Distribution Grid Optimal Power Flow (D-OPF): Modeling, Analysis, and Benchmarking
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Iterative Linearization for Phasor-Defined Optimal Power Dispatch
Optimal power flow (OPF) problems, which dispatch power targets to controllable generating units across a network, must generally account for non-convex constraints on power flow. Furthermore, adapting those problems so as to make them solvable with convex optimization techniques is an area of much academic and operational interest. In this paper, we present a method for solving OPF as a quadratic program by iteratively refining and re-initializing a linearized model of power flow based on the outputs of an associated nonlinear solver. The linear model on which we demonstrate this method is an adapted version of an approximation designed for use with unbalanced distribution networks. As an important benefit, the model allows for the explicit inclusion of nodal voltage phasor values in both the OPF problem's objective and its constraints, which opens the door to the idea of phasor-based control (PBC) design. We show in simulations on the IEEE 13-node test feeder that our method quickly converges to a set of phasor targets that are sufficiently precise for use in operations at the distribution level.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Scalable Risk Assessment of Rare Events in Power Systems With Uncertain Wind Generation and Loads
Risk assessment of rare events has become increasingly important in power system planning and operation with the increasing integration of renewable energy and the presence of system uncertainties. However, quantifying the risk posed by rare events via the traditional method, i.e., Monte Carlo sampling (MCS), incurs substantial computational expense stemming from the vast ensemble of power flow simulations. To accelerate the assessment, this paper proposes a Deep Neural Network (DNN)-kernelized vector-valued Gaussian Process (VVGP) approach with excellent computational efficiency while maintaining high accuracy. Consequently, serving as a surrogate model for the power flow solver, the DNN-kernelized VVGP enables significantly faster but accurate risk assessment compared to the power flow solver. The developed surrogate model evaluates low-order N - k events that contain more than 90% instances by adeptly capturing the topological features while the high-order N - k events are assessed via a power flow solver, thereby striking a balance between computational efficiency and uncertainty quantification accuracy. Moreover, the model incorporates a Support Vector Machine (SVM) classifier to resample concerning low-probability tail events to counteract the biases potentially introduced during the DNN-kernelized VVGP evaluations. Simulations conducted on the modified IEEE 24-bus, 118-bus, and European 1354-bus systems demonstrate that the proposed method maintains the accuracy benchmark set by MCS while significantly reducing computational demands in large-scale power systems as compared to other state-of-the-art methods.
17 WIND ENERGY↗
Scalable Unit Commitment with Security Constrained AC Power Flow via ADMM and Hybrid Modeling Strategies
This research introduces a more efficient way to optimize power grid operations, breaking the problem into manageable steps and using advanced mathematical techniques to speed up calculations. By incorporating smart heuristics, improved preprocessing, and contingency analysis, the approach allows operators to make better decisions faster. These innovations enhance our understanding of how to optimize energy generation, making it possible to anticipate failures before they happen, reduce system costs, and improve overall grid performance. Ultimately, this research helps bridge the gap between theoretical models and real-world applications, paving the way for a smarter, more resilient power grid. This research directly benefits the public by making electricity more affordable, reliable, and sustainable. By improving how power grids schedule and distribute electricity, the project helps energy providers reduce operational costs, which can lead to lower electricity prices for consumers. Additionally, the ability to predict and prevent power system failures enhances grid reliability, reducing the likelihood of blackouts that can disrupt homes, businesses, and critical infrastructure such as hospitals. From an environmental perspective, optimizing power generation reduces energy waste and lowers carbon emissions, contributing to cleaner air and a more sustainable energy system. Furthermore, with extreme weather events becoming more frequent, these advancements make the power grid more resilient, ensuring communities are better prepared for emergencies and natural disasters. By strengthening the nation's energy infrastructure, this research plays a crucial role in improving economic stability, public safety, and environmental sustainability.
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Design and analysis of a wake model for spatially heterogeneous flow
Abstract. Methods of turbine wake modeling are being developed to more accurately account for spatially variant atmospheric conditions within wind farms. Most current wake modeling utilities are designed to apply a uniform flow field to the entire domain of a wind farm. When this method is used, the accuracy of power prediction and wind farm controls can be compromised depending on the flow-field characteristics of a particular area. In an effort to improve strategies of wind farm wake modeling and power prediction, FLOw Redirection and Induction in Steady State (FLORIS) was developed to implement sophisticated methods of atmospheric characterization and power output calculation. In this paper, we describe an adapted FLORIS model that features spatial heterogeneity in flow-field characterization. This model approximates an observed flow field by interpolating from a set of atmospheric measurements that represent local weather conditions. The objective of this method is to capture heterogeneous atmospheric effects caused by site-specific terrain features, without explicitly modeling the geometry of the wind farm terrain. The implemented adaptations were validated by comparing the simulated power predictions generated from FLORIS to the actual recorded wind farm output from the supervisory control and data acquisition (SCADA) recordings and large eddy simulations (LESs). When comparing the performance of the proposed heterogeneous model to homogeneous FLORIS simulations, the results show a 14.6 % decrease for mean absolute error (MAE) in wind farm power output predictions for cases using wind farm SCADA data and a 18.9 % decrease in LES case studies. The results of these studies also indicate that the efficacy of the proposed modeling techniques may vary with differing site-specific operational conditions. This work quantifies the accuracy of wind plant power predictions under heterogeneous flow conditions and establishes best practices for atmospheric surveying for wake modeling.
17 WIND ENERGY↗
Probabilistic Power Flow Based on a Gaussian Process Emulator
In this letter, a novel Gaussian process emulator is proposed, for the first time, to conduct the probabilistic power-flow calculation. Based on Bayesian inference, a Gaussian process emulator is trained and served as a nonparametric, reduced-order model of the nonlinear power-flow model. This emulator has allowed us to evaluate the time-consuming power-flow solver at the sampled values with a negligible computational cost. The simulations reveal the excellent performance of this method.
42 ENGINEERING↗
AC Power Flow Based DLMP Calculation and Decomposition Method to Smooth Power Fluctuation of Distributed Renewable Energy Sources
As the penetration of renewable energy sources increases, the growing renewable power variability brings ramping issues to power systems. Meanwhile, the development of distributed energy resources (DERs) makes the distribution systems to provide both energy and ancillary services. To incentivise individual resources and customers to alleviate ramping issues on the demand side, a two-stage distribution locational marginal price (DLMP) calculation and decomposition method is developed to formulate the marginal power ramping price for DERs. In the first stage of the proposed method, a distribution system operator market scheduling model based on AC optimal power flow is designed to estimate the optimal operating point of the distribution system. Subsequently, the voltage and power flow constraints are linearised in stage two to calculate DLMP. Finally, based on the Lagrange function and sensitivity factors, DLMP is decomposed to the marginal costs for active/reactive power, voltage management, power loss and power variability. Case studies demonstrate that the proposed model can effectively smooth the power fluctuation and reduce the ramping flexibility requirements of distribution systems.
AC optimal power flow↗
An Optimal Neighborhood Energy Sharing Scheme Applied to Islanded DC Microgrids for Cooperative Rural Electrification
Not Available
24 POWER TRANSMISSION AND DISTRIBUTION↗
Distributionally Robust Bilevel Optimization Model for Distribution Network With Demand Response Under Uncertain Renewables Using Wasserstein Metrics
Here, we consider a distribution network integrating demand response (DR) participants in the presence of uncertain renewable suppliers and outdoor temperatures. A bilevel optimization model is proposed to capture the intricate dynamics between price-incentivized DR participants and distribution system operations, including energy procurement and active/reactive power flows. The model is formulated as a distributional robust bilevel optimization using Wasserstein metrics. We show favorable data-driven properties including out-of-sample guarantee and asymptotic consistency. Furthermore, we present a tractable mixed-integer linear programming reformulation and characterize the worst-case distribution. Computational experiments are conducted on a modified 33-bus system. Our findings underscore the efficacy of the pricing strategies derived from the proposed bilevel optimization model. These strategies not only effectively manage DR participants' behavior but also bring equity considerations among households with various characteristics to light. The results contribute to a deeper understanding of the interplay between distribution system operators and DR participants.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Hybrid-RL-MPC4CLR (Hybird-Reinforcement-Learning-Model-Predictive-Control-for-Reserve-Policy-Assisted-Critical-Load-Restoration-in-Distribution-Grids)
Hybrid-RL-MPC4CLR was developed as a hybrid controller for active distribution grid critical load restoration, combining deep reinforcement learning (RL) and model predictive control (MPC) aiming at maximizing total restored load following an extreme event. The RL determines a policy for quantifying operating reserve requirements, thereby hedging against uncertainty, while the MPC models grid operations incorporating the RL policy actions (i.e., reserve requirements), renewable (wind and solar) power predictions, and load demand forecasts. The developers formulated the reserve requirement determination problem as a sequential decision-making problem based on the Markov Decision Process (MDP) and design an RL learning environment based on the OpenAI Gym framework and MPC simulation. The RL agent reward and MPC objective function aim to maximize and monotonically increase total restored load and minimize load shedding and renewable power curtailment. The software is developed using various software packages in Python. The MPC's optimal power flow (OPF) model is implemented using the Pyomo package, the RL simulation environment is implemented using the MPC simulation with various scenarios of renewable energy and load demand profiles and power outage beginning times, based on the OpenAI Gym framework. The RL agent training is performed using the RLlib Ray package. The RL algorithm is trained offline using historical forecasts of renewable generation and load demand profiles. Simulation analysis and performance tests are conducted using a modified IEEE 13-bus distribution test feeder containing wind turbine, photovoltaic, microturbine, and battery.
Eseye, Abinet Tesfaye↗
Computational Algorithms for Unit Commitment with AC Power Flows (Final Report)
Security-constrained unit commitment (SCUC) is a key component in power system operations. When AC power flow constraints are considered in the SCUC model (AC-SCUC), the problem becomes extremely difficult due to its discrete and non-convex nature, as described in “Grid Optimization Competition Challenge 3 Problem Formulation (GOCC)”. There are four main challenges: (i) Discrete decisions regarding unit online/offline status and start-up/shut-down procedures for every single unit. The number of discrete decision variables increases considerably when a system integrates multiple generators; (ii) Configuration-based combined-cycle formulations, and multi-commodity models that include ramping products, spin/non-spin products, and regulation up/down products. The combined-cycle units introduce additional discrete decision variables and auxiliary service products further complicate the model by connecting multi-commodity products’ continuous and discrete variables; (iii) SCUC models with AC power flow constraints are far more complex due to massive bilinear terms in the large-scale nonlinear power balance equations. The nonlinear power balance equations are further complicated by the discrete step control variables of shunts; (iv) N − 1 contingency analysis. The size of the model increases linearly with the number of contingencies considered, greatly increasing the size of the optimization model. Accordingly, there is an emergent need to develop a robust algorithm capable of deriving a high-quality solution in a short time and passing through contingency tests simultaneously. In this project, we explore innovative techniques to address this challenging problem by integrating advanced polyhedral theory, approximation methods, relaxation strategies, decomposition techniques, and parallel computing. Each technique approaches the problem from a different perspective, leveraging its specific strengths to tackle distinct challenges. Each individual method has demonstrated its effectiveness in the PI’s previous research. Their integration is expected to significantly reduce the computational time required to solve the proposed complex problem. Successful completion of this project has the potential to transform the industry by enhancing optimization solvers capable of handling large-scale day-ahead energy market clearing models within strict time constraints, while incorporating AC power flow constraints. This advancement will lead to reduced overall generation costs and, consequently, increased social welfare.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Linear Approximation Line Pack Model for Integrated Electricity and Natural Gas Systems OPF
With the increasing installation of renewable energy electricity generation capacity, the penetration of natural gas fired generation is also substantailly increasing in power systems due to their fast response capability to mitigate system variability and uncertainty. The dependencies between the electricity system and the natural gas system are becoming more important to maintain the reliability of both systems. In integrated electricity and natural gas systems (IEGSs) operations, the nonlinearity of the natural gas system brings challenges to the system operators. In this paper, the IEGSs optimal power flow (OPF) model is proposed that includes the line pack of the gas system via linear approximation. The simulation results demonstrate that the proposed model can obtain optimal solutions efficiently that are comparable in accuracy as the nonlinear line pack model.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Modeling a divertor with mid-leg pumping for high-power H-mode scenarios in DIII-D considering E x B drift flows
Edge-plasma simulations of a baffled, long-legged divertor in DIII-D, performed using the multi-fluid code UEDGE, indicate that the position of the detachment front is constrained to the location of the pump duct along the low-field side (LFS) baffle. Simulations including magnetic and E x B drifts were performed for 12.5 MW deuterium plasmas including intrinsic carbon and seeded neon to assess the optimal location of the LFS divertor pump to create a stable detachment front between the target and the X-point. The radiation front position in the simulations, taken to be indicative of the detachment front, can be controlled between the pump and X-point in the favorable magnetic field direction for H-mode access by moving the pump duct location upstream of the target along the LFS baffle. In the unfavorable magnetic field direction, the radial E θ x B drift flows are directed towards the pumping surface, efficiently removing the injected deuterium gas and limiting the sensitivity of the radiation front location to the gas injection rate. The role of pumping rate and drift direction on the pumping efficiency are also found to affect the divertor plasma conditions and detachment front location in UEDGE simulations.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A Modular Optimal Power Flow Method for Integrating New Technologies in Distribution Grids
This work proposes a modular concept to build optimal power flow (OPF) models for distribution networks containing various emerging technologies under diverse ownership structures, to efficiently deal with evolving technology capabilities and information sharing or privacy constraints. This concept will support any typical OPF application (e.g., optimal dispatch of a given asset without violating grid constraints) by coordinating between grid module and technology module without the need to recreate various modeling elements as technology capability changes due to innovation. Moreover, the modularity of the proposed concept enables achieving system level objectives without sharing detailed information on module level objectives and constraints among modules. To achieve this, the proposed work develops a gradient-descent algorithm which builds upon the literature on the state-of-the-art power flow approximation. The proposed concept is demonstrated with two case studies of i) controllable loads and ii) battery energy storage system (BESS) on an actual large-scale distribution grid.
Hanif, Sarmad↗
An Interior-Point Solver for Optimal Power Flow Problem Considering Distributed FACTS Devices
In this paper, we propose an AC optimal power flow (ACOPF) model considering distributed flexible AC transmission system (D-FACTS) devices, in which the reactance of D-FACTS equipped lines are introduced as decision variables. This is motivated by increasing interests in using D-FACTS devices to address system operational and cyber-security concerns. First, D-FACTS devices can be incorporated in real-time operations for economic benefits such as managing power congestions and reducing system losses. Second, D-FACTS devices can be utilized by moving target defense (MTD), an emerging concept against cyber-attacks, to prevent attackers from knowing true system configurations. Therefore, system operators can use the proposed ACOPF model to achieve economic benefits and provide the setpoints of D-FACTS devices for MTD at the same time. In addition, we rigorously derive the gradient and Hessian matrices of the objective function and constraints, which are further used to build an interior-point solver of the proposed ACOPF. Numerical results on the IEEE 118-bus transmission system show the validity of the proposed ACOPF model as well as the efficacy of the interior-point solver in minimizing system losses and generation costs.
Liu, Bo↗
Analysis of Electricity Price Differentials for the Utah Office of Energy Development
Operation Gigawatt is a vision for Utah to meet its growing energy needs with a focus on doubling energy generation. One of the greatest challenges to meet this goal will be the transmission and distribution system. Utah seeks analysis to inform discussions on new generation, the likely network congestion based on new power flows, and modeling of the state's energy infrastructure. To support this need, LBNL developed a baseline understanding of recent historical congestion in the existing transmission system based on electricity market prices. The resulting products visualize and provide metrics on congestion within Utah and between Utah and its neighbors during 2015-2023.
24 POWER TRANSMISSION AND DISTRIBUTION↗
MPC4CLR (Model-Predictive-Control-for-Critical-Load-Restoration-in-Power-Distribution-Systems) [SWR-22-24]
Model predictive control (MPC) is a system or process control technique for making decisions under uncertainty via rolling look-ahead optimizations at each control step where only the current step decisions are applied, and the rest are discarded. In this work, we developed an MPC for a critical load restoration (CLR) in power distribution systems to recover system service (electricity delivery) following an extreme event-triggered substation outage. The method considers the problem of controlling distributed energy resources (DERs) of the distribution system with the objective of achieving maximum load pick up while satisfying distribution network flow and voltage constraints. A linearized optimal power flow (OPF) model is employed to represent the physics of the network. The problem formulation is augmented with a ramping (up) reserve product for the DERs to ensure improved and upward monotonic load restoration as time evolves. Simulation analysis and performance tests are performed using a modified IEEE 13-bus test feeder integrated with wind, solar, microturbine, and energy storage battery. The software is developed using various software packages in Julia and Python. The MPC model is implemented using the JuMP optimization language in Julia while the data analytics including renewable generation and load demand forecasts, running the MPC simulation and visualizations is performed in Python.
Eseye, Abinet Tesfaye↗
An Integrated High-performance Computing and Digital Real-time Simulation Testbed to Benchmark Closed-loop Load Shedding Algorithms in Power Systems
An integrated testbed using digital real-time simulator (DRTS) and a high-performance computing (HPC) cluster is presented here to compare speed and performance of computational schemes to mitigate time-critical issues in electric power systems. The first approach in this testbed validation is taken by running a set of closed-loop load shedding algorithms to compare and contrast two paradigms of arresting cascading failure propagation. Two algorithms involve solving DC and AC power flow model-based optimization problems to compute load shedding at different buses, while a model-based stochastic search using parallel computing provides a viable alternative. The algorithms are implemented in the DRTS-HPC testbed for the IEEE 14-bus benchmark transmission system. As a proof of the concept, simulation results are presented for implementation of closed-loop load-shedding algorithms for cascading failures in the DRTS-HPC testbed
24 POWER TRANSMISSION AND DISTRIBUTION↗