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Assessing multiple operationally-stable power flow solutions in unbalanced impedance-grounded systems: initialization procedure and analysis
- Citation Author(s):
- Submitted by:
- Bruno Cortes
- Last updated:
- Mon, 11/30/2020 - 11:45
- DOI:
- 10.21227/4b4n-az50
- Data Format:
- License:
- Categories:
- Keywords:
Abstract
The power flow is usually formulated by nonlinear equations and may present multiple solutions. However, most of these solutions do not represent a practical situation but are mathematical findings. Remarkably, in unbalanced multiphase systems with impedance-grounded loads, a phenomenon can occur where two or more solutions may especially show practical significance. These solutions are called operationally-stable solutions (solutions which for a given loading level the nodal voltages, currents, and losses are feasible) and may be obtained in Distribution Systems (DS). In this paper, some relevant aspects regarding the multiple solutions in unbalanced grounded systems are explored: (i) the development of a simple analytical model considering the feeder and loads to analyze the multiple solutions generically; (ii) a direct procedure for initializing neutral voltages to find possible operationally-stable solutions or reduce the number of iterations to achieve convergence; (iii) a study on multiple solutions using the continuation power flow to analyze their behavior and verify their impacts on DS. The proposed assumptions have been confirmed with numerical experiments over IEEE 123, Simple NEV, and IEEE 8500 test feeders.
Please, if you modify or use any of the following contents, you should cite the paper under the DOI: 10.1109/TPWRS.2020.3037464
4 files are found attached in this IEEE DataPort:
1) "NonLinear Equations_IEEE TPWRS-PES 2020 Dataport.pdf" - This file is the annex of the paper entitled “Assessing multiple operationally-stable power flow solutions in unbalanced impedance-grounded systems: initialization procedure and analysis”. Here, it is provided to the readers the step-by-step derivation for the nonlinear equations mentioned in the manuscript.
2) "NonLinear_Equations.m" - In this Matlab file, it is available the final nonlinear equations to support the research community in the matter. In the paper, the authors solved these equations by using Bertini, which can be used without setting an initial point for the state variables.
3) "solve_2Bus.m" - In this Matlab file, it is available a code that uses "fsolve" function to solve the nonlinear equations for the two-bus system presented in the paper. Note that initial points must be individually-set to enable "fsolve" to find multiple solutions.
4) "restrictions.m" - This Matlab file has the nonlinear equations that "fsolve" must solve and are called inside the "solve_2Bus.m" file.
Dataset Files
- 3 Nonlinear systems of equations NonLinear_Equations.m (11.19 kB)
- Code to solve the nonlinear equations of a two-bus system solve_2Bus.m (5.81 kB)
- Restrictions used inside the file "solve_2Bus.m" restrictions.m (1.96 kB)
Documentation
Attachment | Size |
---|---|
PROOF OF THE DEVELOPED EQUATIONS IN THE MANUSCRIPT | 422.18 KB |