Optimal Power Flow
In the load flow analysis problem, generator voltage magnitudes, active power generation (except for the slack bus), and P and Q loads at all the busses is known beforehand. Consequently, to determine the power system state, we have to solve 2n - g - 1 equations in as many unknowns, where n is the number of busses in the system and g is the number of generators. Therefore, the resulting system of equations is neither underdetermined nor overdetermined. In contrast, in the state estimation problem, to filter noise, we deliberately work with an overdetermined system (more measurements than unknowns). In both of the above scenario, controller settings, like generator voltages, MW injections, transformer taps, reactive power compensation etc have been decided beforehand. The criteria used for setting these controllers is not relevant to the problem. However, the next logical question that arises is how best to choose the controller settings for a given load condition. Clearly, there exist multiple choices. If the controller settings are also made variable, then a computational problem on the lines of load flow analysis will have to deal with an underdetermined system of equations. For example, if generator voltage magnitudes are not fixed in load flow analysis, as many additional columns (g) will appear in the load flow Jacobian while the number of rows or equations will remain unchanged.
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