  Residential heating, primarily powered by natural gas, accounts for a
significant portion of residential sector energy use and carbon emissions in
many parts of the world. Hence, there is a push towards decarbonizing
residential heating by transitioning to energy-efficient heat pumps powered by
an increasingly greener and less carbon-intensive electric grid. However, such
a transition will add additional load to the electric grid triggering
infrastructure upgrades, and subsequently erode the customer base using the gas
distribution network. Utilities want to guide these transition efforts to
ensure a phased decommissioning of the gas network and deferred electric grid
infrastructure upgrades while achieving carbon reduction goals. To facilitate
such a transition, we present a network-aware optimization framework for
decarbonizing residential heating at city scale with an objective to maximize
carbon reduction under budgetary constraints. Our approach operates on a graph
representation of the gas network topology to compute the cost of transitioning
and select neighborhoods for transition. We further extend our approach to
explicitly incorporate equity and ensure an equitable distribution of benefits
across different socioeconomic groups. We apply our framework to a city in the
New England region of the U.S., using real-world gas usage, electric usage, and
grid infrastructure data. We show that our network-aware strategy achieves 55%
higher carbon reductions than prior network-oblivious work under the same
budget. Our equity-aware strategy achieves an equitable outcome while
preserving the carbon reduction benefits of the network-aware strategy.
