Power market comes to being with the reformation of the power industry. Now it is studied extensively by many scholars. In this dissertation, transmission service and market stability are researched. The main results are as follows:i) The defects of the existing Pool model are investigated via economic theory. An improved transmission scheduling method is proposed, based on the average transmission cost analysis.ii) A new congestion management method based on bid is proposed.iii) A method to allocation of transmission loss is obtained, based on the N-person cooperative game theory.iv) A general definition for the generalized state solutions to linear discrete shift-varying singular systems is proposed. And the sufficient and necessary conditions for the solvability and uniformly asymptotic stability are presented for linear discrete periodic singular systems. Based on these conditions, the definition and criterion of power market are investigated, by which the default reason of California power market and the influence of congestion and future market are analyzed.v) A new bargain model is explored and some feasible results are presented.