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This paper presents a number of refinements to the formulation as well as the solution procedure for a coordinated reactive power control scheme using conventional reactive power sources, transformer tap, and also the DC converters of a multiterminal DC network. The proposed approach offers considerable improvements in the computational efficiency. These improvements can be attributed to (a) a reduction in the dimensionality of the formulation by exploiting the decoupled nature of the real and reactive power flows in the AC network, (b) sparse matrix techniques to selectively generate the required sensitivity relationships as opposed to computing the entire sensitivity matrix, (c) an efficient dual simplex LP scheme adapted to solve for the desired controls. Numerical examples are presented to demonstrate the effectiveness of the new approach and to show that even for a small 30 bus, 5 DC terminal system significant reduction in computing time can be obtained.