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The method used in Vision to calculate the voltages and currents in a power system is the loadflow according to the Newton-Raphson method. The method was first described in 1961 and 1967. The loadflow quickly converges to a solution and from the introduction of sparse matrix techniques and optimal ordering for the elimination process, memory space and computing time were no longer a problem. The Newton-Raphson loadflow has been successfully tested and accepted worldwide.
For more information, see: http://www.phasetophase.nl/pdf/newton-raphson.pdf (in Dutch).
Transformers and synchronous generators with voltage control exist in the network. The control actions of these components influences the voltage in the network and thus the current flows. During the solving of the network equations, it is assumed that the generators first control and then the tap switches of the transformers. The automatic control of the transformers can be switched off; the control of the generators is assumed to always be active.
Most of the networks are connected to an external network, from which the network to be studied is fed. That external grid is represented by an external grid, possibly with a reduced model (the most important transport connections) of the external grid. If a network is not connected to an external grid, the network is in island mode, if the network is powered by a synchronous generator with voltage control and frequency power droop. Vision controls the power of the synchronous generators present in such a way that the generation is in balance with the load in the network. For more information, see: Island mode.
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