  The problem of heat system pricing is considered. A direct extension of
locational marginal prices (LMP) in electricity markets to heat systems may
lead to revenue inadequate issues. The underlying reason for such a problem is
that, unlike electric power, heat has different grades and cannot be considered
as homogenized commodity. Accordingly, an energy-grade double pricing rule is
proposed in this paper. Heat energy and grade prices are explained as the
shadow prices related to the nodal heat balance constraints and temperature
requirements constraints at the optimal solution. The resulting merchandise
surplus at each dispatch interval can be decomposed into several explainable
parts, namely, congestion rent, impact from the last period, and impact from
the upcoming period. And the total merchandise surplus over all dispatch
intervals can be decomposed into several non-negative interpretable parts,
including congestion rent and impact from the initial state, thus guaranteeing
the revenue adequacy for the heat system operator. Simulations verify the
effectiveness of the proposed mechanism.
