  The problem of heat and electricity pricing in combined heat and power
systems regarding the time scales of electricity and heat, as well as thermal
energy quality, is studied. Based on the asynchronous coordinated dispatch of
the combined heat and power system, an energy-grade double pricing mechanism is
proposed. Under the pricing mechanism, the resulting merchandise surplus of the
heat system operator at each heat dispatch interval can be decomposed into
interpretable parts and its revenue adequacy can be guaranteed for all heat
dispatch intervals. And the electric power system operator's resulting
merchandise surplus is composed of non-negative components at each electricity
dispatch interval, also ensuring its revenue adequacy. In addition, the effects
of different time scales and cogeneration are analyzed in different kinds of
combined heat and power units' pricing.
