Electric Distribution Network Planning pp 41-63 | Cite as

# Static and Dynamic Convex Distribution Network Expansion Planning

## Abstract

This chapter presents static and dynamic optimization-based models for planning the electric distribution network. Based on a branch flow model, two Mixed-Integer Conic Quadratic Programming (MICQP) convex formulations are proposed to solve the network expansion planning models including high modeling fidelity of the intrinsic interaction of the manifold elements of the networks. The objective of the presented models is to minimize investment and operation costs by optimally deciding on installing new feeders and/or changing existing ones for others with larger capacities, installing new substations or expanding existing ones and, finally, installing capacitor banks and voltage regulators, modifying the network topology. In addition, discrete tap settings of voltage regulators are modeled as a set of mixed-integer linear equations, which are embedded in an ac optimal power flow. The presented MICQP models are convex optimization problems. Therefore globality and convergence are guaranteed. Computational results to verify the efficiency of the proposed methodology are obtained for a 24-node test system. Finally, conclusions are duly drawn.

## Keywords

Capacitor banks Convex optimization Dynamic model Electric distribution network expansion planning Static models Voltage regulators## References

- 1.I.J. Ramirez-Rosado, J.A. Dominguez-Navarro, Possibilistic model based on fuzzy sets for the multiobjective optimal planning of electric power distribution networks. IEEE Trans. Power Syst.
**19**(4), 1801–1810 (2004)CrossRefGoogle Scholar - 2.I.J. Ramirez-Rosado, J.A. Dominguez-Navarro, New multiobjective tabu search algorithm for fuzzy optimal planning of power distribution systems. IEEE Trans. Power Syst.
**21**(1), 224–233 (2006)CrossRefGoogle Scholar - 3.T. Gönen,
*Electric Power Distribution Systems Engineering*(McGraw-Hill, New York, 1986)Google Scholar - 4.S.F. Mekhamer, M.E. El-Hawary, S.A. Soliman, M.A. Moustafa, M.M. Mansour, New heuristic strategies for reactive power compensation of radial distribution feeders. IEEE Trans. Power Delivery
**17**(4), 1128–1135 (2002)CrossRefGoogle Scholar - 5.J.Y. Park, J.M. Sohn, J.K. Park, Optimal capacitor allocation in a distribution system considering operation costs. IEEE Trans. Power Syst.
**24**(1), 462–468 (2009)CrossRefGoogle Scholar - 6.N.C. Sahoo, S. Ganguly, D. Das, Recent advances on power distribution system planning: a stage-of-the-art survey. Energy Syst.
**4**(2), 165–193 (2013)CrossRefGoogle Scholar - 7.K. Nara, T. Satoh, H. Kuwabara, K. Aoki, M. Kitagawa, T. Ishihara, Distribution systems expansion planning by multi-stage branch exchange. IEEE Trans. Power Syst.
**7**(1), 208–214 (1992)CrossRefGoogle Scholar - 8.E. Míguez, J. Cidrás, E. Díaz-Dorado, J. García-Dornelas, An improved branch-exchange algorithm for large-scale distribution network planning. IEEE Trans. Power Syst.
**17**(4), 931–936 (2002)CrossRefGoogle Scholar - 9.M. Lavorato, M. Rider, A.V. Garcia, R. Romero, A constructive heuristic algorithm for distribution system planning. IEEE Trans. Power Syst.
**25**(3), 1734–1742 (2010)CrossRefGoogle Scholar - 10.G. Yang, Z. Dong, K. Wong, A modified differential evolution algorithm with fitness sharing for power system planning. IEEE Trans. Power Syst.
**23**(2), 514–522 (2008)CrossRefGoogle Scholar - 11.V. Miranda, J.V. Ranito, L.M. Proença, Genetic algorithm in optimal multistage distribution network planning. IEEE Trans. Power Syst.
**9**(4), 1927–1933 (1994)CrossRefGoogle Scholar - 12.I. Ramirez-Rosado, J. Bernal-Agustín, Genetic algorithms applied to the design of large power distribution systems. IEEE Trans. Power Syst.
**13**(2), 696–703 (1998)CrossRefGoogle Scholar - 13.J. Gómez, H. Khodr, P. Oliveira, L. Ocque, J. Yusta, R. Villasana, A. Urdaneta, Ant colony system algorithm for the planning of primary distribution circuits. IEEE Trans. Power Syst.
**19**(2), 996–1004 (2004)CrossRefGoogle Scholar - 14.V. Parada, J. Ferland, M. Arias, K. Daniels, Optimization of electrical distribution feeders using simulated annealing. IEEE Trans. Power Del.
**19**(3), 1135–1141 (2004)CrossRefGoogle Scholar - 15.J.M. Nahman, D.M. Peric, Optimal planning of radial distribution networks by simulated annealing technique. IEEE Trans. Power Syst.
**23**(2), 790–795 (2008)CrossRefGoogle Scholar - 16.S. Ganguly, N. Sahoo, D. Das, Mono- and multi-objective planning of electrical distribution networks using particle swarm optimization. Appl. Soft Comput.
**11**(2), 2391–2405 (2011)CrossRefGoogle Scholar - 17.R. Lotero, J. Contreras, Distribution system planning with reliability. IEEE Trans. Power Del.
**26**(4), 2552–2562 (2011)CrossRefGoogle Scholar - 18.S. Ganguly, N. Sahoo, D. Das, Multi-objective planning of electrical distribution systems using dynamic programming. Int. J. Electr. Power Energy Syst.
**46**, 65–78 (2013)CrossRefGoogle Scholar - 19.S.N. Ravadanegh, R.G. Roshanagh, On optimal multistage electric power distribution networks expansion planning. Electr. Power Energy Syst.
**54**, 487–497 (2014)CrossRefGoogle Scholar - 20.R.A. Jabr, Polyhedral formulations and loop elimination constraints for distribution network expansion planning. IEEE Trans. Power Syst.
**28**, 1888–1897 (2013)CrossRefGoogle Scholar - 21.R. Gallego, J. Monticelli, R. Romero, Optimal capacitor placement in radial distribution networks. IEEE Trans. Power Syst.
**16**(4), 630–637 (2001)CrossRefGoogle Scholar - 22.D.F. Pires, A.G. Martins, C.H. Antunes, A multiobjective model for VAR planning in radial distribution networks based on tabu search. IEEE Trans. Power Syst.
**20**(2), 1089–1094 (2005)CrossRefGoogle Scholar - 23.I.C. Silva Junior, S. Carneiro Junior, E.J. Oliveira, J.S. Costa, J.L.R. Pereira, P.A.N. Garcia, A heuristic constructive algorithm for capacitor placement on distribution system. IEEE Trans. Power Syst.
**23**(4), 1619–1626 (2008)CrossRefGoogle Scholar - 24.C.A.N. Pereira, C.A. Castro, Optimal placement of voltage regulators in distribution systems, in
*Proceedings of IEEE Bucharest Power Tech*(Bucharest, Romania, 2009), pp. 1–5Google Scholar - 25.A.S. Safigianni, G.J. Salis, Optimum voltage regulator placement in a radial power distribution network. IEEE Trans. Power Syst.
**15**(2), 879–886 (2000)CrossRefGoogle Scholar - 26.J. Mendoza, D. Morales, R. López, J. Vannier, C. Coello, Multiobjetive location of automatic voltage regulators in radial distribution network using a micro genetic algorithm. IEEE Trans. Power Syst.
**22**(1), 404–412 (2007)CrossRefGoogle Scholar - 27.J.F. Franco, M.J. Rider, M. Lavorato, R.A. Romero, A mixed integer LP model for the optimal allocation of voltage regulators and capacitors in radial distribution systems. Electr. Power Energy Syst.
**48**, 123–130 (2013)CrossRefGoogle Scholar - 28.E.P. Madruga, L.N. Canha, Allocation and integrated configuration of capacitor banks and voltage regulators considering multi-objective variables in smart grid distribution system, in
*Proceedings of International Conference on Industry Applications*(São Paulo, Brazil, Nov. 2010), pp. 1–6Google Scholar - 29.B.A. de Souza, A.M.F. de Almeida, Multiobjective optimization and fuzzy logic applied to planning of the volt/var problem in distributions systems. IEEE Trans. Power Syst.
**25**(3), 1274–1281 (2010)CrossRefGoogle Scholar - 30.J. Sugimoto, R. Yokoyama, Y. Fukuyama, V.V.R. Silva, H. Sasaki, Coordinated allocation and control of voltage regulators based on reactive tabu search, in
*IEEE Russian Power Tech*(St. Petersburg, Russia, 27–30 June 2005), pp. 1–6Google Scholar - 31.H. Fletcher, K. Strunz, Optimal distribution system horizon planning-part I: formulation. IEEE Trans. Power Syst.
**22**(2), 791–799 (2007)CrossRefGoogle Scholar - 32.S. Haffner, L.F.A. Pereira, L.A. Pereira, L.S. Barreto, Multistage model for distribution expansion planning with distributed generation—part I: problem formulation. IEEE Trans. Power Delivery
**23**(2), 915–923 (2008)CrossRefGoogle Scholar - 33.S. Haffner, L.F.A. Pereira, L.A. Pereira, L.S. Barreto, Multistage model for distribution expansion planning with distributed generation—part II: numerical results. IEEE Trans. Power Delivery
**23**(2), 924–929 (2008)CrossRefGoogle Scholar - 34.A. Sorokin, S. Rebennack, P. Pardalos, N. Iliadis, M. Pereira,
*Handbook of Networks in Power Systems I. Energy Systems*(Springer, Berlin, 2012)Google Scholar - 35.J. Tate, T. Overbye, A comparison of the optimal multiplier in polar and rectangular coordinates. IEEE Trans. Power Syst.
**20**(4), 1667–1674 (2005)CrossRefGoogle Scholar - 36.S.C. Tripathy, G.D. Prasad, O.P. Malik, G. S. Hope, Load-flow solutions for ill-conditioned power systems by a Newton-like method. IEEE Trans. Power App. Syst.
**PAS-101**(10), 3648–3657 (1982)CrossRefGoogle Scholar - 37.R.A. Jabr, Radial distribution load flow using conic programming. IEEE Trans. Power Syst.
**21**, 1458–1459 (2006)CrossRefGoogle Scholar - 38.M.E. Baran, F.F. Wu, Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans. Power Delivery
**4**, 1401–1407 (1989)CrossRefGoogle Scholar - 39.M.E. Baran, F.F. Wu, Optimal capacitor placement on radial distribution systems. IEEE Trans. Power Delivery
**4**, 725–734 (1989)CrossRefGoogle Scholar - 40.M.E. Baran, F.F. Wu, Optimal sizing of capacitors placed on a radial distribution system. IEEE Trans. Power Delivery
**4**, 735–743 (1989)CrossRefGoogle Scholar - 41.M. Farivar, S.H. Low, Branch flow model: relaxations and convexification—part I. IEEE Trans. Power Syst.
**28**(3), 2554–2564 (2013)CrossRefGoogle Scholar - 42.D. Luenberger, Y. Ye,
*Linear and Nonlinear Programming*(Springer, 2008)Google Scholar - 43.R.A. Jabr, Optimal placement of capacitors in a radial network using conic and mixed integer linear programming. Electr. Power Syst. Res.
**78**, 941–948 (2008)CrossRefGoogle Scholar - 44.J. López, D. Pozo, J. Contreras, J.R.S. Mantovani, A multiobjective minimax regret robust VAr planning model. IEEE Trans. Power Syst.
**32**, 1761–1771 (2017)CrossRefGoogle Scholar - 45.I. Gönen, I. Ramirez-Rosado, Review of distribution system planning models: a model for optimal multi-stage planning. IEE Proc. Gen. Trans. Dist.
**133**(7), 397–408 (1986)Google Scholar - 46.IBM, IBM ILOG CPLEX V12.1. User’s Manual for CPLEX (2009)Google Scholar
- 47.R. Fourer, D.M. Gay, B.W. Kernighan,
*AMPL: A Modeling Language for Mathematical Programming*(Duxbury Press, 2002)Google Scholar