  Demand response for electrical power networks is a mature field that has
yielded numerous efficiency and resilience benefits like managing the peaks and
valleys of electricity usage, reduction in peak electricity usage, to name a
few. However, only recently has the study of the counterpart to demand response
for electric power in natural gas started to receive similar levels of
attention. Natural gas systems are increasingly operating at or near capacity,
which challenges these systems to meet all the needs for gas, especially during
severe winter weather. However, unlike demand response programs in electrical
networks, demand response in gas networks cannot shift peak usage. Here, we
develop analogues to demand response that can help improve the resilience of
natural gas systems by reducing peak consumption and thereby limiting potential
disruptions such events can cause. This paper develops a mathematical
formulation to support a residential-level demand response analogue for natural
gas based on current and anticipated smart thermostat technologies. The
mathematical formulation takes the form of an optimal control problem (OCP)
that leverages physics constraints to model temperature changes, balance
equitable service, and optimize the gas consumption for collections of houses.
On test problems, the formulation demonstrates significant benefits, including
the ability to cut peak demand by 15% while still ensuring equitable service to
customers.
