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## Complex Flow-Based Non-Linear ATC Screening

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**Complex Flow-Based Non-Linear ATC Screening**Santiago Grijalva The Power Affiliates Program Urbana, May 23, 2002**Motivation**• Electricity markets have to deal with the effect of network constraints. • Transfer capability: • Flow-based transmission rights • Transmission operations • Generation and transmission planning**1st Limiter**Thermal @Line X 2nd Limiter Thermal @ Line Y 3rd Limiter Low Voltage @ Bus Z 0 700 950 1300 Static ATC • Supervises: • Line Thermal Limits • Bus High and Low Voltage Limits • Static Collapse • Exact determination requires non-linear continuation algorithms • Transfer limiter sequences are required Transfer size (MW)**Static ATC**• Contingency conditions • Several directions • System patterns Contingency Pattern Need Fast Methods Linear ATC Direction**Linear ATC**• Thermal limits only • Often thermal limits appear as first limiters • Distribution Factors (PTDF’s) • Good for large combinatorial studies • Drawback: • No Bus Voltage Supervision • No Static Collapse Supervision**ATC Cases**Cases correctly assessed with Linear ATC Cases that need Non-Linear ATC Linear and Non-linear ATC Cases • Unexpected non-linear constraints can have a significant impact in security • We don’t know which cases until we run the full non-linear simulation • ATC Screening**Non-Linear ATC Screening**• Research on new methods to estimate the distance to security constraints • Methods based on the state variables: • Bus high and low voltage • Methods based on branch complex flow: • Thermal limits • Generator reactive power limits • Static collapse**Estimated**Thermal Actual Low Voltage Reactive Support Collapse 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Transfer Size (p.u.) Non-Linear ATC Screening**1. Linear ATC with Reactive Flows**Qjk Line is Overloaded Limiting Circle: (0,0,MVA rating) Operating Circle: (Pjk,0,Qjk,0,Sjk,0) Pjk Pjk0 MVA rating Pjkmax**Change in system state:**• Mismatches in rectangular coordinates: • Corrected state change: Can get transfer size p from here 2. Bus Voltage Constraints Transfer Direction T=Tsell+TBuy • Define a transfer: pT Transfer Size in (MW) or p.u.**Transfer #**32 28 24 20 16 12 8 4 0 0 5 10 15 20 25 30 35 Transfer Size, p (p.u.) 2. Bus Voltage Constraints**3. Static Collapse** Line Static Transfer Stability Limit (STSL) • Complex flow trajectory. At least one line must hit the STSL before collapse**3. Static Collapse**Typical Simulation Result Qjk/Yjk First STSL Pjk/Yjk**32**Transfer # 28 24 20 16 12 8 4 0 35 40 25 30 20 15 0 5 10 Transfer Size, p (p.u) 3. Static Collapse**Reactive Support Qj**2.25 2 Actual 1.75 1.5 Circle 1.25 1 Vcrit 0.75 Fourth Order 0.5 0.25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 0 Transfer Size, p (p.u.) 4. Generator Reactive Power Limits • PV bus supports voltage for changes in complex flows due to the transfer.**32**Transfer # 28 24 20 16 12 8 4 0 18 20 12 14 16 10 4 0 2 6 8 Transfer Size, p (p.u.) 4. Generator Reactive Power Limits**Estimated**Thermal Actual Low Voltage Reactive Support Collapse 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Screening Logic • Decision Rule • Statistical • Adaptive • Heuristic If the first limiter is thermal and limiters of other type occur beyond +%, then linear ATC is sufficient. Otherwise non-linear simulation is required.**Transfer Limiter Sequences**Transfer # 15 V L Q C 14 L V Q C L V Q C 13 L Q V C V Q L C 12 V L Q C L V Q C 11 L Q V C V Q L C 10 V L Q C V Q C L 9 V Q L C V Q L C 8 V Q L C V C L Q 7 V C L V C Q 6 V L Q C L V Q C 5 L V Q C V L C Q 4 V L Q C L V Q C 3 L V Q C L V C Q 2 L V Q C V L C Q 1 V L Q C 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Transfer Size, p (p.u.)**Result**• Screening based on the decision rule was successful in 95% of cases. • Less than 5% of cases that did require non-linear simulation were classified as linear.**Conclusions**• Linear ATC is enhanced by estimating the effect of reactive power flows. • A consistent prediction of the point of collapse is obtained with indicators based on the complex-flow of individual elements. • The distance to non-linear security constraints can be estimated with information from the base case. • ATC cases that require non-linear simulation are identified with high significance by the ATC screening algorithm.