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Optimal sizing of distributed generation units and shunt capacitors in the distribution system considering uncertainty resources by the modified evolutionary algorithm

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Abstract

Distributed generation units (DGUs) as auxiliary sources of power generation can play an effective role in meeting the load consumption of the distribution network, also have positive effects such as reducing loss and improving voltage. Moreover, capacitors by reactive power compensation produce positive effects similar to DGUs in the distribution networks. The idea of joint operation of DGUs and shunt capacitors (SCs) in the presence of demand response program (DRP) to derive maximum benefits from their installation is proposed in this paper. The time of use (TOU) mechanism is used as one of the demand response programs (DRPs) to alter the consumption pattern of subscribers and improve the performance of the distribution system. Objective functions include minimization of energy loss, operational cost, and energy not supplied (ENS). In general, the problem of determining the optimal capacity of DGUs and SCs is complex due to the demand variation. Also, considering the effect of uncertainty sources complicate the optimization problem. Hence, a modified shuffled frog leaping algorithm (MSFLA) is proposed to overcome the complexities of this problem. The proposed approach is tested on two 95, and 136-node test networks, and the results are compared with other evolutionary algorithms. According to the obtained results, after using the proposed approach in determining the optimal capacity of DGUs and SCs in the first system, the amount of energy loss, operational cost and ENS dropped by 11, 25.5 and 5% compared to baseline values. After applying the TOU mechanism in allocation of DGUs and SCs simultaneously in the second system by proposed method, the values obtained for the mentioned objectives reduced by 29, 65 and 7% compared to initial values.

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Abbreviations

\({{\varphi }}_{Pd}{{\varphi }}_{Ep}\) :

Occurrence probability of load demand and electricity price

\({\mathrm{C}}_{Ep}\,\,{\mathrm{C}}_{Ep}\) :

Numerical values extracted from probabilistic distributions for load demand and electricity purchase price

\({\mathrm{P}}_{t,i}^{MDF}\) :

Modified demand of the ith feeder at time t

Ns :

Number of scenarios

\({\mathrm{P}}_{t,i}^{\mathrm{TOU}}\,\,\) \({\mathrm{P}}_{t,i}^{\mathrm{INI}}\) :

Surge or drop in the demand for this mechanism and the initial demand values in ith feeder at time t without TOU mechanism

\({\mathrm{TOU }}^{\mathrm{max}}\) :

Maximum speed of demand surge or drop in the TOU mechanism

\(\upmu\) :

Mean value

\(\upsigma\) :

Standard deviation

\({\mathrm{X}}_{w}{\mathrm{X}}_{b}\) :

Worst and best frogs

\({\mathrm{P}}_{DG,j}\) :

Active power of jth DG unit

\({\mathrm{P}}_{Sub,s}\) :

Active power of sth sub-station

\({\mathrm{Price}}_{DG,j}\) :

Purchase price of electricity from jth DG unit

\({\mathrm{Price}}_{Sub,s}\) :

Purchase price of electricity from sth sub-station

\({\mathrm{U}}_{i,j }{\mathrm{ U}}_{i,j}^{\prime}\) :

Repair time (hours per year) and the compensation time for the branches related to bus i

\({\uplambda }_{i,j}{\mathrm{ d}}_{i,j}\) :

Failure rate and line length

\({\mathrm{N}}_{Sub}\) :

Number of sub-stations

\(\mathrm{C}\) :

Constant value

\({\mathrm{Y}}_{ij}{{\theta}}_{ij}\) :

Magnitude and branch admittance angle between buses i and j

\({\mathrm{KK}}_{\mathrm{max}}\) :

Number of current iteration and maximum iteration number

\(\mathrm{W}\) :

Inertia weight

\({\mathrm{f}}_{i}^{\mathrm{min}}{\mathrm{f}}_{i}^{\mathrm{max}}\) :

Lower and upper limits of ith objective function

\({\upmu }_{i}\) :

Fuzzy membership function of ith objective function

\({\upbeta }_{k}\) :

kTh weight of objective function

\({\mathrm{E}}^{\mathrm{pr}}\) :

Distribution function parameter

\({\mathrm{R}}_{i}\) :

Resistance of the ith line

\({\mathrm{I}}_{i}\) :

Current of ith line

\({\mathrm{N}}_{\mathrm{brch}}\) :

Number of branches

\(\mathrm{X}\) :

Vector of decision variables

\({\mathrm{X}}_{G}\) :

Best frog between all memblexes

\(\mathrm{rand}\) :

Random number in [0,1]

\({\mathrm{D}}_{\mathrm{min}}\,\,{\mathrm{D}}_{\mathrm{max}}\) :

Minimum and Maximum displacement of ith frog

\({\mathrm{V}}_{\min}{\mathrm{V}}_{\max}\) :

Minimum and maximum allowable values ​​of ith bus voltage

\({\mathrm{Q}}_{C,i} {\mathrm{Q}}_{d}\,\,{\mathrm{I}}_{f,i}{\mathrm{I}}_{f,i}^{\mathrm{Max}}\) :

Current amplitude at time t and the maximum current of ith feeder

\({\mathrm{P}}_{DG}^{\mathrm{min}}{\mathrm{P}}_{DG}^{\mathrm{max}}\) :

Minimum and maximum output power of ith DG unit

\({\mathrm{N}}_{\mathrm{Cap}}\) :

Number of capacitors

\({\mathrm{t}}_{i,j} {\mathrm{t}}_{i,j}^{\prime}\) :

Average repair time and the average line recovery time between the ith and jth buses

\({\mathrm{P}}_{\mathrm{j}}\,\, {\mathrm{Q}}_{\mathrm{j}}\) :

Active and reactive power injected by the network in the ith bus

\({\mathrm{N}}_{\text{Bus}}\) :

Number of buses

\({\mathrm{V}}_{i}{\updelta }_{i}\) :

Voltage magnitude and Voltage angel of the ith bus

\(\mathrm{m}\,\,\mathrm{n}\) :

Number of non-dominated solution and objective functions

\({\mathrm{W}}_{\mathrm{min}}{\mathrm{W}}_{\mathrm{max}}\) :

Boundaries of inertia weight

\({\mathrm{N}}_{DG}\) :

Number of DG units

\({\mathrm{N}}_{\mu j}\) :

Normalized membership function of each for each member

References

  • Abdelaziz A, Ali E, Abd Elazim S (2016) Optimal sizing and locations of capacitors in radial distribution systems via flower pollination optimization algorithm and power loss index. Eng Sci Technol Int J 19(1):610–618

    Google Scholar 

  • Abou El-Ela AA, El-Sehiemy RA, Kinawy A-M, Mouwafi MT (2016) Optimal capacitor placement in distribution systems for power loss reduction and voltage profile improvement. IET Gener Transm Distrib 10(5):1209–1221

    Article  Google Scholar 

  • Abou El-Ela AA, El-Sehiemy RA, Abbas AS (2018) Optimal placement and sizing of distributed generation and capacitor banks in distribution systems using water cycle algorithm. IEEE Syst J 12(4):3629–3636

    Article  Google Scholar 

  • Al-Ammar EA, Ghazi GA, Ko W, Khan Y, Beroual A, Hong J, Song S-H (2021) Comprehensive impact analysis of ambient temperature on multi-objective capacitor placements in a radial distribution system. Ain Shams Eng J 12(1):717–727

    Article  Google Scholar 

  • Askarzadeh A (2016) Capacitor placement in distribution systems for power loss reduction and voltage improvement: a new methodology. IET Gener Transm Distrib 10(14):3631–3638

    Article  Google Scholar 

  • Azizivahed A, Naderi E, Narimani H, Fathi M, Narimani MR (2017) A new bi-objective approach to energy management in distribution networks with energy storage systems. IEEE Trans Sustain Energy 9(1):56–64

    Article  Google Scholar 

  • Azizivahed A, Barani M, Razavi S-E, Ghavidel S, Li L, Zhang J (2018) Energy storage management strategy in distribution networks utilised by photovoltaic resources. IET Gener Transm Distrib 12(21):5627–5638

    Article  Google Scholar 

  • Azizivahed A, Lotfi H, Ghadi MJ, Ghavidel S, Li L, Zhang J (2019) Dynamic feeder reconfiguration in automated distribution network integrated with renewable energy sources with respect to the economic aspect. In: Paper presented at the 2019 IEEE Innovative Smart Grid Technologies-Asia (ISGT Asia)

  • Barani M, Aghaei J, Akbari MA, Niknam T, Farahmand H, Korpås M (2018) Optimal partitioning of smart distribution systems into supply-sufficient microgrids. IEEE Trans Smart Grid 10(3):2523–2533

    Article  Google Scholar 

  • Biswas PP, Mallipeddi R, Suganthan PN, Amaratunga GA (2017) A multiobjective approach for optimal placement and sizing of distributed generators and capacitors in distribution network. Appl Soft Comput 60:268–280

    Article  Google Scholar 

  • Das S, Das D, Patra A (2019) Operation of distribution network with optimal placement and sizing of dispatchable DGs and shunt capacitors. Renew Sustain Energy Rev 113:109219

    Article  Google Scholar 

  • Din FU, Ahmad A, Ullah H, Khan A, Umer T, Wan S (2019) Efficient sizing and placement of distributed generators in cyber-Physical power systems. J Syst Archit 97:197–207

    Article  Google Scholar 

  • Elattar EE, ElSayed SK (2020) Optimal location and sizing of distributed generators based on renewable energy sources using modified moth flame optimization technique. IEEE Access 8:109625–109638

    Article  Google Scholar 

  • Elbeltagi E, Hegazy T, Grierson D (2007) A modified shuffled frog-leaping optimization algorithm: applications to project management. Struct Infrastruct Eng 3(1):53–60

    Article  Google Scholar 

  • El-Fergany AA, Abdelaziz AY (2014) Artificial bee colony algorithm to allocate fixed and switched static shunt capacitors in radial distribution networks. Electr Power Compon Syst 42(5):427–438

    Article  Google Scholar 

  • Eusuff M, Lansey K, Pasha F (2006) Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization. Eng Optimiz 38(2):129–154

    Article  MathSciNet  Google Scholar 

  • Galgali VS, Ramachandran M, Vaidya G (2019) Multi-objective optimal sizing of distributed generation by application of Taguchi desirability function analysis. SN Appl Sci 1(7):742

    Article  Google Scholar 

  • Grisales-Noreña LF, Gonzalez Montoya D, Ramos-Paja CA (2018) Optimal sizing and location of distributed generators based on PBIL and PSO techniques. Energies 11(4):1018

    Article  Google Scholar 

  • Jahani MTG, Nazarian P, Safari A, Haghifam M (2019) Multi-objective optimization model for optimal reconfiguration of distribution networks with demand response services. Sustain Cities Soc 47:101514

    Article  Google Scholar 

  • Kavousi-Fard A, Samet H (2013) Multi-objective performance management of the capacitor allocation problem in distributed system based on adaptive modified honey bee mating optimization evolutionary algorithm. Electr Power Compon Syst 41(13):1223–1247

    Article  Google Scholar 

  • Kumari RL, Kumar GN, Nagaraju SS, Jain MB (2017) Optimal sizing of distributed generation using particle swarm optimization. Paper presented at the 2017 International Conference on Intelligent Computing, Instrumentation and Control Technologies (ICICICT)

  • Liu W, Luo F, Liu Y, Ding W (2019) Optimal siting and sizing of distributed generation based on improved nondominated sorting genetic algorithm II. Processes 7(12):955

    Article  Google Scholar 

  • López JC, Lavorato M, Rider MJ (2016) Optimal reconfiguration of electrical distribution systems considering reliability indices improvement. Int J Electr Power Energy Syst 78:837–845

    Article  Google Scholar 

  • Lotfi H (2020) Multi-objective energy management approach in distribution grid integrated with energy storage units considering the demand response program. Int J Energy Res 44(13):10662–10681

    Article  Google Scholar 

  • Lotfi H, Ghazi R (2020) Optimal participation of demand response aggregators in reconfigurable distribution system considering photovoltaic and storage units. J Ambient Intell Humaniz Comput 12:2233–2255

    Article  Google Scholar 

  • Lotfi H, Samadi M, Dadpour A (2016) Optimal capacitor placement and sizing in radial distribution system using an improved Particle Swarm Optimization algorithm. Paper presented at the 2016 21st Conference on Electrical Power Distribution Networks Conference (EPDC)

  • Lotfi H, Ghazi R, Sistani MBN (2019) Providing an optimal energy management strategy in distribution network considering distributed generators and energy storage units. Paper presented at the 2019 International Power System Conference (PSC)

  • Lotfi H, Ghazi R, bagher Naghibi-Sistani M (2020) Multi-objective dynamic distribution feeder reconfiguration along with capacitor allocation using a new hybrid evolutionary algorithm. Energy Syst 11:779–809

    Article  Google Scholar 

  • Niknam T, Kavousifard A, Aghaei J (2012) Scenario-based multiobjective distribution feeder reconfiguration considering wind power using adaptive modified particle swarm optimisation. IET Renew Power Gener 6(4):236–247

    Article  Google Scholar 

  • Parvizi E, Rezvani MH (2020) Utilization-aware energy-efficient virtual machine placement in cloud networks using NSGA-III meta-heuristic approach. Cluster Comput 23:2945–2967

    Article  Google Scholar 

  • Ravindran S, Victoire TAA (2018) A bio-geography-based algorithm for optimal siting and sizing of distributed generators with an effective power factor model. Comput Electr Eng 72:482–501

    Article  Google Scholar 

  • Reddy P, Prasad D (2014) Sensitivity based capacitor placement using cuckoo search algorithm for maximum annual savings. IOSR J Eng 4(4):6

    Article  Google Scholar 

  • Su H (2019) Siting and sizing of distributed generators based on improved simulated annealing particle swarm optimization. Environ Sci Pollut Res 26(18):17927–17938

    Article  Google Scholar 

  • Tah A, Das D (2016) Novel analytical method for the placement and sizing of distributed generation unit on distribution networks with and without considering P and PQV buses. Int J Electr Power Energy Syst 78:401–413

    Article  Google Scholar 

  • Veera Reddy VC (2018) Ant Lion optimization algorithm for optimal sizing of renewable energy resources for loss reduction in distribution systems. J Electr Syst Inf Technol 5(3):663–680

    Article  Google Scholar 

  • Zeinalzadeh A, Mohammadi Y, Moradi MH (2015) Optimal multi objective placement and sizing of multiple DGs and shunt capacitor banks simultaneously considering load uncertainty via MOPSO approach. Int J Electr Power Energy Syst 67:336–349

    Article  Google Scholar 

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  1. Department of Electrical Engineering, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran

    Hossein Lotfi

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Lotfi, H. Optimal sizing of distributed generation units and shunt capacitors in the distribution system considering uncertainty resources by the modified evolutionary algorithm. J Ambient Intell Human Comput 13, 4739–4758 (2022). https://doi.org/10.1007/s12652-021-03194-w

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