This paper introduces a unified approach to solving convex hull pricing (CHP) and average incremental cost (AIC) pricing problems. By developing a convex hull and convex envelope formulation for individual resources, a CHP model that minimizes uplift can be solved by linear programming (LP) using relaxation of the binary terms of the security constrained unit commitment (SCUC) problem. This paper proves that by adjusting resource upper bounds based on the SCUC solution, the one-pass LP relaxation of the SCUC problem can also be used to derive AIC prices, eliminating make-whole payments. Case studies using both small systems and the MISO day ahead system are presented to compare make-whole payments, uplift and generator profit under LMP, CHP and AIC.
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