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Commercial power systems are usually too complex to allow for hand solution of the power flow. Special purpose [[Network analyzer (AC power)|network analyzers]] were built between 1929 and the early 1960s to provide laboratory-scale physical models of power systems. Large-scale digital computers replaced the analog methods with numerical solutions.
In addition to a power-flow study, computer programs perform related calculations such as [[short-circuit]] fault analysis, stability studies (transient and steady-state), [[unit commitment]] and [[economic dispatch]].<ref>{{Cite book | last1 = Low | first1 = S. H. | chapter = Convex relaxation of optimal power flow: A tutorial | doi = 10.1109/IREP.2013.6629391 | title = 2013 IREP Symposium Bulk Power System Dynamics and Control - IX Optimization, Security and Control of the Emerging Power Grid | pages = 1–06 | year = 2013 | isbn = 978-1-4799-0199-9 | s2cid = 14195805 }}</ref> In particular, some programs use [[linear programming]] to find the ''optimal power flow'', the conditions which give the lowest cost per [[kilowatt hour]] delivered.
A load flow study is especially valuable for a system with multiple load centers, such as a refinery complex. The power flow study is an analysis of the system’s capability to adequately supply the connected load. The total system losses, as well as individual line losses, also are tabulated. Transformer tap positions are selected to ensure the correct voltage at critical locations such as motor control centers. Performing a load flow study on an existing system provides insight and recommendations as to the system operation and optimization of control settings to obtain maximum capacity while minimizing the operating costs. The results of such an analysis are in terms of active power, reactive power, voltage magnitude and phase angle. Furthermore, power-flow computations are crucial for [[Unit_commitment_problem_in_electrical_power_production|optimal operations of groups of generating units]].
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