Periodic Reporting for period 1 - TRUST-ML (Trust-ML: An Optimization-based Platform for Building Trust in Machine Learning Models used for Power Systems)
Reporting period: 2022-06-15 to 2024-06-14
Deep decarbonization of the energy sector will require massive penetration of stochastic renewable energy resources and an enormous amount of grid asset coordination; this represents a challenging paradigm for power system operators. With its ability to learn in complex environments and provide predictive solutions on fast timescales, machine learning (ML) is posed to help overcome these challenges and dramatically transform power systems in coming decades. Emerging EU verification standards, however, will require that all ML and Reinforcement Learning (RL) used in safety critical applications be demonstrably trustworthy. In this project, we developed a set of tools, all under the project's Trust-ML framework, for assessing the quantitative trustworthiness of the neural network models commonly used in power system applications. Trust-ML uses novel data-generation and convex optimization-based approach to assess ML trustworthiness across three key dimensions: performance, robustness, and interpretability. The approaches designed in this project are engineered to be scalable, and by design, they generates exact verification guarantees. Furthermore, the associated verification tools are designed to meet the emerging needs of actual power systems. The resulting verification tools are published as open-source software packages and shared with researchers and industry. This project advanced state-of-the-art methods across several interdisciplinary fields (power systems, ML, computing), it helped remove the barriers associated with machine learning deployment in power systems, and its outcomes, ultimately, will help push European power grids into competitive spaces.
This project focused primarily on designing scalable verification techniques for power and energy system applications. On this theme, this project advanced multiple new methodologies for analyzing ML models relative to ground truth (i.e. known) grid physics. A key enabling methodology which we pioneered, termed Sequential Targeted Tightening (STT), leverages a loosely convexified reformulation of the original verification problem, which is a nonconvex mixed integer quadratic program (MIQP). Using the sequential addition of targeted cuts, we showed how we can iteratively tighten our formulation until either the solution is sufficiently tight or a satisfactory performance guarantee has been generated. After learning neural network models of the 14, 57, 118, and 200-bus PGLib test cases, we compared the performance guarantees generated by our STT procedure with ones generated by a state-of-the-art MIQP solver, Gurobi 9.5. We showed that STT often generates performance guarantees which are orders of magnitude tighter than the MIQP upper bound.
A complementary verification approach, built on advanced solvers from the ML community, enabled the simultaneous verification of multiple verification problems (e.g. checking for the violation of all line flow constraints simultaneously and not by solving individual verification problems). For that, we introduced an exact transformation that converts the "worst-case" violation across a set of potential violations to a series of ReLU-based layers that augment the original neural network. This allows verifiers to interpret these outputs directly directly. Additionally, since power system ML models often must be verified to satisfy power flow constraints, we proposed a dualization procedure which encodes linear equality and inequality constraints directly into the verification problem; and in a manner which is mathematically consistent with the specialized verification tools. To demonstrate these innovations, we verified problems associated with data-driven security constrained DC-OPF solvers. We built and tested our first set of innovations using the α,β-CROWN solver, and we benchmarked against Gurobi 10.0. Our contributions achieved a speedup that can exceed 100x and allow higher degrees of verification flexibility.
On top of verification, this project also designed scalable techniques to collect high-fidelity, maximally representative training data for ML model construction. To that end, we designed two key new approaches. In the first approach, we performed a systematic investigation into the various nonlinear objective functions which can be used to explore the feasible space associated with the optimal power flow (OPF) problem. A total of 40 nonlinear objective functions were tested, and their results were compared to the data generated by a novel exhaustive rejection sampling routine. The Hausdorff distance, which is a min-max set dissimilarity metric, was then used to assess how well each nonlinear objective function performed (i.e. how well the tested objective functions were able to explore the nonconvex power flow space). Exhaustive test results were collected from five PGLib test-cases and systematically analyzed. In the second approach, using bilevel optimization, we introduced a data collection routine that sequentially solves for optimal power flow solutions which are “optimally far” from previously acquired voltage, power, and load profile data points. The routine, termed RAMBO, samples critical data close to a system’s boundaries much more effectively than a random sampling benchmark. Simulated test results were collected on the 30-, 57-, and 118-bus PGLib test cases.
A complementary verification approach, built on advanced solvers from the ML community, enabled the simultaneous verification of multiple verification problems (e.g. checking for the violation of all line flow constraints simultaneously and not by solving individual verification problems). For that, we introduced an exact transformation that converts the "worst-case" violation across a set of potential violations to a series of ReLU-based layers that augment the original neural network. This allows verifiers to interpret these outputs directly directly. Additionally, since power system ML models often must be verified to satisfy power flow constraints, we proposed a dualization procedure which encodes linear equality and inequality constraints directly into the verification problem; and in a manner which is mathematically consistent with the specialized verification tools. To demonstrate these innovations, we verified problems associated with data-driven security constrained DC-OPF solvers. We built and tested our first set of innovations using the α,β-CROWN solver, and we benchmarked against Gurobi 10.0. Our contributions achieved a speedup that can exceed 100x and allow higher degrees of verification flexibility.
On top of verification, this project also designed scalable techniques to collect high-fidelity, maximally representative training data for ML model construction. To that end, we designed two key new approaches. In the first approach, we performed a systematic investigation into the various nonlinear objective functions which can be used to explore the feasible space associated with the optimal power flow (OPF) problem. A total of 40 nonlinear objective functions were tested, and their results were compared to the data generated by a novel exhaustive rejection sampling routine. The Hausdorff distance, which is a min-max set dissimilarity metric, was then used to assess how well each nonlinear objective function performed (i.e. how well the tested objective functions were able to explore the nonconvex power flow space). Exhaustive test results were collected from five PGLib test-cases and systematically analyzed. In the second approach, using bilevel optimization, we introduced a data collection routine that sequentially solves for optimal power flow solutions which are “optimally far” from previously acquired voltage, power, and load profile data points. The routine, termed RAMBO, samples critical data close to a system’s boundaries much more effectively than a random sampling benchmark. Simulated test results were collected on the 30-, 57-, and 118-bus PGLib test cases.
This work has coupled domain expertise (power system modeling) with advanced ML verification methodologies. In particular, we have repeatedly exploited a key convex relaxation model, known as semidefinite programming, in order to relax a very challenging nonconvex verification problem. The cuts that we identify to iteratively "tighten" this verification model have shown to be extremely, even surprisingly, successful. Next, we have laid the groundwork for using dualization-based techniques for verifying model performance within the context of highly complex network constraints. Furthermore, we have shown that a small signal stability model of an offshore wind power hub (based in the North Sea) is tractable. Future work will focus on pushing scalability of these methods and enhancing their generality to enable the infusion of physics-based models from other safety-critical engineering domains (e.g. autonomous vehicles).