  We consider the coupled problems of optimal thermostat programming and
optimal pricing of electricity. Our framework consists of a single user and a
single provider (a regulated utility). The provider sets prices for the user,
who pays for both total energy consumed (\$/kWh, including peak and off-peak
rates) and the peak rate of consumption in a month (a demand charge) (\$/kW).
The cost of electricity for the provider is based on a combination of capacity
costs (\$/kW) and fuel costs (\$/kWh). In the optimal thermostat programming
problem, the user minimizes the amount paid for electricity while staying
within a pre-defined temperature range. The user has access to energy storage
in the form of thermal capacitance of the interior structure of the building.
The provider sets prices designed to minimize the total cost of producing
electricity while meeting the needs of the user. To solve the user-problem, we
use a variant of dynamic programming. To solve the provider-problem, we use a
descent algorithm coupled with our dynamic programming code - yielding optimal
on-peak, off-peak and demand prices. We show that thermal storage and optimal
thermostat programming can reduce electricity bills using current utility
prices from utilities Arizona Public Service (APS) and Salt River Project
(SRP). Moreover, we obtain optimal utility prices which lead to significant
reductions in the cost of generating electricity and electricity bills.
