Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left">Generated power</td><td align="center">HGA</td><td align="center">PCPD</td><td align="center">IPLS</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left"><svg height="15.25" id="M267" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 17.275 15.25" width="17.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><use xlink:href="#x31"></use></g>
</svg> (MW)</td><td align="center">20,1367</td><td align="center">17,36596</td><td align="center">17,36596</td></tr><tr><td align="left"><svg height="15.25" id="M268" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 17.275 15.25" width="17.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><use xlink:href="#x32"></use></g>
</svg> (MW)</td><td align="center">14,8645</td><td align="center">10,00000</td><td align="center">10,00000</td></tr><tr><td align="left"><svg height="15.4" id="M269" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 17.275 15.4" width="17.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><use xlink:href="#x33"></use></g>
</svg> (MW)</td><td align="center">72,4008</td><td align="center">61,340667</td><td align="center">61,340667</td></tr><tr><td align="left"><svg height="15.25" id="M270" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 17.275 15.25" width="17.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg> (MW)</td><td align="center">72,4008</td><td align="center">77,97487</td><td align="center">77,97487</td></tr><tr><td align="left"><svg height="15.4" id="M271" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 17.275 15.4" width="17.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
l-26 -65h-233z" id="x35"></path></g>
</svg> (MW)</td><td align="center">180,0617</td><td align="center">177,81828</td><td align="center">177,81828</td></tr><tr><td align="left"><svg height="15.4" id="M272" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 17.275 15.4" width="17.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><path d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5
t96 -62.5q53 0 78 45.5t25 105.5q0 68 -35 116t-99 48z" id="x36"></path></g>
</svg> (MW)</td><td align="center">139,5865</td><td align="center">155,500216</td><td align="center">155,500216</td></tr><tr><td align="left"><svg height="15.4" id="M273" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 24.975 15.4" width="24.975" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x3A3"></use></g><g transform="matrix(.017,-0,0,-.017,10.228,11.112)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,21.037,15.187)"><use xlink:href="#x1D456"></use></g>
</svg> (MW)</td><td align="center">500,0000</td><td align="center">500,0000</td><td align="center">500,0000</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Comparison of the power generation outputs obtained for the system with 6 generators.

Mathematical Problems in Engineering

tab5

Table 5

Table 5: Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis 