Electrical Engineering

, Volume 101, Issue 3, pp 829–843 | Cite as

Stochastic economic analysis of FACTS devices on contingent transmission networks using hybrid biogeography-based optimization

  • Sina Ghaemi
  • Farid Hamzeh Aghdam
  • Amin SafariEmail author
  • Meisam Farrokhifar
Original Paper


Flexible AC transmission systems (FACTS) devices have advantages of enhancing AC system controllability and stability, increasing power transfer capability and relieving congestion. Finding the best sizing and siting of them is obligatory to obtain the maximum benefit. In this paper, the optimum planning is done for determining the suitable sizing and siting of the FACTS devices during their lifetime span. The proposed planning approach is implemented to the networks, which are suffering from the contingency to demonstrate that how proper sizing and siting of the FACTS devices are able to deal with the existing problems in such networks. In fact, the maximum social welfare, reducing load shedding cost and construction cost of the new branches besides of the technical issues such as voltage improvement are the main concerns of the present work. To accomplish these aims accurately and reduce the computation time, a hybrid approach, consisting of mathematical and heuristic methods, is proposed for solving the proposed planning problem. The mentioned algorithm is a combination of biogeography-based optimization (BBO) as a heuristic algorithm and nonlinear programming as a mathematical approach. Furthermore, since the stochastic natures of renewable energy sources and load variations contribute to the optimum decisions, the stochastic formulation has been considered in the planning problem using the efficient point estimation (\( 2m + 1 \)) scheme. Finally, the proposed planning approach is tested on different test systems, namely IEEE 14-bus, IEEE 57-bus and IEEE 300-bus, in order to verify its effectiveness from a different point of views.


Biogeography-based optimization (BBO) Nonlinear programming FACTS Contingency management 

List of symbols


Index for load

n, m

Indices for node


Index for generator


Index for hour


Index for year


Index for scenario


Index for FACTS devices


Index for uncertain variable in (\( 2m + 1 \)) scheme

\( \omega \)

Index for habitat

\( \varphi \)

Index for SIV in each habitat


Index for iteration


Index for net present value of the variable


State with FACTS devices


State without FACTS devices


Superscript for expected value of the variable


Superscript for maximum amount of the variable


Superscript for minimum amount of the variable


Superscript for updated variable


Biogeography-based optimization


\( A,B \)

Shape and scale of the Weibull distribution

\( P_{\text{wr}} \)

Rated power of the wind

a, b, c

Coefficients of bid function of the interruptible loads

\( v_{\text{i}} \)

Cut-in speed

\( v_{\text{r}} \)

Rated speed

\( v_{\text{o}} \)

Cut-out speed

\( N_{\text{TCSC}} \)

Number of the TCSC

\( N_{\text{SVC}} \)

Number of the SVC

\( N_{\text{scen}} \)

Number of the scenarios

\( n_{G} \)

Number of the generators

\( n_{l} \)

Number of the load

\( n_{\text{lifetime}} \)

Lifetime of the FACTS devices


Rate of interest

\( {\text{price}}^{\text{shed}} \)

Price of the load shedding ($/MW)

\( L_{\text{int}} \)

Set of the interruptible load

\( \alpha \)

Fixed coefficient in BBO algorithm


\( v \)

Velocity of wind

\( P_{w} \)

Wind output power

\( P_{g} \)

Generator output active power (MW)

\( Q_{g} \)

Generator output reactive power (MW)

\( P^{\text{load}} \)

Active load in each node (MW)

\( Q^{\text{load}} \)

Reactive load in each node (MW)

\( P^{\text{fc}} \)

Forecasted active power in each node (MW)

\( P^{\text{shed}} \)

Active shed power in each node (MW)

\( C_{\text{Gen}} \)

Cost function of the diesel generator

\( {\text{Cost}}_{\text{TCSC}} \)

Investment cost of the TCSC per kVAr

\( {\text{Cost}}_{\text{SVC}} \)

Investment cost of the SVC per kVAr

\( {\text{Cost}}_{\text{Install,FACTS}} \)

Total investment cost of the FACTS devices


The obtained benefit of the TRANSCO

\( S_{\text{SVC}} \)

SVC capacity in MVAr

\( S_{\text{TCSC}} \)

TCSC capacity in MVAr


Interruptible load bid


Voltage magnitude of each node

\( I^{\text{line}} \)

Line current


Probability of each scenario


Locational marginal price ($/MW)

\( \chi \)

Location of the particular concentration in (\( 2m + 1 \)) scheme

\( \xi \)

Standard deviation of the particular variable

\( \lambda \)

Standard control moment of the uncertain variable


Weight of the calculated concentration


Decision variable in each habitat in BBO algorithm

\( \mu_{\text{BBO}} \)

Emigration rate in BBO algorithm

\( \lambda_{\text{BBO}} \)

Immigration rate in BBO algorithm


\( f_{\text{wind}} \)

Probability density function of the wind speed

\( f_{\text{load}} \)

Probability density function of the load

\( F(.) \)

Active power balance

\( G(.) \)

Reactive power balance

\( N(.) \)

Normal distribution

\( f \)

Probability distribution density of particular uncertain variable


Compliance with ethical standards

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of this paper.


  1. 1.
    Dugan RC, McGranaghan MF, Beaty HW (1996) Electrical power systems quality. McGraw-Hill, New YorkGoogle Scholar
  2. 2.
    Shayeghi H, Shayanfar HA, Jalilzadeh S, Safari A (2010) TCSC robust damping controller design based on particle swarm optimization for a multi-machine power system. Energy Convers Manag 51(10):1873–1882CrossRefGoogle Scholar
  3. 3.
    Bashardoust A, Farrokhifar M, Yousefzadeh Fard A, Safari A, Mokhtarpour E (2016) Optimum network reconfiguration to improve power quality and reliability in distribution system. Int J Grid Distrib Comput 9(4):101–110CrossRefGoogle Scholar
  4. 4.
    Aghdam FH, Salehi J, Ghaemi S (2018) Contingency based energy management of multi-microgrid based distribution network. Sustain Cities Soc 41:265–274CrossRefGoogle Scholar
  5. 5.
    Patton DB, LeeVanSchaick P, Chen J, Unit MM (2016) 2015 State of the market report for the New York ISO markets. Potom EconGoogle Scholar
  6. 6.
    Sahraei-Ardakani M, Hedman KW (2017) Computationally efficient adjustment of FACTS set points in DC optimal power flow with shift factor structure. IEEE Trans Power Syst 32(3):1733–1740CrossRefGoogle Scholar
  7. 7.
    Elmitwally A, Eladl A (2016) Planning of multi-type FACTS devices in restructured power systems with wind generation. Int J Electr Power Energy Syst 77:33–42CrossRefGoogle Scholar
  8. 8.
    Shahidehpour M, Yamin H, Li Z (2002) Market operations in electric power systems: forecasting, scheduling, and risk management. Wiley, HobokenCrossRefGoogle Scholar
  9. 9.
    Gotham DJ, Heydt G (1998) Power flow control and power flow studies for systems with FACTS devices. IEEE Trans Power Syst 13(1):60–65CrossRefGoogle Scholar
  10. 10.
    Mutale J, Strbac G (1999) Transmission network reinforcement versus FACTS: an economic assessment. In: 21st International conference on power industry computer applications, pp 279–285Google Scholar
  11. 11.
    Alhasawi FB, Milanovic JV (2012) Techno-economic contribution of FACTS devices to the operation of power systems with high level of wind power integration. IEEE Trans Power Syst 27(3):1414–1421CrossRefGoogle Scholar
  12. 12.
    Acharya N, Mithulananthan N (2007) Locating series FACTS devices for congestion management in deregulated electricity markets. Electr Power Syst Res 77(3):352–360CrossRefGoogle Scholar
  13. 13.
    Donsion MP, Guemes J, Rodriguez J (2007) Power quality, benefits of utilizing FACTS devices in electrical power systems. In: 7th International symposium on electromagnetic compatibility and electromagnetic ecologyGoogle Scholar
  14. 14.
    Singh S, David A (2001) Optimal location of FACTS devices for congestion management. Electr Power Syst Res 58(2):71–79CrossRefGoogle Scholar
  15. 15.
    Lu Y, Abur A (2002) Static security enhancement via optimal utilization of thyristor-controlled series capacitors. IEEE Trans Power Syst 17(2):324–329CrossRefGoogle Scholar
  16. 16.
    Singh J, Singh S, Srivastava S (2007) An approach for optimal placement of static VAr compensators based on reactive power spot price. IEEE Trans Power Syst 22(4):2021–2029CrossRefGoogle Scholar
  17. 17.
    Yang GY, Hovland G, Majumder R, Dong ZY (2007) TCSC allocation based on line flow based equations via mixed-integer programming. IEEE Trans Power Syst 22(4):2262–2269CrossRefGoogle Scholar
  18. 18.
    Lima FG, Galiana FD, Kockar I, Munoz J (2003) Phase shifter placement in large-scale systems via mixed integer linear programming. IEEE Trans Power Syst 18(3):1029–1034CrossRefGoogle Scholar
  19. 19.
    Chang RW, Saha TK (2014) A novel MIQCP method for FACTS allocation in complex real-world grids. Int J Electr Power Energy Syst 62:735–743CrossRefGoogle Scholar
  20. 20.
    Chang R, Saha T (2010) Maximizing power system loadability by optimal allocation of SVC using mixed integer linear programming. IEEE PES general meetingGoogle Scholar
  21. 21.
    Nikoobakht A, Aghaei J, Parvania M, Sahraei-Ardakani M (2018) Contribution of FACTS devices in power systems security using MILP-based OPF. IET Gener Transm Distrib 12(15):3744–3755CrossRefGoogle Scholar
  22. 22.
    Zhang X, Tomsovic K, Dimitrovski A (2018) Optimal allocation of series FACTS devices in large-scale systems. IET Gener Trans Distrib 12(8):1889–1896CrossRefGoogle Scholar
  23. 23.
    Nireekshana T, Rao GK, Raju SSN (2012) Enhancement of ATC with FACTS devices using real-code genetic algorithm. Int J Electr Power Energy Syst 43(1):1276–1284CrossRefGoogle Scholar
  24. 24.
    Eslami M, Shareef H, Khajehzadeh M (2013) Optimal design of damping controllers using a new hybrid artificial bee colony algorithm. Int J Electr Power Energy Syst 52:42–54CrossRefGoogle Scholar
  25. 25.
    Sirjani R, Mohamed A, Shareef H (2012) Optimal allocation of shunt Var compensators in power systems using a novel global harmony search algorithm. Int J Electr Power Energy Syst 43:562–572CrossRefGoogle Scholar
  26. 26.
    Gitizadeh M, Khalilnezhad H, Hedayatzadeh R (2013) TCSC allocation in power systems considering switching loss using MOABC algorithm. Electr Eng 95(2):73–85CrossRefGoogle Scholar
  27. 27.
    Siddiqui AA, Deb T, Singh M (2014) Improved gravitational search algorithm for loadability enhancement of transmission lines using UPFC. Int J Syst Assur Eng Manag 5(3):444–449CrossRefGoogle Scholar
  28. 28.
    Padmavathi SV, Sahu SK, Jayalaxmi A (2019) Power system security improvement by means of fuzzy adaptive gravitational search algorithm-based FACTS devices under fault condition. Soft Comput Data Anal. Springer, Singapore, pp 95–106CrossRefGoogle Scholar
  29. 29.
    Gitizadeh M (2010) Allocation of multi-type FACTS devices using multi-objective genetic algorithm approach for power system reinforcement. Electr Eng 92(6):227–237CrossRefGoogle Scholar
  30. 30.
    Jordehi AR (2015) Optimal setting of TCSCs in power systems using teaching–learning-based optimisation algorithm. Neural Comput Appl 26(5):1249–1256CrossRefGoogle Scholar
  31. 31.
    Naresh G, Raju MR, Narasimham S (2016) Coordinated design of power system stabilizers and TCSC employing improved harmony search algorithm. Swarm Evolut Comput 27:169–179CrossRefGoogle Scholar
  32. 32.
    Hooshmand RA, Morshed MJ, Parastegari M (2015) Congestion management by determining optimal location of series FACTS devices using hybrid bacterial foraging and Nelder–Mead algorithm. Appl Soft Comput 28:57–68CrossRefGoogle Scholar
  33. 33.
    Ersavas C, Karatepe E (2017) Optimum allocation of FACTS devices under load uncertainty based on penalty functions with genetic algorithm. Electr Eng 99(1):73–84CrossRefGoogle Scholar
  34. 34.
    Gerbex S, Cherkaoui R, Germond AJ (2001) Optimal location of multi-type FACTS devices in a power system by means of genetic algorithms. IEEE Trans Power Syst 16(3):537–544CrossRefGoogle Scholar
  35. 35.
    Nagalakshmi S, Kamaraj N (2012) Comparison of computational intelligence algorithms for loadability enhancement of restructured power system with FACTS devices. Swarm Evolut Comput 5:17–27CrossRefGoogle Scholar
  36. 36.
    Raj S, Bhattacharyya B (2018) Optimal placement of TCSC and SVC for reactive power planning using Whale optimization algorithm. Swarm Evolut Comput 40:131–143CrossRefGoogle Scholar
  37. 37.
    Saravanan M, Slochanal SMR, Venkatesh P, Abraham JPS (2007) Application of particle swarm optimization technique for optimal location of FACTS devices considering cost of installation and system loadability. Electr Power Syst Res 77(3):276–283CrossRefGoogle Scholar
  38. 38.
    Jordehi AR (2016) Optimal allocation of FACTS devices for static security enhancement in power systems via imperialistic competitive algorithm (ICA). Appl Soft Comput 48:317–328CrossRefGoogle Scholar
  39. 39.
    Sarker J, Goswami S (2014) Solution of multiple UPFC placement problems using gravitational search algorithm. Int J Electr Power Energy Syst 55:531–541CrossRefGoogle Scholar
  40. 40.
    Kumar BV, Srikanth N (2017) A hybrid approach for optimal location and capacity of UPFC to improve the dynamic stability of the power system. Appl Soft Comput 52:974–986CrossRefGoogle Scholar
  41. 41.
    Gitizadeh M, Kalantar M (2009) Genetic algorithm-based fuzzy multi-objective approach to congestion management using FACTS devices. Electr Eng 90(8):539–549zbMATHCrossRefGoogle Scholar
  42. 42.
    Elmitwally A, Eladl A, Morrow J (2016) Long-term economic model for allocation of FACTS devices in restructured power systems integrating wind generation. IET Gener Transm Distrib 10(1):19–30CrossRefGoogle Scholar
  43. 43.
    Aghdam FH, Ghaemi S, Kalantari NT (2018) Evaluation of loss minimization on the energy management of multi-microgrid based smart distribution network in the presence of emission constraints and clean productions. J Clean Prod 196:185–201CrossRefGoogle Scholar
  44. 44.
    Myung IJ (2003) Tutorial on maximum likelihood estimation. J Math Psychol 47(1):90–100MathSciNetzbMATHCrossRefGoogle Scholar
  45. 45.
    Gandoman FH, Ahmadi A, Sharaf AM, Siano P, Pou J, Hredzak B, Agelidis VG (2018) Review of FACTS technologies and applications for power quality in smart grids with renewable energy systems. Renew Sustain Energy Rev 82:502–514CrossRefGoogle Scholar
  46. 46.
    Wibowo RS, Yorino N, Eghbal M, Zoka Y, Sasaki Y (2011) FACTS devices allocation with control coordination considering congestion relief and voltage stability. IEEE Trans Power Syst 26(4):2302–2310CrossRefGoogle Scholar
  47. 47.
    Shrieves RE, Wachowicz JM Jr (2001) Free cash flow, economic value added, and net present value: a reconciliation of variations of discounted cash flow valuation. Eng Econ 46(1):33–52CrossRefGoogle Scholar
  48. 48.
    Hong H (1998) An efficient point estimate method for probabilistic analysis. Reliab Eng Syst Saf 59(3):261–267CrossRefGoogle Scholar
  49. 49.
    Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713CrossRefGoogle Scholar
  50. 50.
    Elsaiah S, Cai N, Benidris M, Mitra J (2015) Fast economic power dispatch method for power system planning studies. IET Gener Transm Distrib 9(5):417–426CrossRefGoogle Scholar
  51. 51.
    Zimmerman RD, Murillo-Sánchez CE (2011) Matpower 4.1 user’s manual. Power Systems Engineering Research Center, Cornell University, IthacaGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringAzarbaijan Shahid Madani UniversityTabrizIran
  2. 2.Center for Energy Science and TechnologySkolkovo Institute of Science and TechnologyMoscowRussia

Personalised recommendations