Gurrala, G and Joseph, FC (2023) Application of Homotopy Methods in Power Systems Simulations. [Book Chapter]
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Homotopy Analysis Method (HAM) is a popular semi-analytical method used widely in applied sciences. It stands out from the rest of the semi-analytical methods as it provides a family of solutions to nonlinear equations, including ordinary differential equations (ODEs) and partial differential equations. HAM forms the numerical solution to ODEs as sum of series and number of terms required can be varied. HAM introduces an auxiliary parameter, apart from step time for the numerical solution. The convergence characteristics of the solutions can be varied by changing the auxiliary parameter () in HAM. The convergence region of the solution of ODEs using HAM can be improved by applying it over multiple intervals of time, which is referred to as Multistage Homotopy Analysis Method (MHAM). The applicability of MHAM for power system time-domain simulations has been demonstrated in this chapter. This includes the effect of number of terms, and the time step on the accuracy and stability of the solution. The effectiveness of MHAM has been compared with the Modified Euler (ME) and Midpoint Trapezoidal methods. An alternate application of MHAM as an error estimator is also described. MHAM can help to control the Local Truncation Error at each integration step by adjusting the step size. Hence this is used in ME framework to make the step size adaptive. © 2024 by The Institute of Electrical and Electronics Engineers, Inc.
| Item Type: | Book Chapter |
|---|---|
| Publication: | Power System Simulation Using Semi-Analytical Methods |
| Publisher: | wiley |
| Additional Information: | The copyright for this article belongs to the John Wiley & Sons, Inc. |
| Department/Centre: | Division of Electrical Sciences > Electrical Engineering |
| Date Deposited: | 29 Nov 2023 05:23 |
| Last Modified: | 29 Nov 2023 05:23 |
| URI: | https://eprints.iisc.ac.in/id/eprint/83484 |
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