Design of Robust Current Controller for Two-Level 12-Pulse VSC-based STATCOM

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Capacitive region <svg height="14.6" id="M73" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 51.612499 14.6" width="51.612499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑖</tspan>
</text>
<text transform="matrix(1,0,0,-1,-68.06,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑅</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.61,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="20.592442" y="0">1</tspan>
</text>
</g>
</g>
</svg></td><td align="center">Inductive region  <svg height="14.6" id="M74" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 40.912498 14.6" width="40.912498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑖</tspan>
</text>
<text transform="matrix(1,0,0,-1,-68.06,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑅</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.61,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">1</tspan>
</text>
</g>
</g>
</svg></td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">−1856.7</td><td align="center">−2194.6</td></tr><tr><td align="left">−<svg height="13.7375" id="M75" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 109.8125 13.7375" width="109.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.7375)">
<g transform="translate(72,-61.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="37.158916" y="0">±</tspan>
<tspan style="font-size: 12.50px; " x="48.499138" y="0">𝑗</tspan>
<tspan style="font-size: 12.50px; " x="53.362804" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="59.614304" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="65.865807" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="72.117302" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="78.368805" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="81.494553" y="0">6</tspan>
</text>
</g>
</g>
</svg></td><td align="center">−<svg height="13.8" id="M76" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 109.8125 13.8" width="109.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.8)">
<g transform="translate(72,-60.96)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="37.158916" y="0">±</tspan>
<tspan style="font-size: 12.50px; " x="48.499138" y="0">𝑗</tspan>
<tspan style="font-size: 12.50px; " x="53.362804" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="59.614304" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="65.865807" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="72.117302" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="78.368805" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="81.494553" y="0">3</tspan>
</text>
</g>
</g>
</svg></td></tr><tr><td align="left">−55.556</td><td align="center">−<svg height="13.8" id="M77" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 109.8125 13.8" width="109.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.8)">
<g transform="translate(72,-60.96)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="37.158916" y="0">±</tspan>
<tspan style="font-size: 12.50px; " x="48.499138" y="0">𝑗</tspan>
<tspan style="font-size: 12.50px; " x="53.362804" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="59.614304" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="62.740055" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="68.991554" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="75.243057" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="81.494553" y="0">9</tspan>
</text>
</g>
</g>
</svg></td></tr><tr><td align="left">−23.842</td><td align="center"></td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Eigenvalues with optimal controller parameters based on GA.

Advances in Power Electronics

tab4

Table 4

Table 4: Design of Robust Current Controller for Two-Level 12-Pulse VSC-based STATCOM 