Power-flow study: Difference between revisions

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{{Short description|Numerical analysis of electric power flow}}

In [[power engineering]], thea '''power-flow study''', (also orknown as '''power-flow analysis''' or '''load-flow study''',) is a [[numerical analysis]] of the flow of [[electric power]] in an interconnected system. A power-flow study usually uses simplified notations such as a [[one-line diagram]] and [[per-unit system]], and focuses on various aspects of [[AC power]] parameters, such as voltages[[voltage]], voltage angles, real power and reactive power. It analyzes the power systems in normal steady-state operation.

Power-flow or load-flow studies are important for planning future expansion of power systems as well as in determining the best operation of existing systems. The principal information obtained from the power-flow study is the magnitude and phase angle of the voltage at each [[busbar|bus]], and the real and reactive power flowing in each line.

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==Model==

An '''alternating current power-flow model''' is a model used in electrical engineering to analyze [[power grids]]. It provides a [[Nonlinear systems|nonlinear system]] of equations which describes the energy flow through each transmission line. The problem is non-linear because the power flow into load impedances is a function of the square of the applied voltages. Due to nonlinearity, in many cases the analysis of large network via AC power-flow model is not feasible, and a linear (but less accurate) DC power-flow model is used instead.

Usually analysis of a three-phase power system is simplified by assuming balanced loading of all three phases. Sinusoidal steady-state operation is assumed, with no transient changes in power flow or voltage due to load or generation changes, meaning all current and voltage waveforms are sinusoidal with no DC offset and have the same constant frequency. The previous assumption is the same as assuming the power system is linear time-invariant (even though the system of equations is nonlinear), driven by sinusoidal sources of same frequency, and operating in steady-state, which allows to use [[phasor]] analysis, another simplification. A further simplification is to use the [[per-unit system]] to represent all voltages, power flows, and impedances, scaling the actual target system values to some convenient base. A system [[one-line diagram]] is the basis to build a mathematical model of the generators, loads, buses, and transmission lines of the system, and their electrical impedances and ratings.

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* [[Laurent Power Flow (LPF) method]]: Power flow formulation that provides guarantee of uniqueness of solution and independence on initial conditions for electrical distribution systems. The LPF is based on the current injection method (CIM) and applies the Laurent series expansion. The main characteristics of this formulation are its proven numerical convergence and stability, and its computational advantages, showing to be at least ten times faster than the BFS method both in balanced and unbalanced networks.<ref>Giraldo, J. S., Montoya, O. D., Vergara, P. P., & Milano, F. (2022). A fixed-point current injection power flow for electric distribution systems using Laurent series. Electric Power Systems Research, 211, 108326. https://doi.org/10.1016/j.epsr.2022.108326</ref> Since it is based on the system's admittance matrix, the formulation is able to consider radial and meshed network topologies without additional modifications (contrary to the compensation-based BFS<ref>Shirmohammadi, D., Hong, H. W., Semlyen, A., & Luo, G. X. (1988). A compensation-based power flow method for weakly meshed distribution and transmission networks. IEEE Transactions on power systems, 3(2), 753-762. https://doi.org/10.1109/59.192932</ref>). The simplicity and computational efficiency of the LPF method make it an attractive option for recursive power flow problems, such as those encountered in time-series analyses, metaheuristics, probabilistic analysis, reinforcement learning applied to power systems, and other related applications.

==DC power- flow==

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DirectDC power flow (also known as direct current load flow (DCLF)) gives estimations of lines power flows on AC power systems. DirectDespite the name, DC power flow is not an analysis on [[direct current]], loadbut rather on alternating current; the name comes from the linearity of the analysis, which resembles analysis on direct current. DC power flow looks only at [[active power]] flows and neglects [[reactive power]] flows. This method is non-iterative and absolutely convergent but less accurate than AC Load Flow solutions. DirectDC current loadpower flow is used wherever repetitive and fast load flow estimations are required.<ref>[https://link.springer.com/content/pdf/bbm%3A978-3-642-17989-1%2F1.pdf Seifi, H. &. (2011). Appendix A: DC Load Flow. In H. &. Seifi, Electric power system planning: issues, algorithms and solutions (pp. 245-249). Berlin: Springer]</ref>

==References==