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DOE OSTI2023

Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy *

Abstract Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane n e , s e p O M P and the electron temperature at the outer divertor T e , s e p d i v . Note that T e , s e p d i v is not necessarily the peak value of T e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in T e , s e p d i v , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in n e , s e p O M P and 5%–10% in T e , s e p d i v for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in n e , s e p O M P using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Non-linear Model Predictive Control of Wave Energy Converters with Realistic Power Take-off Configurations and Loss Model

Model Predictive Control (MPC) has been recognized as a well-developed control strategy for optimizing the performance of wave energy converters (WECs). The standard problem involves maximizing the absorbed power from oncoming waves while respecting motion constraints of the device and force constraints of the power take-off (PTO). The generated electrical power is then calculated by assuming an ideal PTO with no power conversion losses or limitations to power flow. In this article, we remove the assumption of an ideal PTO and present four different control options that reflect unique combinations of PTO control and power flow constraints. We also recast the MPC problem to maximize the generated power instead of the absorbed power by accounting for the losses in the power train. Using a WEC with a hydraulic PTO, we develop a loss model suitable for controls optimization. Lastly, we illustrate the process of setting up the non-linear MPC problem and compare the performance of competing control strategies using a common benchmark based on annual energy captured at a reference site.

16 TIDAL AND WAVE POWER↗

DOE OSTI2022

Development and assessment of a model predictive controller enabling anticipatory control strategies for a heat-pipe system

To support the reliable and resilient operation of modular reactors and microreactors, anticipatory control strategies have been proposed for achieving faster-than-real-time predictions and decision-making capabilities in anticipation of potential anomalies, including setpoint changes and cyber incidents. Here this work presents how anticipatory control strategies can be implemented via model predictive control (MPC) of a single heat pipe’s temperature. Considering the uncertainty in developing and applying MPC, this work evaluates MPC performance given three different model forms: a linear response surface model, an artificial neural network (ANN), and an autoregressive model with exogenous input (ARX). This work also evaluates the impacts of different input biases and variance on MPC performance in order to account for potential sensor reading variations due to cyber incidents. We observe that nonparametric models such as the ANN and ARX result in more fluctuated control actions compared to the MPC applied to the linear response surface model. However, when the cyber incidents are of a large magnitude, the linear response surface model produces smaller feasible regions than the nonparametric models under identical constraints.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Transient Efficiency Flexibility and Reliability Optimization of Coal-Fired Power Plants: Model-Predictive Control Library Development (Report)

This document pertains to the reporting requirements of DOE contract FE-0031767. The document covers the development of a model predictive control (MPC) library for implementing MPC for a general dynamic system. The library is implemented in a standardized manner in Matlab/Simulink, where core functions on model prediction, linearization and formulation and solution of a quadratic programming (QP) optimization problem is done in the core library - independent of the specific application. The user can provide the application-specific dynamic model in continuous and discrete time, to rapidly implement and test the MPC performance in a desktop simulation. The MPC optimization objective and constraints are also easily configured via an Excel file to allow iterative refinement as needed. Finally, the MPC library enables a rapid deployment to a target environment through auto C-code generation and containerization. The MPC library works seamlessly with the model based estimation (MBE) library to obtain the overall output feedback control solution. In this program, the reduced order model (ROM) of a coal-fired power plant (CFPP) is used to implement and test the MPC solution.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2021

A comparison of efficiency-aware model-predictive control approaches for wave energy devices

In this study, we compare four different formulations of model predictive control that attempt to maximise electrical power generated by a wave energy converter (WEC). Control laws include (1) pure maximisation of mechanical power, (2) maximisation of mechanical power with a control penalty factor, (3) maximisation of electrical power using power conversion efficiency, and (4) maximisation of electrical power using the full electro-mechanical model of a system. For this study, a wave-to-wire model is developed for a floating spherical buoy connected to a permanent magnet synchronous generator. The performance of the controllers, including the mechanical and electrical power outputs, is compared in irregular wave conditions for the unconstrained and force-constrained scenarios. The results demonstrate that the controller designed to maximise mechanical power is not suitable for practical applications and may lead to negative electrical power output due to the non-ideal power take-off efficiency. Moreover, the replacement of the power take-off dynamics by the efficiency coefficient does not guarantee the maximum electrical power production.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

Stochastic Model Predictive Control With Gaussian Wind Direction Preview for Wake Steering

This article addresses the problem of wake steering control for wind farms that explicitly consider the tradeoff between farm-level power generation and yaw duty cycle under variable and uncertain wind conditions. A novel stochastic model predictive control (MPC) algorithm is presented, which utilizes a stochastic model of the freestream wind field components in a receding horizon framework to compute optimal yaw set points that maximize the expected value of the farm power while constraining the yaw actuation. Different configurations of the algorithm are evaluated using a steady-state wind farm simulator. The proposed stochastic MPC algorithm can plan control actions over a future prediction horizon based on probabilistic estimates of the incoming wind magnitude and direction.

17 WIND ENERGY↗

DOE OSTI2022

Model Predictive Control of Discrete-Continuous Energy Systems via Generalized Disjunctive Programming

Generalized Disjunctive Programming (GDP) provides an alternative framework to model optimization problems with both discrete and continuous variables. The key idea behind GDP involves the use of logical disjunctions to represent discrete decisions in the continuous space, and logical propositions to denote algebraic constraints in the discrete space. Compared to traditional mixed-integer programming (MIP), the inherent logic structure in GDP yields tighter relaxations that are exploited by global branch and bound algorithms to improve solution quality. In this paper, we present a general GDP model for optimal control of hybrid systems that exhibit both discrete and continuous dynamics. Specifically, we use GDP to formulate a model predictive control (MPC) model for piecewise-affine systems with implicit switching logic. As an example, the GDP-based MPC approach is used as a supervisory control to improve energy efficiency in residential buildings with binary on/off, relay-based thermostats. A simulation study is used to demonstrate the validity of the proposed approach, and the improved solution quality compared to existing MIPbased control approaches.

Bhattacharya, Arnab↗

DOE OSTI2019

Model Predictive Control of GTAW Weld Pool Penetration

Weld pool penetration is a major implication of weld integrity but it is not directly measurable. The key to solving this issue is to find or create observable phenomena that can be used to derive the penetration. An innovative method has recently been proposed/developed to derive the penetration from the reflection of projected laser from an oscillating weld pool surface. Yet, in addition to the penetration, the oscillation, thus the reflection determined by it, also depends on the pulse amplitude of the current, which needs to be adjusted as the control variable to feedback control the penetration as the output. This dependence imposes a constraint on the control algorithm such that the adjustment of the control variable must be relatively slow to minimize additional sources that affect the oscillation/sensor. This restriction on the control variable adjustment also brings challenges to the identification of the dynamic model of the weld process to be controlled, which has to apply a varying control signal to stimulate the dynamics. To solve these issues, this letter proposes using a low order model to catch the dominant dynamics such that a high speed variation in the control signal can be avoided when choosing the model predictive control algorithm. This allows use of relatively poor models to determine the adjustment on the pulsing amplitude, and still achieves relatively accurate control. Experimental results verified the effectiveness of the resultant penetration control system despite the restrictions imposed by the penetration sensor, which affect the identification of high order dynamics and free adjustments of control variables.

42 ENGINEERING↗

DOE OSTI2020

A Generic Multivector Model Predictive Control With Symmetric Pulse Pattern for Hybrid Multilevel Converters

This article presents a generic multivector model predictive control (MV-MPC) method that has the potential to be applied to all hybrid multilevel converters (HMCs). It first locates the reference voltage vector in the 120° oblique coordinate to select the three adjacent voltage vectors to be applied over one control cycle. Then, the current tracking is guaranteed through duty cycle optimization and dc capacitor voltages are balanced by evaluating possible switching sequences that belong to the voltage vectors with optimal duty cycles. At last, the optimal switching sequence with a symmetric five- or seven-segment pulse pattern is generated using an external modulator. Here, the proposed generic MV-MPC can significantly improve the quality of the output current, while achieving a constant equivalent switching frequency at the same time. Experimental studies on an all silicon carbide HMC prototype, i.e., an active neutral point clamped converter with cascaded H-bridge, are presented to validate the effectiveness of the proposed MV-MPC strategy.

42 ENGINEERING↗

DOE OSTI2019

Coordinated Model Predictive Control on Multi-Lane Roads

There are significant economic, environmental, energy, and other societal costs incurred by the road transportation sector. With the advent and penetration of connected and autonomous vehicles there are vast opportunities to optimize the control of individual vehicles for reducing energy consumption and increasing traffic flow. Model predictive control is a useful tool to achieve such goals, while accommodating ego-centric objectives typical of heterogeneous traffic and explicitly enforcing collision and other constraints. In this paper, we describe a multi-agent distributed maneuver planning and lane selection model predictive controller that includes an information sharing and coordination scheme. The energy saving potential of the proposed coordination scheme is then evaluated via large scale microscopic traffic simulations considering different penetration levels of connected and automated vehicles.

Goulet, Nathan↗

DOE OSTI2022

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↗

DOE OSTI2016

Model Predictive Control of the Exit Part Temperature for an Austenitization Furnace

Quench hardening is the process of strengthening and hardening ferrous metals and alloys by heating the material to a specific temperature to form austenite (austenitization), followed by rapid cooling (quenching) in water, brine or oil to introduce a hardened phase called martensite. The material is then often tempered to increase toughness, as it may decrease from the quench hardening process. The austenitization process is highly energy-intensive and many of the industrial austenitization furnaces were built and equipped prior to the advent of advanced control strategies and thus use large, sub-optimal amounts of energy. The model computes the energy usage of the furnace and the part temperature profile as a function of time and position within the furnace under temperature feedback control. In this paper, the aforementioned model is used to simulate the furnace for a batch of forty parts under heuristic temperature set points suggested by the operators of the plant. A model predictive control (MPC) system is then developed and deployed to control the the part temperature at the furnace exit thereby preventing the parts from overheating. An energy efficiency gain of 5.3% was obtained under model predictive control compared to operation under heuristic temperature set points tracked by a regulatory control layer.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Adaptive Data-Driven Model Predictive Control for Heat Pipe Microreactors

To establish a technical basis for self-regulating microreactors, a model predictive control (MPC) system is investigated to proactively respond to anomalies and disturbances in anticipation of potential deviations from operating setpoints. Due to the difficulty of developing a physics-based surrogate model that can accurately match plant data in various operating conditions, machine learning algorithms are used in MPC, which allow for learning from both simulation and operation data, thus efficiently describing the targeted transient with arbitrary accuracy. However, one of the biggest concerns in applying ML algorithms like artificial neural networks (ANNs) is that the predictive capabilities of ANN are limited by training data. If there are gaps between the training and target domain, the accuracy of an ANN can degrade significantly when it is used to predict unseen data. To improve the predictive capability of ANN and enable a confident use of data-driven MPCs outside the training data, this study proposes an adaptive data-driven MPC framework. The system will monitor the discrepancy between plant responses and surrogate predictions, fine-tune the ANN-based surrogate when a large discrepancy is detected, and continue MPC operation with updated surrogates. The framework is demonstrated on a point kinetic model for microreactors. The hyperparameters of the update strategy, including layers to update, error thresholds, learning rate discount, and number of data points used for fine-tuning, are optimized so the simulated microreactor is able to follow changes in setpoint with the smallest of deviations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Adaptable Data Driven Model Predictive Control for Heat Pipe Microreactors

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

An Average Model Predictive Control of Quasi-Z-Source Modular Cascaded Photovoltaic Converter

An average model predictive control (AMPC) is proposed for dc grid integration of the front-end isolated quasi-Z-source modular cascaded converter (qZS-MCC) photovoltaic (PV) power system. The qZS-MCC deals with PV maximum power point tracking (MPPT), dc grid integration, and de-link voltage balance by the post-stage qZS half-bridge (HB) dc-dc converters, while a unified duty cycle is used in the front-end isolation converters of all submodules (SMs). Thus, it reduces the control resources while overcoming the dc-bus voltage limit because of the PV panel insulation demand. The proposed AMPC of qZS-MCC PV power system predicts the shoot-through duty cycle of each SM for dc-link voltage control, and the total modulation index for dc grid-connected current control; only one proportional-integral (PI) regulator for PV MPPT is required in each SM. Thus, PI regulators are significantly reduced, whereas system dynamic responses are improved, with low computation and simple implementation. Simulation and downscaled experimental results demonstrate the effectiveness of the proposed control.

Liu, Yushan↗

DOE OSTI2022

A machine learning approach for clinker quality prediction and nonlinear model predictive control design for a rotary cement kiln

Abstract Cement manufacturing is energy‐intensive (5Gj/t) and comprises a significant portion of the energy footprint of concrete systems. Incorporating modern monitoring, simulation and control systems will allow lower energy use, lower environmental impact, and lower costs of this widely used construction material. One of the goals of the CESMII roadmap project on the Smart Manufacturing of Cement included developing an analytical process model for clinker quality that includes the chemistry of the kiln feed and accounts for critical process variables. This predictive model will be used in nonlinear model predictive control system designed to significantly reduce process energy use while maintaining or improving product quality. In the cement manufacturing plant used in this study, the kiln feed (meal) is tested every 12 h and used to estimate the mineral composition of the cement kiln output (clinker) using the stoichiometry‐based Bogue's model and the expertise of the plant operators. During kiln operation, kiln output (clinker) is sampled and tested every 2 h to measure its chemical and mineral composition. The predicted and measured values of the clinker composition are used by the plant operators to adjust the kiln input stream and the production process characteristics to maintain stable operation and uniform product quality. However, the time delay between prediction and testing, along with inaccuracies inherent in the Bogue's model have made any process changes designed to minimize energy use problematic, especially in‐light of potential clinker quality issues that process changes often pose. A new analytical model that integrates quality information and process operation information has been developed from data collected from 2 years of production from an operating cement facility. To make the model fuel‐type‐independent, consumed heat energy was computed in the model instead of fuel type and amount. A Feedforward Network was trained and tailored from collected data. Many data‐based simulations were conducted to quantitatively evaluate the proposed model and the 5‐fold cross‐validation procedure was used to test the models. The resulting predictive model was shown to have a low root mean square error (MSE) with respect to the estimated clinker mineral composition compared to that using the industry standard “Bogue’ model”. The end goal of this work was to develop a single machine learning tool that allows the use of quality control data and process control variables to improve energy efficiency of the process in a continuous fashion. The proposed nonlinear model predictive control system (NMPC) can generate predicted kiln production characteristics based on manipulated variables in manner that accurately follows the target product quality values. Simulation results also show that the proposed model produced accurate predictions of kiln outputs that fell within the required constraints, while manipulating control variables within typical operational ranges.

Ali, Asem M.↗

DOE OSTI2020

Model predictive control of KSTAR equilibrium parameters enabled by TRANSP

Due to the complex behavior of tokamak plasmas and the importance of optimizing performance while avoiding instabilities and machine limits, plasma control algorithms are becoming increasingly dependent on sophisticated model-based control approaches. It is anticipated that the use of integrated modeling codes in the model-based control design process will reduce the amount of experimental time needed to implement new control algorithms by facilitating development of control-oriented models and enabling higher-fidelity closed-loop simulations. In this work, a reduced model is developed from a series of TRANSP simulations and is used to develop a model predictive control (MPC) algorithm for controlling important equilibrium parameters in KSTAR [1] discharges. The control algorithm uses the KSTAR neutral beam injection system and the target plasma current and plasma boundary as actuators, and optimizes the plasma stored energy, loop voltage, and internal inductance while avoiding constraints that could lead to disruptions. Higher fidelity testing of the control algorithm is performed using a flexible framework for enabling external processes to actively control plasma parameters in TRANSP simulations. Furthermore, closed-loop simulations demonstrate the ability of the control algorithm to respond to disturbances in density and confinement, handle actuator failures, and move the discharge to high non-inductive fraction conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Limits on the Range and Rate of Change in Power Take-Off Load in Ocean Wave Energy Conversion: A Study Using Model Predictive Control

Previous work comparing power take-off (PTO) architectures for ocean wave-powered reverse osmosis suggests that variable displacement in the wave energy converter (WEC)-driven pump does not offer a significant performance advantage. A limitation of that study is that the WEC was subject to a constant load within a given sea state (“Coulomb damping”) and did not account for controlled, moment-to-moment variation of the PTO load enabled by a variable displacement pump. This study explores the potential performance advantage of a variable PTO load over Coulomb damping. Model predictive control is used to provide optimal load control with constraints on the PTO load. The constraints include minimum and maximum loads and a limit on the rate of load adjustment. Parameter studies on these constraints enable conclusions about PTO design requirements in addition to providing an estimated performance advantage over Coulomb damping. Numerical simulation of the Oyster 1 WEC is carried out with performance weighted by historical sea state data from Humboldt Bay, CA. The results show a performance advantage of up to 20% higher yearly-average power absorption over Coulomb damping. Additionally, the parameter studies suggest that the PTO load should be adjustable down to at least 25% of the maximum load and should be adjustable between the minimum and maximum loads within a few seconds.

16 TIDAL AND WAVE POWER↗