Example 5.5 except that the generators must satisfy the following limitations: 80 "p1" 1200 MW 450 "P2" 750 MW 150 "P3" 250 MW

Question

Repeat Example 5.5 except that the generators must satisfy the following limitations:

[latex]80 \ ^{\prime \prime}P_{1} \ ^{\prime \prime} 1200 MW[/latex]

[latex]450 \ ^{\prime \prime}P_{2} \ ^{\prime \prime} 750 MW[/latex]

[latex]150 \ ^{\prime \prime}P_{1} \ ^{\prime \prime} 250 MW[/latex]

Accepted Answer

From the solution of Example 5.5, the output of generator 3 exceeds the maximum limit of 0.25 pu. Therefore after the first iteration in the previous example [latex] P_{3} [/latex] is set to 0.25 pu. The new partial derivatives become

[latex] \left[\frac{∂g}{∂u} ight]= \left[\begin{matrix} 0 \1 \end{matrix} ight] [/latex] (5.71)

[latex]\left[\frac{∂g}{∂x} ight]= same[/latex] (5.72)

[latex]\left[\frac{∂f}{∂u} ight]=\left[1+0.025P_{2} ight] [/latex] (5.73)

[latex]\left[\frac{∂f}{∂x} ight]=same [/latex] (5.74)

From the constrained steepest descent, the new values of generation become

[latex]\left[\begin{matrix}P_{1} \ P_{2} \ P_{3} \end{matrix} ight] =\left[\begin{matrix}117.1 \ 588.3 \ 250.0 \end{matrix} ight] MW[/latex]

with a cost of $7703/MWh, which is higher than the unconstrained cost of generation of $7664/MWh. As more constraints are added to the system, the system is moved away from the optimal operating point, increasing the cost of generation.

Question 5.6: Example 5.5 except that the generators must satisfy the foll...

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