Skip to main content

Advertisement

SpringerLink
Log in

A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks

  • Original Paper
  • Published:
Energy Systems Aims and scope Submit manuscript

Abstract

This paper proposes a quadratic convex model for optimal operation of battery energy storage systems in a direct current (DC) network that approximates the original nonlinear non-convex one. The proposed quadratic convex model uses Taylor’s series expansion to transform the product between voltage variables in the power balance equations into a linear combination of them. Numerical simulations in the general algebraic modeling system (GAMS) for both models show small differences in the daily energy losses, which are lower than \(3.00\%\). The main advantage of the proposed quadratic model is that its optimal solution is achievable with interior point methods guaranteeing its uniqueness (convexity properties of the solution space and objective function), which is not possible to guarantee with the exact nonlinear non-convex model. The 30-bus DC test feeder with four distributed generators (with power generation forecast via artificial neural networks with errors lower than \(1\%\) between real and predicted generation curves) and three batteries is used to validate the proposed convex and exact models. Numerical results obtained by GAMS show the effectiveness of the proposed quadratic convex model for different simulation scenarios tested, which was confirmed by the CVX tool for convex optimization in MATLAB.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Abbreviations

\(\Delta {t}\) :

Length of the period of time where the loads are constants (h)

\({\mathcal {N}}\) :

Set that contains all the nodes of the network

\({\mathcal {T}}\) :

Set that contains all the nodes of the periods of time

\(CoE_{t}\) :

Cost of the energy in period t (COP$/Wh)

\(G_ij\) :

Conductance value that associates nodes i and j (\(\Omega ^{-1}\))

\(p^{{\rm max}}_i,t\) :

Maximum bound of the power generated in the conventional source connected at node i in the period t (W)

\(p^{{\rm min}}_i,t\) :

Minimum bound of the power generated in the conventional source connected at node i in the period t (W)

\(p^{{\rm b,max}}_i\) :

Maximum discharge capability of a battery connected at node i (W)

\(p^{{\rm b,min}}_i\) :

Minimum charge capability of a battery connected at node i (W)

\(p^{{\rm b}}_i,t\) :

Power injected/absorbed in the battery connected at node i in the period t (W)

\(p^{dg}_i,t\) :

Power generated in the distributed generator connected at node i in the period t (W)

\(p^{d}_i,t\) :

Power demanded in node i in the period t (W)

\(p_{i,t}\) :

Power generated in the conventional source connected at node i in the period t (W)

\(SoC^{{\rm b,max}}_i\) :

Maximum bound of the state of charge of the battery in the ith node (pu)

\(SoC^{{\rm b,min}}_i\) :

Minimum bound of the state of charge of the battery in the ith node (pu)

\(SoC^{{\rm b,fin}}_i\) :

Final state of charge of the battery in the \(i^th\) node (pu)

\(SoC^{{\rm b,ini}}_i\) :

Initial state of charge of the battery in the ith node (pu)

\(SoC^{{\rm b}}_i,t\) :

state of charge of the battery in the ith node at the t th time period (pu)

\(v^{{\rm max}}_i\) :

Maximum voltage regulation bound at node i (V)

\(v^{{\rm min}}_i\) :

Minimum voltage regulation bound at node i (V)

\(v_i,t\) :

Voltage value at node i at the period of time t (V)

\(v_i,t\) :

Voltage value at node j at the period of time t (V)

z :

Value of the objective function regarding the costs of the energy losses (COP$/day)

\(\mathbf{BESS}\) :

Battery energy storage system

\(\mathbf{GAMS}\) :

General algebraic modeling system

\(\mathbf{NLP}\) :

Nonlinear programming

\(p^{{\rm dg,max}}_i,t\) :

Maximum bound of the power generated in the distributed generator connected at node i in the period t (W)

\(p^{{\rm dg,max}}_i,t\) :

Minimum bound of the power generated in the distributed generator connected at node i in the period t (W)

References

  1. Alharbi, T., Bhattacharya, K.: Optimal scheduling of energy resources and management of loads in isolated/islanded microgrids. Can. J. Electr. Comput. Eng. 40(4), 284–294 (2017)

    Article  Google Scholar 

  2. Schoendienst, T., Vokkarane, V.M.: Reducing greenhouse gas emissions with power source-aware multidomain multilayer networks. IEEE Syst. J. 11(2), 673–683 (2017)

    Article  Google Scholar 

  3. Bogaerts, M., Cirhigiri, L., Robinson, I., Rodkin, M., Hajjar, R., Junior, C.C., Newton, P.: Climate change mitigation through intensified pasture management: estimating greenhouse gas emissions on cattle farms in the Brazilian Amazon. J. Clean. Prod. 162, 1539–1550 (2017)

    Article  Google Scholar 

  4. Crosson, P., Shalloo, L., O’Brien, D., Lanigan, G., Foley, P., Boland, T., and Kenny, D.: A review of whole farm systems models of greenhouse gas emissions from beef and dairy cattle production systems, Anim. Feed Sci. Technol. 166–167, 29–45 (2011). Special Issue: Greenhouse Gases in Animal Agriculture—Finding a Balance between Food and Emissions

  5. Thaker, S., Oni, A.O., Gemechu, E., Kumar, A.: Evaluating energy and greenhouse gas emission footprints of thermal energy storage systems for concentrated solar power applications. J. Energy Storage 26, 100992 (2019)

    Article  Google Scholar 

  6. Karmaker, A.K., Rahman, M.M., Hossain, M.A., Ahmed, M.R.: Exploration and corrective measures of greenhouse gas emission from fossil fuel power stations for Bangladesh. J. Clean. Prod. 244, 118645 (2020)

    Article  Google Scholar 

  7. Bauer, A., Menrad, K.: Standing up for the Paris Agreement: do global climate targets influence individuals’ greenhouse gas emissions? Environ. Sci. Policy 99, 72–79 (2019)

    Article  Google Scholar 

  8. Ferreira, A., Pinheiro, M.D., de Brito, J., Mateus, R.: Decarbonizing strategies of the retail sector following the Paris Agreement. Energy Policy 135, 110999 (2019)

    Article  Google Scholar 

  9. Montoya, O.D., Gil-González, W., Grisales-Norena, L., Orozco-Henao, C., Serra, F.: Economic dispatch of BESS and renewable generators in DC microgrids using voltage-dependent load models. Energies 12(23), 4494 (2019)

    Article  Google Scholar 

  10. Yan, Q., Zhang, B., Kezunovic, M.: Optimized operational cost reduction for an EV charging station integrated with battery energy storage and PV generation. IEEE Trans. Smart Grid 10(2), 2096–2106 (2019)

    Article  Google Scholar 

  11. Adefarati, T., Bansal, R.C., John Justo, J.: Techno-economic analysis of a PV-wind-battery-diesel standalone power system in a remote area. J. Eng. 2017(13), 740–744 (2017)

    Article  Google Scholar 

  12. Naumann, M., Karl, R.C., Truong, C.N., Jossen, A., Hesse, H.C.: Lithium-ion battery cost analysis in PV-household application. Energy Procedia 73, 37–47 (2015). 9th International Renewable Energy Storage Conference, IRES 2015

  13. Wentker, M., Greenwood, M., Leker, J.: A bottom-up approach to lithium-ion battery cost modeling with a focus on cathode active materials. Energies 12(3), 504 (2019)

    Article  Google Scholar 

  14. Montoya, O.D., Grajales, A., Garces, A., Castro, C.A.: Distribution systems operation considering energy storage devices and distributed generation. IEEE Lat. Am. Trans. 15(5), 890–900 (2017)

    Article  Google Scholar 

  15. Wang, Z., Du, J., Zhang, M., Yu, J., Liu, H., Chai, X., Yang, B., Zhu, C., Xu, J.: Continuous preparation of high performance flexible asymmetric supercapacitor with a very fast, low-cost, simple and scalable electrochemical co-deposition method. J. Power Sources 437, 226827 (2019)

    Article  Google Scholar 

  16. Krishan, O., Suhag, S.: Grid-independent PV system hybridization with fuel cell-battery/supercapacitor: optimum sizing and comparative techno-economic analysis. Sustain. Energy Technol. Assess. 37, 100625 (2020)

    Google Scholar 

  17. Teyber, R., Rowe, A.: Superconducting magnet design for magnetic liquefiers using total cost minimization. Cryogenics 99, 114–122 (2019)

    Article  Google Scholar 

  18. Gil-González, W., Montoya, O.D., Garces, A.: Control of a SMES for mitigating subsynchronous oscillations in power systems: a PBC-PI approach. J. Energy Storage 20, 163–172 (2018)

    Article  Google Scholar 

  19. Kale, V., Secanell, M.: A comparative study between optimal metal and composite rotors for flywheel energy storage systems. Energy Rep. 4, 576–585 (2018)

    Article  Google Scholar 

  20. Ramli, M.A., Hiendro, A., Twaha, S.: Economic analysis of PV/diesel hybrid system with flywheel energy storage. Renew. Energy 78, 398–405 (2015)

    Article  Google Scholar 

  21. Gil-González, W., Montoya, O.D., Holguín, E., Garces, A., Grisales-Norena, L.F.: Economic dispatch of energy storage systems in dc microgrids employing a semidefinite programming model. J. Energy Storage 21, 1–8 (2019)

    Article  Google Scholar 

  22. Vazquez, L., Majanne, Y., Castro, M., Luukkanen, J., Hohmeyer, O., Vilaragut, M., Diaz, D.: Energy system planning towards renewable power system: energy matrix change in Cuba by 2030. IFAC-PapersOnLine 51(28), 522–527 (2018). 10th IFAC Symposium on Control of Power and Energy Systems CPES 2018

  23. Cepeda, C., Orozco-Henao, C., Percybrooks, W., Pulgarín-Rivera, J.D., Montoya, O.D., Gil-González, W., Vélez, J.C.: Intelligent fault detection system for microgrids. Energies 13(5), 1223 (2020)

    Article  Google Scholar 

  24. Jiang, Q., Xue, M., Geng, G.: Energy management of microgrid in grid-connected and stand-alone modes. IEEE Trans. Power Syst. 28(3), 3380–3389 (2013)

    Article  Google Scholar 

  25. Montoya, O.D., Grisales-Norena, L.F., Gil-González, W., Alcalá, G., Hernandez-Escobedo, Q.: Optimal location and sizing of PV sources in DC networks for minimizing greenhouse emissions in diesel generators. Symmetry 12(2), 322 (2020)

    Article  Google Scholar 

  26. Messo, T., Luhtala, R., Roinila, T., de Jong, E., Scharrenberg, R., Caldognetto, T., Mattavelli, P., Sun, Y., Fabian, A.: Using high-bandwidth voltage amplifier to emulate grid-following inverter for AC microgrid dynamics studies. Energies 12(3), 379 (2019)

    Article  Google Scholar 

  27. Grisales-Norena, L.F., Ramos-Paja, C.A., Gonzalez-Montoya, D., Alcalá, G., Hernandez-Escobedo, Q.: Energy management in PV based microgrids designed for the Universidad Nacional de Colombia. Sustainability 12(3), 1219 (2020)

    Article  Google Scholar 

  28. Xia, Y., Wei, W., Yu, M., Wang, X., Peng, Y.: Power management for a hybrid AC/DC microgrid with multiple subgrids. IEEE Trans. Power Electron. 33(4), 3520–3533 (2018)

    Article  Google Scholar 

  29. Montoya, O.D.: A convex OPF approximation for selecting the best candidate nodes for optimal location of power sources on DC resistive networks. Eng. Sci. Technol. Int. J. 23(3), 527–533 (2020)

    Google Scholar 

  30. Li, J., Liu, F., Wang, Z., Low, S.H., Mei, S.: Optimal power flow in stand-alone DC microgrids. IEEE Trans. Power Syst. 33(5), 5496–5506 (2018)

    Article  Google Scholar 

  31. Iskender, I., Genc, N.: Power electronic converters in DC microgrid. In: Power Systems, pp. 115–137. Springer International Publishing (2019)

  32. Biczel, P.: Power electronic converters in DC microgrid. In: Compatibility in Power Electronics, May 2007, pp. 1–6 (2007)

  33. Murillo-Yarce, D., Garcés-Ruiz, A., Escobar-Mejía, A.: Passivity-based control for DC-microgrids with constant power terminals in island mode operation. Revista Facultad de Ingeniería Universidad de Antioquia 86, 32–39 (2018)

    Article  Google Scholar 

  34. Mahmoodi, M., Shamsi, P., Fahimi, B.: Economic dispatch of a hybrid microgrid with distributed energy storage. IEEE Trans. Smart Grid 6(6), 2607–2614 (2015)

    Article  Google Scholar 

  35. Dominguez-Jimenez, J., Montoya, O., Campillo, J., Gil-González, W.: Economic dispatch in dc microgrids considering different battery technologies: a benchmark study. In: 2020 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC), vol. 4, pp. 1–6. IEEE (2020)

  36. Grisales-Norena, L.F., Montoya, O.D., Ramos-Paja, C.A.: An energy management system for optimal operation of bss in dc distributed generation environments based on a parallel PSO algorithm. J. Energy Storage 29, 101488 (2020)

    Article  Google Scholar 

  37. Montoya, O.D., Gil-González, W., Garces, A.: Optimal power flow on DC microgrids: a quadratic convex approximation. IEEE Trans. Circuits Syst. II 66(6), 1018–1022 (2018)

    Google Scholar 

  38. Molina-Martin, F., Montoya, O.D., Grisales-Norena, L.F., Hernández, J.C., Ramírez-Vanegas, C.A.: Simultaneous minimization of energy losses and greenhouse gas emissions in AC distribution networks using BESS. Electronics 10(9), 1002 (2021)

    Article  Google Scholar 

  39. Garcés, A., Montoya, O.-D.: A potential function for the power flow in DC microgrids: an analysis of the uniqueness and existence of the solution and convergence of the algorithms. J. Control Autom. Electr. Syst. 30(5), 794–801 (2019)

    Article  Google Scholar 

  40. Montoya, O.D., Grisales-na, L., González-Montoya, D., Ramos-Paja, C., Garces, A.: Linear power flow formulation for low-voltage DC power grids. Electr. Power Syst. Res. 163, 375–381 (2018)

    Article  Google Scholar 

  41. Garces, A.: Uniqueness of the power flow solutions in low voltage direct current grids. Electr. Power Syst. Res. 151, 149–153 (2017)

    Article  Google Scholar 

  42. liliana and Napitupulu, T.A.: Artificial neural network application in gross domestic product forecasting: an Indonesia case. In: 2010 Second International Conference on Advances in Computing, Control, and Telecommunication Technologies. IEEE (2010)

  43. Tümer, A.E., Akkuş, A.: Forecasting gross domestic product per capita using artificial neural networks with non-economical parameters. Phys. A Stat. Mech. Appl. 512, 468–473 (2018)

    Article  Google Scholar 

  44. Jung, D.-H., Kim, H.-J., Kim, J.Y., Lee, T.S., Park, S.H.: Model predictive control via output feedback neural network for improved multi-window greenhouse ventilation control. Sensors 20(6), 1756 (2020)

    Article  Google Scholar 

  45. Fente, D.N., Singh, D.K.: Weather forecasting using artificial neural network. In: 2018 Second International Conference on Inventive Communication and Computational Technologies (ICICCT). IEEE (2018)

  46. Antanasijević, D.Z., Ristić, M., Perić-Grujić, A.A., Pocajt, V.V.: Forecasting GHG emissions using an optimized artificial neural network model based on correlation and principal component analysis. Int. J. Greenh. Gas Control 20, 244–253 (2014)

    Article  Google Scholar 

  47. Yu, L., Wang, S., Lai, K.K.: Foreign-Exchange-Rate Forecasting With Artificial Neural Networks. Springer US, New York (2007)

    Book  MATH  Google Scholar 

  48. Montoya, O.D., Gil-González, W.: Dynamic active and reactive power compensation in distribution networks with batteries: a day-ahead economic dispatch approach. Comput. Electr. Eng. 85, 106710 (2020)

    Article  Google Scholar 

  49. Kocer, M.C., Cengiz, C., Gezer, M., Gunes, D., Cinar, M.A., Alboyaci, B., Onen, A.: Assessment of battery storage technologies for a Turkish power network. Sustainability 11(13), 3669 (2019)

    Article  Google Scholar 

  50. Wang, P., Ang, W., Xu, D.: Optimal sizing of distributed generations in DC microgrids with comprehensive consideration of system operation modes and operation targets. IEEE Access 6, 31129–31140 (2018)

    Article  Google Scholar 

  51. Data, s.s.r. time series of solar radiation data. Available online http://www.soda-pro.com/. Accessed 5 July 2019

  52. Montoya, O.D., Grajales, A., Garces, A., Castro, C.A.: Distribution systems operation considering energy storage devices and distributed generation. IEEE Lat. Am. Trans. 15(5), 890–900 (2017)

    Article  Google Scholar 

  53. Giraldo, O.D.M.: Solving a classical optimization problem using gams optimizer package: economic dispatch problem implementation. Ingeniería y Ciencia 13(26), 39–63 (2017)

    Article  Google Scholar 

  54. Montoya, O.D., Gil-González, W., Grisales-Norena, L.: An exact MINLP model for optimal location and sizing of DGs in distribution networks: a general algebraic modeling system approach. Ain Shams Eng. J. 11(2), 409–418 (2020)

    Article  Google Scholar 

  55. Tartibu, L., Sun, B., Kaunda, M.: Multi-objective optimization of the stack of a thermoacoustic engine using GAMS. Appl. Soft Comput. 28, 30–43 (2015)

    Article  Google Scholar 

  56. Skworcow, P., Paluszczyszyn, D., Ulanicki, B., Rudek, R., Belrain, T.: Optimisation of pump and valve schedules in complex large-scale water distribution systems using GAMS modelling language. Procedia Eng. 70, 1566–1574. 12th International Conference on Computing and Control for the Water Industry, CCWI2013 (2014)

  57. Pintér, J.D.: Nonlinear optimization with GAMS /LGO. J. Glob. Optim. 38(1), 79–101 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Carrera 7 No. 40B-53, Bogotá D.C., 110231, Colombia

    Oscar Danilo Montoya

  2. Laboratorio Inteligente de Energía, Universidad Tecnológica de Bolívar, km 1 vía Turbaco, Cartagena, 131001, Colombia

    Oscar Danilo Montoya

  3. Facultad de Ingenierías y Arquitectura, Universidad de Pamplona, Pamplona, 543050, Colombia

    Víctor Manuel Garrido

  4. Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Campus Robledo, Medellín, 050036, Colombia

    Andrés Arias-Londoño & Walter Gil-González

  5. Departamento de Electromecánica y Mecatrónica, Instituto Tecnológico Metropolitano, Medellín, 050013, Colombia

    Luis Fernando Grisales-Noreña

Authors
  1. Oscar Danilo Montoya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrés Arias-Londoño
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Víctor Manuel Garrido
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Walter Gil-González
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Luis Fernando Grisales-Noreña
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oscar Danilo Montoya.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Montoya, O.D., Arias-Londoño, A., Garrido, V.M. et al. A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks. Energy Syst 14, 985–1005 (2023). https://doi.org/10.1007/s12667-021-00495-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12667-021-00495-z

Keywords

Search

Navigation