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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Adaptive primal–dual control for distributed energy resource management

With the increased adoption of distributed energy resources (DERs) in distribution networks, their coordinated control with a DER management system (DERMS) that provides grid services (e.g., voltage regulation, virtual power plant) is becoming more necessary. One particular type of DERMS using primal–dual control has recently been found to be very effective at providing multiple grid services among an aggregation of DERs; however, the main parameter, the primal–dual step size, must be manually tuned for the DERMS to be effective, which can take a considerable amount of engineering time and labor. To this end, we design a simple method that self-tunes the step size(s) and adapts it to changing system conditions. Additionally, it gives the DER management operator the ability to prioritize among possibly competing grid services. Here we evaluate the automatic tuning method on a simulation model of a real-world feeder in Colorado with data obtained from an electric utility. Through a variety of scenarios, we demonstrate that the DERMS with automatically and adaptively tuned step sizes provides higher-quality grid services than a DERMS with a manually tuned step size.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Towards constrained grid-forming control

Grid-forming converters are commonly envisioned to replace conventional synchronous generators as the cornerstone of future power systems. However, compared to synchronous generators, power converters and their power sources (e.g., renewable generation, energy storage) are subject to significant physical constraints (e.g., current limits, modulation limits). Grid-forming controls are commonly designed neglecting these constraints and subsequently augmented with limiters for a subset of constraints. In this work, we propose a systematic approach to constrained grid-forming control of two-level voltage source converters interfacing photovoltaics. We first formulate grid-forming control objectives and constraints of voltage source converters and photovoltaics in a one-step optimal grid-forming control problem. Next, we leverage primal-dual dynamics to obtain a dynamic feedback controller that approximates the solution of the one-step optimal grid-forming control problem. Finally, electromagnetic transient simulations are used to illustrate the results.

Gross, Dominic↗

DOE OSTI2022

Learning-Based Demand Response in Grid Interactive Buildings via Gaussian Processes

This paper presents a predictive controller for a grid-interactive multi-zone building where the temperature dynamics are learned via Gaussian Process (GP) regression. We investigate the development of a learning-based predictive control with two main objectives: (i) continuously learn the temperature dynamics of the building based on data; and, (ii) use the learned dynamics to solve a multi-objective predictive control problem to guarantee occupants' comfort and energy efficiency during normal conditions and demand response events. We leverage the probabilistic non-parametric properties of GPs to estimate the (unknown) non-linear temperature dynamics of the building and to incorporate the uncertainty of those predictions in a multi-objective optimization problem. The GP-based predictive control is solved via a zero-order primal-dual projected-gradient algorithm. We evaluate numerically the performance of the proposed controller using a five-zone commercial building.

demand response↗

DOE OSTI2021

Peer-to-Peer Energy Management System for Distributed Microgrid Coordination [SWR-21-92]

Resiliency is one of the key challenges in today's power system. Natural disasters and cyber-attacks both can limit communications between microgrids and the central management system. Thus, having a Distributed Microgrid Coordination (DMC) algorithm can improve the system resiliency, which enables the microgrids to operate without communication with the central management system. Peer-to-Peer Energy Management System for Distributed Microgrid Coordination adopts a primal-dual approach, where each microgrid controller keeps a local estimate of the dual variables. The estimate is updated with local measurements and peer-to-peer communication, leading to a fully distributed algorithm. While the DMC is developed for microgrid coordination, it can be used for general distributed control purpose.

Li, Yashen↗

DOE OSTI2025

Virtual Agents-Based Attack-Resilient Distributed Control for Islanded AC Microgrid

Due to its dependence on a communication network, distributed secondary control of microgrids is susceptible to denial-of-service (DoS) attacks in channel shutdown mode, which may negatively impact the network connectivity and thus deteriorate the coordination and power sharing among distributed generators (DGs). Honeypot is a common method for cyber deception by introducing fake targets. However, in the context of microgrid, the misleading information spread by honeypots will also impact the system performance. This paper proposes an attack-resilient distributed control for AC microgrids utilizing virtual agents (VAs) to counteract both DoS edge and node attacks. The VAs are designed to not impact the system’s steady state during normal operation but to share information among neighboring real agents and serve as dummy targets for DoS attacks. The control with VAs is implemented by a primal-dual gradient based distributed algorithm to efficiently obtain a practical solution for voltage/frequency regulation and power sharing. The simulation results on a 4-DG test system and a modified IEEE 34-bus system show that 1) VAs do not impact the normal functionality of the test system, and 2) deploying VAs can enhance the resilience of the microgrid control against DoS edge and node attacks.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1974

The discrete complementary variational principle and optimal control systems

A discrete complementary variational principle is developed and applied to linear and nonlinear discrete-time optimal control systems. Using the variational approach, a primal-dual relationship is established. This relationship provides a precise measure of system suboptimality independent of any a priori knowledge of the optimal solution.

Chan, W. L.↗

DOE OSTI2022

Online data-enabled predictive control

We develop an online data-enabled predictive (ODeePC) control method for optimal control of unknown systems, building on the recently proposed DeePC (Coulson et al., 2019). Our proposed ODeePC method leverages a primal-dual algorithm with real-time measurement feedback to iteratively compute the corresponding real-time optimal control policy as system conditions change. The proposed ODeePC conceptual-wise resembles standard adaptive system identification and model predictive control (MPC), but it provides a new alternative for the standard methods. ODeePC is enabled by computationally efficient methods that exploit the special structure of the Hankel matrices in the context of DeePC with Fast Fourier Transform (FFT) and primal-dual algorithm We provide theoretical guarantees regarding the asymptotic behavior of ODeePC, and we demonstrate its performance through numerical examples.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Optimal Power Flow With State Estimation in the Loop for Distribution Networks

Here in this article, we propose a framework for running optimal control-estimation synthesis in distribution networks. Our approach combines a primal-dual gradient-based optimal power flow solver with a state estimation feedback loop based on a limited set of sensors for system monitoring, instead of assuming exact knowledge of all states. The estimation algorithm reduces uncertainty on unmeasured grid states based on certain online state measurements and noisy "pseudomeasurements." We analyze the convergence of the proposed algorithm and quantify the statistical estimation errors based on a weighted least-squares estimator. The numerical results on a 4521-node network demonstrate that this approach can scale to extremely large networks and provide robustness to both large pseudomeasurement variability and inherent sensor measurement noise.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Primal-Dual Differentiable Programming for Distribution System Critical Load Restoration: Preprint

Swift and reliable critical load restoration (CLR) can help make a distribution system resilient towards extreme events. To optimally achieve that, alongside practical concerns such as limiting online computational burden, some studies leverage model-free reinforcement learning (RL) to train control policies. Despite the advantages provided by RL algorithms, these approaches suffer from two issues: 1) the lack of a proper mechanism for constraint enforcement, and 2) poor sample efficiency. Therefore, in this paper, a primal-dual differentiable programming (PDDP) method is developed for guiding the training leading to a constraint-satisfying policy. Additionally, the model-based nature of the proposed method aims at improving sample efficiency. The experiment on a CLR problem demonstrates that PDDP can effectively train a control policy that both achieves desirable performance and satisfies required constraints.

differentiable programming↗

DOE OSTI2024

Time-Varying Feedback Optimization for Quadratic Programs with Heterogeneous Gradient Step Sizes

Online feedback-based optimization has become a promising framework for real-time optimization and control of complex engineering systems. This tutorial paper surveys the recent advances in the field as well as provides novel convergence results for primal-dual online algorithms with heterogeneous step sizes for different elements of the gradient. The analysis is performed for quadratic programs and the approach is illustrated on applications for adaptive step-size and model-free online algorithms, in the context of optimal control of modern power systems.

gradient methods↗

DOE OSTI2021

Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation

Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a sub-optimal (but applicationally acceptable) solution with significantly reduced computational effort. We employ an economic Model Predictive Control (MPC) strategy to obtain a feedback control. The MPC sub-problems are based on a linear-quadratic optimal control problem subjected to mixed control and state constraints and a convection-diffusion equation, reduced with proper orthogonal decomposition. Finally, to solve each sub-problem, we apply a primal-dual active set strategy. The method can be fully parallelized, which enables the solution of large problems with real-world parameters.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Performance Evaluation of Peer-to-Peer Distributed Microgrids Coordination for Voltage Regulation

This paper presents the performance evaluation of a peer-to-peer microgrids coordination algorithm for sub-transmission systems. As distributed energy resources (DERs) in distribution system start to show negative impact to the bulk power system, a paradigm shift is needed for transmission planning and operation. Because distribution substations are located far from the sub-transmission system, and it is hard to use traditional centralized control for real-time control and coordination. Thus, distributed control is a natural choice because it requires less communication and central computation. In this paper, each distribution substation is treated as a microgrid, and the peer-to-peer distributed microgrids control is formulated as a real-time optimal power flow problem to reduce the negative impact in sub-transmission systems. A distributed primal-dual optimization algorithm is adopted to solve the problem. Validation of the peer-to-peer algorithm is performed through the simulation of a real-world sub-transmission system composing of many distribution systems with high renewable penetration. Simulation results show that the peer-to-peer algorithm can achieve satisfactory performance (e.g., voltage regulation) in sub-transmission system by coordinating and controlling DERs in distribution systems.

distributed control↗

DOE OSTI2022

Performance Evaluation of Peer-to-Peer Distributed Microgrids Coordination for Voltage Regulation: Preprint

distributed control↗

DOE OSTI2022

On the Convergence of Overlapping Schwarz Decomposition for Nonlinear Optimal Control

Here, we study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all subproblems defined over subdomains in parallel. The convergence is attained by updating primal-dual information at the boundaries of overlapping subdomains. We show that the algorithm exhibits local linear convergence, and that the convergence rate improves exponentially with the overlap size. We also establish global convergence results for a general quadratic programming, which enables the application of the Schwarz scheme inside second-order optimization algorithms (e.g., sequential quadratic programming). The theoretical foundation of our convergence analysis is a sensitivity result of nonlinear OCPs, which we call "exponential decay of sensitivity" (EDS). Intuitively, EDS states that the impact of perturbations at domain boundaries (i.e., initial and terminal time) on the solution decays exponentially as one moves into the domain. Here, we expand a previous analysis available in the literature by showing that EDS holds for both primal and dual solutions of nonlinear OCPs, under uniform second-order sufficient condition, controllability condition, and boundedness condition. We conduct experiments with a quadrotor motion planning problem and a partial differential equations (PDE) control problem to validate our theory, and show that the approach is significantly more efficient than alternating direction method of multipliers and as efficient as the centralized interior-point solver.

42 ENGINEERING↗

DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗

NASA NTRS2007

Implementation of a Point Algorithm for Real-Time Convex Optimization

The primal-dual interior-point algorithm implemented in G-OPT is a relatively new and efficient way of solving convex optimization problems. Given a prescribed level of accuracy, the convergence to the optimal solution is guaranteed in a predetermined, finite number of iterations. G-OPT Version 1.0 is a flight software implementation written in C. Onboard application of the software enables autonomous, real-time guidance and control that explicitly incorporates mission constraints such as control authority (e.g. maximum thrust limits), hazard avoidance, and fuel limitations. This software can be used in planetary landing missions (Mars pinpoint landing and lunar landing), as well as in proximity operations around small celestial bodies (moons, asteroids, and comets). It also can be used in any spacecraft mission for thrust allocation in six-degrees-of-freedom control.

Acikmese, Behcet↗

DOE OSTI2023

Interpreting Primal-Dual Algorithms for Constrained Multiagent Reinforcement Learning: Preprint

We study multiagent reinforcement learning (MARL) with constraints. This setting is gaining importance as MARL algorithms find new applications in real-world systems ranging from power grids to drone swarms. Most constrained MARL (C-MARL) algorithms use a primal-dual approach to enforce constraints through a penalty function added to the reward. In this paper, we study the structural effects of the primal-dual approach on the constraints and value function. First, we show that using the constraint evaluation as the penalty leads to a weak notion of safety, but by making simple modifications to the penalty function, we can enforce meaningful probabilistic safety constraints. Second, we show that the penalty term changes the value function in a way that is easy to model, and demonstrate the consequences of not doing so. We conclude with simulations in a simple constrained multiagent environment to back up the theoretical results.

data-driven control↗

NASA NTRS1995

Modified Interior Distance Functions (Theory and Methods)

In this paper we introduced and developed the theory of Modified Interior Distance Functions (MIDF's). The MIDF is a Classical Lagrangian (CL) for a constrained optimization problem which is equivalent to the initial one and can be obtained from the latter by monotone transformation both the objective function and constraints. In contrast to the Interior Distance Functions (IDF's), which played a fundamental role in Interior Point Methods (IPM's), the MIDF's are defined on an extended feasible set and along with center, have two extra tools, which control the computational process: the barrier parameter and the vector of Lagrange multipliers. The extra tools allow to attach to the MEDF's very important properties of Augmented Lagrangeans. One can consider the MIDFs as Interior Augmented Lagrangeans. It makes MIDF's similar in spirit to Modified Barrier Functions (MBF's), although there is a fundamental difference between them both in theory and methods. Based on MIDF's theory, Modified Center Methods (MCM's) have been developed and analyzed. The MCM's find an unconstrained minimizer in primal space and update the Lagrange multipliers, while both the center and the barrier parameter can be fixed or updated at each step. The MCM's convergence was investigated, and their rate of convergence was estimated. The extension of the feasible set and the special role of the Lagrange multipliers allow to develop MCM's, which produce, in case of nondegenerate constrained optimization, a primal and dual sequences that converge to the primal-dual solutions with linear rate, even when both the center and the barrier parameter are fixed. Moreover, every Lagrange multipliers update shrinks the distance to the primal dual solution by a factor 0 less than gamma less than 1 which can be made as small as one wants by choosing a fixed interior point as a 'center' and a fixed but large enough barrier parameter. The numericai realization of MCM leads to the Newton MCM (NMCM). The approximation for the primal minimizer one finds by Newton Method followed by the Lagrange multipliers update. Due to the MCM convergence, when both the center and the barrier parameter are fixed, the condition of the MDF Hessism and the neighborhood of the primal ninimizer where Newton method is 'well' defined remains stable. It contributes to both the complexity and the numerical stability of the NMCM.

Polyak, Roman A.↗