-area algorithm to exactly and efficiently solve the WLS problem. The proposed algorithm enables distributed and parallel computation of the state estimation problem without compromising any performance. Numerical results on a 4,521-node test feeder show that the designed algorithm features fast convergence and accurate estimation results. Comparison with traditional Gauss-Newton method shows that the proposed method has much better performance in distribution systems with a limited amount of reliable measurement. The real-time implementation of the algorithm tracks time-varying system states with high accuracy.

Concise and reliable modeling for the aggregated power flexibility of distributed energy resources (DERs) in active distribution networks (ADNs) is essential for coordinating transmission and distribution networks. Inner approximated aggregation models are desirable for power system operators because they ensure a safe dispatchable range for the distribution network. However, previous inner approximation methods often rely on experience and intuition due to the absence of an explicit expression of the exact aggregation model (EAM), leading to accuracy and computational efficiency challenges. This paper proposes a novel inner approximation method to overcome these challenges, leveraging the properties of our recently derived closed-form EAM. Specifically, we divide the process of inner approximation methods into two steps: defining a geometric prototype and calculating its parameters. The first step is accomplished by selecting a subset of all the coefficient vectors forming the EAM so as to improve accuracy. When calculating parameters, on the other hand, we exploit the regularity of these coefficient vectors to improve the computational efficiency. The inner approximated flexibility model of ADNs is further incorporated into the security-constrained unit commitment problem as an application, which helps improve the system’s economic benefits. Numerical simulations verify the effectiveness of the proposed method.

This is the second part of a two-part paper on data-based distributionally robust stochastic optimal power flow (OPF). The general problem formulation and methodology have been presented in a companion paper [1]. Here, we present extensive numerical experiments in both distribution and transmission networks to illustrate the effectiveness and flexibility of the proposed methodology for balancing efficiency, constraint violation risk, and out-of-sample performance. On the distribution side, the method mitigates overvoltages due to high photovoltaic penetration using local energy storage devices. On the transmission side, the method reduces N-1 security line flow constraint risks due to high wind penetration using reserve policies for controllable generators. In both cases, the data-based distributionally robust model predictive control (MPC) algorithm explicitly utilizes forecast error training datasets, which can be updated online. The numerical results illustrate inherent tradeoffs between the operational costs, risks of constraints violations, and out-of-sample performance, offering systematic techniques for system operators to balance these objectives.

An accurate and cost-effective islanding detection is in a great need for distributed generation (DG) integration. An onsite contactless islanding detection scheme is proposed in this paper, based on a small number of tiny and portable electric field (EF) sensors. In contrast to the existing mainstream detection techniques, which are heavily depended on the instrument transformer measurement in substations, the proposed contactless scheme is able to be deployed on the ground below the overhead feeders, enabled by a compact EF sensor and the associated accurate frequency measurement algorithm. The effectiveness, robustness, efficiency and security advantages of the proposed method are investigated and verified by the simulations using various feeder configurations. It is further supported by the laboratory experiments based on a scale-down overhead feeder test bed.

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 metric-optimization to obtain optimal SP. These metrics include minimizing intrusion detection time, thereby 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 that 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.