SEARCH · Search NASA

Results for “deterministic”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 811 records · Page 45

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Volt-VAR Optimization in Distribution Networks Using Twin Delayed Deep Reinforcement Learning

Modern distribution grids are undergoing new challenges due to the stochastic nature of distributed energy resources (DERs). High penetration of DERs has a significant impact on Volt-VAR profile and system power losses. This work proposes a deep reinforcement learning (DRL)-based Volt-VAR optimization approach for improving voltage profile and reducing system power loss under high penetration of distributed energy resources, such as battery energy storage and solar photovoltaic units in distribution grids. The twin delayed deep deterministic policy gradient (TD3) method-based DRL agent is proposed to configure optimal set-points of reactive power outputs of fast responding smart inverters. The agent schedules the reactive power of inverters according to their physical capabilities, such as minimum allowed power factor, e.g., 0.9 leading/lagging. The reward function of the proposed DRL scheme is designed carefully to ensure a proper voltage profile of the grids with effective scheduling of reactive power outputs from inverters. The performance of the proposed model is verified on modified IEEE 34- and 123-bus systems and compared with base case with no reactive supply by inverters, and local droop Volt-VAR control approach. The results show that the proposed method performs better than the local droop control and deep deterministic policy gradient (DDPG)-based DRL method for reducing voltage fluctuation and minimizing power loss.

Hossain, Rakib↗

DOE OSTI2021

Stochastic Pricing Game for Aggregated Demand Response Considering Comfort Level

In recent years, demand response (DR) has been explored as a fundamental strategy for demand-side management due to its advantages in mediating intermittency of renewable energy generation, load shifting, etc. To engage customers in DR programs, several deterministic price-based DR strategies have been developed and implemented. However, the stochastic weather conditions and occupants' consumption behaviors often make the deterministic solution less robust to uncertainties. In this paper, with the consideration of the uncertainties, a stochastic Stackelberg game is proposed to model the price-demand negotiation between a distributed system operator and load aggregators, where the virtual battery constraints are extracted from the building thermostatically controlled loads (TCLs)‘ characteristics to guarantee comfortable TCLs' levels. Following the negotiation, a priority-based control method is used to allocate the optimal aggregated power DR profile at the building level and track the power signal. Several groups of experiments have demonstrated the effectiveness and robustness of the stochastic solutions.

Chen, Yang↗

DOE OSTI2024

Short-Term Load Forecasting Considering EV Charging Loads with Prediction Interval Evaluation

Short-term load forecasting plays a critical role in power system planning and operation. Along with the electrification of various loads, electricity demands are becoming increasingly hard to predict. Notably, the recent rise in electric vehicles (EVs) has further contributed to this unpredictability. To address this issue, this paper proposes a probabilistic load forecasting strategy utilizing Gaussian process regression, structured in a day-ahead manner. While many works focus on deterministic prediction, probabilistic forecasting offers additional insights into variability and uncertainty, enabling more flexible and reliable operation for power systems. To enhance the accuracy of the load forecasting model, the inputs include features related to EV charging habits as well as commonly used weather information. The load forecasting results are evaluated using various metrics, including conventional ones that assess the accuracy of point forecasts, as well as additional metrics that test the reliability of prediction intervals. The proposed load forecasting method is finally tested on real residential power consumption data and EV charging data sampled from real-world sources. The results prove that the new features can greatly improve the performance of the load forecasting method.

electrical vehicle↗

DOE OSTI2020

Allocation and Operation of A Hydropneumatic Energy Storage with Building Microgrid

Behind-meter application for a recently invented hydropneumatic Ground-Level Integrated Diverse Energy Storage (GLIDES) is focused in this research. Considering possible uncertainties from solar radiation and electricity load in a building microgrid, two-stage stochastic programming is adopted for 15-min operation and a mixed-integer nonlinear stochastic model is built with integrated energy systems of GLIDES, solar panel and power generating unit. In order to make the model computationally tractable, we use sample average approximate method to decrease associated complexity with sample size and improve solving efficiency. The experimental results in deterministic and stochastic operation indicate that best candidate solution from SAA are superior to the solution from expected value problem in terms of optimality gap and variance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Occlusion-Perturbed Deep Learning for Probabilistic Solar Forecasting via Sky Images

Solar forecasting is shifting to the probabilistic paradigm due to the inherent uncertainty within the solar resource. Input uncertainty quantification is one of the widely used and best-performing ways to model solar uncertainty. However, compared to other sources of inputs, such as numerical weather prediction models, pure sky image-based probabilistic solar forecasting lags behind. In this research, an occlusion-perturbed convolutional neural network, named the PSolarNet, is developed. The PSolarNet provides very short-term deterministic forecasts, forecast scenarios, and probabilistic forecasts of the global horizontal irradiance from sky image sequences. Case studies based on 6 years of open-source data show that the developed PSolarNet is able to generate accurate 10-minute ahead deterministic forecasts with a 5.62% normalized root mean square error, realistic and diverse forecast scenarios with a 0.966 average correlation with the actual time series, and reliable and sharp probabilistic forecasts with a 2.77% normalized continuous ranked probability score.

Bayesian model averaging↗

DOE OSTI2024

Short-Term Probabilistic Solar Forecasting via Reinforcement Learning over ECMWF

In this paper, we present an innovative reinforcement learning approach for short-term solar forecasting, leveraging data from the European Centre for Medium-Range Weather Forecasts (ECMWF). The methodology begins with the application of the System Advisor Model (SAM) to transform various ECMWF numerical weather prediction members into predictive photovoltaic power generation. To enhance the precision of deterministic forecasting, we introduce a dynamic model selection algorithm based on Q-learning. This algorithm dynamically identifies and utilizes the most accurate ensemble member for forecasting purposes. Furthermore, we employ a support vector regression surrogate model with a Gaussian distribution to generate probabilistic forecasts, providing a holistic view of solar energy generation uncertainty. To expedite the training process and make it more practical for real-world applications, we integrate a rolling update workflow. This innovative workflow reduces the training period from months to a mere 19 days, making our method highly efficient. Numerical results of the case study show that in comparison to benchmark models, the proposed method improves the deterministic and probabilistic solar forecasting accuracy by up to 40.84% and 48.42%, respectively.

ensemble forecasting↗

DOE OSTI2018

Correlation between EVs and Other Loads in Probabilistic Load Flow for Distribution Systems

To date, most probabilistic studies have assumed independence between the various loads and other inputs on the distribution system. It is well know however, that this is typically not the case. The work presented in the paper expands upon a previous unbalanced three-phase probabilistic load flow study on a residential feeder with a 50 % penetration of electric vehicles, under three different charging schemes where different correlation scenarios between the load flow inputs are considered. The data for the probabilistic load flow study are derived from a voltage dependent time-variant deterministic load flow. Here the deterministic load flow data are examined further to gain a better understanding of the correlation between the customer and electric vehicle charging loads, and how different charging schemes may impact it further. Four different correlation scenarios are then created and details on how the probabilistic load flow inputs are created is also presented; demonstrating the need for better analysis on the correlation between system inputs. This paper hopes to open the discussion and start the push for future research into understanding the correlation and effects of various system inputs on the probabilistic nature of distribution systems, and how to apply this knowledge to future studies.

Melhorn, Alexander C.↗

DOE OSTI2015

Stochastic Optimization for Unit Commitment-A Review

Optimization models have been widely used in the power industry to aid the decision-making process of scheduling and dispatching electric power generation resources, a process known as unit commitment (UC). Since UC's birth, there have been two major waves of revolution on UC research and real life practice. The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation. With the high penetration of renewable energy, increasing deregulation of the electricity industry, and growing demands on system reliability, the next wave is focused on transitioning from traditional deterministic approaches to stochastic optimization for unit commitment. Since the literature has grown rapidly in the past several years, this paper is to review the works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC. Relevant lines of future research are also discussed to help transform research advances into real-world applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2016

A robust approach to chance constrained optimal power flow with renewable generation

Optimal Power Flow (OPF) dispatches controllable generation at minimum cost subject to operational constraints on generation and transmission assets. The uncertainty and variability of intermittent renewable generation is challenging current deterministic OPF approaches. Recent formulations of OPF use chance constraints to limit the risk from renewable generation uncertainty, however, these new approaches typically assume the probability distributions which characterize the uncertainty and variability are known exactly. We formulate a robust chance constrained (RCC) OPF that accounts for uncertainty in the parameters of these probability distributions by allowing them to be within an uncertainty set. The RCC OPF is solved using a cutting-plane algorithm that scales to large power systems. We demonstrate the RRC OPF on a modified model of the Bonneville Power Administration network, which includes 2209 buses and 176 controllable generators. In conclusion, deterministic, chance constrained (CC), and RCC OPF formulations are compared using several metrics including cost of generation, area control error, ramping of controllable generators, and occurrence of transmission line overloads as well as the respective computational performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2017

Ensemble Kalman Filter for Dynamic State Estimation of Power Grids Stochastically Driven by Time-correlated Mechanical Input Power

State and parameter estimation of power transmission networks is important for monitoring power grid operating conditions and analyzing transient stability. Wind power generation depends on fluctuating input power levels, which are correlated in time and contribute to uncertainty in turbine dynamical models. The ensemble Kalman filter (EnKF), a standard state estimation technique, uses a deterministic forecast and does not explicitly model time-correlated noise in parameters such as mechanical input power. However, this uncertainty affects the probability of fault-induced transient instability and increased prediction bias. Here a novel approach is to model input power noise with time-correlated stochastic fluctuations, and integrate them with the network dynamics during the forecast. While the EnKF has been used to calibrate constant parameters in turbine dynamical models, the calibration of a statistical model for a time-correlated parameter has not been investigated. In this study, twin experiments on a standard transmission network test case are used to validate our time-correlated noise model framework for state estimation of unsteady operating conditions and transient stability analysis, and a methodology is proposed for the inference of the mechanical input power time-correlation length parameter using time-series data from PMUs monitoring power dynamics at generator buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Observability Analysis of a Power System Stochastic Dynamic Model Using a Derivative-Free Approach

Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. In this work, facing these challenges, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Multi-Stage Modeling With Recourse Decisions for Solving Stochastic Complementarity Problems With an Application in Energy

This paper presents a multi-stage model with recourse decisions for solving complementarity problems in a competitive electricity market under uncertainty, while also considering renewable energy technologies and battery storage utilization. The model is based on a Nash-Cournot formulation of imperfect competition among power producers. We analyze the value of variable renewable energy (VRE) and battery storage under different uncertainties, such as demand level and VRE availability. To illustrate the proposed model, we apply it to three- bus five-player model and analyze different cases varying costs, including a user-optimal perspective (with market power) and a system-optimal perspective (with central planning). We also consider the potential for congestion in the system by restricting the transmission capacity between a single interface that connects two buses. Our findings show that increasing the battery storage capacity results in a decrease in the need for perfect information about future uncertainties. Additionally, as the model allows for more uncertainty, it becomes more apparent that the stochastic mixed complementarity problem (MCP) has an advantage over a deterministic equivalent. We propose the use of the Value of the Stochastic Equilibrium Solution (VSES) as a quality metric to compare the stochastic MCP with its deterministic equivalent. Overall, expanding battery storage capacity can lower the maximum, mean, and variance values of delivered prices, but there are diminishing returns to this approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2015

Robust Distribution Network Reconfiguration

We propose a two-stage robust optimization model for the distribution network reconfiguration problem with load uncertainty. The first-stage decision is to configure the radial distribution network and the second-stage decision is to find the optimal a/c power flow of the reconfigured network for given demand realization. We solve the two-stage robust model by using a column-and-constraint generation algorithm, where the master problem and subproblem are formulated as mixed-integer second-order cone programs. Computational results for 16, 33, 70, and 94-bus test cases are reported. We find that the configuration from the robust model does not compromise much the power loss under the nominal load scenario compared to the configuration from the deterministic model, yet it provides the reliability of the distribution system for all scenarios in the uncertainty set.

distribution network↗

DOE OSTI2020

Switch Opening and Exchange Method for Stochastic Distribution Network Reconfiguration

The purpose of distribution network reconfiguration (DNR) is to determine the optimal topology of an electricity distribution network, which is an efficient measure to reduce network power losses. Electricity load demand and photovoltaic (PV) output are uncertain and vary with time of day, and will affect the optimal network topology. Single-hour deterministic DNR is incapable of handling this uncertainty and variability. Therefore, this paper proposes to solve a multi-hour stochastic DNR (SDNR). Existing solution methods for DNR are either inaccurate or excessively time-consuming, and are therefore incapable of solving multi-hour SDNRs for large distribution networks. In this regard, a switch opening and exchange (SOE) method is proposed. Starting from a looped network with all switches closed, the SOE consists of three steps. The first step is to sequentially open the switches until all of the loops are opened. The second and third steps modify the status of branches obtained in the first step to obtain better radial topologies. Five test systems are used to validate the accuracy and fast solution speed of the SOE and the superiority of multi-hour SDNR over single-hour deterministic DNR.

distribution network reconfiguration↗

DOE OSTI2015

Endogenous Assessment of the Capacity Value of Solar PV in Generation Investment Planning Studies

There exist several different reliability-and approximation-based methods to determine the contribution of solar resources toward resource adequacy. However, most of these approaches require knowing in advance the installed capacities of both conventional and solar generators. This is a complication since generator capacities are actually decision variables in capacity planning studies. In this paper, we study the effect of time resolution and solar PV penetration using a planning model that accounts for the full distribution of generator outages and solar resource variability. We also describe a modification of a standard deterministic planning model that enforces a resource adequacy target through a reserve margin constraint. Our numerical experiments show that at least 50 days worth of data are necessary to approximate the results of the full-resolution model with a maximum error of 2.5% on costs and capacity. We also show that the amount of displaced capacity of conventional generation decreases rapidly as the penetration of solar PV increases. We find that using an exogenously defined and constant capacity value based on time-series data can yield relatively accurate results for small penetration levels. For higher penetration levels, the modified deterministic planning model better captures avoided costs and the decreasing value of solar PV.

14 SOLAR ENERGY↗

DOE OSTI2022

Deep Reinforcement Learning From Demonstrations to Assist Service Restoration in Islanded Microgrids

Microgrids can be operated in island mode during utility grid outages to support service restoration and improve system resilience. To schedule and dispatch distributed energy resources (DERs) in an islanded microgrid, conventional model-based methods rely on accurate distribution network models and lack generalization and adaptability. Data-driven methods are promising for DER coordination but face practical challenges such as potential hazards to microgrids during online training and insufficient online training opportunities due to low outage rates. This paper presents a novel two-stage learning framework that builds on the deep deterministic policy gradient from demonstrations to identify an optimal restoration strategy. At the pre-training stage, imitation learning is applied to equip the control agent with expert experiences to guarantee acceptable initial performance. At the online training stage, action clipping, reward shaping, and expert demonstrations are leveraged to ensure safe exploration while accelerating the training process. In conclusion, the proposed method is illustrated using the IEEE 123-node system and compared with a representative model-based method and the standard deep deterministic policy gradient method to prove solution accuracy and demonstrate increased computational efficiency.

Du, Yan↗

DOE OSTI2023

A Multi-Fidelity Gaussian Process Regression Method for Probabilistic Wind Farm Power Curve Estimation

Accurate estimation of the power curve for wind turbines or wind farms is crucial to ensure their efficient operation and management. However, conventional methods for power curve estimation rely either on expensive and infrequent measurements or on low-quality numerical simulations. Moreover, the majority of previous studies on power curve estimation for wind turbines or wind farms focused on deterministic estimation, which provides a point estimate of the relationship between wind speed and power generation. Nevertheless, the deterministic approach fails to consider the inherent uncertainty associated with wind energy production resulting from varying turbine characteristics. This can lead to inaccurate power generation estimation and suboptimal decisions regarding energy management. In this paper, a kernel density estimation (KDE) based Multi-Fidelity Gaussian Process Regression (MFGPR) model is proposed to fuse theoretical power curve data and the ground true measurements to create a mapping of wind speed and wind power. By conducting a case study on an actual wind farm in China, the efficacy of the proposed MFGPR model was demonstrated in characterizing the variability of wind power. The probabilistic MFGPR model was also able to generate confidence intervals that encompassed the measured power, thereby improving the accuracy and confidence in wind power estimation or wind resource assessment. Overall, the proposed MFGPR model offers a reliable approach to integrate high-fidelity ground measurements and theoretical power curve data, resulting in precise wind resource assessment and power estimation.

Gaussian process regression↗

DOE OSTI2015

Application of High Performance Computing for Studying Cyclic Variability in Dilute Internal Combustion Engines

Combustion instabilities in dilute internal combustion engines are manifest in cyclic variability (CV) in engine performance measures such as integrated heat release or shaft work. Understanding the factors leading to CV is important in model-based control, especially with high dilution where experimental studies have demonstrated that deterministic effects can become more prominent. Observation of enough consecutive engine cycles for significant statistical analysis is standard in experimental studies but is largely wanting in numerical simulations because of the computational time required to compute hundreds or thousands of consecutive cycles. We have proposed and begun implementation of an alternative approach to allow rapid simulation of long series of engine dynamics based on a low-dimensional mapping of ensembles of single-cycle simulations which map input parameters to output engine performance. This paper details the use Titan at the Oak Ridge Leadership Computing Facility to investigate CV in a gasoline direct-injected spark-ignited engine with a moderately high rate of dilution achieved through external exhaust gas recirculation. The CONVERGE™ CFD software was used to perform single-cycle simulations with imposed variations of operating parameters and boundary conditions selected according to a sparse grid sampling of the parameter space. Using an uncertainty quantification technique, the sampling scheme is chosen similar to a design of experiments grid but uses algorithms designed to minimize the number of samples required to achieve a desired degree of accuracy. The simulations map input parameters to output metrics of engine performance for a single cycle, and by mapping over a large parameter space, results can be interpolated from within that space. This interpolation scheme forms the basis for a low-dimensional ‘metamodel’ (or model of a model) which can be used to mimic the dynamical behavior of corresponding high-dimensional simulations. Simulations of high-EGR spark-ignition combustion cycles within a parametric sampling grid were performed and analyzed statistically, and sensitivities of the physical factors leading to high CV are presented. With these results, the prospect of producing low-dimensional metamodels to describe engine dynamics at any point in the parameter space will be discussed. Additionally, modifications to the methodology to account for nondeterministic effects in the numerical solution environment are proposed.

Finney, Charles E. A.↗