With the deregulation of power industry and the market competition, reliable power supply and secured system operation are major concerns of the independent system operator (ISO). Power system operation under deregulated environment is very complicated with various possibilities of decisions involved. A robust and fast network analysis tool is one of important functions of conventional EMS, and this function will be reserved for the on-line analysis to deal with varied behaviors of the new deregulated environment. Firstly, a multiple-frequency three-phase load flow model was developed in this dissertation. There are two new sub-models including the fundamental power flow (FPF) and harmonic frequency power flow (HPF) model. In FPF, models of electrical elements and injected power on buses were treated in the form of current injections in a transmission system. The standard Fourier analysis was used to deal with the harmonic loads to get injection currents. With harmonic currents as equivalent current sources, the HPF can be derived. Besides, the fast assumptive model and decoupled model of FPF and HPF, called AFPF, DFPF and DHPF, were also proposed to improve execution time of the load flow programs. Test results show that the proposed general-purpose methods are better performers than conventional power flow solutions and are very robust. Secondly, the novel method, Upstream Tracing Model (UTM) and Downstream Tracing Model (DTM), to trace the power flow in transmission systems based on the converged AC power flow solution was proposed. The method is formulated by using the transmission network structure, the equivalent current-injection and load-admittances from the engineering viewpoint. Four steps are used to trace the linear relationship between each line flow and generator injection power without any assumption and the counter flow can be traced out, then the power consumption on each load can be represented as generators¡¦ contribution. According to the result of tracing, the loss of each line can be allocated to each generator by using a fair line usage concept. This tracing algorithm can calculate each generator¡¦s contribution quickly and fairly, and can be integrated into the existent tariffs of charging for transmission losses and services.