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Complex-Flow Network Limits and Static System Collapse

Complex-Flow Network Limits and Static System Collapse. Santiago Grijalva The Power Affiliates Program Meeting Urbana, May 11, 2001. j. k. Motivation. Linear ATC programs are based on “line flow limits” such as thermal constraints. They use Power Transfer Distribution Factors (PTDFs):.

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Complex-Flow Network Limits and Static System Collapse

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  1. Complex-Flow Network Limits and Static System Collapse Santiago Grijalva The Power Affiliates Program Meeting Urbana, May 11, 2001

  2. j k Motivation • Linear ATC programs are based on “line flow limits” such as thermal constraints. • They use Power Transfer Distribution Factors (PTDFs):

  3. Motivation • There is a need to check other phenomena such as margin to collapse. Goal • “Describe the system-wide collapse limit in terms of line flow limits”.

  4. 5 1 1 5 0 3 2 0 0 3 2 2 Network Theory

  5. Network Theory • Does the system-wide transfer limit depend on the limits of individual lines?

  6. Complex Flow Limits • T/L complex flow trajectory. • Static Transfer Stability Limit (STSL): • [Pjkmx,st–, Pjkmx,st+]

  7. Main Result: A Line Flow Based Necessary Condition for Collapse • Let p be a scalar parameter. The system has solution for all p such that 0 < p0 < p < p* and no solution if p  p*. • Proposition:Let a power network with a power flow solution for a parameter p=p0, giving flows at each line side Pjk(p0) feasible with respect to line side STSLs. If p varies until the point of collapse, then at least the trajectory of one line side must have reached its STSL.

  8. Results Typical Simulation Result Qjk/Yjk Pjk/Yjk

  9. Numerical Results Table 1: Point of First STSL and Point of Collapse IEEE 118-bus case with p=change in MW bus load

  10. Numerical Results Table 2: Point of First STSL and Point of Collapse IEEE 118-bus case: p=change in system active load

  11. Numerical Results Table 3: Point of First STSL and Point of Collapse IEEE 118-bus case: p=change in active and reactive system load

  12. Numerical Results: Margin to Collapse Margin(MW) Actual Value Using PTDF Using CTDF Pi(MW)

  13. Conclusions and Further Work • A necessary condition for system-wide collapse limit using individual line properties has been developed. • This necessary condition is not severely conservative. • The necessary condition may point towards a fast approximate mapping of the system-wide collapse limit into a check for use with linear ATC programs and other security applications.

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