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A Quadratically Constrained Optimization Problem for Determining the Optimal Nominal Power of a PV System in Net-Metering Model: A Case Study for Croatia

Author

Listed:
  • Luka Budin

    (Department of Energy and Power Systems, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia)

  • Goran Grdenić

    (Department of Energy and Power Systems, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia)

  • Marko Delimar

    (Department of Energy and Power Systems, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia)

Abstract

The world’s demand for electrical energy is increasing rapidly while the use of fossil fuels is getting limited more and more by energy policies and the need for reducing the impact of climate change. New sources of energy are required to fulfill the world’s demand for electricity and they are currently found in renewable sources of energy, especially in solar and wind power. Choosing the optimal PV nominal power minimizes the unnecessary surplus of electrical energy that is exported to the grid and thus is not making any impact on the grid more than necessary. Oversizing the PV system according to the Croatian net-metering model results in switching the calculation of the costs to the prosumer model which results in a decrease of the project’s net present value (NPV) and an increase in the payback period (PP). This paper focuses on formulating and solving the optimization problem for determining the optimal nominal power of a grid-connected PV system with a case study for Croatia using multiple scenarios in the variability of electricity production and consumption. In this paper, PV systems are simulated in the power range that corresponds to a typical annual high-tariff consumption in Croatian households. Choosing the optimal power of the PV system maximizes the investor’s NPV of the project as well as savings on the electricity costs. The PP is also minimized and is determined by the PV production, household consumption, discount rate, and geographic location. The optimization problem is classified as a quadratically constrained discrete optimization problem, where the value of the optimal PV power is not a continuous variable because the PV power changes with a step of one PV panel power. Modeling and simulations are implemented in Python using the Gurobi optimization solver.

Suggested Citation

  • Luka Budin & Goran Grdenić & Marko Delimar, 2021. "A Quadratically Constrained Optimization Problem for Determining the Optimal Nominal Power of a PV System in Net-Metering Model: A Case Study for Croatia," Energies, MDPI, vol. 14(6), pages 1-23, March.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:6:p:1746-:d:521493
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    References listed on IDEAS

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    1. Chul-Yong Lee & Jaekyun Ahn, 2020. "Stochastic Modeling of the Levelized Cost of Electricity for Solar PV," Energies, MDPI, vol. 13(11), pages 1-18, June.
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    1. Pavlos Nikolaidis, 2023. "Solar Energy Harnessing Technologies towards De-Carbonization: A Systematic Review of Processes and Systems," Energies, MDPI, vol. 16(17), pages 1-39, August.
    2. Dariusz Kurz & Damian Głuchy & Michał Filipiak & Dawid Ostrowski, 2023. "Technical and Economic Analysis of the Use of Electricity Generated by a BIPV System for an Educational Establishment in Poland," Energies, MDPI, vol. 16(18), pages 1-23, September.
    3. Ludwik Wicki & Robert Pietrzykowski & Dariusz Kusz, 2022. "Factors Determining the Development of Prosumer Photovoltaic Installations in Poland," Energies, MDPI, vol. 15(16), pages 1-19, August.
    4. Anna Mularczyk & Iwona Zdonek & Marian Turek & Stanisław Tokarski, 2022. "Intentions to Use Prosumer Photovoltaic Technology in Poland," Energies, MDPI, vol. 15(17), pages 1-15, August.
    5. Akram Al-Mahrouk & Emad Awada & Wasseem Al-Rousan & Dana Al-Mahrouk, 2024. "The Design of a PV System of a Multi-Location Large Consumer: A Case Study from Al-Balqa Applied University," Sustainability, MDPI, vol. 16(21), pages 1-18, October.
    6. Rezaeimozafar, Mostafa & Monaghan, Rory F.D. & Barrett, Enda & Duffy, Maeve, 2022. "A review of behind-the-meter energy storage systems in smart grids," Renewable and Sustainable Energy Reviews, Elsevier, vol. 164(C).

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