Maximum hosting capacity of distributed generation in three-phase distribution systems: an approach based on an optimization model / Máxima capacidade de hospedagem de geração distribuída em sistemas de distribuição trifásicos: uma abordagem baseada em um modelo de otimização

Igor Delgado de Melo, Heitor Magno Rodrigues Junior, Mariana Escarati de Oliveira



In this paper, an optimization problem is formulated with the main purpose of determining the maximum hosting capacity of distributed generation in three-phase electric power distribution systems. The objective function to be maximized is the sum of the active powers injected into the system buses in which distributed generation is considered. Inequality constraints are used to determine lower and upper bounds for voltage magnitudes, unbalance factor, reverse power flow at the substation bus and active power insertion. Power flow equations are modelled as equality constraints according to the three-phase current injection method. Simulations are performed using a modified IEEE 33-bus to show the effectiveness of the proposed methodology for determining the maximum hosting capacity in three-phase distribution feeders assuming dispersed generation previously allocated in the network. An index is proposed to calculate the maximum hosting capacity based on the response of the optimization problem. Additionally, daily load profiles are considered to test the proposed methodology assuming system load variation. The main contribution of this paper is the optimization model which assumes bounds for reverse power flow and unbalance factor in a systemic analysis based on the three-phase current injection method equations (TPCIM).




hosting capacity, electric distribution systems, distributed generation, computational simulations.

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Abad MSS, Ma J, Han X (2019) Distribution systems hosting capacity assessment: Relaxation and linearization. In: Smart Power Distribution Systems, Elsevier, pp 555–586

Almeida D, Abeysinghe S, Ekanayake MP, Godaliyadda RI, Ekanayake J, Pasupuleti J (2020) Generalized approach to assess and characterise the impact of solar pv on lv networks. International Journal of Electrical Power & Energy Systems 121:106058

Alturki M, Khodaei A, Paaso A, Bahramirad S (2018) Optimization-based distribu- tion grid hosting capacity calculations. Applied Energy 219:350–360

Celli G, Chowdhury N, Pilo F, Soma GG, Troncia M, Gianinoni IM (2018) Multi- criteria analysis for decision making applied to active distribution network plan- ning. Electric Power Systems Research 164:103–111

Fu YY, Chiang HD (2018) Toward optimal multiperiod network reconfiguration for increasing the hosting capacity of distribution networks. IEEE Transactions on Power Delivery 33(5):2294–2304

Garcia PA, Pereira JLR, Carneiro S, Da Costa VM, Martins N (2000) Three-phase power flow calculations using the current injection method. IEEE Transactions on Power Systems 15(2):508–514.

Holguin JP, Rodriguez DFC, Ramos G (2020) Reverse power flow (rpf) detection and impact on protection coordination of distribution systems. IEEE Transactions on Industry Applications

Khani H, El-Taweel N, Farag HE (2018) Real-time optimal management of reverse power flow in integrated power and gas distribution grids under large renewable power penetration. IET Generation, Transmission & Distribution 12(10):2325– 2331

Lakshmi S, Ganguly S (2018) Simultaneous optimization of photovoltaic hosting capacity and energy loss of radial distribution networks with open unified power quality conditioner allocation. IET Renewable Power Generation 12(12):1382–1389

Lee J, Bérard JP, Razeghi G, Samuelsen S (2020) Maximizing pv hosting capacity of distribution feeder microgrid. Applied Energy 261:114400

Mahroo-Bakhtiari R, Izadi M, Safdarian A, Lehtonen M (2019) Distributed load management scheme to increase pv hosting capacity in lv feeders. IET Renewable Power Generation 14(1):125–133

Melo ID, Pereira JL, Variz AM, Garcia PA (2017) Harmonic state estimation for distribution networks using phasor measurement units. Electric Power Systems Research 147:133–144

Melo ID, Pereira JL, Ribeiro PF, Variz AM, Oliveira BC (2019) Harmonic state estimation for distribution systems based on optimization models considering daily load profiles. Electric Power Systems Research 170:303–316

Mulenga E, Bollen MH, Etherden N (2020) A review of hosting capacity quantifi- cation methods for photovoltaics in low-voltage distribution grids. International Journal of Electrical Power & Energy Systems 115:105445

de Oliveira C, Elias T, Bollen M, Ribeiro PF, de Carvalho P, Zambroni AC, Bon- atto BD (2019) The concept of dynamic hosting capacity for distributed energy resources: Analytics and practical considerations. Energies 12(13):2576

Oliveira EJ, Oliveira LW, Pereira J, Honório LM, Junior ICS, Marcato A (2015) An optimal power flow based on safety barrier interior point method. International Journal of Electrical Power & Energy Systems 64:977–985

Quijano DA, Wang J, Sarker MR, Padilha-Feltrin A (2017) Stochastic assessment of distributed generation hosting capacity and energy efficiency in active distribution networks. IET Generation, Transmission & Distribution 11(18):4617–4625

Raja AA, Mansoor M, Zahid F (2018) Optimal sitting of distributed generation based on hosting capacity approach. In: 2018 International Conference on Engineering and Emerging Technologies (ICEET), IEEE, pp 1–5

Sahu SK, Ghosh D (2019) Hosting capacity enhancement in distribution system in highly trenchant photo-voltaic environment: A hardware in loop approach. IEEE Access 8:14440–14451

Schultis DL (2019) Comparison of local volt/var control strategies for pv hosting capacity enhancement of low voltage feeders. Energies 12(8):1560

Wang S, Dong Y, Wu L, Yan B (2019) Interval overvoltage risk based pv hosting capacity evaluation considering pv and load uncertainties. IEEE Transactions on Smart Grid



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