ECE PhD QE PE1 2011 Problem2 - Rhea

Problem 2

Coenergy Calculation

Coenergy will be calculated in steps using a sequential ramping process. Before any steps can be completed, the contribution to coenergy of fixing the mechanical system should be documented (zero unless the mechanical system can store energy in its position).

$ \begin{equation} W_{c,0} = 0 \end{equation} $

The first step in the coenergy calculation will ramp dummy variable $ i_{as}' $ from $ 0 $ to its final value of $ i_{as} $ while dummy variable $ i_{bs}' = 0 $ is held at its initial value.

$ \begin{align} W_{c,1} &= \left.\int_{i_{as}' = 0}^{i_{as}} \lambda_{as}\left(i_{as}', i_{bs}', \theta_{rm}\right) \, di_{as}'\right|_{i_{bs}' = 0} + \left.\int_{i_{as}' = 0}^{i_{as}} \lambda_{bs}\left(i_{as}', i_{bs}', \theta_{rm}\right) \, di_{as}'\right|_{i_{bs}' = 0} \\ \end{align} $

Discussion

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