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State estimation (SE) is one of the principal components in any energy management system for secure and reliable operation of power systems. The aim of state estimation process is to obtain the voltage magnitude and phase angles of buses which are further utilized in various real-time practice in power systems. This paper presents two new SE methods with the direct utilization of complex synchronized measurements obtained from optimally placed phasor measurements units (PMUs). Both the proposed methods use a linear measurement model to provide optimal solution avoiding iterative procedure compared to sub-optimal results provided by most of the existing iterative SE methods. The first method portrays a new static state estimation (NSSE) and the second one presents a new dynamic state estimation (NDSE) method using the more pragmatic Brown's triple exponential (BTE) smoothing method for one step ahead prediction. The proposed approaches also include a unique detection, identification and correction of bad data method. The proposed methods have been tested on various IEEE bus test systems as well on two Indian practical systems, viz. 38-bus system of Damodar Valley Corporation and 246-bus system of Northern Regional Power Grid. The accomplishments of the proposed approaches have been evaluated by comparing it with conventional static state estimation (SSE) and dynamic state estimation (DSE) as well as newly proposed unscented Kalman filter-(UKF) and cubature Kalman filter (CKF)-based DSE methods under different simulated operating conditions. Simulation results provided validates the superiority of the proposed schemes. [ABSTRACT FROM AUTHOR]