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AC-Optimal Power Flow Solutions with Security Constraints from Deep Neural Network Models

Computer Aided Chemical Engineering

Kilwein, Zachary; Boukouvala, Fani; Laird, Carl D.; Castillo, Anya; Blakely, Logan; Eydenberg, Michael S.; Jalving, Jordan H.; Batsch-Smith, Lisa

In power grid operation, optimal power flow (OPF) problems are solved several times per day to find economically optimal generator setpoints that balance given load demands. Ideally, we seek an optimal solution that is also “N-1 secure”, meaning the system can absorb contingency events such as transmission line or generator failure without loss of service. Current practice is to solve the OPF problem and then check a subset of contingencies against heuristic values, resulting in, at best, suboptimal solutions. Unfortunately, online solution of the OPF problem including the full N-1 contingencies (i.e., two-stage stochastic programming formulation) is intractable for even modest sized electrical grids. To address this challenge, this work presents an efficient method to embed N-1 security constraints into the solution of the OPF by using Neural Network (NN) models to represent the security boundary. Our approach introduces a novel sampling technique, as well as a tuneable parameter to allow operators to balance the conservativeness of the security model within the OPF problem. Our results show that we are able to solve contingency formulations of larger size grids than reported in literature using non-linear programming (NLP) formulations with embedded NN models to local optimality. Solutions found with the NN constraint have marginally increased computational time but are more secure to contingency events.

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Scalable preconditioning of block-structured linear algebra systems using ADMM

Computers and Chemical Engineering

Rodriguez, Jose S.; Laird, Carl D.; Zavala, Victor M.

We study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation, optimal control, network optimization, and stochastic programming. Our approach uses a Krylov solver (GMRES) that is preconditioned with an alternating method of multipliers (ADMM). We show that this ADMM-GMRES approach overcomes well-known scalability issues of Schur complement decomposition in problems that exhibit a high degree of coupling. The effectiveness of the approach is demonstrated using linear systems that arise in stochastic optimal power flow problems and that contain up to 2 million total variables and 4000 coupling variables. We find that ADMM-GMRES is nearly an order of magnitude faster than Schur complement decomposition. Moreover, we demonstrate that the approach is robust to the selection of the augmented Lagrangian penalty parameter, which is a key advantage over the direct use of ADMM.

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A mathematical programming approach for the optimal placement of flame detectors in petrochemical facilities

Process Safety and Environmental Protection

Zhen, Todd; Klise, Katherine A.; Cunningham, Sean; Marszal, Edward; Laird, Carl D.

Flame detectors provide an important layer of protection for personnel in petrochemical plants, but effective placement can be challenging. A mixed-integer nonlinear programming formulation is proposed for optimal placement of flame detectors while considering non-uniform probabilities of detection failure. We show that this approach allows for the placement of fire detectors using a fixed sensor budget and outperforms models that do not account for imperfect detection. We develop a linear relaxation to the formulation and an efficient solution algorithm that achieves global optimality with reasonable computational effort. We integrate this problem formulation into the Python package, Chama, and demonstrate the effectiveness of this formulation on a small test case and on two real-world case studies using the fire and gas mapping software, Kenexis Effigy.

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Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations

AIChE Journal

Bynum, Michael L.; Castillo, Anya; Watson, Jean-Paul W.; Laird, Carl D.

While peak shaving is commonly used to reduce power costs, chemical process facilities that can reduce power consumption on demand during emergencies (e.g., extreme weather events) bring additional value through improved resilience. For process facilities to effectively negotiate demand response (DR) contracts and make investment decisions regarding flexibility, they need to quantify their additional value to the grid. We present a grid-centric mixed-integer stochastic programming framework to determine the value of DR for improving grid resilience in place of capital investments that can be cost prohibitive for system operators. We formulate problems using both a linear approximation and a nonlinear alternating current power flow model. Our numerical results with both models demonstrate that DR can be used to reduce the capital investment necessary for resilience, increasing the value that chemical process facilities bring through DR. However, the linearized model often underestimates the amount of DR needed in our case studies. Published 2018. This article is a U.S. Government work and is in the public domain in the USA. AIChE J, 65: e16508, 2019.

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Results 1–25 of 90
Results 1–25 of 90