The simulation results show that the determined optimal PMU placements by the proposed method can guarantee good observability of the system states, which further leads to smaller estimation errors and larger number of convergent states for dynamic state estimation compared with random PMU placements. The proposed method is tested on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system by performing dynamic state estimation with square-root unscented Kalman filter. The implementation, validation, and also the robustness to load fluctuations and contingencies of the proposed method are carefully discussed. An optimal PMU placement method for power system dynamic state estimation is further formulated as an optimization problem which maximizes the determinant of the empirical observability gramian and is efficiently solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search (MADS) algorithm. In this paper the empirical observability gramian calculated around the operating region of a power system is used to quantify the degree of observability of the system states under specific phasor measurement unit (PMU) placement. The procedure adopted can be applied to any complex geometry in a relatively simple way for preliminary designing of grain configuration. Equilibrium pressure method is used to calculate the internal ballistics. Grain burn back is achieved by making new surfaces at each web increment and calculating geometrical properties at each step. Initial geometry is defined in the form of a surface which defines the grain configuration. The design process involves parametric modeling of the geometry in CAD software through dynamic variables that define the complex configuration. ![]() In this study, grain burn back analysis for 3-D star grain geometries for solid rocket motor was investigated. ![]() The performance prediction of the solid rocket motor can be achieved easily if the burn back steps of the grain are known. Determination of the grain geometry is an important and critical step in the design of solid propellant rocket motors, because accurate calculation of grain geometrical properties plays a vital role in performance prediction.
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