Grounded, Compute-Efficient LLM Policy Agents for Energy-Poverty Equity in Physically-Constrained Peer-to-Peer Energy Markets Researchers introduced EqGrid, a closed-loop simulation where a low-frequency, open-weight LLM policy agent sets price, carbon bounds, and targeted subsidies for peer-to-peer energy markets, reducing the Gini of energy burden to 0.305 from 0.351 and mean burden by 28% while cutting costs. The decoupled-safety design achieved zero grid-constraint violations versus 55 under direct LLM control, and a 3B-active model retained 95% of the equity benefit at roughly 9x lower inference energy than a 235B teacher, with a 0.8B on-device model retaining 92% at roughly 24x lower energy. arXiv:2609.01918v1 Announce Type: new Abstract: Energy poverty is nearly absent from NLP-for-social-good, and the little existing work is either static retrieval/QA or relies on carbon-intensive cloud LLMs, a self-defeating "computational irony" for a humanitarian setting. We present EqGrid, a closed-loop simulation in which a low-frequency, open-weight LLM policy agent sets price and carbon bounds and targeted subsidies over a community of empirically-grounded household personas, while high-frequency multi-agent RL traders clear a continuous double auction constrained by a physical distribution grid IEEE-33-bus with Dynamic Operating Envelopes . Our contribution is threefold and directly addresses how to measure the social impact of AI: i grounded personas region-matched socio-demographics whose load curves are checked for shape and level realism against real smart-meter data; ii formal energy-poverty equity metrics Energy Burden, Gini of EB, LIHC showing the intervention reduces burden inequality without raising net grid cost; and iii a compute-efficiency frontier that measures how much equity performance survives compressing the policy agent from a 235B teacher down to a sub-1B model deployable on a laptop, in estimated energy/carbon per decision. A decoupled-safety design the LLM sets bounds; a validate-and-project grid gate executes yields zero grid-constraint violations versus 55 under direct LLM control. On energy-poverty equity, the LLM policy lowers the Gini of energy burden to 0.305 from 0.351 and mean burden by 28% while cutting cost outperforming a tuned rule baseline , and a 3B-active model retains 95% of the benefit at roughly 9x lower inference energy than the teacher, with even a 0.8B on-device model retaining 92% at roughly 24x lower energy. We will release code and configs.