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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 | pmid = | pmc = | 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, 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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==Other power-flow methods==
*[[Gauss–Seidel method]]: This is the earliest devised method. It shows slower rates of convergence compared to other iterative methods, but it uses very little memory and does not need to solve a matrix system.
*[[Fast-decoupled-load-flow method]] is a variation on Newton-Raphson that exploits the approximate decoupling of active and reactive flows in well-behaved power networks, and additionally fixes the value of the [[Jacobian matrix and determinant|Jacobian]] during the iteration in order to avoid costly matrix decompositions. Also referred to as "fixed-slope, decoupled NR". Within the algorithm, the Jacobian matrix gets inverted only once, and there are three assumptions. Firstly, the conductance between the buses is zero. Secondly, the magnitude of the bus voltage is one per unit. Thirdly, the sine of phases between buses is zero. Fast decoupled load flow can return the answer within seconds whereas the Newton Raphson method takes much longer. This is useful for real-time management of power grids.<ref>{{Cite journal|
*[[Holomorphic embedding load flow method]]: A recently developed method based on advanced techniques of complex analysis. It is direct and guarantees the calculation of the correct (operative) branch, out of the multiple solutions present in the power flow equations.
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