# An economic dispatch algorithm for congestion management of smart power networks

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## Abstract

We present a novel oblivious routing economic dispatch (ORED) algorithm for power systems. The method is inspired by the oblivious network design which works perfectly for networks in which different sources (generators) send power flow toward their destinations (load points) while they are unaware of the current network state and other flows. Basically, our focus is on the economic dispatch while managing congestion and mitigating power losses. Furthermore, we studied a loss-minimizing type of the economic dispatch which aims to minimize the emission by optimizing the total power generation rather than system cost. Comparing to state-of-the-art economic dispatch methods, our algorithm is independent of network topology and works for both radial and non-radial networks. Our algorithm is thus suited for large-scale economic dispatch problems that will emerge in the future smart distribution grids with host of small, decentralized, and flexibly controllable prosumers; i.e., entities able to consume and produce electricity. The effectiveness of the proposed ORED is evaluated via the IEEE 57-bus standard test system. The simulation results verify the superior performance of the proposed method over the current methods in the literature in terms of congestion management and power loss minimization.

### Keywords

Congestion management Economic dispatch Loss minimization Oblivious network design Smart power network### References

- 1.Kar, S., Hug, G., Mohammadi, J., Moura, J.M.F.: Distributed state estimation and energy management in smart grids: a consensus+ innovations approach. IEEE Trans. Select. Topics Signal Process.
**8**(6), 1022–1038 (2014)CrossRefGoogle Scholar - 2.U.S. Department of Energy: The Smart Grid: An Introduction. (2008)Google Scholar
- 3.Zidan, A., El-Saadany, E.F.: A cooperative multi-agent framework for self-healing mechanisms in distribution systems. IEEE Trans. Smart Grid
**3**(3), 1525–1539 (2012)CrossRefGoogle Scholar - 4.Brown, R.E.: Impact of smart grid on distribution system design. In: Proceedings of IEEE Power and Energy Society General Meeting, pp. 1–4, Pittsburgh, PA (2008)Google Scholar
- 5.Chowdhury, B.H., Rahman, S.: A review of recent advances in economic dispatch. IEEE Trans. Power Syst.
**5**(4), 1248–1259 (1990)MathSciNetCrossRefGoogle Scholar - 6.Pappu, V., Carvalho, M., Pardalos, P.: Optimization and Security Challenges in Smart Power Grids. Springer, New York (2013)CrossRefGoogle Scholar
- 7.Zhu, J.: Optimization of Power System Operation. Wiley, Amsterdam (2014)Google Scholar
- 8.Padhy, N.: Unit commitment: a bibliographical survey. IEEE Trans. Power Syst.
**19**(2), 1196–1205 (2004)CrossRefGoogle Scholar - 9.Selvakumar, A.I., Thanushkodi, K.: A new particle swarm optimization solution to nonconvex economic dispatch problems. IEEE Trans. Power Syst.
**22**(1), 42–51 (2007)CrossRefGoogle Scholar - 10.Amini, M.H., Nabi, B., Haghifam, M.-R.: Load management using multi-agent systems in smart distribution network. In: Proceedings of IEEE Power and Energy Society General Meeting, Vancouver, BC, Canada, pp. 1–5 (2013)Google Scholar
- 11.Lavaei, J., Tse, D., Zhang, B.: Geometry of power flows and optimization in distribution networks. IEEE Trans. Power Syst.
**29**(2), 572–583 (2014)CrossRefGoogle Scholar - 12.Sanjari, M.J., Karami, H., Gooi, H.B.: Micro-generation dispatch in a smart residential multi-carrier energy system considering demand forecast error. Energy Convers. Manag.
**120**, 90–99 (2016)CrossRefGoogle Scholar - 13.Kellerer, E., Steinke, F.: Scalable economic dispatch for smart distribution networks. IEEE Trans. Power Syst.
**99**, 1–8 (2014)Google Scholar - 14.Carrion, M., Arroyo, J.: A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Trans. Power Syst.
**21**(3), 1371–1378 (2006)CrossRefGoogle Scholar - 15.Botterud, A., Zhi, Z., Wang, J., et al.: Demand dispatch and probabilistic wind power forecasting in unit commitment and economic dispatch: a case study of Illinois. IEEE Trans. Sustain. Energy
**4**(1), 250–261 (2012)CrossRefGoogle Scholar - 16.Li, Z., Guo, Q., Sun, H., Wang, J.: Sufficient conditions for exact relaxation of complementarity constraints for storage-concerned economic dispatch. IEEE Trans. Power Syst.
**99**, 1–2 (2015)Google Scholar - 17.Khator, S.K., Leung, L.C.: Power distribution planning: a review of models and issues. IEEE Trans. Power Syst.
**12**(3), 1151–1159 (1997)CrossRefGoogle Scholar - 18.Liu, Y., Ul Hassan, N., Huang, S., Yuen, C.: Electricity cost minimization for a residential smart grid with distributed generation and bidirectional power transactions. IEEE Innovat. Smart Grid Technol. (ISGT), pp. 1–6, Washington, DC (2013)Google Scholar
- 19.Papavasiliou, A., Oren, S.S.: Supplying renewable energy to deferrable loads: algorithms and economic analysis. In: Proceedings of IEEE Power and Energy Society General Meeting, pp. 1–8, Minneapolis, MN (2010)Google Scholar
- 20.Boroojeni, K.G., et al.: Optimal two-tier forecasting power generation model in smart grids. Int. J. Inf. Process.
**8**(4), 79–88 (2014)Google Scholar - 21.Iyengar, S.S., Boroojeni, K.G.: Oblivious Network Routing: Algorithms and Applications. MIT Press, New York (2015)MATHGoogle Scholar
- 22.Gupta, A., Hajiaghayi, M.T., Racke, H.: Oblivious network design. In: SODA 06: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithm. New York, NY, USA: ACM, pp. 970–979 (2006)Google Scholar
- 23.Maknouninejad, A., Lin, W., Harno, H.G., Qu, Z., Simaan, M.A.: Cooperative control for self-organizing microgrids and game strategies for optimal dispatch of distributed renewable generations. Energy Syst.
**3**(1), 23–60 (2012)CrossRefGoogle Scholar - 24.Tuffaha, M., Gravdahl, J.T.: Discrete state-space model to solve the unit commitment and economic dispatch problems. Energy Syst. pp. 1–23, in Press (2016)Google Scholar
- 25.Frank, S., Rebennack, S.: An introduction to optimal power flow: theory, formulation, and examples. IIE Trans. to appear (2016)Google Scholar
- 26.Nolden, C., Schönfelder, M., Eßer-Frey, A., Bertsch, V., Fichtner, W.: Network constraints in techno-economic energy system models: towards more accurate modeling of power flows in long-term energy system models. Energy Syst.
**4**(3), 267–287 (2013)CrossRefGoogle Scholar - 27.Kargarian, A., Mohammadi, J., Guo, J., Chakrabarti, S., Barati, M., Hug, G., Kar, S., Baldick, R.: Toward distributed/decentralized DC optimal power flow implementation in future electric power systems. IEEE Trans Smart Grid (2016, to appear)Google Scholar
- 28.Rebennack, S., Flach, B., Pereira, M.V.F., Pardalos, P.M.: Stochastic hydro-thermal scheduling under CO2 emissions constraints. IEEE Trans. Power Syst.
**27**(1), 58–68 (2012)CrossRefGoogle Scholar - 29.Shortle, J., et al.: Transmission-capacity expansion for minimizing blackout probabilities. IEEE Trans. Power Syst.
**29**(1), 43–52 (2014)CrossRefGoogle Scholar - 30.Tucker, A.: A note on convergence of the Ford–Fulkerson flow algorithm. Math. Oper. Res.
**2**(2), 143–144 (1977)MathSciNetCrossRefMATHGoogle Scholar - 31.Kumar, A., Gupta, A., Roughgarden, T.: Simpler and better approximation algorithms for network design. In: Proceedings of the 35th STOC, pp. 365–372 (2003)Google Scholar
- 32.Bartal, Y.: On approximating arbitrary metrics by tree metrics. In: Proceedings of the 30th STOC, pp. 161–168 (1998)Google Scholar
- 33.Alman, F.S.S., Heriyan, J.C., Avi, R.R., Ubramanian, S.S.: Approximating the single-sink link-installation problem in network design. SIAM J. Optim.
**11**, 595–610 (2000)MathSciNetCrossRefGoogle Scholar - 34.Arger, D.R.K., Inkoff, M.M.: Building Steiner trees with incomplete global knowledge. In: Proceedings of the 41st FOCS, pp. 613–623 (2000)Google Scholar
- 35.Uha, S.G., Eyerson, A.M., Ungala, K.M.: Hierarchical placement and network design problems. In: Proceeding of the 41st FOCS, pp. 603–612 (2000)Google Scholar
- 36.Uha, S.G., Eyerson, A.M., Ungala, K.M.: A constant factor approximation for the single sink edge installation problem. In: Proceedings of the 33rd STOC, pp. 383–388 (2001)Google Scholar
- 37.Eyerson, A.M., Ungala, K.M., Lotkin, S.A.P.: Cost-distance: two metric network design. In: Proceedings of the 41st FOCS, pp. 624–630 (2000)Google Scholar
- 38.Rebennack, S., Nahapetyan, A., Pardalos, P.M.: Bilinear modeling solution approach for fixed charge network flow problems. Optim. Lett.
**3**(3), 347–355 (2009)MathSciNetCrossRefMATHGoogle Scholar - 39.Srinivasagopalan, S., Busch, C., Iyengar, S.S.: An oblivious spanning tree for single-sink buy-at-bulk in low doubling-dimension graphs. IEEE Trans. Comput.
**61**(5), 700–712 (2012)MathSciNetCrossRefGoogle Scholar - 40.Kumar, A., Gupta, A., Roughgarden, T.: Approximations via cost-sharing: a simple approximation algorithm for the multicommodity rent-or-buy problem. In: Proceedings of the 44th FOCS, pp. 606–615 (2003)Google Scholar
- 41.Garg, N., Khandekar, R., Konjevod, G., Ravi, R., Salman, F.S., Sinha, A.: On the integrality gap of a natural formulation of the single-sink buy-at-bulk network design formulation. In: Proceedings of the 8th IPCO, pp. 170–184 (2001)Google Scholar
- 42.Charikar, M., Karagiozova, A.: On non-uniform multicommodity buy-at-bulk network design. In: Proceedings of the 37th STOC, pp. 176–182 (2005)Google Scholar
- 43.Alwar, K.T.: Single-sink buy-at-bulk LP has constant integrality gap. In: Proceedings of the 9th IPCO, pp. 475–486 (2002)Google Scholar
- 44.Kumar, A., Gupta, A., Roughgarden, T.: A constant-factor approximation algorithm for the multicommodity rent-or-buy problem. In: Proceedings of the 43rd FOCS, pp. 333–342 (2002)Google Scholar
- 45.Werbuch, B.A., Zar, Y.A.: Buy-at-bulk network design. In: Proceedings of the 38th FOCS, pp. 542–547 (1997)Google Scholar
- 46.Frank, S., Steponavice, I., Rebennack, S.: Optimal power flow: a bibliographic survey I: formulations and deterministic methods. Energy Syst.
**3**(3), 221–258 (2012)CrossRefGoogle Scholar - 47.Frank, S., Steponavice, I., Rebennack, S.: Optimal power flow: a bibliographic survey II: non-deterministic and hybrid methods. Energy Syst.
**3**(3), 259–289 (2012)CrossRefGoogle Scholar - 48.Amini, M.H., et al.: Distributed security constrained economic dispatch. IEEE Innovative Smart Grid Technologies-Asia (ISGT ASIA) (2015)Google Scholar
- 49.Wood, A.J., Wollenberg, B.F.: Power Generation, Operation, and Control. Wiley, Amsterdam (2012)Google Scholar
- 50.Fakcharoenphol, J., Rao, S.B., Talwar, K.: A tight bound on approximating arbitrary metrics by tree metrics. In: Proceedings of the 35th STOC, pp. 448–455 (2003)Google Scholar
- 51.MATLAB version 8.5. Miami, Florida: The MathWorks Inc. (2015)Google Scholar
- 52.Abdollahi, A., Moghaddam, M.P., Rashidinejad, M., Sheikh-El-Eslami, M.K.: Investigation of economic and environmental-driven demand response measures incorporating UC. IEEE Trans. Smart Grids
**3**(1), 12–25 (2012)CrossRefGoogle Scholar - 53.Power systems test case archive, 57 Bus Power Flow Test Case. [Online]. Available: http://www2.ee.washington.edu/research/pstca/pf57/pg_tca57bus.htm (1993). Accessed 10 May 2016
- 54.Zimmerman, R.D., Murillo-Sanchez, C.E., Thomas, R.J.: MATPOWER: Steady-state operations, planning and analysis tools for power systems research and education. IEEE Trans. Power Syst.
**26**(1), 12–19 (2011)CrossRefGoogle Scholar