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Table 2 Objective function under different fault conditions

From: Equivalent model of multi-type distributed generators under faults with fast-iterative calculation method based on improved PSO algorithm

 

Equivalent model of the DGs

Voltage relationship

Fault boundary constraints

3P-SC-F

\(\begin{gathered} \left\{ {\begin{array}{*{20}c} {Mag_{I - IIDG} = \sqrt {i_{IIDGdref}^{2} + i_{IIDGqref}^{2} } } \\ {Phi_{I - IIDG} = \arctan \left( {\frac{{i_{IIDGdref} }}{{i_{IIDGqref} }}} \right)} \\ \end{array} } \right. \hfill \\ \left\{ {\begin{array}{*{20}c} {Mag_{I - DFIG} = \sqrt {i_{DFIGdref}^{2} + i_{DFIGqref}^{2} } } \\ {Phi_{I - DFIG} = \arctan \left( {\frac{{i_{DFIGdref} }}{{i_{DFIGqref} }}} \right)} \\ \end{array} } \right. \hfill \\ \end{gathered}\)

\(\left\{ {\begin{array}{*{20}l} {\dot{E}_{s} = \dot{I}_{s} Z_{s} - \dot{U}_{IIDG} + \dot{I}_{IDG} Z_{LT1} } \hfill \\ {\dot{U}_{IIDG} - \dot{I}_{IDG} Z_{LT1} = \dot{U}_{DFIG} - \dot{I}_{DFIG} Z_{LT2} } \hfill \\ {\dot{U}_{IIDG} - \dot{I}_{IIDG} Z_{LT1} = \left( {\dot{I}_{s} + \dot{I}_{IDG} + \dot{I}_{DFIG} } \right)Z_{L2} - \dot{U}_{f(1)} } \hfill \\ {\dot{U}_{f(1)} = \left( {\dot{I}_{f(1)} + \dot{I}_{s} + \dot{I}_{IIDG} + \dot{I}_{DFIG} } \right)Z_{LD3} } \hfill \\ {\dot{U}_{f(2)} = \frac{{\left( {Z_{s(2)} + Z_{L2(2)} } \right)Z_{LD3(2)} }}{{Z_{s(2)} + Z_{L2(2)} + Z_{LD3(2)} }}\dot{I}_{f(2)} } \hfill \\ \end{array} } \right.\)

\(\dot{U}_{f(2)} = 0\)

2P-SC-F

\(\left\{ {\begin{array}{*{20}l} {\dot{U}_{f(1)} = \dot{U}_{f(2)} } \hfill \\ {\dot{I}_{f(1)} + \dot{I}_{f(2)} = 0} \hfill \\ \end{array} } \right.\)

2P-G-F

\(\left\{ {\begin{array}{*{20}l} {\dot{U}_{f(1)} = \dot{U}_{f(2)} } \hfill \\ {\dot{I}_{f(1)} + \dot{I}_{f(2)} = 0} \hfill \\ \end{array} } \right.\)

1P-G-F

\(\left\{ {\begin{array}{*{20}l} {\dot{U}_{f(1)} = \dot{U}_{f(2)} = 0} \hfill \\ {\dot{I}_{f(1)} + \dot{I}_{f(2)} } \hfill \\ \end{array} } \right.\)