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Load flow methods in Radial system

Load flow methods in Radial system. Outline. Definition Methods Gauss-Seidel Newton-Raphson Distflow Direct approach Decoupling compensation Discussion and Conclusion. What is load flow?. Given specific quantities, determine the behavior of bus voltage and power flows

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Load flow methods in Radial system

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  1. Load flow methods in Radial system

  2. Outline • Definition • Methods • Gauss-Seidel • Newton-Raphson • Distflow • Direct approach • Decoupling compensation • Discussion and Conclusion

  3. What is load flow? • Given specific quantities, determine the behavior of bus voltage and power flows • Important way to analysis any power system

  4. What is load flow? 1

  5. Characteristics of distribution system • Radial or weakly meshed structure • Multiphase and unbalanced operation • Unbalanced distribution load • Extremely large number of branches and nodes • Wide-ranging resistance and reactance values

  6. Gauss-Seidel method • Slow iterative problem-solving technique • Use a full matrix • Require a large number of processors

  7. Gauss-Seidel method 1 1

  8. Gauss-Seidel method 1

  9. Gauss-Seidel method • Comparably slow convergance rate • matrix is sparse and can’t be inverted • Usually solve for linear power system

  10. Newton-Raphson method • Solve nonsquare and nonlinear problems • Relatively high iteration • Require a good initial guess of the solution

  11. Newton-Raphson method • Active power cost optimization • Active power loss minimization • Minimum control-shift • Minimum number of controls rescheduled

  12. Newton-Raphson method • First order • Second order 2 2

  13. Newton-Raphson method • Y=Yij; • i=n(p-1)+k; • J=n(q-1)+1; • S is three phase bus complex power vector • E is diagonal three phase bus voltage matrix • Y is complex conjugation of three phase bus admittance matrix 2 2

  14. Newton-Raphson method • Very complicated • Lead to partial derivations of nonlinear complex • It is involved Jacobian -J complex form • It has relatively slow convergence time

  15. DistFlow method • Don’t require the admittance matrix calculation • Use a set of recursive equations • Estimating the power loss reduction due to a branch exchange.

  16. DistFlow method • Basic equation 3

  17. DistFlow method • Pi represents the real power • Qi represents reactive power • Vi represents voltage magnitudes

  18. DistFlow method • Had a greater speed of convergence and fewer iterations to obtain an optimal solution • Minimize the feeder losses • Make it possible for the power industry to supply energy in the most cost effective manner • Still need to reconfiguration of the network

  19. 3

  20. 3

  21. Direct approach • Bus injection to branch-current matrix (BIBC) • Branch-current to bus-voltage matrix (BCBV)

  22. Direct approach • Accuracy: They both have almost same accuracy as Gauss-Seidel • Performance:1. BCBV has more efficiency, especially when the network size increases. 4

  23. Direct approach • 2.The normalized time increases since the network increase the nonzero terms of the BIBC and BCBV metrics 4

  24. Decoupling compensation • Sequence Decoupling compensation Newton-Raphson (SDCNR) • Sequence Decoupling Compensation Fast Decoupling (SDCFD) 5

  25. Decoupling compensation • Use to analysis both normal and abnormal three phase power system steady state operation • Computation accuracy and speed improved • Convergence reliable • Simplify computation procedure • Positive-sequence impedance of generator

  26. Conclusion • Introduce Some load flow LF-methods • Some other methods: • Bus-impedance • Fast decoupling • Unique features of each LF-method • How to use these methods

  27. Questions?

  28. Reference • 1:A parallel Gauss-Seidel algorithm for sparse power system matricesKoester, D.P.; Ranka, S.; Fox, G.C.;Supercomputing '94. Proceedings14-18 Nov. 1994 Page(s):184 - 193 2: Newton-Raphson method in complex form [power flow analysis]Hieu Le Nguyen;Transmission and Distribution Conference, 1996. Proceedings., 1996 IEEE15-20 Sept. 1996 Page(s):591 - 595 3:A comparison of load flow analysis using DistFlow, Gauss-Seidel, and optimal load flow algorithmsGilbert, G.M.; Bouchard, D.E.; Chikhani, A.Y.;Electrical and Computer Engineering, 1998. IEEE Canadian Conference onVolume 2, 24-28 May 1998 Page(s):850 - 853 vol.2 • 4:A direct approach for distribution system load flow solutionsJen-Hao Teng;Power Delivery, IEEE Transactions onVolume 18, Issue 3, July 2003 Page(s):882 - 887 • 5:Fast three phase load flow methodsXiao-Ping Zhang;Power Systems, IEEE Transactions onVolume 11, Issue 3, Aug. 1996 Page(s):1547 - 1554

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