Firstly, this paper reviews optimal power flow and security-constrained economic dispatch problem, focusing on the principle of locational marginal price. This paper discusses some drawbacks of the pricing mechanism based on security-constrained economic dispatch and security-constrained unit commitment under non-convexity conditions, and explains how to use extended locational marginal price algorithm to reduce uplift cost and promote incentive- compatible pricing scheme. Then, using duality theory, this paper gives a rigorous proof on the uplift cost under typical pricing mechanism: convex hull price, locational marginal price, and integer relaxation price, and particularly elaborates its physical meaning from geometric perspective. Finally, this paper implements a set of optimization algorithms with mixed integer programming and Lagrangian relaxation for unit commitment. Numerical results prove correctness of the proposed relationship between the uplift cost induced by locational marginal price and integer relaxation price, and the minimum uplift cost by convex hull price. Research on incentive-compatible pricing mechanisms will facilitate integration of distributed renewable energy resources into power grid, thereby driving transformation and upgrading of power systems to clean, efficient, and smart goals.