Solving Multiperiod OPF Problems Using an AC-QP Algorithm Initialized with an SOCP Relaxation

IEEE Transactions on Power Systems

Volumn 32, Issue 5, 2017, Pages 3538-3548

  Marley, Jennifer F ^a   Molzahn, Daniel K ^b   Hiskens, Ian A ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

^b ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

Convex relaxation; global solution; large scale power system optimization; optimal power flow

Indexed keywords

ACOUSTIC GENERATORS; ELECTRIC LOAD FLOW; OPTIMIZATION; QUADRATIC PROGRAMMING; RELAXATION PROCESSES; VIRTUAL STORAGE;

CONVEX RELAXATION; GLOBAL SOLUTIONS; IMPROVED CONVERGENCE; LARGE-SCALE POWER SYSTEMS; OPTIMAL POWER FLOW PROBLEM; OPTIMAL POWER FLOWS; SECOND-ORDER CONE PROGRAMMING; SUCCESSIVE QUADRATIC PROGRAMMING;

PROBLEM SOLVING;

EID: 85028920007     PISSN: 08858950     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPWRS.2016.2636132     Document Type: Article

References (56)

1. A. Wood, B. Wollenberg, G. Sheble, Power Generation, Operation and Control. 3rd ed. New York, NY, USA: Wiley, 2013.
2. M. Huneault and F. Galiana, "A survey of the optimal power flow literature, " IEEE Trans. Power Syst., vol. 6, no. 2, pp. 762-770, May 1991.
3. J. Momoh, R. Adapa, M. El-Hawary, "A review of selected optimal power flow literature to 1993. Parts I & II, " IEEE Trans. Power Syst., vol. 14, no. 1, pp. 96-111, Feb. 1999.
4. A. Castillo and R. O'Neill, "Survey of approaches to solving the ACOPF (OPF Paper 4), " US Federal Energy Regulatory Commission, Tech. Rep., Mar. 2013.
5. A. Motto, F. Galiana, A. Conejo, J. Arroyo, "Network-constrained multiperiod auction for a pool-based electricity market, " IEEE Trans. Power Syst., vol. 17, no. 3, pp. 646-653, Aug. 2002.
6. T. Overbye, X. Cheng, Y. Sun, "A comparison of the AC and DC power flow model for LMP calculations, " in Proc. 37th Hawaii Int. Conf. Syst. Sci., Jan. 2006, pp. 1-9.
7. M. Amini, R. Jaddivada, S. Mishra, O. Karabasoglu, "Distributed security constrained economic dispatch, " in Proc. IEEE Innovative Smart Grid Technol. Conf., Bangkok, Thailand, Nov. 2015, pp. 1-6.
8. K. Purchala, L. Meeus, D. Van Dommelen, R. Belmans, "Usefulness of DC power flow for active power flow analysis, " in Proc. IEEE Power Eng. Soc. General Meeting, Jun. 2005, pp. 454-459.
9. B. Stott, J. Jardim, O. Alsac, "DC power flow revisited, " IEEE Trans. Power Syst., vol. 24, no. 3, pp. 1290-1300, Aug. 2009.
10. K. Dvijotham and D. Molzahn, "Error bounds on linear power flow approximations: A convex relaxation approach, " in Proc. IEEE 55th Annu. Conf. Decision Control, Dec. 2016, pp. 2411-2418.
11. X. Bai, H.Wei, K. Fujisawa, Y.Wang, "Semidefinite programming for optimal power flow problems, " Int. J. Elect. Power Energy Syst., vol. 30, no. 6, pp. 383-392, Feb. 2008.
12. J. Lavaei and S. Low, "Zero duality gap in optimal power flow problem, " IEEE Trans. Power Syst., vol. 27, no. 1, pp. 92-107, Feb. 2012.
13. S. Low, "Convex relaxation of optimal power flow-part I: Formulations and equivalence, " IEEE Trans. Control Netw. Syst., vol. 1, no. 1, pp. 15-27, Mar. 2014.
14. D. Molzahn, J. Holzer, B. Lesieutre, C. DeMarco, "Implementation of a large-scale optimal power flow solver based on semidefinite programming, " IEEE Trans. Power Syst., vol. 28, no. 4, pp. 3987-3998, Nov. 2013.
15. D. Molzahn and I. Hiskens, "Moment-based relaxation of the optimal power flow problem, " in Proc. 18th Power Syst. Comput. Conf., Aug. 18-22, 2014, pp. 1-7.
16. B. Ghaddar, J. Marecek, M. Mevissen, "Optimal power flow as a polynomial optimization problem, " IEEE Trans. Power Syst., vol. 31, no. 1, pp. 539-546, Jan. 2016.
17. C. Josz, J. Maeght, P. Panciatici, J. Gilbert, "Application of the moment-SOS approach to global optimization of the OPF problem, " IEEE Trans. Power Syst., vol. 30, no. 1, pp. 463-470, Jan. 2015.
18. D. Molzahn and I. Hiskens, "Sparsity-exploiting moment-based relaxations of the optimal power flow problem, " IEEE Trans. Power Syst., vol. 30, no. 6, pp. 3168-3180, Nov. 2015.
19. B. Kocuk S. Dey, A. Sun, "Strong SOCP relaxations of the optimal power flow problem, " Oper. Res., vol. 64, no. 6, pp. 1177-1196, 2016.
20. C. Coffrin, H. Hijazi, P. Van Hentenryck, "The QC relaxation: Theoretical and computational results on optimal power flow, " IEEE Trans. Power Syst., vol. 31, no. 4, pp. 3008-3018, Jul. 2016.
21. E. Dall'Anese, H. Zhu, andG.Giannakis, "Distributed optimal power flow for smart microgrids, " IEEE Trans. Smart Grid, vol. 4, no. 3, pp. 1464-1475, Sep. 2013.
22. D. Molzahn and I. Hiskens, "Mixed SDP/SOCP moment relaxations of the optimal power flow problem, " in Proc. IEEE Eindhoven PowerTech, Jun. 2015, pp. 1-6.
23. R. Madani, S. Sojoudi, J. Lavaei, "Convex relaxation for optimal power flow problem: Mesh networks, " IEEE Trans. Power Syst., vol. 30, no. 1, pp. 199-211, Jan. 2015.
24. B. Lesieutre, D. Molzahn, A. Borden, C. DeMarco, "Examining the limits of the application of semidefinite programming to power flow problems, " in Proc. 49th Annu. Allerton Conf. Commun., Control, Comput., Sep. 2011, pp. 1492-1499.
25. D. Molzahn, B. Lesieutre, C. DeMarco, "Investigation of non-zero duality gap solutions to a semidefinite relaxation of the optimal power flow problem, " in Proc. 47th Hawaii Int. Conf. Syst. Sci., Jan. 6-9, 2014, pp. 2325-2334.
26. D. Molzahn and I. Hiskens, "Convex relaxations of optimal power flow problems: An illustrative example, " IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 63, no. 5, pp. 650-660, May 2016.
27. K. Chandy, S. Low, U. Topcu, H. Xu, "A simple optimal power flow model with energy storage, " in Proc. IEEE 49th Annu. Conf. Decision Control, Atlanta, GA, USA, Dec. 2010, pp. 1051-1057.
28. M. Almassalkhi and I. Hiskens, "Cascade mitigation in energy hub networks, " in Proc. IEEE 50th Annu. Conf. Decision Control, Orlando, FL, USA, Dec. 2011, pp. 2181-2188.
29. R. Jabr, S. Karaki, J. Korbane, "Robust multi-period OPF with storage and renewables, " IEEE Trans. Power Syst., vol. 30, no. 5, pp. 2790-2799, Sep. 2015.
30. N. Nguyen, D. Bovo, A. Berizzi, "Optimal power flow with energy storage systems: Single-period model vs. multi-period model, " in Proc. IEEE Eindhoven PowerTech, Jun. 2015, pp. 1-6.
31. D. Gayme and U. Topcu, "Optimal power flow with large-scale storage integration, " IEEE Trans. Power Syst., vol. 28, no. 2, pp. 709-717, May 2013.
32. A. Gopalakrishnan, A. U. Raghunathan, D. Nikovski, L. T. Biegler, "Global optimization of multi-period optimal power flow, " in Proc. Amer. Control Conf., Washington, DC, USA, Jun. 2013, pp. 1157-1164.
33. J. Marley and I. Hiskens, "Multi-period AC-QP optimal power flow including storage, " in Proc. 19th Power Syst. Comput. Conf., Jun. 2016, pp. 1-7.
34. S. Low, "Convex relaxation of optimal power flow: Parts I & II, " IEEE Trans. Control Netw. Syst., vol. 1, no. 1, pp. 15-27, Mar. 2014.
35. L. Gan and S. Low, "Convex relaxations and linear approximation for optimal power flow in multiphase radial networks, " in Proc. 18th Power Syst. Comput. Conf., Aug. 2014, pp. 1-9.
36. M. Baran and F. Wu, "Optimal capacitor placement on radial distribution systems, " IEEE Trans. Power Del., vol. 4, no. 1, pp. 725-734, Jan. 1989.
37. Z. Li, Q. Guo, H. Sun, J.Wang, "Sufficient conditions for exact relaxation of complementarity constraints for storage-concerned economic dispatch, " IEEE Trans. Power Syst., vol. 31, no. 2, pp. 1653-1654, Mar. 2016.
38. Z. Li, Q. Guo, H. Sun, J. Wang, "Further discussions on sufficient conditions for exact relaxation of complementarity constraints for storageconcerned economic dispatch, " Jun. 2015, arXiv:1505.02493.
39. A. Giacomoni and B. Wollenberg, "Linear programming optimal power flow utilizing a trust region method, " in Proc. North Amer. Power Symp., Sep. 2010, pp. 1-6.
40. J. Felder and I. Hiskens, "Optimal power flow with storage, " in Proc. 18th Power Syst. Comput. Conf., Aug. 2014, pp. 1-7.
41. D. Molzahn, C. Josz, I. Hiskens, P. Panciatici, "Solution of optimal power flow problems using moment relaxations augmented with objective function penalization, " in Proc. IEEE 54th Annu. Conf. Decision Control, Dec. 2015, pp. 31-38.
42. Siemens PTI, "Volume II: Program application guide, " Power Syst. Simulation Eng., Dec. 2007, vol. 31.0.
43. R. Zimmerman, C. Murillo-Sánchez, R. Thomas, "MATPOWER: Steady-state operations, planning, analysis tools for power systems research and education, " IEEE Trans. Power Syst., vol. 26, no. 1, pp. 12-19, Feb. 2011.
44. W. Bukhsh, A. Grothey, K. McKinnon, P. Trodden, "Local solutions of optimal power flow problem, " IEEE Trans. Power Syst., vol. 28, no. 4, pp. 4780-4788, Nov. 2013, Test Case Archive. [Online]. Available: Http://www.maths.ed.ac.uk/optenergy/LocalOpt/
45. S. Fliscounakis, P. Panciatici, F. Capitanescu, L. Wehenkel, "Contingency ranking with respect to overloads in very large power systems taking into account uncertainty, preventive and corrective actions, " IEEE Trans. Power Syst., vol. 28, no. 4, pp. 4909-4917, Nov. 2013.
46. E. Camacho and C. Bordons, Model Predictive Control. 2nd ed. New York, NY, USA: Springer-Verlag, 2004.
47. N. Janssens and A. Kamagate, "Loop flows in a ring AC power system, " in Proc. 14th Power Syst. Comput. Conf., Jun. 2002, pp. 591-597.
48. D. Bienstock and G. Munoz, "Approximate method for AC transmission switching based on a simple relaxation for ACOPF problems, " in Proc. IEEE Power Energy Soc. General Meeting, Denver, CO, 2015, pp. 1-5.
49. C. Coffrin and P. V. Hentenryck, "A linear-programming approximation of AC power flows, " INFORMS J. Comput., vol. 26, no. 4, pp. 718-734, May 2014.
50. F. Bouffard and F. Galiana, "Stochastic security for operations planning with significant wind power generation, " IEEE Trans. Power Syst., vol. 23, no. 2, pp. 306-316, May 2008.
51. A. Papavasiliou, S. Oren, R. ONeill, "Reserve requirements for wind power integration: A scenario-based stochastic programming framework, " IEEE Trans. Power Syst., vol. 26, no. 4, pp. 2197-2206, Nov. 2011.
52. J. Morales, A. Conejo, J. Perez-Ruiz, "Economic valuation of reserves in power systems with high penetration of wind power, " IEEE Trans. Power Syst., vol. 24, no. 2, pp. 900-910, May 2009.
53. L. Roald, F. Oldewurtel, T. Krause, G. Andersson, "Analytical reformulation of security constrained optimal power flow with probabilistic constraints, " in Proc. IEEE PowerTech Conf., Jun. 2013, pp. 1-6.
54. D. Bienstock, M. Chertkov and S. Harnett, "Chance-constrained optimal power flow: Risk-aware network control under uncertainty, " SIAM Rev., vol. 56, no. 3, pp. 461-495, Jan. 2014.
55. M. Campi, S. Garatti, F. Ramponi, "Non-convex scenario optimization with application to system identification, " in Proc. 54th IEEE Conf. Decision Control, Dec. 2015, pp. 4023-4028.
56. M. Vrakopoulou, M. Katsampani, K. Margellos, J. Lygeros, G. Andersson, "Probabilistic security-constrained AC optimal power flow, " in Proc. IEEE PowerTech Conf., Jun. 2013, pp. 1-6.