Christoph Graf

Maya Domeshek, Christoph Graf, Burçin Ünel

Coordinated planning of generation, storage, and transmission more accurately captures the interactions among these three capacity types necessary to meet electricity demand, at least in theory. However, in practice, U.S. system operators typically follow a sequential planning approach: They first determine future generation and storage additions based on an assumed unconstrained (`copper plate') system. Next, they perform dispatch simulations of this projected generation and storage capacity mix on the existing transmission grid to identify transmission constraint violations. These violations indicate the need for transmission upgrades. We describe a multistage, multi-locational planning model that co-optimizes generation, storage, and transmission investments. The model respects reliability constraints as well as state energy and climate policies. We test the two planning approaches using a current stakeholder-informed 20-zone model of the PJM region, developed for the current FERC Order No. 1920 compliance filing process. In our most conservative model specification, we find that the co-optimized approach estimates 67% lower transmission upgrade needs than the sequential model, leading to total system costs that are .6% lower and similar reliability and climate outcomes. Our sensitivities show larger transmission and cost savings and reliability and climate benefits from co-optimized planning.

Christoph Graf, Viktor Zobernig, Johannes Schmidt et al.

We test the performance of deep deterministic policy gradient (DDPG), a deep reinforcement learning algorithm, able to handle continuous state and action spaces, to learn Nash equilibria in a setting where firms compete in prices. These algorithms are typically considered model-free because they do not require transition probability functions (as in e.g., Markov games) or predefined functional forms. Despite being model-free, a large set of parameters are utilized in various steps of the algorithm. These are e.g., learning rates, memory buffers, state-space dimensioning, normalizations, or noise decay rates and the purpose of this work is to systematically test the effect of these parameter configurations on convergence to the analytically derived Bertrand equilibrium. We find parameter choices that can reach convergence rates of up to 99%. The reliable convergence may make the method a useful tool to study strategic behavior of firms even in more complex settings. Keywords: Bertrand Equilibrium, Competition in Uniform Price Auctions, Deep Deterministic Policy Gradient Algorithm, Parameter Sensitivity Analysis