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Let i and j be two marginal units with (C_j > C_i), belonging to different buses.
Let (i, j) and (p, q) be two pairs of marginal units with cost functions (C_j > C_i) and (C_q > C_p), corresponding to before and after the topology error, respectively.
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Indeed, in this situation the generator at slack bus 1 is still the marginal unit with the topology error.
Open image in new window Fig. 6 Impact of a varying gap between the marginal costs with and without topology error on LMP change in Case 4: a pair of marginal units (p, q) with topology error.
Staffing: The decreasing marginal unit cost with increasing utilization is based on the assumption that health care institutions could either meet the demand within their given labour capacity or acquire sufficient additional staff.
In Case 3, the congested line varies from lines 9, 10 to lines 1, 2. Case 4 includes the same changing marginal units in Case 2, along with the different congested lines 5, 6.
In addition, Cases 3 and 4 have a more significant effect on LMP than Cases 1 and 2. We can conjecture from this that the impact of the line exclusion with varying marginal units or the congested line on LMP is larger than without them.
Equation (7) represents the LMP change equation for Case 4. This equation can be modified to illustrate the other three cases with varying conditions for network congestion and marginal units due to topology error.
Our current work involves a more realistic broad set of scenarios including Cases 2, 3, and 4 with the changing conditions for network congestion and marginal units (i.e. part-loaded generators) due to topology error.
We can observe from Fig. 6 that as the gap between the energy costs of the marginal units increases, the value of LMP change increases at only buses 2 and 3 with positive (W_{l,l'}^{(4 }).
Case 1: both unchanging congestion line and marginal units.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com