LACE-S: Toward Sensitivity-consistent Locational Average Carbon Emissions via Neural Representation

Abstract

Carbon-aware grid optimization relies on accurate locational emission metrics to effectively guide demand-side decarbonization tasks such as spatial load shifting. However, existing metrics are only valid around limited operating regions and unfortunately cannot generalize the emission patterns beyond these regions. When these metrics are used to signal carbon-sensitive resources, they could paradoxically increase system-wide emissions. This work seeks to develop a sensitivity-consistent metric for locational average carbon emissions (LACE-S) using a neural representation approach. To ensure physical validity, the neural model enforces total emission balance through an explicit projection layer while matching marginal emission sensitivities across the entire loading region. Jacobian-based regularization is further introduced to capture the underlying partition of load buses with closely aligned generator responses. Moreover, we present a scalable zonal aggregation strategy, ZACE-S, to reduce the model complexity by mapping nodal inputs to predefined market zones. Numerical tests on the IEEE 30-bus system have verified the performance improvements of LACE-S in matching total emissions and their sensitivities over the non-regularized design. Crucially, while spatial load shifting driven by existing metrics often increases the post-shift emissions, the proposed LACE-S metric has led to a reliable reduction of system-wide emissions, demonstrating its excellent consistency with the global emission patterns.

Figures (9)

• Figure 1: (a) A 2-bus system with two generators and loads; and the LMCE distribution of (b) $d_1$ and (c) $d_2$.
• Figure 2: The proposed neural approximation models estimate LACE-S from load profiles using trainable weights. To mitigate overfitting, cluster-based structured sparsification is applied to the first and last layers.
• Figure 3: Visualization of dispatch Jacobian matrices ($\partial {\mathbf g}^*/\partial {\mathbf d}$) on the IEEE 14-bus system under two distinct congestion patterns.
• Figure 4: Comparison of $\mathcal{L}$ and the regularization losses $\{\mathcal{L}_{\mathrm{bd}},\mathcal{L}_{\mathrm{d}}\}$ on the IEEE 30-bus system. (a) Vary $\gamma_1$ with $\gamma_2$ fixed at 0; (b) Vary $\gamma_2$ with $\gamma_1$ fixed at 0.05.
• Figure 5: The proposed neural approximation models estimate ZACE-S from load profiles using trainable weights.