Abstract
Variable renewable energies are leading the energy transition and power system flexibility has become a global priority. Incorporating short-term assessment into long-term planning is essential to capture the operational characteristics of generation and address flexibility issues. This paper presents a novel model for generation and transmission expansion planning with economic dispatch. In the generation expansion planning, the capacity expansion is optimized. In the economic dispatch problem, power plant operation, hydropower generation, and line transmission power flow are optimized. The model is a mixed-integer linear programming problem solved in MATLAB using Gurobi toolbox. A model is proposed to optimize the reservoir of hydropower systems and run-of-river. A case study for supplying Brazilian demand in 2050 is presented. A scenario with greenhouse gas emission costs and no deficit is proposed. This study has shown that the current penalty cost for loss of load is not sufficient to avoid a deficit. It is possible to supply 2050 demand, without large reservoirs or deficits, with a 5.5% curtailment, using 13% of total storage capacity, however; peaking power plants are required.
Keywords:
Economic Dispatch; Flexibility; Generation Expansion Planning; Hydro Reservoir; Variable Renewable Energy
HIGHLIGHTS
A generation and transmission expansion planning is presented to Brazil in 2050.
Hourly economic dispatch problem is incorporate in the expansion planning.
Power plant and hydropower operation, and transmission power flow are optimized.
The power plant generation was optimized to supply only peak load in the year.
INTRODUCTION
The power sector is responsible for about three-quarters of greenhouse gas (GHG) emissions [11 International Energy Agency. Net Zero by 2050: A Roadmap for the Global Energy Sector [Internet]. Paris: IEA; 2021 May [cited 2024 Apr 13]. 222 p. Available from: https://www.iea.org/reports/net-zero-by-2050
https://www.iea.org/reports/net-zero-by-...
], and renewable energy accounts for only 26% of the power sector [22 REN21. Renewables 2021 Global status report [Internet]. Paris: REN21 Secretariat; 2021 [cited 2024 Apr 13]. 370p. Available from: https://www.ren21.net/wp-content/uploads/2019/05/GSR2021_Full_Report.pdf
https://www.ren21.net/wp-content/uploads...
]. For this reason, many countries had some form of renewable electricity target [22 REN21. Renewables 2021 Global status report [Internet]. Paris: REN21 Secretariat; 2021 [cited 2024 Apr 13]. 370p. Available from: https://www.ren21.net/wp-content/uploads/2019/05/GSR2021_Full_Report.pdf
https://www.ren21.net/wp-content/uploads...
]. The energy transition is a reality, and it is supported by Variable Renewables Energy (VRE). According to the International Renewable Energy Agency (IRENA), by 2050, 60% of the electricity will come from VRE, primarily solar photovoltaic (PV) and wind power [33 International Renewable Energy Agency. Power system flexibility for the energy transition [Internet]. Abu Dhabi: IRENA; 2018 Nov [cited 2024 Apr 13]. Available from: https://www.irena.org/publications/2018/Nov/Power-system-flexibility-for-the-energy-transition
https://www.irena.org/publications/2018/...
]. The energy transition has been led by low-cost VRE, Distributed Energy Resources (DER), sector electrification and digitalization [44 International Energy Agency. Status of Power System Transformation 2019: Power system flexibility [Internet]. Paris: OECD Publishing; 2019 Jun [cited 2024 Apr 13]. 32 p. Available from: https://doi.org/10.1787/7c49400a-en.
https://doi.org/10.1787/7c49400a-en...
]. IRENA defines VRE characterized by variability and uncertainty, such as solar PV and wind power [33 International Renewable Energy Agency. Power system flexibility for the energy transition [Internet]. Abu Dhabi: IRENA; 2018 Nov [cited 2024 Apr 13]. Available from: https://www.irena.org/publications/2018/Nov/Power-system-flexibility-for-the-energy-transition
https://www.irena.org/publications/2018/...
]. If, on the one hand, there is unpredictability of generation, on the other hand, there is unpredictability of demand. The duck-shaped curve affected by distributed solar photovoltaic (DPV) is another challenge for the operation of the power system. Indeed, power system flexibility has become a global priority [44 International Energy Agency. Status of Power System Transformation 2019: Power system flexibility [Internet]. Paris: OECD Publishing; 2019 Jun [cited 2024 Apr 13]. 32 p. Available from: https://doi.org/10.1787/7c49400a-en.
https://doi.org/10.1787/7c49400a-en...
].
Flexibility is defined as the ability of the power system to cope with change. To analyze system flexibility, some researchers argue that time-steps of one hour or less are necessary [55 Brown TW, Bischof-Niemz T, Blok K, Breyer C, Lund H, Mathiesen BV. Response to ‘Burden of proof: A comprehensive review of the feasibility of 100% renewable-electricity systems.’ Renew Sustain Energy Rev [Internet]. 2018 Sep;92:834-47. Available from: https://doi.org/10.1016/j.rser.2018.04.113
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,66 Diesendorf M, Elliston B. The feasibility of 100% renewable electricity systems: A response to critics. Renew Sustain Energy Rev [Internet]. 2018 Oct;93:318-30. Available from: https://doi.org/10.1016/j.rser.2018.05.042
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]. In their review study of generation expansion planning (GEP) with VRE integration, Oree and coauthors [77 Oree V, Sayed Hassen SZ, Fleming PJ. Generation expansion planning optimisation with renewable energy integration: A review. Renew Sustain Energy Rev [Internet]. 2017 Mar;69:790-803. Available from: http://dx.doi.org/10.1016/j.rser.2016.11.120
http://dx.doi.org/10.1016/j.rser.2016.11...
] assert that short-term integration is needed to capture the operational characteristics of generation and integrate flexibility aspects. Therefore, short-term decisions [88 Koltsaklis NE, Georgiadis MC. A multi-period, multi-regional generation expansion planning model incorporating unit commitment constraints. Appl Energy [Internet]. 2015 Nov;158:310-31. Available from: http://dx.doi.org/10.1016/j.apenergy.2015.08.054
http://dx.doi.org/10.1016/j.apenergy.201...
] or unit commitment constraints [99 Palmintier BS, Webster MD. Impact of Operational Flexibility on Electricity Generation Planning with Renewable and Carbon Targets. IEEE Trans Sustain Energy [Internet]. 2016 Apr;7(2):672-84. Available from: https://doi.org/10.1109/TSTE.2015.2498640
https://doi.org/10.1109/TSTE.2015.249864...
] have been incorporated into long-term planning to represent hourly dynamics and ensure success. Simplified models can lead to significant errors in carbon emissions and operating costs [1010 Koltsaklis NE, Dagoumas AS. State-of-the-art generation expansion planning: A review. Appl Energy [Internet]. 2018 Nov;230:563-89. Available from: https://doi.org/10.1016/j.apenergy.2018.08.087
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]. Underestimating hourly variability can result in a mix in which the energy storage system is unable to balance the difference between supply and demand [1111 Da Luz T, Moura P. Power generation expansion planning with complementarity between renewable sources and regions for 100% renewable energy systems. Int Trans Electr Energy Syst [Internet]. 2019 Jan;29(7):e2817. Available from: http://doi.wiley.com/10.1002/2050-7038.2817
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], while neglecting flexibility requirement can result in generation portfolios that are inoperable [99 Palmintier BS, Webster MD. Impact of Operational Flexibility on Electricity Generation Planning with Renewable and Carbon Targets. IEEE Trans Sustain Energy [Internet]. 2016 Apr;7(2):672-84. Available from: https://doi.org/10.1109/TSTE.2015.2498640
https://doi.org/10.1109/TSTE.2015.249864...
]. On the other hand, a detailed model requires a high computational cost, for instance, Flores-Quiroz and coauthors [1212 Flores-Quiroz A, Palma-Behnke R, Zakeri G, Moreno R. A column generation approach for solving generation expansion planning problems with high renewable energy penetration. Electr Power Syst Res [Internet]. 2016 Jul;136:232-41. Available from: http://dx.doi.org/10.1016/j.epsr.2016.02.011
http://dx.doi.org/10.1016/j.epsr.2016.02...
] spent 15 days to solve a problem with 13 typical weeks and a planning horizon of 19 years, using a supercomputer with 2 TB of RAM.
To reduce the spend time and computational cost, some authors simplified the model to annual energy demand [1313 Da Cunha SHF, Pereira Jr AO, Castro G. Emissão de Gases de Efeito Estufa - 2050: Implicações Econômicas e Sociais do Cenário de Plano Governamental [Internet]. Rio de Janeiro: Centro Clima/COPPE/UFRJ; 2016 [cited 2024 Apr 13]. 72 p. Available from: http://www.centroclima.coppe.ufrj.br/images/documentos/ies-brasil-2050/3_-_Cenario_de_Emiss%C3%B5es_de_GEE_-_Setor_de_Transportes_Demanda_de_Energia_-_IES_Brasil_2050.pdf
http://www.centroclima.coppe.ufrj.br/ima...
], load duration curve with energy levels [1414 Melo R, Torres C, Borba B, Dias B. Multi-year two-stage generation and transmission expansion planning: intermittent renewable energy sources integration for Brazilian interconnected power system [Internet]. Electr Eng. 2022 Feb; 104: 2689-701. Available from: https://doi.org/10.1007/s00202-021-01456-6
https://doi.org/10.1007/s00202-021-01456...
], peak load demand [1515 Mahdavi M, Javadi MS, Catalão JPS. Integrated generation-transmission expansion planning considering power system reliability and optimal maintenance activities. Int J Electr Power Energy Syst [Internet]. 2023 Feb;145:108688. Available from: https://doi.org/10.1016/j.ijepes.2022.108688
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], data in monthly resolution [1616 Basu M. Electric Power and Heat Generation Expansion Planning. Electr Power Components Syst [Internet]. 2020 Mar 15;48(4-5):501-11. Available from: https://doi.org/10.1080/15325008.2020.1793840
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,1717 Luz TJ da, Vila CU, Aoki AR. Complementarity Between Renewable Energy Sources and Regions - Brazilian Case. Braz Arch Biol Technol [Internet]. 2023;66:e23220442. Available from: https://doi.org/10.1590/1678-4324-2023220442
https://doi.org/10.1590/1678-4324-202322...
], typical weeks [1212 Flores-Quiroz A, Palma-Behnke R, Zakeri G, Moreno R. A column generation approach for solving generation expansion planning problems with high renewable energy penetration. Electr Power Syst Res [Internet]. 2016 Jul;136:232-41. Available from: http://dx.doi.org/10.1016/j.epsr.2016.02.011
http://dx.doi.org/10.1016/j.epsr.2016.02...
,1818 Greenpeace. Energy [R]evolution: For a Brazil with 100% clean and renewable energy [Internet]. São Paulo: Greenpeace; 2016 [cited 2024 Apr 13]. 31 p. Available from: https://www.greenpeace.org/brasil/publicacoes/
https://www.greenpeace.org/brasil/public...
], typical days [1919 Luz T, Moura P. 100% Renewable energy planning with complementarity and flexibility based on a multi-objective assessment. Appl Energy [Internet]. 2019 Dec;255:113819. Available from: https://doi.org/10.1016/j.apenergy.2019.113819
https://doi.org/10.1016/j.apenergy.2019....
,2020 Karimianfard H, Haghighat H, Zeng B. Co-Optimization of Battery Storage Investment and Grid Expansion in Integrated Energy Systems. IEEE Syst J [Internet]. 2022 Dec;16(4):5928-38. Available from: https://ieeexplore.ieee.org/document/9665771/
https://ieeexplore.ieee.org/document/966...
], or a day is represented by a few groups of hours [2121 English J, Niet T, Lyseng B, Keller V, Palmer-Wilson K, Robertson B, et al. Flexibility requirements and electricity system planning: Assessing inter-regional coordination with large penetrations of variable renewable supplies. Renew Energy [Internet]. 2020 Jan;145:2770-82. Available from: https://doi.org/10.1016/j.renene.2019.07.097
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,2222 Empresa de Pesquisa Energética. Plano Nacional de Energia - 2050 [Internet]. Brasília: MME/EPE; 2020 [cited 2024 Apr 13]. 230 p. Available from: https://www.epe.gov.br/pt/publicacoes-dados-abertos/publicacoes/Plano-Nacional-de-Energia-2050
https://www.epe.gov.br/pt/publicacoes-da...
]. There are few studies with hourly time-steps [33 International Renewable Energy Agency. Power system flexibility for the energy transition [Internet]. Abu Dhabi: IRENA; 2018 Nov [cited 2024 Apr 13]. Available from: https://www.irena.org/publications/2018/Nov/Power-system-flexibility-for-the-energy-transition
https://www.irena.org/publications/2018/...
,2323 Gils H, Simon S, Soria R. 100% Renewable Energy Supply for Brazil-The Role of Sector Coupling and Regional Development. Energies [Internet]. 2017 Nov;10(11):1859. Available from: http://www.mdpi.com/1996-1073/10/11/1859
http://www.mdpi.com/1996-1073/10/11/1859...
]. When short-term problems are modeled, they are typically formulated as day-ahead operation planning [2424 Aquino CCCB de, Blasi TM, Unsihuay-Vila C, Fernandes TSP, Pinto RS, Lara Filho MO de, et al. A Hierarchical Framework for Day-Ahead Optimal Operation Planning of Active Distribution Networks with Multi-Microgrids. Braz Arch Biol Technol [Internet]. 2023;66:e23220379. Available from: https://doi.org/10.1590/1678-4324-2023220379
https://doi.org/10.1590/1678-4324-202322...
]. Hourly time step for a whole year has been applied to design microgrids [2525 Da Luz T, Vila C, Ferreira F. New Benders decomposition and rolling horizon optimisation approaches to design isolated microgrids for Amazon region. Electr Power Syst Res [Internet]. 2023 Aug;221:109447. Available from: https://doi.org/10.1016/j.epsr.2023.109447
https://doi.org/10.1016/j.epsr.2023.1094...
,2626 Felix R, Unsihuay-Vila C. A Model to optimize Mix Power Generation Selection of Distributed Renewable Plants for Expansion Planning with Reliability Criteria: An Application in Puno, Peru. In: 2018 IEEE PES Transmission & Distribution Conference and Exhibition - Latin America (T&D-LA) [Internet]. IEEE; 2018. p. 1-5. Available from: https://ieeexplore.ieee.org/document/8511762/
https://ieeexplore.ieee.org/document/851...
] or in GEP with heuristic decomposition techniques [2727 Cuisinier É, Lemaire P, Penz B, Ruby A, Bourasseau C. New rolling horizon optimization approaches to balance short-term and long-term decisions: An application to energy planning. Energy [Internet]. 2022 Apr;245:122773. Available from: https://linkinghub.elsevier.com/retrieve/pii/S036054422103022X
https://linkinghub.elsevier.com/retrieve...
].
Brazil has been using the Investment Decision Model (IDM) since 2017 [2828 Empresa de Pesquisa Energética. [Investment Decision Model for SIN Expansion] [Internet]. Brasília: EPE; 2020 Dec [cited 2024 Apr 13]. 33 p. Available from: https://www.epe.gov.br/sites-pt/publicacoes-dados-abertos/publicacoes/PublicacoesArquivos/publicacao-490/topico-531/NT EPE-DEE-NT-073_2020 - MDI.PDF
https://www.epe.gov.br/sites-pt/publicac...
], and Paes and coauthors [2929 Paes CE, Gandelman DA, Firmo HT, Bahiense L. The power generation expansion planning in Brazil: Considering the impact of greenhouse gas emissions in an Investment Decision Model. Renew Energy [Internet]. 2022 Jan;184:225-38. Available from: https://doi.org/10.1016/j.renene.2021.11.060
https://doi.org/10.1016/j.renene.2021.11...
] implemented this model adding carbon tax and emission limits. The IDM defines three load levels for each month and the maximum instantaneous demand for each month. The monthly target for hydropower generation is set a priori, and the seasonality of generation and demand is analyzed on the monthly time scale. However, generation flexibility is not tested in this model, nor is the capacity to allocate water resources under the optimization model.
In many countries, hydropower reservoirs are largely responsible for supply flexibility [3030 Silva AR, Pimenta FM, Assireu AT, Spyrides MHC. Complementarity of Brazil׳s hydro and offshore wind power. Renew Sustain Energy Rev [Internet]. 2016 Apr;56:413-27. Available from: http://linkinghub.elsevier.com/retrieve/pii/S1364032115013106
http://linkinghub.elsevier.com/retrieve/...
]. However, construction of large reservoirs has declined. In Brazil, 70% of storage capacity is concentrated in the Southeast and Middle East regions, and construction of new large reservoirs is not planned in the coming years [3131 Hunt JD, Freitas MAV, Pereira Junior AO. Enhanced-Pumped-Storage: Combining pumped-storage in a yearly storage cycle with dams in cascade in Brazil. Energy [Internet]. 2014 Dec;78:513-23. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0360544214011888
http://linkinghub.elsevier.com/retrieve/...
]. In other countries, natural gas and coal-fired power plants take on the role of supply flexibility. Thermal power plants also supply the electricity system in the dry months, however; better use of complementarity among renewables could reduce the use of non-renewable sources [1919 Luz T, Moura P. 100% Renewable energy planning with complementarity and flexibility based on a multi-objective assessment. Appl Energy [Internet]. 2019 Dec;255:113819. Available from: https://doi.org/10.1016/j.apenergy.2019.113819
https://doi.org/10.1016/j.apenergy.2019....
].
When a one hour time-step is not used, water flow is not optimized. In countries with large reservoirs (e.g. Brazil), optimizing hydropower flow is essential to reduce the need for reservoirs. Power generation expansion planning must include spatial planning, shortand long-term asset optimization [33 International Renewable Energy Agency. Power system flexibility for the energy transition [Internet]. Abu Dhabi: IRENA; 2018 Nov [cited 2024 Apr 13]. Available from: https://www.irena.org/publications/2018/Nov/Power-system-flexibility-for-the-energy-transition
https://www.irena.org/publications/2018/...
]. Nevertheless, many authors have used simplified models with annual or monthly averages, ignoring hourly variations and complementarity.
In literature, there are some tools to evaluate the flexibility, such as NREL system evaluation and GIVAR (IEA) to present an overview and characteristics, or FAST2 (IEA), FESTIV (NREL), and InFLEXion (EPRI) to dispatch assessment. To perform capacity expansion and system operation, there are few tools, such as REFlex (NREL), RESOLVE (E3) and IRENA FlexTool [33 International Renewable Energy Agency. Power system flexibility for the energy transition [Internet]. Abu Dhabi: IRENA; 2018 Nov [cited 2024 Apr 13]. Available from: https://www.irena.org/publications/2018/Nov/Power-system-flexibility-for-the-energy-transition
https://www.irena.org/publications/2018/...
]. Soft-linking or two-stage is a heurist approach used to couple longand short-term planning, for instance, Deane and coauthors [3232 Deane JP, Gracceva F, Chiodi A, Gargiulo M, Gallachóir BPÓ. Assessing power system security. A framework and a multi model approach. Int J Electr Power Energy Syst [Internet]. 2015 Dec;73:283-97. Available from: http://dx.doi.org/10.1016/j.ijepes.2015.04.020
http://dx.doi.org/10.1016/j.ijepes.2015....
] applied this approach to connect the PLEXOS and TIMES tools. Table 1 provides an overview of the generation expansion planning models presented.
In the literature, tools capable of solving the economic dispatch and capacity expansion usually group hydropower plants or work in the same way with large hydropower and run-of-river. There are few tools that can solve the combination of generation expansion and short-term planning, and typically some simplifications or approximations are applied. Some heuristics approaches to separate the expansion and economic dispatch problems have been developed in the literature; however, heuristics approaches do not have a formal guarantee of convergence. In fact, a reference model with a single level formulation is needed to validate new emerging methodologies. Therefore, this paper presents a generation and transmission expansion planning with full-year hourly power balance constraints. In the generation and transmission expansion planning problem, capacity expansion is optimized by node. The hydropower with reservoir and run-of-river plants are not grouped and are represented by integer variables.
The proposed model is a mixed integer linear programming (MILP) with a single level formulation solved in MATLAB software using the Gurobi toolbox. The economic dispatch problem is included in the expansion planning. In economic dispatch, power plant operation, hydropower generation, and transmission line power flow are optimized. A case study of Brazilian in 2050 is presented. Three scenarios are performed and the GHG emissions costs and deficit penalty price impact are evaluated. The simulation was performed in Microsoft Azure cloud computation. The simulations were run on virtual machine Standard G2 (4 vCPU, 56 GB). The main contributions are:
-
A novel generation expansion planning model with economic dispatch for evaluating annual complementarity among regions with transmission constraints using a single level formulation;
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A model for optimizing water storage;
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A case study to supply Brazilian demand in 2050, considering a full-year hourly demand and VRE profile;
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An assessment of future Brazilian flexibility;
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A reference result for evaluating decompositions and simplified approaches in new studies.
The remainder of the paper is structured as follows. The proposed model is presented in Section II. The data used in the case study for the Brazilian scenario is presented in Section III. The results and discussion of the case study are presented in section IV. Finally, Section V summarizes the paper and highlights its main conclusions.
FORMULATION
The formulation is based on [33 International Renewable Energy Agency. Power system flexibility for the energy transition [Internet]. Abu Dhabi: IRENA; 2018 Nov [cited 2024 Apr 13]. Available from: https://www.irena.org/publications/2018/Nov/Power-system-flexibility-for-the-energy-transition
https://www.irena.org/publications/2018/...
,1717 Luz TJ da, Vila CU, Aoki AR. Complementarity Between Renewable Energy Sources and Regions - Brazilian Case. Braz Arch Biol Technol [Internet]. 2023;66:e23220442. Available from: https://doi.org/10.1590/1678-4324-2023220442
https://doi.org/10.1590/1678-4324-202322...
], however; with binary variables. For investment in new hydropower plants, binary variables is used based on available projects in [3333 Empresa de Pesquisa Energética. Ten-Year Energy Expansion Plan 2030 [Internet]. Brasília: MME/EPE; 2021 [cited 2024 Apr 13]. 447 p. Available from: https://www.epe.gov.br/sites-pt/publicacoes-dados-abertos/publicacoes/PublicacoesArquivos/publicacao-490/PDE2030_RevisaoPosCP_rv2.pdf
https://www.epe.gov.br/sites-pt/publicac...
]. The model is a MILP problem, with 420,531 continuous and 15 binary decision variables, and 665,672 constraints. The problem was formulated using MatLab, and the optimization problem was solved using Gurobi [3434 Gurobi. Software Gurobi [Internet]. 2023 [cited 2024 Apr 13]. Available from: https://www.gurobi.com
https://www.gurobi.com...
]. The Gurobi (used in [2020 Karimianfard H, Haghighat H, Zeng B. Co-Optimization of Battery Storage Investment and Grid Expansion in Integrated Energy Systems. IEEE Syst J [Internet]. 2022 Dec;16(4):5928-38. Available from: https://ieeexplore.ieee.org/document/9665771/
https://ieeexplore.ieee.org/document/966...
,2525 Da Luz T, Vila C, Ferreira F. New Benders decomposition and rolling horizon optimisation approaches to design isolated microgrids for Amazon region. Electr Power Syst Res [Internet]. 2023 Aug;221:109447. Available from: https://doi.org/10.1016/j.epsr.2023.109447
https://doi.org/10.1016/j.epsr.2023.1094...
,2626 Felix R, Unsihuay-Vila C. A Model to optimize Mix Power Generation Selection of Distributed Renewable Plants for Expansion Planning with Reliability Criteria: An Application in Puno, Peru. In: 2018 IEEE PES Transmission & Distribution Conference and Exhibition - Latin America (T&D-LA) [Internet]. IEEE; 2018. p. 1-5. Available from: https://ieeexplore.ieee.org/document/8511762/
https://ieeexplore.ieee.org/document/851...
]) and CPLEX (used [88 Koltsaklis NE, Georgiadis MC. A multi-period, multi-regional generation expansion planning model incorporating unit commitment constraints. Appl Energy [Internet]. 2015 Nov;158:310-31. Available from: http://dx.doi.org/10.1016/j.apenergy.2015.08.054
http://dx.doi.org/10.1016/j.apenergy.201...
,99 Palmintier BS, Webster MD. Impact of Operational Flexibility on Electricity Generation Planning with Renewable and Carbon Targets. IEEE Trans Sustain Energy [Internet]. 2016 Apr;7(2):672-84. Available from: https://doi.org/10.1109/TSTE.2015.2498640
https://doi.org/10.1109/TSTE.2015.249864...
,1212 Flores-Quiroz A, Palma-Behnke R, Zakeri G, Moreno R. A column generation approach for solving generation expansion planning problems with high renewable energy penetration. Electr Power Syst Res [Internet]. 2016 Jul;136:232-41. Available from: http://dx.doi.org/10.1016/j.epsr.2016.02.011
http://dx.doi.org/10.1016/j.epsr.2016.02...
,2929 Paes CE, Gandelman DA, Firmo HT, Bahiense L. The power generation expansion planning in Brazil: Considering the impact of greenhouse gas emissions in an Investment Decision Model. Renew Energy [Internet]. 2022 Jan;184:225-38. Available from: https://doi.org/10.1016/j.renene.2021.11.060
https://doi.org/10.1016/j.renene.2021.11...
]) are widely-used MILP solvers which employs a linear-programming based branch-and-bound algorithm. Both offer academic license; however, in new versions, MatLab connector has been removed from CPLEX (most recent version to include the connector is 12.10). Both solvers were tested and Gurobi performed better in Matlab. Gurobi includes presolve, cutting planes, heuristics, and parallelism.
The objective function is to minimize the expansion and operation cost (1), as well as: the annualized investment costs of the units (2); the annualized CAPEX of the hydropower (3); annualized investment costs of transmission line (4); annual fixed operation and maintenance (O&M) cost (6); OPEX of hydropower (7); penalty cost of insufficient capacity (8); variable O&M cost (9); emission cost (10); penalty cost of loss of load (11); and penalty cost of curtailment of VRE (12).
Objective function:
where:
The investment cost is converted to annualized cost by using the Capital Recovery Factor (CRF):
The annual fixed cost is calculated by:
The annual variable cost is calculated by:
The energy balance must be guaranteed in all nodes and at all times with a time step of one hour. The energy balance of each node includes: generation from non-dispatchable renewable energy; thermal power and hydropower; energy imports/exports to the node; the slack variable for loss of load and curtailments; and energy demand.
Energy balance
where:
Hydropower constraints need to ensure reservoir capacity constraints, intra-year depreciation and maximum hourly generation. The run-of-river (RoR) reservoir has little flexibility in water storage. In this paper, the water in the reservoir can be managed for twenty-four hours. Therefore, constraint (15) applies to new and (16) to existing plants (16), :
Hydro with large reservoir (ReS) has a large flexibility to storage water for long time. Storage constraint for reservoir capacity, :
However, to avoid reservoir depreciation, maximum annual generation constraints are required, :
Maximum and minimum hourly generation :
Thermal power was simplified to reduces the number of integer variables, therefore, ramp up & down constraints, startup & shut down time ramp limit constraints were not considered. Simplification allows simulation in reasonable time and memory capacity. Constraint (24) presents the maximum and minimum hourly generation :
For transfer between nodes is used the transport model [33 International Renewable Energy Agency. Power system flexibility for the energy transition [Internet]. Abu Dhabi: IRENA; 2018 Nov [cited 2024 Apr 13]. Available from: https://www.irena.org/publications/2018/Nov/Power-system-flexibility-for-the-energy-transition
https://www.irena.org/publications/2018/...
], in this model transmission lines are considered as “pipelines” that can transfer a maximum power :
Maximum and minimum hourly loss of load :
Finally, decision variables limits:
Table 2-4 present the descriptions of the symbols used in the formulation.
BRAZILIAN SCENARIO
The installed capacity of the electrical system in 2021 was considered (generation, storage and transmission), and the investments already programmed for the expansion of the system according to electricity system operator [3535 Operador Nacional do Sistema. [National Electric System Operator] [Internet]. 2024 [cited 2024 Apr 13]. Available from: http://www.ons.org.br
http://www.ons.org.br...
]. Data for solar radiation and wind speed were extracted from ten-year energy expansion plan (EEP 2030), as well as economic data [3333 Empresa de Pesquisa Energética. Ten-Year Energy Expansion Plan 2030 [Internet]. Brasília: MME/EPE; 2021 [cited 2024 Apr 13]. 447 p. Available from: https://www.epe.gov.br/sites-pt/publicacoes-dados-abertos/publicacoes/PublicacoesArquivos/publicacao-490/PDE2030_RevisaoPosCP_rv2.pdf
https://www.epe.gov.br/sites-pt/publicac...
]. As a major cost reduction in wind and solar PV are expected, current costs are projected to 2050 as the analysis of [1919 Luz T, Moura P. 100% Renewable energy planning with complementarity and flexibility based on a multi-objective assessment. Appl Energy [Internet]. 2019 Dec;255:113819. Available from: https://doi.org/10.1016/j.apenergy.2019.113819
https://doi.org/10.1016/j.apenergy.2019....
]. Table 5 summarizes the data used.
For hydropower, it was considered two types: i) reservoir (ReS); and ii) run-of-river (RoR). Table 6-7 summarize hydropower data and the list of available hydropower.
For transmission lines, the installed capacity was considered, plus the capacity already contracted as: N-NE 8,500 MW; N-SE 13,400 MW; NE-SE 7,500 MW; SE-S 11,500 MW. With a cost of: 286 USD/kW for N-NE and NE-SE; 367 USD /kW for N-SE; and 163 USD /kW for SE-S [3333 Empresa de Pesquisa Energética. Ten-Year Energy Expansion Plan 2030 [Internet]. Brasília: MME/EPE; 2021 [cited 2024 Apr 13]. 447 p. Available from: https://www.epe.gov.br/sites-pt/publicacoes-dados-abertos/publicacoes/PublicacoesArquivos/publicacao-490/PDE2030_RevisaoPosCP_rv2.pdf
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]. To DG, the projection of 118 GW for solar PV and 140.1 TWh for self-production was considered, according to National Energy Plan 2050 (NEP 2050) [2222 Empresa de Pesquisa Energética. Plano Nacional de Energia - 2050 [Internet]. Brasília: MME/EPE; 2020 [cited 2024 Apr 13]. 230 p. Available from: https://www.epe.gov.br/pt/publicacoes-dados-abertos/publicacoes/Plano-Nacional-de-Energia-2050
https://www.epe.gov.br/pt/publicacoes-da...
]. Finally, a penalty cost of 1,071 USD/MWh was considered for loss of load and 555,612 USD/MW for insufficient capacity [3636 Empresa de Pesquisa Energética. [Capacity and Flexibility: Concepts for incorporating attributes into planning] [Internet]. Brasília: MME/EPE; 2018 Aug [cited 2024 Apr 13]. 21 p. Available from: https://www.epe.gov.br/sites-pt/publicacoes-dados-abertos/publicacoes/PublicacoesArquivos/publicacao-316/NT_EPE_DEE-NT-067_2018-r0.pdf
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]. There is no set cost for curtailment in Brazilian system.
RESULTS AND DISCUSSION
This section presents some scenarios to Brazilian in 2050, considering the formulation and data presented.
Base scenario
In this base case, the total expansion cost was USD 28,790 million. Figure 1 presents the results for new units. All available ReS units (689 MW), six RoR units (1,190 MW) in the South and Southeast, and no SHP were added. Non-renewables expansion accounted for 27,119 MW, including coal and gas; nuclear was not installed. Wind and sugarcane together accounted for 139,929 MW, while solar PV installed the minimum (2,000 MW) and biomass, biogas, and urban waste were not installed. Although there is no new solar PV (only the minimum), 118 GW were installed in the DPV.
Figure 2 shows hourly operation for a week in April, a period when reservoirs have lower levels and lower wind generation. The duck curve phenomenon is caused by DPV.
Greater flexibility capacity is required to reduce generation at the beginning of the day, resulting in the shutdown of all thermal power plants, reduction of hydro ReS to the minimum allowable generation (15%), and curtailment. In contrast, at the end of the day, there is a need to increase generation due to the decrease in DPV and hourly peak demand, which leads to an increase in hydropower generation and the entry of thermal power plants. With an hourly resolution, it is possible to analyze up-ramping and down-ramping demand.
VRE generation (wind and solar PV) represented 43% of annual demand, with 10.7% curtailments, representing 4.5% of annual demand. The maximum simultaneous peak of curtailments was 90.2 GW. The annual deficit was 374 GWh, equivalent to 0.023% of annual demand, and the maximum coincident loss of load was 23.2 GW. Figure 3 presents the results of the transfers by node. The Southeast region has higher energy demand and therefore receives more energy from other regions. The Northeast region has a large wind potential (Figure 1). However, the energy demand is low, thus, the excess energy is exported to the Southeast. For this purpose, 20 GW transmission lines were installed from the Northeast to the Southeast. Figure 3 shows the importance of complementarity in supplying the Southeast. 4.4 GW of transmission lines were installed from South to Southeast, 8.8 GW from North to Southeast.
GHG scenario
In this scenario, the cost of greenhouse gas (GHG) emissions is taken into account. As a result, the total cost of expansion was USD 29,449 million, an increase of 2.3%. The GHG emissions costs amounted to USD 609 million (2% of the total costs). In addition, non-renewable production was reduced by 25.4%. Coal has the higher GHG emission, as result no new plant was built, and generation decreased by 36%. In addition, CCGT expansion capacity and generation was decreased by 18% and 28% (Figure 4).
Wind and sugarcane were responsible for offsetting the decline in non-renewable, suppling 50% of annual demand. VRE generation met 44% of annual demand, however; curtailments increased by 33%, equivalent to 6.1% of annual demand. Despite deficit increasing by 9.5%, it is only 0.026% of annual demand.
ZDeficit scenario
This study has shown that the current penalty costs for loss of load are not sufficient to avoid a deficit. In this scenario, the costs for GHG emissions are taken into account, and the penalty costs were increased to avoid a deficit, for which the penalty costs had to be multiplied by three. To achieve this result without a deficit, the total expansion costs had to be increased by 5.9% compared to the GHG scenario and reached USD 31,184 million. To reduce the deficit, VRE was reduced by 39.7% in compared to the GHG scenario, while other non-dispatchable energy source were increased by 50.6% to fill the gap. In the GHG scenario, the deficit was 409 GWh, in the ZDeficit scenario there is no deficit, and the curtailment was reduced to 5.5%. This scenario is characterized by the installation of SHP (Figure 5), and the maximum investment in SHP was achieved in the Southeast and Northeast.
Capacity growth was concentrated in the Southeast and the North. Despite the increase in non-renewable capacity (45%), non-renewable generation decreased by 8.7% compared to the GHG scenario, however; GHG emissions increased by 13.4% because coal-fired power plants were installed (8.2 GW). In fact, more flexible power plants were installed to supply peak demand, resulting in a low capacity factor (Figure 6).
Figure 7 presents the management of the reservoirs during the year. It can be observed that the reservoirs reach their minimum in March and their maximum in September, using only 13% of the total storage capacity for management. In the North, the minimum level is reached exactly when there are floods in this region, which complements the wind generation. The correlation between hydropower in the North and wind farms in the South is -0.92 [1919 Luz T, Moura P. 100% Renewable energy planning with complementarity and flexibility based on a multi-objective assessment. Appl Energy [Internet]. 2019 Dec;255:113819. Available from: https://doi.org/10.1016/j.apenergy.2019.113819
https://doi.org/10.1016/j.apenergy.2019....
].
DISCUSSION
The scenario with zero deficit (ZDeficit) is compared in this section with other works (Table 8). Scenario 2020 is the current system composition and NEP is the baseline scenario projection for 2050 developed by NEP. COPPE and GILS have presented a similar share of hydropower. In this paper, the share of hydropower was lower because only four plants with large reservoirs were considered [3333 Empresa de Pesquisa Energética. Ten-Year Energy Expansion Plan 2030 [Internet]. Brasília: MME/EPE; 2021 [cited 2024 Apr 13]. 447 p. Available from: https://www.epe.gov.br/sites-pt/publicacoes-dados-abertos/publicacoes/PublicacoesArquivos/publicacao-490/PDE2030_RevisaoPosCP_rv2.pdf
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]. The RoR expansion was limited by the flexibility of this technology. To compensate for the low share of hydropower, the share of biomass is higher than other studies. Although biomass technology has a high cost and is non-dispatchable, it played an important role in reducing the storage requirements due to its high complementarity with hydropower [1111 Da Luz T, Moura P. Power generation expansion planning with complementarity between renewable sources and regions for 100% renewable energy systems. Int Trans Electr Energy Syst [Internet]. 2019 Jan;29(7):e2817. Available from: http://doi.wiley.com/10.1002/2050-7038.2817
http://doi.wiley.com/10.1002/2050-7038.2...
]. As can be observed, the present study came to a similar conclusion as COPPE, Gils and NEP did for solar PV. Although a more flexible unit is required in the hourly analysis, the non-renewable share was low compared to other studies.
CONCLUSION
A time-steps of one hour in the expansion energy planning is essential to evaluate flexibility. Hourly resolution allowed optimization of water reservoirs, while other studies for the Brazilian case do not. Hourly resolution also made it possible to identify the deficit problem and the need to increase the penalty price. When GHG emissions were taken into account, no coal-fired plant was installed, however; in a zero-deficit scenario, it was necessary. It is possible to supply 2050 demand without large reservoirs or deficits, with a 5.5% curtailment and using 13% of storage capacity, however; peaking power plants are needed to provide flexibility. To improve the low power plant capacity factor, minimum generation constraint can be introduced, as well as battery storage systems and demand response programs. The size of the model was limited by computer capacity. Thermal power ramp up & down constraints, startup & shut down time ramp limit constraints can be implemented in new studies using decomposition technique.
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Funding: This research was funded by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
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Publication Dates
-
Publication in this collection
05 Aug 2024 -
Date of issue
2024
History
-
Received
29 Sept 2023 -
Accepted
12 Jan 2024