The increase in renewable energy sources (RESs), like wind or solar power, results in growinguncertainty also in transmission grids. This affects grid stability through fluctuating energy supplyand an increased probability of overloaded lines. One key strategy to cope with this uncertainty isthe use of distributed energy storage systems (ESSs). In order to securely operate power systemscontaining renewables and use storage, optimization models are needed that both handle uncertaintyand apply ESSs. This paper introduces a compact dynamic stochastic chance-constrained DC optimalpower flow (CC-OPF) model, that minimizes generation costs and includes distributed ESSs. AssumingGaussian uncertainty, we use affine policies to obtain a tractable, analytically exact reformulation asa second-order cone problem (SOCP). We test the new model on five different IEEE networks withvarying sizes of 5, 39, 57, 118 and 300 nodes and include complexity analysis. The results showthat the model is computationally efficient and robust with respect to constraint violation risk. Thedistributed energy storage system leads to more stable operation with flattened generation profiles.Storage absorbed RES uncertainty, and reduced generation cost.
In this paper, we propose a data-driven approach for uncertainty propagation and reachability analysis in a dynamical system. The proposed approach relies on the linear lifting of a nonlinear system using linear Perron-Frobenius (P-F) and Koopman operators. The uncertainty can be characterized in terms of the moments of a probability density function. We demonstrate how the P-F and Koopman operators are used for propagating the moments. Time-series data is used for the finite-dimensional approximation of the linear operators, thereby enabling data-driven approach for moment propagation. Simula…
The increase in renewable energy sources (RESs), like wind or solar power, results in growing uncertainty also in transmission grids. This affects grid stability through fluctuating energy supply and an increased probability of overloaded lines. One key strategy to cope with this uncertainty is the use of distributed energy storage systems (ESSs). In order to securely operate power systems containing renewables and use storage, optimization models are needed that both handle uncertainty and apply ESSs. This paper introduces a compact dynamic stochastic chance-constrained optimal power flow (CC…
This letter presents an analytical path loss model for air-ground (AG) propagation between unmanned aerial vehicles (UAVs) and ground-based vehicles. We consider built-up areas, such as the ones defined by ITU-R. The three-dimensional (3D) path loss model is based on propagation conditions and essential parameters are derived by using geometric methods. Owing to the generality, the analytical model is capable of arbitrary deployments of buildings, such as suburban, urban and dense urban. The analytical model is evaluated numerically, and validations conducted by ray-tracing simulations show th…
We present a proximal algorithm that performs a variational recursion on the space of joint probability measures to propagate the stochastic uncertainties in power system dynamics over high dimensional state space. The proposed algorithm takes advantage of the exact nonlinearity structures in the trajectory-level dynamics of the networked power systems, and is nonparametric. Lifting the dynamics to the space of probability measures allows us to design a scalable algorithm that obviates gridding the underlying high dimensional state space which is computationally prohibitive. The proximal recur…
Certifying Guidance & Control Networks: Uncertainty Propagation to an Event Manifold
Advanced Concepts Team, European Space Research and Technology Centre (ESTEC)（欧洲空间研究与技术中心（ESTEC）先进概念团队）；Surrey Space Centre, University of Surrey（萨里大学萨里空间中心）；ESA/ESOC（欧洲空间局欧洲空间操作中心）
Computer Science and Artificial Intelligence Laboratory (CSAIL)（计算机科学与人工智能实验室（CSAIL））；Massachusetts Institute of Technology (MIT)（麻省理工学院（MIT））
In this paper, we address the problem of uncertainty propagation through nonlinear stochastic dynamical systems. More precisely, given a discrete-time continuous-state probabilistic nonlinear dynamical system, we aim at finding the sequence of the moments of the probability distributions of the system states up to any desired order over the given planning horizon. Moments of uncertain states can be used in estimation, planning, control, and safety analysis of stochastic dynamical systems. Existing approaches to address moment propagation problems provide approximate descriptions of the moments…
The development of a reliable and robust surrogate model is often constrained by the dimensionality of the problem. For a system with high-dimensional inputs/outputs (I/O), conventional approaches usually use a low-dimensional manifold to describe the high-dimensional system, where the I/O data is first reduced to more manageable dimensions and then the condensed representation is used for surrogate modeling. In this study, we present a new solution scheme for this type of problems based on a deep learning approach. The proposed surrogate is based on a particular network architecture, i.e. the…
