Skip to main content

Advertisement

SpringerLink
Log in

Optimal Operation of Unbalanced Microgrid Utilizing Copula-Based Stochastic Simultaneous Unit Commitment and Distribution Feeder Reconfiguration Approach

  • Research Article-Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Currently, the microgrid operators try to operate this special type of the electrical grid in an optimal way due to the energy and cost saving and enhancing the other technical, environmental and economic aspects. Two of the most important tasks of operators to improve the efficiency of the microgrid are the optimal unit commitment and the distribution feeder reconfiguration. If these tasks are individually carried out, it may not lead to the optimal operation. Simultaneously, performing these two tasks in an unbalanced microgrid is a challenging multi-objective problem that this paper is faced with it. The assumed unbalanced microgrid has been equipped by two hybrid energy systems which include the dispatchable distributed generations that are fuel cell units and the non-dispatchable ones that are wind turbines and photovoltaic cells. The stochastic behavior of the non-dispatchable generation units and electrical demand is modeled by a stochastic copula scenario-based framework. The objective functions are minimization of the operational cost of the microgrid, minimization of active power loss, maximization of voltage stability index, minimization of emissions, and minimization of the voltage and current unbalance indices subject to diverse technical constraints. The proposed multi-objective problem is optimized by multi-objective covariance matrix adaption-evolution strategy (MOCMA-ES) algorithm, and a set of Pareto solutions is achieved. The best compromised solution is then chosen by using the fuzzy technique. The capability of the proposed model is investigated on an unbalanced 25-bus microgrid. The simulation results show the efficacy of the proposed model to optimize objective functions, while the constraints are satisfied.

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.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.
Fig. 15.
Fig. 16.
Fig. 17.
Fig. 18.

Similar content being viewed by others

Abbreviations

\(N_{{{\text{BR}}}}\) :

Set of branches

\(N_{{\rm DG_{{ND}} }}\) :

Set of non-dispatchable DGs

\(N_{{\rm DG_{D} }}\) :

Set of dispatchable DGs

\(N_{{{\text{bus}}}}\) :

Set of buses\(N_{p}\)

\(S\) :

Set of scenarios

\(N_{p}\) :

Set of populations

\(D\) :

Set of decision variables

\(K\) :

Set of iterations

\(P\) :

Set of phases

\(P_{{{\text{loss}}}} \left( s \right)\) :

Active power loss and \(s\)th scenario (kW)

\(I^{i} \left( {k\,s} \right)\) :

Current \(i\)th phase in \(k\)th branch and \(s\)th scenario (A)

\({\text{VSI}}_{r} \left( s \right)\) :

Voltage stability index for \(r\)th bus and \(s\)th scenario (pu)

\(V_{z}^{i} \left( s \right)\) :

Voltage for \(z\)th bus in \( i\)th phase and \(s\)th scenario (pu)

\(P_{zr}^{i} \left( s \right)\) :

Active power between \(z\)th and \(r{\rm th}\) buses in \( i\)th phase and \(s\)th scenario (pu)

\(Q_{zr}^{i} \left( s \right)\) :

Reactive power between \(z\)th and \(r{\rm th}\) buses in \( i\)th phase and \(s\)th scenario (pu)

\(C_{{{\text{grid}}}} \left( s \right)\) :

Cost of energy exchanged with upstream grid and \(s\)th scenario ($)

\(i,s)\) :

Cost of active power generated by \(i\)th non-dispatchable DG ($)

\(C_{{\rm DG_{D} }} \left( {j,s} \right)\) :

Cost of active power generated by \(j\)th dispatchable DG and \(s\)th scenario ($)

\(P_{{{\text{grid}}}} \left( s \right)\) :

Active power exchanged with upstream grid (kW)

\(P_{{\rm DG_{{ND}} }} \left( {i,s} \right)\) :

Active power generated by \(i\)th non-dispatchable DG and \(s\)th. scenario (kW)

\(P_{{\rm DG_{D} }} \left( {j,s} \right)\) :

Active power generated by \(j\)th dispatchable DG and \(s\)th scenario (kW)

\({\text{TVUF}}\left( s \right)\) :

Total voltage unbalance factor in \(s\)th scenario

\(V_{2}^{r} \left( s \right)\) :

Negative sequence of voltage in \(r\)th bus and \(s\)th scenario (pu)

\(V_{1}^{r} (s\)):

Positive sequence of voltage in \(r\)th bus and \(s\)th scenario (pu)

\({\text{TCUF}}\left( s \right)\) :

Total current unbalance factor in \(s\)th scenario

\(I_{2}^{k} \left( s \right)\) :

Negative sequence of current in \(k\)th branch and \(s\)th scenario (pu)

\(I_{1}^{k} (s\)):

Positive sequence of current in \(k\)th branch and \(s\)th scenario (pu)

\(f_{i} \left( s \right)\) :

Value of \(i\)th objective function and \(s\)th. scenario

\( f_{i}^{{\min}}\) :

Nadir value for \(i\) th objective function

\( f_{i}^{{\max}}\) :

Ideal value for \(i\) th objective function

\(a_{i} \left( s \right)\) :

Fuzzy membership for \(i\) th objective function and \(s\)th scenario

\({\text{PG}}\left( {i,s} \right)\) :

Generated active power in \(i\) th bus and \(s\)th scenario (pu)

\({\text{PD}}\left( {i,s} \right)\) :

Demanded active power in \(i\) th bus and \(s\)th scenario (pu)

\(\left| {V\left( {i,s} \right)} \right|\) :

Magnitude of voltage in \(i\) th bus and \(s\)th scenario (pu)

\(\delta \left( {i,s} \right)\) :

Phase voltage in \(i\) th bus and \(s\)th scenario (pu)

\(\left| {Y\left( {i,j} \right)} \right|\) :

Magnitude of admittance of between \(i\) th and \(j\)th bus (pu)

\(\varphi \left( {i,j,s} \right)\) :

Phase of admittance of between \(i\)th and \(j\)th bus (pu)

\({\text{QG}}\left( {i,s} \right)\) :

Generated reactive power in \(i\)th bus and \(s\)th scenario (pu)

\({\text{QD}}\left( {i,s} \right)\) :

Demanded reactive power in \(i\)th bus and \(s\)th scenario (pu)

\(\left| {I\left( {i,j,s} \right)} \right|\) :

Magnitude of current of between \(i\)th and \(j\)th bus and \(s\)th scenario (pu)

\(X_{j}^{{\left( {k,i} \right)}}\) :

\(j\)th candidate solution for \(i\)th particle in \(k\)th iteration

\(V_{j}^{{\left( {k,i} \right)}}\) :

\(j\)th element of velocity vector for \(i\)th particle in \(k\)th iteration

\({\text{Gbest}}_{j}^{\left( k \right)}\) :

Global best position all of candidate solution found up to \(k\)th iteration

\({\text{Pbest}}_{j}^{{\left( {k,i} \right)}}\) :

Best previous experience for \(i\)th particle in \(k\)th iteration

\(\psi_{r} \left( {X,Y} \right)\) :

Rank correlation

\(G_{X} \left( X \right)\) :

Calmative distribution function (CDF) of \(X\) random variable

\(G_{Y} \left( Y \right)\) :

Calmative distribution function (CDF) of \(Y\) random variable

\({\text{Cov}}\left( {G_{X} ,G_{Y} } \right)\) :

Covariance of \(G_{X}\) and \(G_{Y} .\)

\(\sigma \left( {G_{X} } \right)\) :

Standard deviation of \(G_{X}\)

\(\sigma \left( {G_{Y} } \right)\) :

Standard deviation of \(G_{Y}\)

\(R^{i} \left( k \right)\) :

Resistance \(i\)th phase of \(k\)th branch (\({\Omega }\))

\(R_{zr}^{i}\) :

Resistance \(i\)th phase between \(z\)th and \(r{\rm th}\) buses (pu)

\(X_{zr}^{i}\) :

Reactance \(i\)th phase between \(z\)th and \(r{\rm th}\) buses (pu)

\(\rho_{{{\text{grid}}}} \left( t \right) \) :

Price of electricity in the upstream market at \(t\)th hour ($/kW)

\(a_{{\rm DG_{{ND}} }} \left( i \right)\) :

Investment (fix) cost of \(i\)th non-dispatchable DG ($)

\(b_{{\rm DG_{{ND}} }} \left( i \right)\) :

Variable cost of \(i\)th non-dispatchable DG ($)

\(a_{{\rm DG_{D} }} \left( i \right)\) :

Investment (fix) cost of \(i\)th dispatchable DG ($)

\(b_{{\rm DG_{D} }} \left( i \right)\) :

Variable cost of \(i\)th non-dispatchable DG ($)

\(\eta_{{{\text{ele}}}}\) :

Electrical efficiency of dispatchable DGs

\({\rm Cost_{Capital }^{{DG}}}\) :

Capital cost of DGs ($/kW)

\(P_{\rm {Capacity}^{DG}}\) :

Capacity of DGs (kW)

\({\text{Gr}}\) :

Annual rate of benefit

\(CF_{{{\text{DG}}}} \left( i \right)\) :

Capacity factor of \(i\)th DG

\(T_{{{\text{Life}}}}\) :

Lifetime of DGs (year)

\({\rm Cost_{{DG_{D} }}^{O\& M}}\) :

Cost of operation and maintenance of dispatchable DGs ($/kW)

\({\rm Cost_{{ DG_{D} }}^{ Fuel} }\) :

Cost of fuel of dispatchable DG ($/kW)

\({\rm Cost_{{DG_{ND}}}^{O\& M} }\) :

Cost of operation and maintenance of non-dispatchable DGs ($/kW)

\(\rho_{{{\text{gas}}}}\) :

Price of natural gas in the upstream market ($/\({\text{m}}^{3}\))

\(\beta_{{{\text{gas}}}}\) :

Rate of exchanging natural gas to electricity (\({\text{m}}^{3}\)/kW)

\({\text{ER}}\left( j \right)\) :

Emission rate of \(j\)th DG (kg/kW)

\({\rm ER_{{grid}}}\) :

Emission rate of grid (kg/kW)

\(I_{ij}^{{\max}}\) :

Permitted current of feeder or cable between \(i\)th and \(j\)th bus (pu)

\(V_{{\min}}\) :

Maximum allowable voltage in each bus (pu)

\(V_{\max }\) :

Minimum allowable voltage in each bus (pu)

\(P_{\rm {DG_{D} }}^{{\min}} \left( i \right)\) :

Minimum allowable active power generated by \(i\)th dispatchable DG (kW)

\(P_{{\rm DG_{D} }}^{{\max}} \left( i \right)\) :

Maximum allowable active power generated by \(i\)th dispatchable DG (kW)

\({\text{VUF}}^{{\max}}\) :

Maximum allowable voltage unbalance at each bus

\({\text{CUF}}^{{\max}}\) :

Maximum allowable current unbalance at each branch

\(r_{1} , r_{2} \) :

Random number from the Gaussian distribution

\(c_{1} , c_{2}\) :

Inertia coefficients

\({\text{si}}\) :

Solar irradiance (\({\text{(kW}}/{\text{m}}^{2} )\)

\(f_{b} \left( {{\text{si}}} \right)\) :

Beta PDF of \({\text{si}}\)

\(\alpha_{s}\) :

Parameters of the Beta PDF

\(\beta_{s}\) :

Parameters of the Beta PDF

\(\mu_{s}\) :

Mean of forecasted solar irradiance (\({\text{kW}}/{\text{m}}^{2} )\)

\(\sigma_{s}\) :

Standard deviation of forecasted solar irradiance (\({\text{kW}}/{\text{m}}^{2} )\)

\(\eta^{{\text{pv}}}\) :

Efficiency of PV module

\(S^{{\text{pv}}}\) :

Area of PV module (\(({\text{m}}^{2} )\)

\(P_{{\text{rated}}}\) :

Rated output power of WT (kW)

\(v_{r}\) :

Rated wind speed (m/s)

\(v\) :

Wind speed (m/s)

\(v_{ct}\) :

Cut-in wind speed (m/s)

\(v_{co}\) :

Cut-out wind speed (m/s)

\(\mu_{d}\) :

Mean of forecasted electrical demand (kW)

\(\sigma_{d}\) :

Standard deviation of forecasted electrical demand (kW)

\(z\) :

a vector of random variables between zero and one

\(\rho \left( s \right)\) :

Probability of scenario s

ASO:

Average stochastic output

CDF:

Cumulative distribution function

DFR:

Distribution feeder reconfiguration

DG:

Distributed generation

FC:

Fuel cell

MOCMA-ES:

Multi-objective covariance matrix adaption-evolution strategy

MG:

Microgrid

MGO:

Microgrid operator

MOP:

Multi-objective problem

CMA-ES:

covariance matrix adaption-evolution strategy

MGO:

Microgrid operator

MLP:

Multi-layer perceptron

O&M:

Operation and maintenance

PV:

Photovoltaic

PDF:

Probability distribution function

PSO:

Particle swarm optimization

SOP:

Single-objective problem

VSI:

Voltage Stability Index (VSI)

WT:

Wind turbine

References

  1. Ben Hamida, I., Salah, S.B., Msahli, F., Mimouni, M.F.: Optimal network reconfiguration and renewable DG integration considering time sequence variation in load and DGs. Renew. Energy 121, 66–80 (2018). https://doi.org/10.1016/j.renene.2017.12.106

    Article  Google Scholar 

  2. Sedghi, L., Emam, M., Fakharian, A., Savaghebi, M.: Decentralized control of an islanded microgrid based on offline model reference adaptive control. J. Renew. Sustain Energy 10(6), 065301 (2018)

    Google Scholar 

  3. Rahmani, R.; Fakharian, A.: Guerrero, J.: An optimal power management system for automatic connection of DC and AC resources of hybrid-microgrid systems. In: 2017 IEEE Second International Conference on DC Microgrids (ICDCM), 2017: IEEE, pp. 181–187

  4. Esmaeili, M., Sedighizadeh, M., Esmaili, M.: Multi-objective optimal reconfiguration and DG (distributed generation) power allocation in distribution networks using Big Bang-Big Crunch algorithm considering load uncertainty. Energy 103, 86–99 (2016). https://doi.org/10.1016/j.energy.2016.02.152

    Article  Google Scholar 

  5. Wang, H., Huang, J.: Joint investment and operation of microgrid. IEEE Trans. Smart Grid 8(2), 833–845 (2015)

    Google Scholar 

  6. Sedighizadeh, M., Esmaili, M., Esmaeili, M.: Application of the hybrid Big Bang-Big Crunch algorithm to optimal reconfiguration and distributed generation power allocation in distribution systems. Energy 76, 920–930 (2014). https://doi.org/10.1016/j.energy.2014.09.004

    Article  Google Scholar 

  7. Leite, J.C., Abril, I.P., Azevedo, M.S.S.: Capacitor and passive filter placement in distribution systems by nondominated sorting genetic algorithm-II. Electric Power Syst. Res. 143, 482–489 (2017)

    Google Scholar 

  8. Sedighizadeh, M., Shaghaghi-shahr, G., Esmaili, M., Aghamohammadi, M.R.: Optimal distribution feeder reconfiguration and generation scheduling for microgrid day-ahead operation in the presence of electric vehicles considering uncertainties. J. Energy Storage 21, 58–71 (2019). https://doi.org/10.1016/j.est.2018.11.009

    Article  Google Scholar 

  9. Jabbari-Sabet, R., Moghaddas-Tafreshi, S.-M., Mirhoseini, S.-S.: Microgrid operation and management using probabilistic reconfiguration and unit commitment. Int. J. Electr. Power Energy Syst. 75, 328–336 (2016)

    Google Scholar 

  10. Gutiérrez-Alcaraz, G., Galván, E., González-Cabrera, N., Javadi, M.: Renewable energy resources short-term scheduling and dynamic network reconfiguration for sustainable energy consumption. Renew. Sustain. Energy Rev. 52, 256–264 (2015)

    Google Scholar 

  11. Gazijahani, F.S., Salehi, J.: Integrated DR and reconfiguration scheduling for optimal operation of microgrids using Hong’s point estimate method. Int. J. Electr. Power Energy Syst. 99, 481–492 (2018)

    Google Scholar 

  12. Kaveh, M.R., Hooshmand, R.-A., Madani, S.M.: Simultaneous optimization of re-phasing, reconfiguration and DG placement in distribution networks using BF-SD algorithm. Appl. Soft Comput. 62, 1044–1055 (2018)

    Google Scholar 

  13. Shukla, J., Das, B., Pant, V.: Stability constrained optimal distribution system reconfiguration considering uncertainties in correlated loads and distributed generations. Int. J. Electr. Power Energy Syst. 99, 121–133 (2018)

    Google Scholar 

  14. E. kianmehr, S. Nikkhah, and A. Rabiee, : Multi-objective stochastic model for joint optimal allocation of DG units and network reconfiguration from DG owner’s and DisCo’s perspectives. Renew. Energy 132, 471–485 (2019). https://doi.org/10.1016/j.renene.2018.08.032

    Article  Google Scholar 

  15. Nguyen, T.T., Truong, A.V., Phung, T.A.: A novel method based on adaptive cuckoo search for optimal network reconfiguration and distributed generation allocation in distribution network. Int. J. Electr. Power Energy Syst. 78, 801–815 (2016). https://doi.org/10.1016/j.ijepes.2015.12.030

    Article  Google Scholar 

  16. Zhang, S., Cheng, H., Wang, D., Zhang, L., Li, F., Yao, L.: Distributed generation planning in active distribution network considering demand side management and network reconfiguration. Appl. Energy 228, 1921–1936 (2018). https://doi.org/10.1016/j.apenergy.2018.07.054

    Article  Google Scholar 

  17. Kanwar, N., Gupta, N., Niazi, K.R., Swarnkar, A.: An integrated approach for distributed resource allocation and network reconfiguration considering load diversity among customers. Sustai. Energy Grids Netw. 7, 37–46 (2016). https://doi.org/10.1016/j.segan.2016.05.002

    Article  Google Scholar 

  18. Zidan, A., Shaaban, M.F., El-Saadany, E.F.: Long-term multi-objective distribution network planning by DG allocation and feeders’ reconfiguration. Electric Power Syst. Res. 105, 95–104 (2013)

    Google Scholar 

  19. Rao, R.S., Ravindra, K., Satish, K., Narasimham, S.: Power loss minimization in distribution system using network reconfiguration in the presence of distributed generation. IEEE Trans. Power Syst. 28(1), 317–325 (2013)

    Google Scholar 

  20. M. K and J. S, : Integrated approach of network reconfiguration with distributed generation and shunt capacitors placement for power loss minimization in radial distribution networks. Appl. Soft Comput. 52, 1262–1284 (2017). https://doi.org/10.1016/j.asoc.2016.07.031

    Article  Google Scholar 

  21. Mohammadi, M., Rozbahani, A.M., Bahmanyar, S.: Power loss reduction of distribution systems using BFO based optimal reconfiguration along with DG and shunt capacitor placement simultaneously in fuzzy framework. J. Central South Univ. 24(1), 90–103 (2017)

    Google Scholar 

  22. Ravadanegh, S.N., Oskuee, M.R.J., Karimi, M.: Multi-objective planning model for simultaneous reconfiguration of power distribution network and allocation of renewable energy resources and capacitors with considering uncertainties. J. Central South Univ. 24(8), 1837–1849 (2017)

    Google Scholar 

  23. Li, K; Zhang, J.; Che, J.; Wang, F.; Ren, H.; Mi, Z.: Capacity configuration optimization for stand-alone microgrid considering the uncertainties of wind and solar resource. In: 2018 IEEE Power and Energy Society Innovative Smart Grid Technologies Conference (ISGT), 2018. IEEE, pp. 1–5

  24. Taher, S.A., Karimi, M.H.: Optimal reconfiguration and DG allocation in balanced and unbalanced distribution systems. Ain Shams Eng. J. 5(3), 735–749 (2014). https://doi.org/10.1016/j.asej.2014.03.009

    Article  Google Scholar 

  25. Ding, F., Loparo, K.A.: Feeder reconfiguration for unbalanced distribution systems with distributed generation: a hierarchical decentralized approach. IEEE Trans. Power Syst. 31(2), 1633–1642 (2015)

    Google Scholar 

  26. Esmaeilian, H.R., Fadaeinedjad, R.: Energy loss minimization in distribution systems utilizing an enhanced reconfiguration method integrating distributed generation. IEEE Syst. J. 9(4), 1430–1439 (2014)

    Google Scholar 

  27. Zidan, A., El-Saadany, E.F.: Distribution system reconfiguration for energy loss reduction considering the variability of load and local renewable generation. Energy 59, 698–707 (2013)

    Google Scholar 

  28. Sedighizadeh, M., Dakhem, M., Sarvi, M., Kordkheili, H.H.: Optimal reconfiguration and capacitor placement for power loss reduction of distribution system using improved binary particle swarm optimization. Int. J. Energy Environ. Eng. 5(1), 3 (2014)

    Google Scholar 

  29. Nasiraghdam, H., Jadid, S.: Optimal hybrid PV/WT/FC sizing and distribution system reconfiguration using multi-objective artificial bee colony (MOABC) algorithm. Sol. Energy 86(10), 3057–3071 (2012)

    Google Scholar 

  30. Niknam, T., Fard, A.K., Seifi, A.: Distribution feeder reconfiguration considering fuel cell/wind/photovoltaic power plants. Renew. Energy 37(1), 213–225 (2012)

    Google Scholar 

  31. Olamaei, J., Niknam, T., Gharehpetian, G.: Application of particle swarm optimization for distribution feeder reconfiguration considering distributed generators. Appl. Math. Comput. 201(1–2), 575–586 (2008)

    MathSciNet  MATH  Google Scholar 

  32. Sedighizadeh, M., Ahmadi, S., Sarvi, M.: An efficient hybrid big bang–big crunch algorithm for multi-objective reconfiguration of balanced and unbalanced distribution systems in fuzzy framework. Electric Power Compon. Syst. 41(1), 75–99 (2013)

    Google Scholar 

  33. Sedighizadeh, M., Ghalambor, M., Rezazadeh, A.: Reconfiguration of radial distribution systems with fuzzy multi-objective approach using modified big bang-big crunch algorithm. Arabian J. Sci. Eng. 39(8), 6287–6296 (2014)

    Google Scholar 

  34. Sedighizadeh, M., Esmaili, M., Mohammadkhani, N.: Stochastic multi-objective energy management in residential microgrids with combined cooling, heating, and power units considering battery energy storage systems and plug-in hybrid electric vehicles. J. Clean. Prod. 195, 301–317 (2018)

    Google Scholar 

  35. Teng, J.-H.: A direct approach for distribution system load flow solutions. IEEE Trans. Power Deliv. 18(3), 882–887 (2003)

    Google Scholar 

  36. Shahryari, E.; Shayeghi, H.; Mohammadi-Ivatloo, B.; Morad Zadeh, M.: Optimal energy management of microgrid in day-ahead and intra-day markets using a copula-based uncertainty modeling method. J. Oper. Autom. Power Eng. (2019).

  37. Hagspiel, S., Papaemannouil, A., Schmid, M., Andersson, G.: Copula-based modeling of stochastic wind power in Europe and implications for the Swiss power grid. Appl. Energy 96, 33–44 (2012)

    Google Scholar 

  38. Sklar, M.: Fonctions de repartition an dimensions et leurs marges. Publ. inst. statist. univ. Paris 8, 229–231 (1959)

    MathSciNet  MATH  Google Scholar 

  39. Zakariazadeh, A., Jadid, S., Siano, P.: Smart microgrid energy and reserve scheduling with demand response using stochastic optimization. Int. J. Electr. Power Energy Syst. 63, 523–533 (2014)

    Google Scholar 

  40. Sedighizadeh, M., Esmaili, M., Jamshidi, A., Ghaderi, M.-H.: Stochastic multi-objective economic-environmental energy and reserve scheduling of microgrids considering battery energy storage system. Int. J. Electr. Power Energy Syst. 106, 1–16 (2019)

    Google Scholar 

  41. Talari, S., Yazdaninejad, M., Haghifam, M.-R.: Stochastic-based scheduling of the microgrid operation including wind turbines, photovoltaic cells, energy storages and responsive loads. IET Gener. Transm. Distrib. 9(12), 1498–1509 (2015)

    Google Scholar 

  42. Motevasel, M., Seifi, A.R.: Expert energy management of a micro-grid considering wind energy uncertainty. Energy Convers. Manag. 83, 58–72 (2014)

    Google Scholar 

  43. Zakariazadeh, A., Jadid, S., Siano, P.: Economic-environmental energy and reserve scheduling of smart distribution systems: A multiobjective mathematical programming approach. Energy Convers. Manag. 78, 151–164 (2014)

    Google Scholar 

  44. Sedighizadeh, M., Mohammadpour, A.H., Alavi, S.M.M.: A two-stage optimal energy management by using ADP and HBB-BC algorithms for microgrids with renewable energy sources and storages. J. Energy Storage 21, 460–480 (2019)

    Google Scholar 

  45. Petrollese, M., Valverde, L., Cocco, D., Cau, G., Guerra, J.: Real-time integration of optimal generation scheduling with MPC for the energy management of a renewable hydrogen-based microgrid. Appl. Energy 166, 96–106 (2016)

    Google Scholar 

  46. Su, W., Wang, J., Roh, J.: Stochastic energy scheduling in microgrids with intermittent renewable energy resources. IEEE Trans. Smart Grid 5(4), 1876–1883 (2014)

    Google Scholar 

  47. Sachs, J., Sawodny, O.: Multi-objective three stage design optimization for island microgrids. Appl. Energy 165, 789–800 (2016)

    Google Scholar 

  48. Jose-Garcia, A., Gómez-Flores, W.: Automatic clustering using nature-inspired metaheuristics: a survey. Appl. Soft Comput. 41, 192–213 (2016)

    Google Scholar 

  49. Fu, M.C.: Handbook of Simulation Optimization. Springer, Berlin (2015)

    MATH  Google Scholar 

  50. Hansen, N.: The CMA evolution strategy: a tutorial. arXiv preprint arXiv:1604.00772.

  51. Hansen, N.: The CMA evolution strategy: a comparing review. In: Towards a new evolutionary computation, pp. 75–102. Springer (2006).

  52. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evolut. Comput. 6(2), 182–197 (2002)

    Google Scholar 

  53. Whitley, D.: A genetic algorithm tutorial. Stat. Comput. 4(2), 65–85 (1994)

    Google Scholar 

  54. Trelea, I.C.: The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf. Process. Lett. 85(6), 317–325 (2003)

    MathSciNet  MATH  Google Scholar 

  55. Karaboga, D.; Basturk, B.: Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. In International Fuzzy Systems Association World Congress. Springer, pp. 789–798 (2007)

  56. Simon, D.: Biogeography-based optimization. IEEE Trans. Evolut. Comput. 12(6), 702–713 (2008)

    Google Scholar 

  57. Zhang, N., Kang, C., Xia, Q., Liang, J.: Modeling conditional forecast error for wind power in generation scheduling. IEEE Trans. Power Syst. 29(3), 1316–1324 (2013)

    Google Scholar 

  58. Vulasala, G., Sirigiri, S., Thiruveedula, R.: Feeder reconfiguration for loss reduction in unbalanced distribution system using genetic algorithm. Int. J. Electr. Power Energy Syst. Eng. 3(12), 754–762 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical, Biomedical, and Mechatronics Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

    Ahmad Fakharian & Masoud Khajehvand

  2. Faculty of Electrical Engineering, Shahid Beheshti University, Evin, Tehran, Iran

    Mostafa Sedighizadeh

Authors
  1. Ahmad Fakharian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mostafa Sedighizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masoud Khajehvand
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmad Fakharian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fakharian, A., Sedighizadeh, M. & Khajehvand, M. Optimal Operation of Unbalanced Microgrid Utilizing Copula-Based Stochastic Simultaneous Unit Commitment and Distribution Feeder Reconfiguration Approach. Arab J Sci Eng 46, 1287–1311 (2021). https://doi.org/10.1007/s13369-020-04965-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-020-04965-x

Keywords

Search

Navigation