A Global Stochastic Programming Approach for the Optimal Placement of Gas Detectors with Nonuniform Unavailabilities.
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This presentation gives an overview of a stochastic look ahead commitment (SLAC) problem for managing transmission grid uncertainty in the near- to medium-term (15 minutes to a few hours). We discuss formulation and solution methods, as well as application to transmission system operations.
As extreme weather events become more frequent and intense, the demand for connecting grid operation and infrastructure planning with extreme event models will increase as well. We present a methodology for creating damage contingencies and scenarios for electric transmission grids during a hurricane strike. Included is an example case study: Hurricane Dolly damaging a synthetic 2000 bus test system during its landing in Southern Texas. Using WIND Toolkit meteorological data in conjunction with fragility curves for various electric grid elements, we generate stochastic damage scenarios that can be used for short- and long-term planning problems including emergency asset management. We perform statistical analysis of damages and quantify topological effects on example synthetic grid. Also, we investigate loss-of-load events during two-day economic dispatch experiment. Finally, we point out various shortcomings of our method and suggest how it can be improved.
The Athena project, funded by the Department of Energy, has worked to identify the critical infrastructure at Dallas Fort Worth (DFW) Airport which influences mobility between the airport and the surrounding city of Dallas. Using scalable methods that can leverage HPC resources we have developed a multi-stage stochastic infrastructure expansion model for determining parking and curb modifications to the DFW Airport over a 20-year horizon. Additionally, we have explored the impacts of congestion pricing in conjunction with infrastructure modifications. Our multi-stage stochastic model is implemented using the mpi-sppy software and solved in parallel using progressive hedging on the National Renewable Energy Laboratory's HPC system Eagle. In this talk we present results from solving this model at scale.
In Multi-Policy Decision-Making (MPDM), many computationally-expensive forward simulations are performed in order to predict the performance of a set of candidate policies. In risk-aware formulations of MPDM, only the worst outcomes affect the decision making process, and efficiently finding these influential outcomes becomes the core challenge. Recently, stochastic gradient optimization algorithms, using a heuristic function, were shown to be significantly superior to random sampling. In this disclosure, it was shown that accurate gradients can be computed-even through a complex forward simulation—using approaches similar to those in dep networks. The proposed approach finds influential outcomes more reliably, and is faster than earlier methods, allowing one to evaluate more policies while simultaneously eliminating the need to design an easily-differentiable heuristic function.
This paper considers the problem of distributed beam scheduling and power allocation problem in millimeter- Wave (mmWave) cellular networks, in which multiple Base Stations (BSs) operate as individual operators over a shared spectrum. We propose a novel learning-aided approach that integrates the Lyapunov Drift-Plus-Penalty (LDPP) framework and Multi-agent Deep Deterministic Policy Gradient (MADDPG) reinforcement learning algorithms. This offers a powerful approach to learning stable and constraint-aware policies, reaping the joint benefit of both LDPP and MADDPG, in complex multiagent environments. The major challenge for this approach is to integrate these two approaches in a meaningful and effective manner. The key idea to solve this problem is to introduce a novel feature of local observation that incorporates potential negative value of the reward function due to the stochastic constraints introduced by the LDPP framework. Empirical results demonstrate that our proposed scheme outperforms the baseline methods under various conditions.
HERON is a modeling toolset and plugin for RAVEN to accelerate stochastic technoeconomic assessment of the economic viability of various grid-energy system configurations, especially with application to electrical grids and integrated energy systems (IES). The frameworks enabling this toolset are INL's RAVEN and its TEAL plugin. The toolset includes automated RAVEN workflow generation tools for performing stochastic analysis and optimization driven by technoeconomic factors. The workflows generated employ RAVEN for parametric or optimizing study of grid component characteristics, and again for stochastic sampling of regulated and deregulated markets, load, and weather histories. The toolset further provides methods for economically-optimal dispatch of system components given the stochastic samples of market, load, and weather histories. The toolset allows assembling of existing and new models through the RAVEN interface to the Modelica process modeling language.
The problem of obtaining an optimal control law, which is constrained to be a feedback of the available measurements, is considered for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise. Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite duration cases. The feedback gain matrices are constrained to be constant for the infinite duration cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. Computational aspects are discussed via application to two continuous time processes, including a helicopter/slung load system subjected to measurement noise and random wind gust input.
We report a prominent challenge to the safe and optimal operation of the modern power grid arises due to growing uncertainties in loads and renewables. Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these uncertainties by computing dispatch decisions and control policies that maintain feasibility under uncertainty. Most SOPF formulations consider simple control policies such as affine policies that are mathematically simple and resemble many policies used in current practice. Motivated by the efficacy of machine learning (ML) algorithms and the potential benefits of general control policies for cost and constraint enforcement, we put forth a deep neural network (DNN)-based policy that predicts the generator dispatch decisions in real time in response to uncertainty. The weights of the DNN are learnt using stochastic primal–dual updates that solve the SOPF without the need for prior generation of training labels and can explicitly account for the feasibility constraints in the SOPF. The advantages of the DNN policy over simpler policies and their efficacy in enforcing safety limits and producing near optimal solutions are demonstrated in the context of a chance constrained formulation on a number of test cases.
Control algorithm for optimization of nonlinear stochastic processes with discounted performance criteria
In this study, we consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their stochastic estimates by, for example, subsampling. We propose a stochastic algorithm based on sequential quadratic programming (SQP) that uses a differentiable exact augmented Lagrangian as the merit function. To motivate our algorithm design, we first revisit and simplify an old SQP method Lucidi developed for solving deterministic problems, which serves as the skeleton of our stochastic algorithm. Based on the simplified deterministic algorithm, we then propose a non-adaptive SQP for dealing with stochastic objective, where the gradient and Hessian are replaced by stochastic estimates but the stepsizes are deterministic and prespecified. Finally, we incorporate a recent stochastic line search procedure Paquette and Scheinberg into the non-adaptive stochastic SQP to adaptively select the random stepsizes, which leads to an adaptive stochastic SQP. The global "almost sure" convergence for both non-adaptive and adaptive SQP methods is established. Numerical experiments on nonlinear problems in CUTEst test set demonstrate the superiority of the adaptive algorithm.
The problem of global maxima of functionals has been examined. Mathematical roots of local maxima are the same as those for a much simpler problem of finding global maximum of a multi-dimensional function. The second problem is instability even if an optimal trajectory is found, there is no guarantee that it is stable. As a result, a fundamentally new approach is introduced to optimal control based upon two new ideas. The first idea is to represent the functional to be maximized as a limit of a probability density governed by the appropriately selected Liouville equation. Then, the corresponding ordinary differential equations (ODEs) become stochastic, and that sample of the solution that has the largest value will have the highest probability to appear in ODE simulation. The main advantages of the stochastic approach are that it is not sensitive to local maxima, the function to be maximized must be only integrable but not necessarily differentiable, and global equality and inequality constraints do not cause any significant obstacles. The second idea is to remove possible instability of the optimal solution by equipping the control system with a self-stabilizing device. The applications of the proposed methodology will optimize the performance of NASA spacecraft, as well as robot performance.
Modern particle accelerator optimization requires sophisticated computational methods to address the inherently stochastic nature of beam dynamics. This research develops a framework applying AD to SDEs that specifically addresses beam dynamics challenges in particle accelerators, focusing on accurately modeling and optimizing beam behavior in regimes dominated by stochastic processes. By incorporating key physical phenomena such as synchrotron radiation, wakefield effects, and quantum excitation, the framework aims to provide auto differentiation on the figure of merit of the phase space evolution and beam dynamics. The methodology will enable effective optimization method in a dynamic system with stochastic process.
A significant difficultly associated with the use of stochastic programming to solve optimal power flow problems on a 5-minute timescale is the quality of renewable energy scenarios input by the user. This is especially true when considering power systems with high penetrations of renewable energy, e.g. wind power. This paper introduces the use of stochastic programming to solve the DCOPF problem with scenarios drawn directly from high-fidelity data sets. Hence, the proposed method avoids the problem of lost physics by finding high-fidelity analogs that can describe future states of the system. Furthermore, this method can be simply extended to output multi-period scenarios to the stochastic program. We demonstrate the effectiveness of this technique on simulated dispatch operations of the RTS-GMLC over a week.