  Electricity prices determined by economic dispatch that do not consider fixed
costs may lead to significant uplift payments. However, when fixed costs are
included, prices become non-monotonic with respect to demand, which can
adversely impact market transparency. To overcome this issue, convex hull (CH)
pricing has been introduced for unit commitment with fixed costs. Several CH
pricing methods have been presented, and a feasible cost has been used as a
quality measure for the CH price. However, obtaining a feasible cost requires a
computationally intensive optimization procedure, and the associated duality
gap may not provide an accurate quality measure. This paper presents a new
approach for quantifying the quality of the CH price by establishing an upper
bound on the optimal dual value. The proposed approach uses Surrogate
Lagrangian Relaxation (SLR) to efficiently obtain near-optimal CH prices, while
the upper bound decreases rapidly due to the convergence of SLR. Testing
results on the IEEE 118-bus system demonstrate that the novel quality measure
is more accurate than the measure provided by a feasible cost, indicating the
high quality of the upper bound and the efficiency of SLR.
