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Distributed Storage for Intermittent Energy Sources: Control Design and Performance Limits

Distributed Storage for Intermittent Energy Sources: Control Design and Performance Limits. Yashodhan Kanoria Stanford University Joint work with: Andrea Montanari , David Tse and Baosen Zhang. The challenge of renewables. Intermittent Intrinsically distributed How to manage?. The

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Distributed Storage for Intermittent Energy Sources: Control Design and Performance Limits

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  1. Distributed Storage for Intermittent Energy Sources: Control Design and Performance Limits YashodhanKanoria Stanford University Joint work with: Andrea Montanari, David Tse and Baosen Zhang

  2. The challenge of renewables • Intermittent • Intrinsically distributed How to manage? The paper

  3. The challenge of renewables • Intermittent • Intrinsically distributed How to manage? This talk

  4. Questions? • Optimal control of grid with transmission and storage? • Infrastructure improvement: • New transmission line? Upgrade in existing line? • New storage facility? • New generation? Which will help more? How to optimally allocate budget?

  5. Our contribution • Control design for discrete time model • Analytical insights quantifying benefits of storage, transmission and overprovisioning

  6. Model 3 2 1 4

  7. Model = Electric load 3 2 1 4

  8. Model = Renewable sources 3 2 1 4

  9. Model 3 2 1 4 −

  10. Model 3 2 1 4

  11. Model 3 2 1 4

  12. Model 3 2 1 4

  13. Model 3 3 2 2 2 1 1 1 4 4 4

  14. Model Energy pushed into

  15. Model • Control inputs: • Dependent variables: • Flows • Storage buffers

  16. Constraints • Storage capacity constraintsHard constraint • Transmission constraintsSoft constraint

  17. Cost function • Cost of fast generation(free disposal of energy) • Cost of violating transmission constraints • Performance criterion: 0 -Ce Ce

  18. What’s the issue? • Centralized control problem • is linear function of controls • Storage constraints cause thresholding • Non-quadratic cost function Idea: Use surrogate cost function (drop storage constraints for now) X X

  19. The surrogate problem • ‘State’ consisting of buffer sizes • ‘Noise’ • State and noise fully observed • Linear state evolution • Quadratic cost • Assume is Gaussian We have an LQG problem! • Can be solved numerically yielding control scheme • Can be mapped back to original problem

  20. The surrogate LQG problem • Is the scheme any good? • Any insights into roles of storage and transmission?

  21. Specific networks • Transmission network is almost a tree • What happens on an infinite line? • What about a two-dimensional grid?

  22. 1-D and 2-D grids Assume: • Storage at each node • Capacity on each line • iid

  23. Storage Transmission 1-D and 2-D grids We find, for original problem: • Analytical expressions for cost of LQG-based schemes • Fundamental limits LQG is near optimal

  24. Storage Transmission Results

  25. Storage Transmission Results

  26. Storage Transmission Results

  27. Storage Transmission Results

  28. Storage Transmission Results

  29. Storage Transmission Results

  30. Storage Transmission Results

  31. Storage Transmission Results and together works best!

  32. Storage Transmission Results

  33. Storage Transmission Results

  34. Storage Transmission Results Averaging over 2-D much more effective than 1-D

  35. Storage Transmission Results seems to provide extra dimension for averaging! Intuition: Time is like extra spatial dimension

  36. Storage Transmission Results

  37. Storage Transmission Results

  38. Spatial averaging is much easier in 2-D 1-D Segment of length 2-D Square of side

  39. Conclusions and future work • Gaussian assumption optimistic • But key insights should remain valid: • 2-D averaging much better than 1-D • Sfacilitates averaging over extra dimension • In the paper: A little overprovisioning can go a long way

  40. Thank you!

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