Electricity markets are known for their nonconvex characteristics due to discrete unit commitment and decommitment decisions. Non-convexity disjoints the scheduling and pricing programs' results. Additionally, clearing prices sometimes cannot cover resources' operating costs or credits based on their schedules or over-adequate to that of the non-market behavior resources. Therefore, pricing challenge and settlement uplift arise out of the inherent nonconvexity. This paper presents a mathematical model on pricing scheme and constructed uplift settlement functions to provide either position or negative uplift on how industry dealt with this situation. Both the primal and the dual form of pricing model are presented and interpreted. The constructed uplift function for both commitment and decommitment consider actual and planned operating statuses, operating costs, and shadow prices formed in a pricing run. The proof of the static incentive equilibrium is presented to demonstrate the effectiveness of the mathematical model. The case studies herein detail the pricing process along with the corresponding make-whole or claw-back of settlement payment or credit based on a small system and a practical system.

Traditionally, power system flexibility in economic dispatch is measured by the ramping up/down capacity with given total demand and locational distributional factors in a system. In this paper, we present the elasticity metrics for the optimal security-constrained economic dispatch (SCED) restoration using the sequential convergence speed of a deformed SCED. The degree of the residual deformation of the SCED solution is denoted by the norm of the Euclid distance between the optimal dispatch point without initial point and some trajectory constraints and sequential dispatches starting from the current operating point. The mathematical proof of the convergence of the sequential SCED is given in this paper. Numerical examples are based on a SCED simulation tool running on a practical power system to verify the convergence and calculate the metrics of the proposed elasticity.