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Topics Addressed at UC Berkeley

Topics Addressed at UC Berkeley. Modeling Wind Variability and Uncertainty Application of HPC to DC Transmission Switching Transmission switching with successive linearization of AC OPF. Modeling Wind Power Variability and Uncertainty (Complete) Task 1.8: Wind Modeling (Due 6/30/13).

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Topics Addressed at UC Berkeley

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  1. Topics Addressed at UC Berkeley Modeling Wind Variability and UncertaintyApplication of HPC to DC Transmission SwitchingTransmission switching with successive linearization of AC OPF

  2. Modeling Wind Power Variability and Uncertainty (Complete) Task 1.8: Wind Modeling (Due 6/30/13)

  3. Obtain a multi-area stochastic model of wind power that capture temporal and spatial statistical and systematic variability of wind power production • Calibrate model to available data bases (e.g. NREL western wind and solar interconnection study) of wind speed and power production. • Use model to bootstrap limited data so as to produce multiple temporal and spatial realization of wind power scenarios that can be used for stochastic optimization and simulation studies (scenarios can be scaled to reflect renewable penetration assumptions) Objectives and Approach

  4. Background

  5. Autoregressive Model

  6. Calibration

  7. Calibration Details

  8. Scenario Generation

  9. Data Sources for Demonstration Example

  10. Reduced WECC Model with Major Wind Sites

  11. Tehachapi County

  12. Remarks

  13. Parallelization of Transmission Switching for Economics in DC network (118 Bus complete, FERC/PJM case in progress) Task 1.6: Parallelization of MIP Heuristic and Greedy Algorithm (Due 6/30/13) Task 1.11 Small Scale Testing: Normal (Due 6/30/13) Task 2.5: High Performance Computing & Parallelization (Due 6/30/14) – Large Scale Parallelization

  14. Test Cases • IEEE 118 Bus System (Standard test case for transmission switching studies (Fisher-2008, Hedman -2010, Fuller-2012) • 118 buses • 186 lines • 19 generators • Solved on Laptop with 3 processors • FERC Dataset • 13867 Buses • 1011 Generators • 18824 Branches • Summer Scenario • DCOPF Base Case (all lines closed) Cost: $541620.75 • Solved on LLNL HPC Cluster • Computational Facility - LLNL Hera cluster • 864 nodes (13824 cores) • Quad-Core AMD Opteron processors 8356 at 1.2 GHz, 32 GB per node • MPI calling on Java CPLEX callable library

  15. Greedy Line Selection (TX1)

  16. Greedy Line Selection with Priority Listing (TX2)

  17. MIP Heuristic (TX3)

  18. Results for IEEE118 Case • (TX3) outperforms (TX2) which outperforms (TX1) • Note (TX2) outperforms (TX1) although (TX1) checks all lines at each iteration • Critical lines: • L132, L153 switched by all • and L132, L162 switched by (TX1) and (TX3) • FULL MIP Solution: Cost = 1537.38 (MIP GAP 0.5%) 32 Lines switched 17 seconds 300 seconds 1,314 seconds FULL MIP (0.5% MIPGAP) 32 Lines OFF 34 seconds 1537.38

  19. Results for FERC/PJM Case K is the number of lines examined before choosing the best improved line to switch • TX1 outperforms TX2. • For TX2, higher K leads to better performance. • No apparent critical line

  20. Results

  21. Conclusions • The model generally takes very long time to solve even with parallel programmingso we need to explore improvements through use of warm starts and other shortcut methods used in industry. • Even though TX1 outperforms TX2, the long computation time renders it impractical, which makes intelligent line search by sensitivity analysis important in real electrical networks. • Using smaller K can effectively reduce the computation time in TX2.

  22. Transmission switching with successive linearization of AC OPF (Continued) Task 1.9: AC and Stability Feasibility (Due 6/30/13) Task 1.11: Small Scale Testing: Normal (Due 6/30/13)

  23. LP-ACOPF Procedure Flat start: vrn =1, vin=0 Compute starting values of line currents AC Feasible or Maximum Iterations Exceeded? Solve LP Approximation Return Solution Yes No Add voltage and current cuts to cut off AC infeasible solutions Reset fixed points in P&Q Taylor series expansions as LP optimal solutions

  24. r tan(π/N) r θ/2=π/N Voltage Approximation Initial Approximation Iterative Cuts New Constraint Solution

  25. IEEE Data & Current Constraints

  26. MIP Methods

  27. Results Linear Objective Value Linear vs. Nonlinear Objective Value

  28. Results – CPU Time Note: MIPs with up to five lines open hit maximum time limit of 1000s

  29. Results Linear Objective Value Linear vs. Nonlinear Objective Value

  30. Results – CPU Time Note: MIPs with up to five lines open hit maximum time limit of 1000s

  31. Voltage Violations:57 Bus, Loose Current ConstraintVoltage Profile

  32. Preventing Voltage Violations With Additional Constraints Remove stepsize restriction. Run first iteration without any constraints on the minimum voltage, then add….. Instant Feasibility Incremental Feasibility -vmax -vmin -vmax -vmin

  33. Additional Constraints

  34. Results LP Objective Value Linear vs. Nonlinear Objective Value

  35. Results LP Objective Value Linear vs. Nonlinear Objective Value

  36. Up to Five Lines Open • One MIP: Solve MIP (switching) on first linear iteration; fix network; solve LP ACOPF in all further iterations • Repeated MIP: Solve MIP at every linear iteration

  37. Conclusions • Inner cuts prevent infeasibility • Opening one line at a time is promising • Need to examine more MIP heuristics with LP

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