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Interval Arithmetic Power Flow Analysis of Radial Distribution System with Probabilistic Load Model and Distributed Generation

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Abstract

The variations in load and generation result in higher degree of uncertainty in power flow calculation and create new challenge for the system operator to develop new tools to assess the current and future state of the system. Therefore, the incorporation of the system uncertainties plays a vital role for sustainable planning of the power system. This paper demonstrates the combined application of the probabilistic and possibilistic approach to address line, load and distributed generation (DG) uncertainties in a radial distribution system. The uncertainty in load demand is represented as a Gaussian distribution function, whereas line and DG uncertainty are varied at a fixed proportion. The load is modelled as composite. Type I (penetrates real power), Type II (penetrates reactive power) and Type IV (penetrates both real and reactive power) DG are considered depending upon the type of power injected. The efficacy of improved power flow techniques with the inclusion of various types of DG and its effect on power losses is verified by four test cases on three IEEE test systems: 33-bus, 34-bus and 69-bus. The obtained results are compared to the possibilistic-only approach and found out to be superior. The convergence characteristic is also analysed at various degree of belongingness. The technique converges in smaller number of iterations as compared to other methods. The lower interval width signifies the numerical stability. The statistical analysis of power losses reduction with DG penetration is also carried out.

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References

  • 1547-2003 IEEE standard for interconnecting distributed resources with electric power systems (2003) In: IEEE Standards, p 1–16.

  • Abdelkader B, Slimani L, Bouktir T (2014) Analysis of radial distribution system power flow under uncertainties with fuzzy arithmetic algorithm. 3rd International Conference on Information Processing and Electrical Engineering.

  • Aiena M, Rashidinejad M, Fotuhi-Firuzabad M (2014) On possibilistic and probabilistic uncertainty assessment of power flow problem: a review and a new approach. Renew Sustain Energy Rev 37:883–895

    Article  Google Scholar 

  • Alefeld G, Herzeberger J (1983) Introduction to interval arithmetic. Academic, New York

    Google Scholar 

  • Ali ES, Elazim SM, Abdelaziz AY (2018) Ant lion optimization algorithm for renewable distributed generations. Electr Eng 100(1):100–109

    Article  Google Scholar 

  • Attari SK, Shakarami MR, Namdari F, Bakhshipour M (2015) Multiobjective optimal reconfiguration of power distribution systems with load uncertainty using a genetic algorithm based on NSGA-II. Int Elect Eng J 6(10):2040–2047

    Google Scholar 

  • Baran ME, Wu F (1989a) Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans Power Delivery 4(2):1401–1407

    Article  Google Scholar 

  • Baran ME, Wu F (1989b) Optimal sizing of capacitor placed on radial distribution systems. IEEE Transaction on Power Delivery 4(1):735–743

    Article  Google Scholar 

  • Carpinelli G, Caramia P, Varilone P (2015) Multi-linear Monte Carlo simulation method for probabilistic load flow of distribution systems with wind and photovoltaic generation systems. Renew Energ 76:283–295

    Article  Google Scholar 

  • Chaturvedi A, Prasad K, Ranjan R (2006) Use of interval arithmetic to incorporate the uncertainty of load demand for radial distribution system analysis. IEEE Trans Power Delivery 21(2):1019–1021

    Article  Google Scholar 

  • Das B (2002) Radial distribution power flow using interval arithmetic. Int J Electr Power Energy Syst 24(10):827–836

    Article  Google Scholar 

  • Das B (2009) Incorporation of uncertainties in radial distribution system load flow with voltage-dependent loads. Electr Power Comp Syst 37:1102–1117

    Article  Google Scholar 

  • Das S, Malakar T (2020) Estimating the impact of uncertainty on optimum capacitor placement in wind-integrated radial distribution system. Int Trans Electr Energ Syst 30(8):1–23

    Article  Google Scholar 

  • Ding T, Bo R, Li F, Guo Q, Sun H, Gu W, Zhou G (2015) Interval power flow analysis using linear relaxation and optimality-based bounds tightening (OBBT) methods. IEEE Trans Power Syst 30(1):177–188

    Article  Google Scholar 

  • Ersavas C, Karatepe E (2017) Optimum allocation of FACTS devices under load uncertainty based on penalty functions with genetic algorithm. Electr Eng 99(1):73–84

    Article  Google Scholar 

  • Esmaeili M, Sedighizahed M, Esmaili M (2016) 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

    Article  Google Scholar 

  • Jagtap KM, Khatod DK (2016) Loss allocation in radial distribution networks with various distributed generation and load models. Int J Electr Power Energ Syst 75:173–186

    Article  Google Scholar 

  • Marin M, Milano F, Defour D (2017) Midpoint-radius interval-based method to deal with uncertainty in power flow analysis. Electr Power Syst Res 147:81–87

    Article  Google Scholar 

  • Nogueira WC, Garcés Negrete LP, López-Lezama JM (2021) Interval load flow for uncertainty consideration in power systems analysis. Energies 14:642–656

    Article  Google Scholar 

  • Noorkami M et al (2014) Effect of temperature uncertainty on polymer electrolyte fuel cell performance. Int J Hydrogen Energy 39(3):1439–1448

    Article  Google Scholar 

  • Parihar SS, Malik N (2017) Interval arithmetic power flow analysis of radial distribution system including uncertainties in input parameters. 7th Int Conf Power Syst 69–74.

  • Parihar SS, Malik N (2020) Optimal allocation of renewable DGs in a radial distribution system based on new voltage stability index. Int Trans Electr Energ Syst 30(4):1–19

    Article  Google Scholar 

  • Pereira LES, Da Costa VM, Rosa ALS (2012) Interval arithmetic in current injection power flow analysis. Int J Electr Power Syst 43(1):1106–1113

    Article  Google Scholar 

  • Pradeepa H, Ananthapadmanabha T, Sandhya RDN, Bandhavya C (2015) Optimal allocation of combined DG and capacitor units for voltage stability enhancement. Procedia Technol 21:216–223

    Article  Google Scholar 

  • Raj V, Kumar BK (2019) A modified affine arithmetic-based power flow analysis for radial distribution system with uncertainty. Int J Electr Power Energy Syst 107:395–402

    Article  Google Scholar 

  • Ranjan R, Venkatesh B, Das D (2003) Load flow algorithm of radial distribution networks incorporating composite load model. Int J Power Energ Syst 23(1):71–76

    Google Scholar 

  • Salama MMA, Chikhani AY (1993) A simplified network approach to the VAR control problem for radial distribution systems. IEEE Trans Power Delivery 8(3):1529–1535

    Article  Google Scholar 

  • Teng JH (2003) A direct approach for distribution system power flow solution. IEEE Trans Power Delivery 18(3):882–887

    Article  Google Scholar 

  • Vaccaro A, Canizares CA, Villacci D (2010) An affine arithmetic-based methodology for reliable power flow analysis in the presence of data uncertainty. IEEE Trans Power Syst 25(2):624–632

    Article  Google Scholar 

  • Vidovic PM, Saric AT (2017) A novel correlated interval-based algorithm for distribution power flow calculation. Int J Electr Power Energ Syst 90:245–255

    Article  Google Scholar 

  • Walling RA, Saint R, Dugan RC, Burke J, Kojovic LA (2008) Summary of distributed resources impact on power delivery systems. IEEE Trans Power Delivery 23(3):1636–1644

    Article  Google Scholar 

  • Wang S, Wang C, Zhang G, Zhao G (2009) Fast decoupled power flow using interval arithmetic considering uncertainty in power systems. Int Symp Neural Networks Advanc Neural Networks 1171–1178.

  • Wang Y, Wu Z, Duo X, Hu M, Xu Y (2017) Interval power flow analysis via multi-stage affine arithmetic for unbalanced distribution network. Electric Power Systems Res 142:1–8

    Article  Google Scholar 

  • Wang Z, Alvarado FL (1992) Interval arithmetic in power flow analysis. IEEE Trans Power Syst 7(3):1341–1349

    Article  Google Scholar 

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  1. The NorthCap University, Gurgaon, Haryana, India

    Shradha Singh Parihar & Nitin Malik

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  1. Shradha Singh Parihar
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  2. Nitin Malik
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Correspondence to Nitin Malik.

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Parihar, S.S., Malik, N. Interval Arithmetic Power Flow Analysis of Radial Distribution System with Probabilistic Load Model and Distributed Generation. Process Integr Optim Sustain 6, 3–15 (2022). https://doi.org/10.1007/s41660-021-00200-8

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  • DOI: https://doi.org/10.1007/s41660-021-00200-8

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