Mathematical Modeling and Fault Tolerance Control for a Three-Phase Soft-Switching Mode Rectifier

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left" rowspan="2">Operating condition</td><td align="center" colspan="3">Switch</td></tr><tr class="thead"><td align="center">SW1</td><td align="center">SW2</td><td align="center">SW3</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left">Normal operation</td><td align="center"><i>ⓐ</i></td><td align="center"><i>ⓐ</i></td><td align="center"><i>ⓐ</i></td></tr><tr><td align="left">SSMR <svg height="7.9499998" id="M196" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 9.2749996 7.9499998" width="9.2749996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M515 96q-37 -44 -84.5 -76t-71.5 -32q-12 0 -18 7t-6 34t10 75l19 89h-2q-87 -113 -181 -176q-43 -29 -83 -29q-46 0 -46 63q0 31 9 67l52 222q7 36 -1 36q-10 0 -76 -50l-13 24q47 45 92 71.5t67 26.5q18 0 21 -16.5t-8 -65.5l-56 -242q-16 -67 13 -67q41 0 114 74
t114 146l32 145l74 26h11q-52 -199 -80 -347q-8 -39 6 -39q7 0 32 17.5t47 39.5z" id="x1D462"></path></g>
</svg> fault</td><td align="center"><i>ⓐ</i></td><td align="center"><i>ⓐ</i></td><td align="center"><i>ⓑ</i></td></tr><tr><td align="left">SSMR <svg height="7.9499998" id="M197" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.2875004 7.9499998" width="8.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M457 332q0 -81 -41 -161.5t-105.5 -131.5t-129.5 -51q-46 0 -79 30.5t-33 86.5q0 18 7 51q18 95 46 187q6 19 6 33q0 7 -7 7q-24 0 -78 -64l-20 23q32 48 73 77t78 29q33 0 33 -46q0 -38 -10 -70q-28 -92 -39 -152q-7 -38 -7 -57q0 -78 69 -78q68 0 118 75.5t50 194.5
q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D463"></path></g>
</svg> fault</td><td align="center"><i>ⓑ</i></td><td align="center"><i>ⓐ</i></td><td align="center"><i>ⓐ</i></td></tr><tr><td align="left">SSMR <svg height="7.9499998" id="M198" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 12.225 7.9499998" width="12.225" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152
q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D464"></path></g>
</svg> fault</td><td align="center"><i>ⓐ</i></td><td align="center"><i>ⓑ</i></td><td align="center"><i>ⓐ</i></td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Positions of toggle switches SW1~SW3 under various operating conditions.

Mathematical Problems in Engineering

tab3

Table 3

Table 3: Mathematical Modeling and Fault Tolerance Control for a Three-Phase Soft-Switching Mode Rectifier 