Fig 4 - uploaded by Yize Chen
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Example when the middle region has no data. But as long as the other two regions are well trained (black lines), the slopes in the middle region are bounded (blue and red dashed lines) by Theorem 5.5. Then the active constraint detection (Algorithm 1) would still be correct.
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The DC optimal power flow (DCOPF) problem is a fundamental problem in power systems operations and planning. With high penetration of uncertain renewable resources in power systems, DCOPF needs to be solved repeatedly for a large amount of scenarios, which can be computationally challenging. As an alternative to iterative solvers, neural networks a...
Contexts in source publication
Context 1
... the curve in Fig 1. Suppose we learned the two end pieces correctly but there was no training data for the middle piece, as shown in Fig. 4. Then by Theorem 5.5, the slope of the middle piece is constrained to be between the slope of the two end pieces. Furthermore, even if the neural network is trained in such a way that there are more than one piece of the middle region, the slopes of all of the pieces are still bounded between the two end pieces. Since Algorithm 1 only ...
Context 2
... is trained in such a way that there are more than one piece of the middle region, the slopes of all of the pieces are still bounded between the two end pieces. Since Algorithm 1 only relies on getting µ to be in the correct range, the active constraints would be identified correctly for all of these cases. Theorem 5.5 formalizes the picture in Fig. 4 to higher dimensions, but the geometric intuition remains the ...
Context 3
... the curve in Fig 1. Suppose we learned the two end pieces correctly but there was no training data for the middle piece, as shown in Fig. 4. Then by Theorem 5.5, the slope of the middle piece is constrained to be between the slope of the two end pieces. Furthermore, even if the neural network is trained in such a way that there are more than one piece of the middle region, the slopes of all of the pieces are still bounded between the two end pieces. Since Algorithm 1 only ...
Context 4
... is trained in such a way that there are more than one piece of the middle region, the slopes of all of the pieces are still bounded between the two end pieces. Since Algorithm 1 only relies on getting µ to be in the correct range, the active constraints would be identified correctly for all of these cases. Theorem 5.5 formalizes the picture in Fig. 4 to higher dimensions, but the geometric intuition remains the ...
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