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DOE OSTI2020

Stochastic DC optimal power flow with reserve saturation

We propose an optimization framework for stochastic optimal power flow with uncertain loads and renewable generator capacity. Our model follows previous work in assuming that generator outputs respond to load imbalances according to an affine control policy, but introduces a model of saturation of generator reserves by assuming that when a generator’s target level hits its limit, it abandons the affine policy and produces at that limit. This is a particularly interesting feature in models where wind power plants, which have uncertain upper generation limits, are scheduled to provide reserves to balance load fluctuations. Here, the resulting model is a nonsmooth nonconvex two-stage stochastic program, and we use a stochastic approximation method to find stationary solutions to a smooth approximation. Computational results on 6-bus and 118-bus test instances demonstrate that by considering the effects of saturation, our model can yield solutions with lower expected generation costs (at the same target line violation probability level) than those obtained from a model that enforces the affine policy to stay within generator limits with high probability.

17 WIND ENERGY↗

DOE OSTI2021

The impacts of convex piecewise linear cost formulations on AC optimal power flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. Furthermore, these results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, an important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2020

Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow

We develop, in this paper, a machine learning approach to optimize the real-time operation of electric power grids. In particular, we learn feasible solutions to the AC optimal power flow (OPF) problem with negligible optimality gaps. The AC OPF problem aims at identifying optimal operational conditions of the power grids that minimize power losses and/or generation costs. Due to the computational challenges with solving this nonconvex problem, many efforts have focused on linearizing or approximating the problem in order to solve the AC OPF on faster timescales. However, many of these approximations can be fairly poor representations of the actual system state and still require solving an optimization problem, which can be time consuming for large networks. In this work, we learn a mapping between the system loading and optimal generation values, enabling us to find near-optimal and feasible AC OPF solutions. This allows us to bypass solving the traditionally nonconvex AC OPF problem, resulting in a significant decrease in computational burden for grid operators.

machine learning↗

DOE OSTI2021

A learning-augmented approach for AC optimal power flow

Because of the high nonlinearity of AC optimal power flow (OPF), numerous efforts have been made in recent decades to find efficient methods. Machine learning (ML) has proven to significantly reduce the computational costs in many real-world problems. Thus, this paper develops a learning-augmented method for solving AC OPF, which integrates both power network equations and ML to yield near-optimal solutions. More specifically, ML models are developed to first predict bus voltage magnitudes and angles. Then, physics-based network equations are employed to calculate the power injection at different buses. Three ML algorithms, i.e., random forest, multi-target decision tree, and extreme learning machine, are explored and compared. To evaluate the efficiency of the proposed learning-augmented AC OPF solver, the MATPOWER Interior Point Solver is adopted as a baseline. Case studies on both 500-bus and 4918-bus test networks show that the proposed learning-augmented method has reduced the computational time by 15–100 times depending on the network size with a minimal loss in optimality.

42 ENGINEERING↗

DOE OSTI2020

Solving Optimal Power Flow for Distribution Networks with State Estimation Feedback

Conventional optimal power flow (OPF) solvers assume full observability of the involved system states. However in practice, there is a lack of reliable system monitoring devices in the distribution networks. To close the gap between the theoretic algorithm design and practical implementation, this work proposes to solve the OPF problems based on the state estimation (SE) feedback for the distribution networks where only a part of the involved system states are physically measured. The SE feedback increases the observability of the under-measured system and provides more accurate system states monitoring when the measurements are noisy. We analytically investigate the convergence of the proposed algorithm. The numerical results demonstrate that the proposed approach is more robust to large pseudo measurement variability and inherent sensor noise in comparison to the other frameworks without SE feedback.

distirbution systems↗

DOE OSTI2023

Linearized Distribution Optimal Power Flow for OEDI SI

This research is to meant to demonstrate the OEDI SI use case for distributed optimal power flow (DOPF). The goal was to formulate the optimal power flow problem in the distribution system for active and reactive power setpoints of PV systems using topology information and voltage measurements. The co-simulation runs every 15 minutes as outlined within the scenario file for the given feeder configuration. The linked GitHub repository includes five federates to achieve DOPF for the small, medium, large, and IEEE 123 feeder scenarios. We are using the OEDI SI framework, as well as the example feeder, sensor, recorder, and estimator federates provided in the example repository for OEDI SI. We also provide a runner script for switching between scenarios.

algorithm↗

DOE OSTI2025

Sensitivity-based voltage constraints for optimal power flow in low-voltage distribution feeders

The optimal power flow (OPF) problem for distribution systems can include network details down to the low-voltage (LV) points of interconnection of individual customers. This paper addresses the implementation of voltage magnitude constraints, and sets forth a practicable approach for capturing the effects on voltage from the switching behavior of loads (e.g., heat pumps, air conditioners, water heaters, or pool pumps) and from the variability of renewable generation (e.g., rooftop solar). The proposed method adjusts the OPF voltage constraints based on forecasts of load and generation upper and lower bounds, in conjunction with sensitivity factors derived from the power flow equations. An illustrative OPF formulation is also provided, which incorporates transformer models that include core loss. We demonstrate that accurate modeling of these LV network components is critical to avoid voltage violations at customer points of interconnection. Furthermore, the ideas are validated through numerical case studies on a realistic distribution feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow: Preprint

machine learning↗

DOE OSTI2020

Multi-Level Optimal Power Flow Solver in Large Distribution Networks: Preprint

Solving optimal power flow (OPF) problem for large distribution networks incurs high computational complexity. We consider a large multi-phase distribution networks of tree topology with deep penetration of active devices. We divide the network into collaborating areas featuring subtree topology and subareas featuring subsubtree topology. We design a multi-level implementation of the primal-dual gradient algorithm for solving the voltage regulation OPF problems while preserving nodal voltage information and topological information within areas and subareas. Numerical results on a 4,521-node system verifies that the proposed algorithm can significantly improve computational speed without compromising any optimality.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2020

Model-Free Primal-Dual Methods for Network Optimization with Application to Real-Time Optimal Power Flow: Preprint

This paper examines the problem of real-time optimization of networked systems and develops online algorithms that steer the system towards the optimal trajectory without explicit knowledge of the system model. The problem is modeled as a dynamic optimization problem with time-varying performance objectives and engineering constraints. The design of the algorithms leverages the online zero-order primal-dual projected-gradient method. In particular, the primal step that involves the gradient of the objective function (and hence requires networked systems model) is replaced by its zero-order approximation with two function evaluations using a deterministic perturbation signal. The evaluations are performed using the measurements of the system output, hence giving rise to a feedback interconnection, with the optimization algorithm serving as a feedback controller. The paper provides some insights on the stability and tracking properties of this interconnection. Finally, the paper applies this methodology to a real-time optimal power flow problem in power systems, and shows its efficacy on the IEEE 37-node distribution test feeder for reference power tracking and voltage regulation.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2021

Computational and numerical analysis of AC optimal power flow formulations on large-scale power grids

We report that alternating current optimal power flow (AC-OPF) is a fundamental tool in electric utilities to determine optimal operation of the various resources. Typically, the AC-OPF problem uses power balance formulation containing voltages and power equations. Yet, there is no comprehensive comparison of the different AC-OPF formulations, especially for large-scale networks. This paper presents a detailed comparative evaluation of different formulations of the AC-OPF problem on networks ranging from 9-bus to 25,000 buses. Three different formulations: 1) power balance with polar voltages, 2) power balance with Cartesian voltages, and 3) current balance with Cartesian voltages are discussed in detail by comparing their characteristics, and numerical and computational performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow

With the increasing penetration of distributed energy resources, distributed optimization algorithms have attracted significant attention for power systems applications due to their potential for superior scalability, privacy, and robustness to a single point-of-failure. The Alternating Direction Method of Multipliers (ADMM) is a popular distributed optimization algorithm; however, its convergence performance is highly dependent on the selection of penalty parameters, which are usually chosen heuristically. In this work, we use reinforcement learning (RL) to develop an adaptive penalty parameter selection policy for alternating current optimal power flow (ACOPF) problem solved via ADMM with the goal of minimizing the number of iterations until convergence. We train our RL policy using deep Q-learning and show that this policy can result in significantly accelerated convergence (up to a 59% reduction in the number of iterations compared to existing, curvatureinformed penalty parameter selection methods). Furthermore, we show that our RL policy demonstrates promise for generalizability, performing well under unseen loading schemes as well as under unseen losses of lines and generators (up to a 50% reduction in iterations). This work thus provides a proof-of-concept for using RL for parameter selection in ADMM for power systems applications.

alternating current optimal power flow↗

DOE OSTI2022

Hierarchical Optimal Power Flow with Improved Gradient Evaluation

Existing algorithms to solve alternating-current optimal power flow (AC-OPF) often exploit linear approximations to simplify system models and accelerate computations. In this paper, we improve a recent hierarchical OPF algorithm, which rested on primal-dual gradients evaluated in a linearized distribution power flow model. Specifically, we identify a risk of voltage violation arising from the model linearization, and propose a more accurate gradient evaluation method to eliminate that risk. We further develop a hierarchical primal-dual algorithm to solve OPF based on the proposed gradient evaluation method. Numerical results on IEEE networks show that our algorithm can enhance voltage safety with satisfactory computational efficiency.

distributed algorithm↗

DOE OSTI2020

A Real-Time Optimization with Warm-Start of Multiperiod AC Optimal Power Flows

We present a real-time optimization strategy based on warm-start for solving a moving horizon of multi period AC optimal power flow (ACOPF) problems. In each horizon, ACOPFs are temporally interlinked via generator ramp constraints, and we assume that each horizon needs to be solved every few seconds or minutes. We introduce two approximate tracking schemes that closely follow a solution path consisting of strongly regular points. We present theoretical results bounding the tracking error by the square of the parameter changes between time periods. Experimental results for networks of sizes up to 9K buses show a fast computation time while maintaining a good solution quality, thus making our approach well suited for real-time circumstances.

moving horizon↗

DOE OSTI2021

Learning Optimal Power Flow Solutions using Linearized Models in Power Distribution Systems

Solving nonlinear optimal power flow (OPF) problem is computationally expensive, and poses scalability challenges for power distribution networks. An alternative to solving the original nonlinear OPF is the linear approximated OPF models. Although, these linear approximated OPF models are fast, the resulting solutions may result in significant optimality gap. Lately, the application of machine learning (ML) methods in successfully solving the nonlinear OPF has been reported. These methods learn and estimate the nonlinear control policies using a purely data-driven approach. In this paper, we propose an approach to complements the ML based approach to solving OPF using solutions from known linearized OPF model. Specifically, we use supervised learning to map the solutions of linear OPF to nonlinear control variables. Unlike, the traditional ML based methods for OPF that approximate the full distribution feeder model using function approximation, our approach uses a two-node approximation of radial networks. The proposed approach is validated using IEEE 123 bus test system for OPF solutions obtained using the nonlinear OPF models.

optimal power flow, power distribution systems, su↗

DOE OSTI2020

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↗

DOE OSTI2021

Evaluation of AC optimal power flow on graphical processing units

This paper investigates the performance of alternating current optimal power flow (ACOPF) on hardware accelerators such as graphical processing units (GPUs). We describe the strategies employed and the software used to port the ACOPF application to GPU. Through reorganizing the flow of fundamental calculations, restructuring data organization for the GPUs, and using portability libraries, maximum utilization of GPU is attempted. We present details of our efforts with representative results on 200, 500, and 2000-bus networks.

Abhyankar, Shrirang G.↗

DOE OSTI2023

Optimal Power Flow Derived Sparse Linear Solver Benchmarks

Due to the changing nature of the power grid, it is increasingly important to be able to solve a high-fidelity optimal power-flow models on large power networks. This high-fidelity problem, called AC Optimal Power Flow (ACOPF), is a nonlinear, nonconvex optimization problem. One of the few reliable ways of solving such a problem is interior point methods. These methods result in sparse linear systems where the coefficient matrix is symmetric, indefinite and nearly always ill-conditioned. As such, they are particularly challenging for sparse linear solvers and represent a considerable computational bottleneck in solving the ACOPF problem. In this paper, we introduce a repository of linear systems captured from ACOPF problems when solved by the open-source optimizer IPOPT. These matrices are meant to be used as a test suite for sparse linear solver development.

97 MATHEMATICS AND COMPUTING↗