State estimation is widely used as a tool to evaluate the real time power system prevailing conditions. State estimation algorithms could suffer divergence under stressed system conditions. This dissertation first investigates impacts of variations of load levels and topology errors on the convergence property of the commonly used weighted least square (WLS) state estimator. The influence of topology errors on the condition number of the gain matrix in the state estimator is also analyzed. The minimum singular value of gain matrix is proposed to measure the distance between the operating point and state estimation divergence. To study the impact of the load increment on the convergence property of WLS state estimator, two types of load increment are utilized: one is the load increment of all load buses, and the other is a single load increment. In addition, phasor measurement unit (PMU) measurements are applied in state estimation to verify if they could solve the divergence problem and improve state estimation accuracy. The dissertation investigates the impacts of variations of line power flow increment and topology errors on convergence property of the WLS state estimator. A simple 3-bus system and the IEEE 118-bus system are used as the test cases to verify the common rule. Furthermore, the simulation results show that adding PMU measurements could generally improve the robustness of state estimation. Two new approaches for improving the robustness of the state estimation with PMU measurements are proposed. One is the equality-constrained state estimation with PMU measurements, and the other is Hachtel's matrix state estimation with PMU measurements approach. The dissertation also proposed a new heuristic approach for optimal placement of phasor measurement units (PMUs) in power system for improving state estimation accuracy. In the problem of adding PMU measurements into the estimator, two methods are investigated. Method I is to mix PMU measurements with conventional measurements in the estimator, and method II is to add PMU measurements through a post-processing step. These two methods can achieve very similar state estimation results, but method II is a more time-efficient approach which does not modify the existing state estimation software.