power grid sizing via convex programming peng du, shih-hung weng, xiang hu, chung-kuan cheng...
TRANSCRIPT
Power Grid Sizing via Convex Programming
Peng Du, Shih-Hung Weng, Xiang Hu, Chung-Kuan Cheng
University of California, San Diego
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Outline
• Problem Formulation• Convex Programming Reduction• Optimizer of the Convex Programming Problem– Interior point and gradient descent methods– A Krylov space method to evaluate effective
resistances– Close form of the derivative of effective resistances
• Experimental Results
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Problem Formulation
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• Power Network N(V,E)• Voltage source at node u• Current loads in set W• Variables: conductance
g(e) for each edge e• Objective: min max
voltage drop at all nodes and over all possible current loads
Problem Formulation
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• D(v,g,I): the voltage drop between nodes u and v for given conductance assignment g and current profile I.
• We assume the current profile satisfies the normalization constraint I(w1)+I(w2)+…+I(wr)=1 where W={w1,w2,…,wr}.
Optimizer for Larger Cases
• Interior point method.• Gradient descent method.• Obstacles:– Evaluate the objective: effective resistances.– Evaluate the derivative of effective resistances
relative to conductance.
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Experimental Results (Regular Grids)
The effective resistances before (blue plane) and after (green plane) optimization.
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Experimental Results (Regular Grids)
(R,C) MaxR(uni) MaxR(opt) Improvement
(4,4) 44.57 36.00 19.23%
(7,5) 142.21 100.00 29.68%
(10,10) 542.10 324.89 40.07%
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Voltage Map of Layer M1
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The worst voltage drop is achieved near the origin which is the farthest point to the voltage source.
Resource Transformation between M6 and AP
• “Adjust Percentage” indicates the ratio of M6 resource obtained from AP.• A monotonically decreasing curve means that with more resource to M6 we can
reduce worst voltage drop.
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Conclusion• A power grid sizing method to minimize the maximum voltage
drop over all test locations and current source distributions.• We reduce the original problem into a convex programming
problem whose objective is to minimize the maximum effective resistance.
• We adopt a Krylov space method to evaluate the effective resistances and devise a formula to update the derivative of effective resistance.
• Experimental results show that our method can achieve up to 40% improvement for regular 2D grids and 7.32% improvement for a practical power grid with only top two layers tunable.