Energy Systems

, Volume 9, Issue 3, pp 529–550 | Cite as

Optimal siting and sizing of renewable energy sources, storage devices, and reactive support devices to obtain a sustainable electrical distribution systems

  • Ozy D. Melgar Dominguez
  • Mahdi Pourakbari Kasmaei
  • Marina Lavorato
  • José R. Sanches Mantovani
Original Paper


This paper presents an integrated planning framework to optimally determine the location and allocation of renewable-based distributed generation (DG) units, energy storage systems (ESSs), and capacitor banks (CBs). This planning aim at improving the performance of electrical distribution systems (EDSs). In the proposed model, the cost of energy delivered by the substation and the investment costs are minimized. The environmental aspects are taken into account to obtain an efficient environmentally committed plan. The uncertainties due to PV generation and demand profile are considered via external uncertainty indexes in a deterministic environment. The proposed model is a mixed-integer nonlinear programming (MINLP) problem, which is recast to a mixed-integer linear programming (MILP) problem using appropriate linearization techniques. This approximated MILP model is implemented in the mathematical language AMPL, while the commercial solver CPLEX is used to obtain the global optimal solutions. The proposed model is validated by testing on a medium voltage distribution system with 135 nodes under different conditions and topologies.


Capacitor banks Energy storage systems Environmental aspects Planning framework Renewable generation 



Capacitor bank


Distribution company


Distributed generation


Depth of discharge


Electrical distribution system


Energy storage system


Mixed integer linear programming


Mixed integer nonlinear programming



Sets and indexes

\({\varOmega }^{ cb}\)

Set of CB capacities


Set of planning horizon (years)


Set of circuits


Set of nodes


Set of time intervals


Index of reactive power capacity of installed CB


Index of years


Index of nodes


Index of circuits


Index of PV modules


Index of time intervals


\(\zeta _{t,d}^{G} \)

Energy cost at time interval t, at year d

\(\zeta _b^{CB^{f/sw}} \)

Installation cost of fixed/switchable CB with power capacity b

\(\zeta ^{PV}\)

Installation cost of PV modules

\( \zeta _{d}^{o \& m^{ PV}}\)

Operation and maintenance cost of installed PV modules at year d

\( \zeta _n^{D \& R}\)

Disposal and recycling cost of ESS at present net value (n)

\( \zeta _{d}^{o \& m^{ ESS}}\)

Operation and maintenance cost of installed ESS at year d

\(\zeta ^{PC^{ ESS}}\)

Investment charging and discharging power capacity cost of ESS

\(\zeta ^{RC^{ ESS}}\)

Investment storage reservoir cost of ESS

\({\varDelta }_d \)

Duration of the year d (8760 h)

\({\varDelta }_t \)

Duration of time interval t

\(\underline{{\varPhi }}^S,\overline{{\varPhi }}^S \)

Lower and upper limit of power factor for substation

\({\varPhi }^{ pv}\)

Power factor for PV-based DG units

\(\eta \)

Efficiency of the ESS

\(\overline{E}^{ ESS}\)

Maximum energy reservoir capacity of ESS that can be installed

\(\underline{E}^{ ESS}\)

Minimum energy reservoir capacity of ESS that can be installed

\(e ^p \)

Emission coefficient

\(f_{t,d}^{G^{ pv}}\)

PV generation factor; time t, year d

\(\overline{I}_{ ij}\)

Maximum current magnitude allowed on the circuit ij

\({IC^{ CB}}\)

Investment cost limit of CB

\({IC^{ PV}}\)

Investment cost limit of PV-based DG units

\({IC^{ ESS}}\)

Investment cost limit of ESS

\({N}^{ PV}\)

Maximum number of PV plants that can be installed

\(P_{i,t,d}^{ Ld}\)

Active power demand at node i, time t, year d

\(\overline{P}^{ ESS}\)

Maximum power rating of ESS that can be installed

\(\overline{P}^{ PV}\)

Active power capacity of PV module

\(\overline{ PE}_d \)

Pollutant emission limit at year d

\(Q_{b}^{ esp}\)

Nominal reactive power of the CB with capacity b

\(Q_{i,t,d}^{ Ld}\)

Reactive power demand at node i, time t, and year d

\(R,X,Z_{ ij}\)

Resistance, reactance, and impedance of the circuit ij

\(\overline{V}, \underline{V}\)

Upper and lower voltage magnitude limits

\(V^{ nom} \)

Nominal voltage magnitude


Estimated voltage magnitude at node i, time t, and year d

Continuous variables

\(\tilde{E}_{i}^{ ESS} \)

Energy reservoir of installed ESS at node i

\(E_{i,t,d}^{ ESS} \)

State of charge of installed ESS at node i, time t, and year d

\(I^{ sqr}_{ij,t,d}\)

Square of current flow magnitude of circuit ij in time t, and year d


Active power flow of circuit ij in time t, and year d

\(\tilde{P}_{i}^{ ESS}\)

Power rating of installed ESS at node i

\(P_{i,t,d}^{ES{S^c}} \)

Charging power of installed ESS at node i in time t, and year d

\(P_{i,t,d}^{ES{S^d}} \)

Discharging power of installed ESS at node i in time t, and year d

\(P_{i,t,d}^{ PV}\)

PV active power generation at node i in time t, and year d


Active power supplied by substation in time t, and year d


Reactive power flow of circuit ij in time t, and year d

\(Q_{i,d}^{ CB}\)

Reactive power delivered by installed CB at node i in year d

\(Q_{i,t}^{ PV}\)

PV reactive power generated at node i in time t


Reactive power supplied by substation in time t, and year d


Square of voltage at node i in time t, and year d

Binary and integer variables


Binary variables that define the capacity b and CB type (fixed or switchable) to be installed at node i

\(y_{i}^{ ESS}\)

Binary variable that define the ESS to be installed at node i


Binary variable that define the PV modules k to be installed at node i

\(B_{i,d} \)

Integer variable for the CB modules to be installed at node i in year d


Integer variable for the maximum CB bank to be installed in node i



The authors would like to gratefully acknowledge the financial support for this research by FAPESP (Grant nos. 2014/22828-3, 2016/14319-7), CNPq no. 305371/2012-6, and CAPES.


  1. 1.
    Abul-Wafa, A.: Optimal capacitor allocation in radial distribution systems for loss reduction: a two stage method. Elect. Power Syst Res. 95, 168–174 (2013)CrossRefGoogle Scholar
  2. 2.
    Mohamed-Shuaib, Y., Surya, K.M., Christober, C.: Optimal capacitor placement in radial distribution system using gravitational search algorithm. Int. J. Elect. Power Energy Syst. 64, 384–397 (2015)Google Scholar
  3. 3.
    Abou El-Ela, A., El-Sehiemy, R., Kinawy, A., Mouwafi, M.: Optimal capacitor placement in distribution systems for power loss reduction and voltage profile improvement. IET Gener. Transm. Distrib. 10, 1209–1221 (2016)Google Scholar
  4. 4.
    Gampa, S.R., Das, D.: Optimum placement of shunt capacitors in a radial distribution system for substation power factor improvement using fuzzy GA method. Int. J. Elect. Power Energy Syst. 77, 314–326 (2016)CrossRefGoogle Scholar
  5. 5.
    Karimi, H., Dashti, R.: Comprehensive framework for capacitor placement in distribution networks from the perspective of distribution system management in a restructured environment. Int. J. Elect. Power Energy Syst. 82, 11–18 (2016)CrossRefGoogle Scholar
  6. 6.
    Ramadan, H.S., Bendary, A.F., Nagy, S.: Particle swarm optimization algorithm for capacitor allocation problem in distribution systems with wind turbine generators. Int. J. Elect. Power Energy Syst. 84, 143–152 (2017)CrossRefGoogle Scholar
  7. 7.
    World energy outlook. I.E.A. International Energy Agency (2012)Google Scholar
  8. 8.
    El-Khattam, W., Hegazy, Y., Salama, M.: An integrated distributed generation optimization model for distribution system planning. IEEE Trans. on Power Syst. 20, 1158–1165 (2005)CrossRefGoogle Scholar
  9. 9.
    Atwa, Y., El-Saadany, E., Salama, M., Seethapathy, R.: Optimal renewable resources mix for distribution system energy loss minimization. IEEE Trans. on Power Syst. 25, 360–370 (2010)CrossRefGoogle Scholar
  10. 10.
    Ganguly, S., Samajpati, D.: Distributed generation allocation on radial distribution networks under uncertainties of load and generation using genetic algorithm. IEEE Trans. Sustain. Energy 6, 688–697 (2015)CrossRefGoogle Scholar
  11. 11.
    Jamian, J., Mustafa, M., Mokhlis, H.: Optimal multiple distributed generation output through rank evolutionary particle swarm optimization. Neuro-computing 152, 190–198 (2015)Google Scholar
  12. 12.
    Montoya-Bueno, S., Muñoz, J., Contreras, J.: A stochastic investment model for renewable generation in distribution systems. IEEE Trans. Sustai. Energy. 6, 1466–1474 (2015)CrossRefGoogle Scholar
  13. 13.
    Tanwar, S.S., Khatod, D.K.: Techno-economic and environmental approach for optimal placement and sizing of renewable DGs in distribution system. Energy. 127, 52–67 (2017)CrossRefGoogle Scholar
  14. 14.
    Moradi, M., Zeinalzadeh, A., Mohammadi, Y., Abedini, M.: An efficient hybrid method for solving the optimal sitting and sizing problem of DG and shunt capacitor banks simultaneously based on imperialist competitive algorithm and genetic algorithm. Int. J. Elect. Power Energy Syst. 54, 101–111 (2014)CrossRefGoogle Scholar
  15. 15.
    Pereira, B., da Costa, G., Contreras, J., Mantovani, J.: Optimal distributed generation and reactive power allocation in electrical distribution systems. IEEE Trans. Sustain. Energy. 7, 975–984 (2016)CrossRefGoogle Scholar
  16. 16.
    Jannat, M., Savić, A.: Optimal capacitor placement in distribution networks regarding uncertainty in active power load and distributed generation units production. IET Gener. Transm. Distrib. 10, 3060–3067 (2016)CrossRefGoogle Scholar
  17. 17.
    Kayal, P., Chanda, C.K.: Strategic approach for reinforcement of intermittent renewable energy sources and capacitor bank for sustainable electric power distribution system. Int. J. Elect. Power Energy Syst. 83, 335–351 (2016)CrossRefGoogle Scholar
  18. 18.
    Macedo, L.H., Franco, J.F., Rider, M.J., Romero, R.: Optimal operation of distribution networks considering energy storage devices. IEEE Trans. Smart Grid. 6, 2825–2836 (2015)CrossRefGoogle Scholar
  19. 19.
    Sabillon, C., Melgar Dominguez, O., Franco, J.F., Lavorato, M., Rider, M.J.: Volt-VAr control and energy storage device operation to improve the electric vehicle charging coordination in unbalanced distribution networks. IEEE Trans. Sustain. Energy. 8, 1560–1570 (2017)Google Scholar
  20. 20.
    Atwa, Y., El-Saadany, E.: Optimal allocation of ESS in distribution systems with a high penetration of wind energy. IEEE Trans. Power Syst. 25, 1815–1822 (2010)CrossRefGoogle Scholar
  21. 21.
    Mostafa, N., Cherkaoui, R., Paolone, M.: Optimal allocation of dispersed energy storage systems in active distribution networks for energy balance and grid support. IEEE Trans. Power Syst. 29, 2300–2310 (2014)CrossRefGoogle Scholar
  22. 22.
    Mostafa, N., Cherkaoui, R., Paolone, M.: Optimal siting and sizing of distributed energy storage systems via alternating direction method of multipliers. Int. J. Elect. Power Energy Syst. 72, 33–39 (2015)CrossRefGoogle Scholar
  23. 23.
    Motalleb, M., Reihani, E., Ghorbani, R.: Optimal placement and sizing of the storage supporting transmission and distribution networks. Renew. Energy. 94, 651–659 (2016)CrossRefGoogle Scholar
  24. 24.
    Babacan, O., Torre, W., Kleissl, J.: Siting and sizing of distributed energy storage to mitigate voltage impact by solar PV in distribution systems. Solar Energy. 146, 199–208 (2017)CrossRefGoogle Scholar
  25. 25.
    Baker, K., Hug, g., Li, X.: Energy storage sizing taking into account forecast uncertainties and receding horizon operation. IEEE Trans. Sustain. Energy. 8, 331–340 (2017)Google Scholar
  26. 26.
    Misener, R., Floudas, C.A.: ANTIGONE: algorithms for continuous/integer global optimization of nonlinear equations. J. Global Optim. 59, 503–526 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Alguacil, N., Motto, A., Conejo, A.: Transmission expansion planning: a mixed-integer lp approach. IEEE Trans. Power Syst. 18, 1070–1077 (2003)CrossRefGoogle Scholar
  28. 28.
    Rueda-Medina, A.C., Franco, J.F., Rider, M.J., Padilha-Feltrin, A., Romero, R.: A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems. Elect. Power Syst Res. 97, 133–143 (2013)CrossRefGoogle Scholar
  29. 29.
    Rebennack, S.: Computing tight bounds via piecewise linear functions through the example of circle cutting problems. Math. Methods Oper. Res. 84, 3–57 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Pereira, B., Cossi, A., Mantovani, J.: Multiobjective short-term planning of electric power distribution systems using NSGA-II. J. Control Autom. Elect. Syst. 24, 286–299 (2013)CrossRefGoogle Scholar
  31. 31.
    Cavanagh, K., Ward, J., Behrens, S., Bhatt, A., Ratnam, E., Oliver, E., Hayward, J.: Electrical energy storage: technology overview and applications. CSIRO, Australia. EP154168 (2015)Google Scholar
  32. 32.
    Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: A modeling language for mathematical programming. CA: Brooks/Cole-Thomson Learning, Pacific Grove, 2nd Ed. (2003)Google Scholar
  33. 33.
    IBM ILOG CPLEX V12.1 User’s Manual for CPLEX. CPLEX Division, ILOG Inc., Incline Village, NV, USA (2009)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Ozy D. Melgar Dominguez
    • 1
  • Mahdi Pourakbari Kasmaei
    • 1
  • Marina Lavorato
    • 2
  • José R. Sanches Mantovani
    • 1
  1. 1.Power System Planning Lab., Department of Electrical EngineeringState University of São PauloSão PauloBrazil
  2. 2.Electrical Engineering FacultyPUC/CAMPINAS-Pontifical Catholic University of CampinasSão PauloBrazil

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