Michael Baldea

Jiyong Lee, Melody Agustin, Joanne Langsdorf et al.

In this paper, we consider the expansion of power grids under emerging large loads from data centers and electrified manufacturing. We develop a multi-period grid capacity expansion model to determine optimal investment profiles for power generation, storage, and transmission capacity while accounting for hourly power dispatch, such that electricity demand is satisfied and the total planning and operation cost is minimized. We also propose a new modeling approach regarding the spatial distribution of demand from large loads. The model is used to analyze the expansion of a synthetic grid that follows key characteristics of the ERCOT system over a seven-year planning horizon, under loads from data centers and electrified oil refining, which account for 17.5% and 4.7% of total annual electricity demand by the end of the planning horizon. The optimal investment policy leads to an 83.6% increase in generation capacity and exploits the short construction times of solar and storage as well as the operational flexibility of thermal generators. Finally, sensitivity analysis reveals that the construction time of grid assets substantially impacts investment timing, generation technology mix, and transmission capacity expansion. The proposed modeling framework is general and can be extended to other grid systems, enabling the exploration of diverse demand scenarios, policy assumptions, and regional characteristics.

Joshua E. Hammond, Tyler A. Soderstrom, Brian A. Korgel et al.

Data-driven models of dynamical systems require extensive amounts of training data. For many practical applications, gathering sufficient data is not feasible due to cost or safety concerns. This work uses the Subset Extended Kalman Filter (SEKF) to adapt pre-trained neural network models to new, similar systems with limited data available. Experimental validation across damped spring and continuous stirred-tank reactor systems demonstrates that small parameter perturbations to the initial model capture target system dynamics while requiring as little as 1% of original training data. In addition, finetuning requires less computational cost and reduces generalization error.

Calvin Tsay, Michael Baldea

Given their increasing participation in fast-changing markets, the integration of scheduling and control is an important consideration in chemical process operations. This generally involves computing optimal production schedules using dynamic models, which is challenging due to the nonlinearity and high-dimensionality of the models of chemical processes. In this paper, we begin by observing that the intrinsic dimensionality of process dynamics (as relevant to scheduling) is often much lower than the number of model state and/or algebraic variables. We introduce a data mining approach to "learn" closed-loop process dynamics on a low-dimensional, latent manifold. The manifold dimensionality is selected based on a tradeoff between model accuracy and complexity. After projecting process data, system identification and optimal scheduling calculations can be performed in the low-dimensional, latent-variable space. We apply these concepts to schedule an air separation unit under time-varying electricity prices. We show that our approach reduces the computational effort, while offering more detailed dynamic information compared to previous related works.

Joshua E. Hammond, Tyler Soderstrom, Brian A. Korgel et al.

We present the Subset Extended Kalman Filter (SEKF) as a method to update previously trained model weights online rather than retraining or finetuning them when the system a model represents drifts away from the conditions under which it was trained. We identify the parameters to be updated using the gradient of the loss function and use the SEKF to update only these parameters. We compare finetuning and SEKF for online model maintenance in the presence of systemic drift through four dynamic regression case studies and find that the SEKF is able to maintain model accuracy as-well if not better than finetuning while requiring significantly less time per iteration, and less hyperparameter tuning.

Joshua Edward Hammond, Ricardo A. Lara Orozco, Michael Baldea et al.

We report a data-parsimonious machine learning model for short-term forecasting of solar irradiance. The model inputs include sky camera images that are reduced to scalar features to meet data transmission constraints. The output irradiance values are transformed to focus on unknown short-term dynamics. Inspired by control theory, a noise input is used to reflect unmeasured variables and is shown to improve model predictions, often considerably. Five years of data from the NREL Solar Radiation Research Laboratory were used to create three rolling train-validate sets and determine the best representations for time, the optimal span of input measurements, and the most impactful model input data (features). For the chosen test data, the model achieves a mean absolute error of 74.34 $W/m^2$ compared to a baseline 134.35 $W/m^2$ using the persistence of cloudiness model.

Fernando Lejarza, Michael Baldea

Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon Optimization (DySMHO), a scalable machine learning framework for identifying governing laws in the form of differential equations from large-scale noisy experimental data sets. DySMHO consists of a novel moving horizon dynamic optimization strategy that sequentially learns the underlying governing equations from a large dictionary of basis functions. The sequential nature of DySMHO allows leveraging statistical arguments for eliminating irrelevant basis functions, avoiding overfitting to recover accurate and parsimonious forms of the governing equations. Canonical nonlinear dynamical system examples are used to demonstrate that DySMHO can accurately recover the governing laws, is robust to high levels of measurement noise and that it can handle challenges such as multiple time scale dynamics.