Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the Western System Coordinating Council (WSCC) 9-bus test system using synthetic multi-device outage scenarios. Towards integrating our modeling framework with real threats and more realistic power systems, we explore applying hybrid dynamics to power systems. Our work is applied to basic RL circuits with the ultimate goal of using the methodology to model protective tripping schemes in the grid. Finally, we survey mitigation techniques for HEMP threats and describe a GIS application developed to create threat scenarios in a grid with geographic detail.
This report summarizes the guidance provided to Sustainable Engineering to help them learn about equation-oriented optimization and the Sandia-developed software packages Pyomo and IDAESPSE. This was a short 10-week project (October 2021 – December 2021) and the goal was to help the company learn about the IDAES framework and how it could be used for their future projects. The company submitted an SBIR proposal related to developing a green ammonia process model with IDAES and if that proposal is successful this NMSBA project could lead to future collaboration opportunities.
Nicholson, Bethany L.; Thierry, David T.; Parker, Robert B.; Eslick, John C.; Ma, Jinliang M.; Le, Quang M.; Bhattacharyya, Debangsu B.; Biegler, Larry B.
We study connections between the alternating direction method of multipliers (ADMM), the classical method of multipliers (MM), and progressive hedging (PH). The connections are used to derive benchmark metrics and strategies to monitor and accelerate convergence and to help explain why ADMM and PH are capable of solving complex nonconvex NLPs. Specifically, we observe that ADMM is an inexact version of MM and approaches its performance when multiple coordination steps are performed. In addition, we use the observation that PH is a specialization of ADMM and borrow Lyapunov function and primal-dual feasibility metrics used in ADMM to explain why PH is capable of solving nonconvex NLPs. This analysis also highlights that specialized PH schemes can be derived to tackle a wider range of stochastic programs and even other problem classes. Our exposition is tutorial in nature and seeks to to motivate algorithmic improvements and new decomposition strategies
Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming. We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.
We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.
New modelling and optimization platforms have enabled the creation of frameworks for solution strategies that are based on solving sequences of dynamic optimization problems. This study demonstrates the application of the Python-based Pyomo platform as a basis for formulating and solving Nonlinear Model Predictive Control (NMPC) and Moving Horizon Estimation (MHE) problems, which enables fast on-line computations through large-scale nonlinear optimization and Nonlinear Programming (NLP) sensitivity. We describe these underlying approaches and sensitivity computations, and showcase the implementation of the framework with large DAE case studies including tray-by-tray distillation models and Bubbling Fluidized Bed Reactors (BFB).
Real-time energy pricing has caused a paradigm shift for process operations with flexibility becoming a critical driver of economics. As such, incorporating real-time pricing into planning and scheduling optimization formulations has received much attention over the past two decades (Zhang and Grossman, 2016). These formulations, however, focus on 1-hour or longer time discretizations and neglect process dynamics. Recent analysis of historical price data from the California electricity market (CAISO) reveals that a majority of economic opportunities come from fast market layers, i.e., real-time energy market and ancillary services (Dowling et al., 2017). We present a dynamic optimization framework to quantify the revenue opportunities of chemical manufacturing systems providing frequency regulation (FR). Recent analysis of first order systems finds that slow process dynamics naturally dampen high frequency harmonics in FR signals (Dowling and Zavala, 2017). As a consequence, traditional chemical processes with long time constants may be able to provide fast flexibility without disrupting product quality, performance of downstream unit operations, etc. This study quantifies the ability of a distillation system to provide sufficient dynamic flexibility to adjust energy demands every 4 seconds in response to market signals. Using a detailed differential algebraic equation (DAE) model (Hahn and Edgar, 2002) and historic data from the Texas electricity market (ECROT), we estimate revenue opportunities for different column designs. We implement our model using the algebraic modeling language Pyomo (Hart et al., 2011) and its dynamic optimization extension Pyomo.DAE (Nicholson et al., 2017). These software packages enable rapid development of complex optimization models using high-level modelling constructs and provide flexible tools for initializing and discretizing DAE models.
Continuous or regularly scheduled monitoring has the potential to quickly identify changes in the environment. However, even with low - cost sensors, only a limited number of sensors can be deployed. The physical placement of these sensors, along with the sensor technology and operating conditions, can have a large impact on the performance of a monitoring strategy. Chama is an open source Python package which includes mixed - integer, stochastic programming formulations to determine sensor locations and technology that maximize monitoring effectiveness. The methods in Chama are general and can be applied to a wide range of applications. Chama is currently being used to design sensor networks to monitor airborne pollutants and to monitor water quality in water distribution systems. The following documentation includes installation instructions and examples, description of software features, and software license. The software is intended to be used by regulatory agencies, industry, and the research community. It is assumed that the reader is familiar with the Python Programming Language. References are included for addit ional background on software components. Online documentation, hosted at http://chama.readthedocs.io/, will be updated as new features are added. The online version includes API documentation .