A Quadratically Constrained Optimization Problem for Determining the Optimal Nominal Power of a PV System in Net-Metering Model: A Case Study for Croatia
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 curre...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-03-01
|
| Series: | Energies |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1996-1073/14/6/1746 |
| _version_ | 1797540465708367872 |
|---|---|
| author | Luka Budin Goran Grdenić Marko Delimar |
| author_facet | Luka Budin Goran Grdenić Marko Delimar |
| author_sort | Luka Budin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T13:01:48Z |
| format | Article |
| id | doaj.art-02c11e27014944e1962d8900a4f878ac |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T13:01:48Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-02c11e27014944e1962d8900a4f878ac2023-11-21T11:25:42ZengMDPI AGEnergies1996-10732021-03-01146174610.3390/en14061746A Quadratically Constrained Optimization Problem for Determining the Optimal Nominal Power of a PV System in Net-Metering Model: A Case Study for CroatiaLuka Budin0Goran Grdenić1Marko Delimar2Department of Energy and Power Systems, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, CroatiaDepartment of Energy and Power Systems, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, CroatiaDepartment of Energy and Power Systems, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, CroatiaThe 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.https://www.mdpi.com/1996-1073/14/6/1746photovoltaicnet-metering modelprosumer modelfeed-in tariff modeloptimal PV powerrenewable energy sources |
| spellingShingle | Luka Budin Goran Grdenić Marko Delimar 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 photovoltaic net-metering model prosumer model feed-in tariff model optimal PV power renewable energy sources |
| title | A Quadratically Constrained Optimization Problem for Determining the Optimal Nominal Power of a PV System in Net-Metering Model: A Case Study for Croatia |
| title_full | A Quadratically Constrained Optimization Problem for Determining the Optimal Nominal Power of a PV System in Net-Metering Model: A Case Study for Croatia |
| title_fullStr | A Quadratically Constrained Optimization Problem for Determining the Optimal Nominal Power of a PV System in Net-Metering Model: A Case Study for Croatia |
| title_full_unstemmed | A Quadratically Constrained Optimization Problem for Determining the Optimal Nominal Power of a PV System in Net-Metering Model: A Case Study for Croatia |
| title_short | A Quadratically Constrained Optimization Problem for Determining the Optimal Nominal Power of a PV System in Net-Metering Model: A Case Study for Croatia |
| title_sort | quadratically constrained optimization problem for determining the optimal nominal power of a pv system in net metering model a case study for croatia |
| topic | photovoltaic net-metering model prosumer model feed-in tariff model optimal PV power renewable energy sources |
| url | https://www.mdpi.com/1996-1073/14/6/1746 |
| work_keys_str_mv | AT lukabudin aquadraticallyconstrainedoptimizationproblemfordeterminingtheoptimalnominalpowerofapvsysteminnetmeteringmodelacasestudyforcroatia AT gorangrdenic aquadraticallyconstrainedoptimizationproblemfordeterminingtheoptimalnominalpowerofapvsysteminnetmeteringmodelacasestudyforcroatia AT markodelimar aquadraticallyconstrainedoptimizationproblemfordeterminingtheoptimalnominalpowerofapvsysteminnetmeteringmodelacasestudyforcroatia AT lukabudin quadraticallyconstrainedoptimizationproblemfordeterminingtheoptimalnominalpowerofapvsysteminnetmeteringmodelacasestudyforcroatia AT gorangrdenic quadraticallyconstrainedoptimizationproblemfordeterminingtheoptimalnominalpowerofapvsysteminnetmeteringmodelacasestudyforcroatia AT markodelimar quadraticallyconstrainedoptimizationproblemfordeterminingtheoptimalnominalpowerofapvsysteminnetmeteringmodelacasestudyforcroatia |