Lucas Valenzuela


Email: lucasfv at stanford dot edu

Lucas Valenzuela

ASL Publications

  1. 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, 2024.

    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 almost 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, i.e., models with temporal constraints such as ramping and storage. Using real data from the U.S. electricity system, we validate the proposed method by comparing emissions predictions with another state-of-the-art method. We show that incorporating dynamic constraints improves prediction 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. Namely, static LMEs and dynamic LMEs exhibit an average RMS deviation of 28.40%, implying dynamic constraints are essential to accurately modeling emissions rates.

      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}},
      note = {In Press},
      year = {2024},
      url = {},
      owner = {rdyro},
      timestamp = {2024-01-08},
      keywords = {pub}
  2. 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.

      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 = {},
      owner = {rabrown1},
      timestamp = {2024-03-05},
      keywords = {sub}