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Cited by 10Optimal Power Flow DistributionElectric Power System OptimizationSmart Grid Energy Management

Dynamic Optimal Power Dispatch in Unbalanced Distribution Networks with Single-Phase Solar PV Units and BESS

Open access
Radosavljević, Jordan, Ktena, Aphrodite, Gajić, Milena, Milovanović, Miloš, Živić, Jovana·2023·Energies
DOI 10.3390/en16114356

Published version of a preprint

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Abstract

Battery energy storage systems (BESSs) are a promising solution for increasing efficiency and flexibility of distribution networks (DNs) with a significant penetration level of photovoltaic (PV) systems. There are various issues related to the optimal operation of DNs with integrated PV systems and BESS that need to be addressed to maximize DN performance. This paper deals with day-ahead optimal active–reactive power dispatching in unbalanced DNs with integrated single-phase PV generation and BESS. The objectives are the minimization of cost for electricity, energy losses in the DN, and voltage unbalance at three-phase load buses by optimal management of active and reactive power flows. To solve this highly constrained non-linear optimization problem, a hybrid particle swarm optimization with sigmoid-based acceleration coefficients (PSOS) and a chaotic gravitational search algorithm (CGSA)called the PSOS-CGSA algorithm is proposed. A scenario-based approach encompassing the Monte Carlo simulation (MCS) method with a simultaneous backward reduction algorithm is used for the probabilistic assessment of the uncertainty of PV generation and power of loads. The effectiveness of the proposed procedure is evaluated through aseries test cases in a modified IEEE 13-bus feeder. The simulation results show that the proposed approach enables a large reduction in daily costs for electricity, as well as a reduction in expected daily energy losses in the DN by 22% compared to the base case without BESS while ensuring that the phase voltage unbalance rate (PVUR) is below the maximum limit of 2% for all three-phase buses in the DN.

AI snapshot

Written from the paper’s full text.

TL;DR

This paper proposes a two-stage day-ahead optimal active-reactive power dispatch for unbalanced distribution networks with single-phase PV and BESS, using a hybrid PSOS-CGSA metaheuristic and scenario-based uncertainty modeling. Tests on a modified IEEE 13-bus feeder show reduced electricity cost, lower energy losses, and voltage unbalance below the 2% limit.

Key findings

  • The proposed OAPD achieves an optimal expected daily electricity cost of 453.16 €; PSOS-CGSA provides lower costs in each of the 10 reduced scenarios than PSO, GSA, PSOS, and CGSA, and reduces costs versus the base case and the prior scheduling approach in [12].
  • The proposed ORPD reduces expected active energy losses by 22% compared with the base case and lowers the expected maximum PVUR from 9.10% to 1.91%, below the IEEE 141-1993 2% limit.
  • For loss minimization (Case 1), the best scenario is scenario 9; for voltage unbalance minimization (Case 2), the best scenario is scenario 1.
  • Single-phase PV inverters and BESS can serve as additional reactive power management resources in unbalanced DNs.

Methods

  • Two-stage nonlinear optimization: OAPD controls BESS charge/discharge through coefficients aφ(t) to minimize expected electricity cost; ORPD controls PV/BESS inverter reactive powers and slack bus voltage magnitudes to minimize expected energy losses or expected maximum PVUR.
  • Uncertainty modeling uses a Beta PDF for solar irradiance and a Gaussian PDF for load; Monte Carlo simulation generates 2000 scenarios, which are reduced to 10 using the simultaneous backward reduction algorithm over a 24-h horizon.
  • The test system is a modified IEEE 13-bus feeder with 250 kW single-phase PV units at buses 634, 645, 646, 611, 675, 692, and 652, and 0.9 MW/3.6 MWh single-phase BESS at bus 680 in all three phases; PSOS-CGSA uses N=50 and itmax=200 and is compared with PSO, GSA, PSOS, and CGSA.

Limitations

  • The paper states no explicit limitations section.
  • Evident from the text: evaluation uses only one modified IEEE 13-bus feeder and one day-ahead dataset based on Serbian spot-market prices for January–February 2023, so generalizability is not demonstrated.
  • Evident from the text: the probabilistic assessment reduces 2000 MCS scenarios to 10, and no sensitivity analysis of the scenario reduction or algorithm parameter choices is reported.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.3390/en16114356

Cites

35 of 35 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

11 of 21 cited sources checked · 1 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    PV generators suffer from variability and stochasticity of their output power, which is their main drawback.

    “However, they suffer from variability and stochasticity of the output power which is their main drawback [2] and a challenge attracting the interest of research community.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [2] Ktena, 2020, Optimal placement and sizing of renewable distributed generation using hybrid metaheuristic algorithm, J. Mod. Power Syst. Clean Energy source

      The PV Generation Modeling section (page unavailable) describes solar irradiance as stochastic and says PV power output depends on its possible states. The Simulation Results section shows PV generation varying by season and falling to zero at night. These passages support variable, stochastic output, but the paper does not identify it as PV generators’ main drawback. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
  • Findingown data

    The proposed PSOS-CGSA-based approach for OAPD leads to a large reduction in costs for electricity compared to the base case and the approach for OAPD in [12].

    “The results in Figure 9 clearly indicate that the proposed PSOS-CGSA-based approach for OAPD leads to a large reduction in costs for electricity compared to the base case and the approach for OAPD in [12].”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [12] Prudhviraj, 2020, Stochastic energy management of microgrid with nodal price, J. Mod. Power Syst. Clean Energy source
  • Interpretationnone given

    Charging/discharging powers of BESS determined by the price-based coefficient aφ(t) as in [12] and [16] do not guarantee optimal dispatch of active power according to the adopted objective function.

    “However, the charging/discharging powers of the BESS determined in this way do not guarantee the optimal dispatch of the active power according to the adopted objective function.”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites [12] Prudhviraj, 2020, Stochastic energy management of microgrid with nodal price, J. Mod. Power Syst. Clean Energy source

      The BESS Modeling section defines charging and discharging powers as variables constrained by battery limits, and the Objective Function section describes minimizing expected energy cost; neither discusses a price-based coefficient aφ(t). Searches for that coefficient and for a claim that it cannot guarantee optimal active-power dispatch found no supporting passage in our copy. The paper’s optimization approach does not, by itself, establish the claimed limitation of a different approach. (LLM, conf=0.72)

      Experimental — accuracy not yet measured
    • cites [16] 2021, Voltage regulation in LV distribution networks with PV generation and battery storage, J. Electr. Eng.

      Not checked in the free run.

  • Premisecitation

    The equality constraints for the ORPD problem are typical nonlinear power flow equations for three-phase unbalanced distribution networks.

    “The equality constraints for the ORPD problem are typical nonlinear power flow equations for three-phase unbalanced DNs [22,23].”
    Quote in the paperNot a substantial claim2 of 2 sources checked
    • cites [22] Ali, 2021, Probabilistic approach for hosting high PV penetration in distribution systems via optial oversized inverter with watt-var functions, IEEE Syst. J. source

      Section III (Problem Formulation; page unavailable) describes distribution-system constraints using bus voltages, voltage-angle differences, conductance, susceptance, and active and reactive power. Section VI (Solution Process; page unavailable) says the optimization uses a nonlinear method. These passages support the power-flow aspect, but our copy does not establish that the stated constraints are for three-phase unbalanced networks; that phrase appears in the title of a different work in the References. (LLM, conf=0.78)

      Experimental — accuracy not yet measured
    • cites [23] Xavier, L.S., Amorim, W.C.S., Cupertino, A.F., Mendes, V.F., Boaventura, W.C., and Pereira, H.A. (2019). Power converters for battery energystorage systems connected to mediumvoltage systems: A comprehensive review. BMC Energy, 1. source

      The BESS control strategies section discusses converter current control and reactive-power references, not equality constraints for optimal reactive power dispatch. Searches for ORPD and three-phase unbalanced distribution-network power-flow equations found no passage addressing the claim. The indexed passages provide no page numbers. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
  • Findingown data

    The proposed hybrid PSOS-CGSA method finds better solutions for the OAPD problem, providing lower costs in each of 10 scenarios compared to PSO, GSA, PSOS and CGSA algorithms.

    “It is clear that the proposed hybrid PSOS-CGSA method finds better solutions for the OAPD problem, i.e., provides lower costs in each of 10 scenarios compared to PSO, GSA, PSOS and CGSA algorithms.”
    • Also stated in: § Additional information · boosted
      “The proposed PSOS-CGSA solution technique provides better solutions for the optimal power dispatch problems compared to other well-established metaheuristic algorithms such as PSO, GSA, and modified PSOS and CGSA.”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites [24] Girigoudar, 2019, On the impact of different voltage unbalance metrics in distribution system optimization, Electr. Power Syst. Res. source

      The Simulation Results (p. 6) describe three-phase optimal power flow solved with Ipopt on two test feeders, not an OAPD comparison. Searches for PSOS-CGSA, OAPD, the four comparator algorithms, and costs across ten scenarios found no passage addressing the claim in our copy. (LLM, conf=0.78)

      Experimental — accuracy not yet measured
    • cites [25] (1994). Recommended Practice for Electric Power Distribution for Industrial Plants (Standard No. IEEE Standard 141–1993).

      Not checked in the free run.

  • Classified as probably not a substantial claim. 4
  • May combine two claims. 3

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The hybrid PSOS-CGSA algorithm has demonstrated performance in solving various complex optimization problems such as distribution system state estimation, dynamic economic dispatch, and optimal power flow in distribution networks.

    “Its performance in terms of simplicity, efficiency and robustness has been demonstrated in solving various complex optimization problems such as distribution system state estimation [23], dynamic economic dispatch [26], and optimal power flow in DNs [12].”
    Quote in the paperNot a substantial claim2 of 3 sources checked
    • cites [23] Xavier, L.S., Amorim, W.C.S., Cupertino, A.F., Mendes, V.F., Boaventura, W.C., and Pereira, H.A. (2019). Power converters for battery energystorage systems connected to mediumvoltage systems: A comprehensive review. BMC Energy, 1. source

      The BESS control strategies section discusses converter power and current control, not the PSOS-CGSA algorithm. Searches for PSOS-CGSA, distribution system state estimation, dynamic economic dispatch, and optimal power flow found no passage in our copy addressing the claimed performance. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [26] Khushalani, 2007, Development of three-phase unbalanced power flow using PV and PQ models for distributed generation and study of the impact of DG models, IEEE Trans. Power Syst. source
    • cites [12] Prudhviraj, 2020, Stochastic energy management of microgrid with nodal price, J. Mod. Power Syst. Clean Energy source

      The System Model describes solving an optimal power flow problem to calculate nodal prices, and the Simulation Results test the approach on a 15-node distribution network. But the Simulation Results say the optimization is solved with GAMS and KNITRO, not the hybrid PSOS-CGSA algorithm; this paper therefore does not demonstrate that algorithm’s claimed performance. (LLM, conf=0.86)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Premisecitation

    PV and battery inverters have the ability to control generation/absorption of reactive power and can be used as an additional regulation resource in distribution networks.

    “Depending on the nominal apparent power of the converter and the active power level of the corresponding PV source or battery, they have the ability to control the generation/absorption of reactive power, that is, they can be used as an additional regulation resource in DNs [12,20], as illustrated in Figure 1.”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites [12] Prudhviraj, 2020, Stochastic energy management of microgrid with nodal price, J. Mod. Power Syst. Clean Energy source

      The Network Modeling section (page unavailable) includes reactive-power flows, but its local-generation equation includes only active power from DG, PV and batteries. The Simulation Results section (page unavailable) reports improved voltage profiles with BESS and local generation, without attributing that improvement to inverter reactive-power control. Searches for reactive power, inverters and apparent power found no passage addressing the claimed inverter capability. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [20] (2023, February 22). LNesp. Scenred. GitHub. Available online: https://github.com/supsi-dacd-isaac/scenred.

      Not checked in the free run.

    • The authors state this as an assumption: PV arrays and batteries are connected to unbalanced distribution networks via single-phase converters.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    A BESS is a combination of a voltage source converter and a battery pack, such that active and reactive power can be controlled independently.

    “The BESS is a combination of a voltage source converter and a battery pack, such that the active and reactive power can be controlled independently [4][5][6][7][8][9].”
    Quote in the paperNot a substantial claim2 of 6 sources checked
    • cites [4] Thango, B.A., and Bokoro, P.N. (2022). Battery Energy Storage for Photovoltaic Application in South Africa: A Review. Energies, 15. source

      The BESS installation tables in the Conclusions list batteries and inverters, and §4.1 (Regulation) discusses energy storage providing reactive-power support. Neither passage identifies the inverter as a voltage-source converter or says that active and reactive power can be controlled independently. Page numbers are unavailable in our copy. (LLM, conf=0.83)

      Experimental — accuracy not yet measured
    • cites [5] Gabash, 2012, Active-reactive optimal power flow in distribution networks with embedded generation and battery storage, IEEE Trans. Power Syst. source
    • cites [6] Mehrjerdi, 2019, Modeling and optimal scheduling of battery energy storage systems in electric power distribution networks, J. Clean. Prod. source
    • cites [7] Adewuyi, 2019, Static voltage stability improvement with battery energy storage considering optimal control of active and reactive power injection, Electr. Power Syst. Res. source
    • cites [8] Li, 2022, Optimal dispatch for battery energy storage station in distribution network considering voltage distribution improvement and peak load shifting, J. Mod. Power Syst. Clean Energy source

      The “Operation Constraints of BESS” section models active and reactive power as separately controlled outputs within a shared capacity limit, and identifies a power converter. The “Simulation Background” section identifies the battery type. Our copy does not specify a voltage-source converter or describe the BESS as precisely a converter-and-battery-pack combination; control of the two outputs is also bounded by the shared capacity limit. (LLM, conf=0.85)

      Experimental — accuracy not yet measured
    • cites [9] 2020, Technique for stability enhancement of microgrids during unsymmetrical disturbances using nattery connected by single-phase converters, IET Renew. Power Gener. source

  • May combine two claims.

    Findingown data

    In Case 1, ORPD reduces the active energy losses compared to the base case, while the voltages are within the permissible limits.

    “In Case 1, ORPD reduces the active energy losses compared to the base case, while the voltages are within the permissible limits, as shown in Figure 12.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    All algorithms were employed to solve the problem of OAPD under the same terms and input data.

    “All algorithms were employed to solve the problem of OAPD under the same terms and input data.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    Significant voltage unbalance may lead to higher network losses, increased heating of network components such as transformers, and costly damage or derating of three-phase motors.

    “It is well known that significant voltage unbalance may lead to higher network losses, increased heating of network components such as transformers, as well as costly damage or derating of three-phase motors [21].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [21] Maheshwari, 2023, Flow direction algorithm-based optimal power flow analisys in the presence of stochastic renewable energy sources, Electr. Power Syst. Res. source

  • Classified as probably not a substantial claim.

    Interpretationnone given

    Single-phase PV inverters and BESS can serve as additional reactive power management resources.

    “It has been shown that single-phase PV inverters and BESS can serve as additional reactive power management resources.”
    Quote in the paperSubstantial claim
7 of 7

  • The authors state this as an assumption.

    Retail electricity prices have the same daily profile as wholesale electricity prices and fluctuate hourly.

    “The retail electricity prices have the same daily profile as the wholesale electricity prices and fluctuate hourly.”

  • The authors state this as an assumption.

    The distribution network transacts with wholesale markets through some energy agent such as an aggregator.

    “The DN transacts with the wholesale markets through some energy agent such as an aggregator.”

  • The authors state this as an assumption.

    The load level is a random variable following the same probability density function within each hour of a given daily load diagram.

    “Generally, the load level is assumed to be a random variable (L) following the same PDF within each hour of a given daily load diagram [2].”

  • The authors state this as an assumption.

    PV arrays and batteries are connected to unbalanced distribution networks via single-phase converters.

    “In this paper, it is assumed that PV arrays and batteries are connected to unbalanced DNs via single-phase converters.”

  • The paper relies on this without support.

    The optimal power dispatch in distribution networks with integrated renewable energy sources and BESS is a non-linear, non-convex, large-scale, dynamic optimization problem with constraints.

    “In its most general mathematical formulation, the optimal power dispatch in DNs with integrated RES and BESS is a non-linear, non-convex, large-scale, dynamic optimization problem with constraints.”

  • The paper relies on this without support.

    The operating costs of the distribution network mostly depend on the value of the energy from/to the source grid.

    “The operating costs of the distribution network mostly depend on the value of the energy from/to the source grid.”

  • The paper relies on this without support.

    The power output of a PV source is determined by the solar irradiation at a given moment, and its value cannot be influenced.

    “The power output of a PV source is determined by the solar irradiation at a given moment, and its value cannot be influenced.”

  • The paper relies on this without support.

    High penetration of single-phase PV systems and relative variations in per-phase loading lead to an increase in voltage imbalance in distribution networks.

    “High penetration of single-phase PV systems and relative variations in per-phase loading lead to an increase in voltage imbalance in distribution networks.”
8 of 8

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • PVUR exceeds the claimed 2% limit in several scenarios

    Minor

    The paper says the ORPD results keep PVUR below 2% at all three-phase buses, but Table 8 reports Case 2 maximum PVUR values above 2% in scenarios 2, 3, 5, 6, and 10. This contradicts the stated conclusion even though the expected maximum is 1.91%.

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 4

  1. Radosavljević, J., Milovanović, M., Arsić, N., Jovanović, A., Perović, B., and Vukašinović, J. (2022, January 6–9). Optimal power dispatch in distribution networks with PV generation and battery storage. Proceedings of the IX International Conference on Electrical, Electronic and Computing Engineering IcETRAN 2022, Novi Pazar, Serbia.
  2. (1994). Recommended Practice for Electric Power Distribution for Industrial Plants (Standard No. IEEE Standard 141–1993).
  3. (2023, February 18). IEEE PES Test Feeder. Available online: https://cmte.ieee.org/pes-testfeeders/resources/.
  4. Kennedy, J., and Eberhart, R.C. (December1995, January 27). Particle swarm optimizaton. Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia.

Cited by

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Related

Authors
Radosavljević, J., Ktena, A., Gajić, M., Milovanović, M., & Živić, J.
Affiliations
  • University of Priština - Kosovska Mitrovica (XK)
  • National and Kapodistrian University of Athens (GR)
  • University of Belgrade (RS)
  • Faculty of Technical Sciences, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia
Corresponding author
Ktena, Aphrodite
ORCID
Venue
Energies
Publisher
MDPI AG
Published
2023-05-26
Volume
16
Issue
11
Pages
4356
ISSN
1996-1073 (ISSN-L)
DOI
10.3390/en16114356
OpenAlex
W4378528326
Cited by
10
References
34
Citations by year
2026: 3 · 2025: 3 · 2024: 3 · 2023: 1
FWCI
0.74
Type
journal article
Language
en
Open access
Licence
Locations
  • Energies (publishedVersion, cc-by)
  • Preprints.org (acceptedVersion, cc-by)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
Government of the Republic of Serbia (TR 33046)
Topics
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Optimal Power Flow Distribution
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Electric Power System Optimization
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Smart Grid Energy Management
Keywords
optimal power dispatch, unbalanced distribution systems, battery energy storage, voltage unbalance, energy loss minimization, hybrid particle swarm optimization, photovoltaic uncertainty, load uncertainty, day-ahead scheduling

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