Contacts:
Lucas Valenzuela
ASL Publications
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L. F. Valenzuela, R. Brown, and M. Pavone, “Decentralized Implicit Differentiation,” IEEE Transactions on Control of Network Systems, 2024. (Submitted)
Abstract: The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that exploiting problem structure can yield significant computation gains for optimization and, in some cases, enable distributed computation. One should expect that this structure can be similarly exploited for gradient computation. In this work, we discuss a decentralized framework for computing gradients of constraint-coupled optimization problems. First, we show that this framework results in significant computational gains, especially for large systems, and provide sufficient conditions for its validity. Second, we leverage exponential decay of sensitivities in graph-structured problems towards building a fully distributed algorithm with convergence guarantees. Finally, we use the methodology to rigorously estimate marginal emissions rates in power systems models. Specifically, we demonstrate how the distributed scheme allows for accurate and efficient estimation of these important emissions metrics on large dynamic power system models.
@article{ValenzuelaBrownEtAl2024, author = {Valenzuela, L. F. and Brown, R. and Pavone, M.}, title = {Decentralized Implicit Differentiation}, journal = {{IEEE Transactions on Control of Network Systems}}, note = {Submitted}, year = {2024}, url = {https://arxiv.org/abs/2403.01260}, owner = {rabrown1}, timestamp = {2024-03-05}, keywords = {sub} } -
A. Degleris, L. F. Valenzuela, R. Rajagopal, M. Pavone, and A. E. Gamal, “Fast Grid Emissions Sensitivities using Parallel Decentralized Implicit Differentiation,” 2024. (Submitted)
Abstract: Marginal emissions rates – the sensitivity of carbon emissions to electricity demand – are important for evaluating the impact of emissions mitigation measures. Like locational marginal prices, locational marginal emissions rates (LMEs) can vary geographically, even between nearby locations, and may be coupled across time periods because of, for example, storage and ramping constraints. This temporal coupling makes computing LMEs computationally expensive for large electricity networks with high storage and renewable penetrations. Recent work demonstrates that decentralized algorithms can mitigate this problem by decoupling timesteps during differentiation. Unfortunately, we show these potential speedups are negated by the sparse structure inherent in power systems problems. We address these limitations by introducing a parallel, reverse-mode decentralized differentiation scheme that never explicitly instantiates the solution map Jacobian. We show both theoretically and empirically that parallelization is necessary to achieve non-trivial speedups when computing grid emissions sensitivities. Numerical results on a 500 node system indicate that our method can achieve greater than 10x speedups over centralized and serial decentralized approaches.
@inproceedings{DeglerisValenzuelaEtAl2024, author = {Degleris, A. and Valenzuela, L. F. and Rajagopal, R. and Pavone, M. and Gamal, A. E.}, title = {Fast Grid Emissions Sensitivities using Parallel Decentralized Implicit Differentiation}, booktitle = {}, year = {2024}, keywords = {sub}, owner = {amine}, timestamp = {2024-09-19}, url = {https://arxiv.org/abs/2408.10620} } -
L. F. Valenzuela, A. Degleris, A. E. Gamal, M. Pavone, and R. Rajagopal, “Dynamic Locational Marginal Emissions via Implicit Differentiation,” IEEE Transactions on Power Systems, vol. 39, no. 1, pp. 1138–1147, 2023.
Abstract: Locational marginal emissions rates (LMEs) estimate the rate of change in emissions due to a small change in demand in a transmission network, and are an important metric for assessing the impact of various energy policies or interventions. In this work, we develop a new method for computing the LMEs of an electricity system via implicit differentiation. The method is model agnostic; it can compute LMEs for any convex optimization-based dispatch model, including some of the complex dispatch models employed by system operators in real electricity systems. In particular, this method lets us derive LMEs for dynamic dispatch models, which have temporal constraints such as ramping and storage. Using real data from the U.S. electricity system, we validate the proposed method against a state-of-the-art merit-order-based method and show that incorporating dynamic constraints improves model accuracy by 8.2%. Finally, we use simulations on a realistic 240-bus model of WECC to demonstrate the flexibility of the tool and the importance of incorporating dynamic constraints. In this example, static and dynamic LMEs deviate from one another by 28.4% on average, implying dynamic constraints are essential in accurately modeling emissions rates.
@article{ValenzuelaDeglerisEtAl2022, author = {Valenzuela, L. F. and Degleris, A. and Gamal, A. E. and Pavone, M. and Rajagopal, R.}, title = {Dynamic Locational Marginal Emissions via Implicit Differentiation}, journal = {{IEEE Transactions on Power Systems}}, year = {2023}, volume = {39}, number = {1}, pages = {1138--1147}, doi = {10.1109/TPWRS.2023.3247345}, owner = {jthluke}, timestamp = {2024-10-28}, url = {https://arxiv.org/abs/2302.14282} }