Reference	Temporal representation	Comment
A: Long-term planning
Luz and Moura [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... ]	Two days with hourly resolution	Optimize capacity expansion with monthly balance demand and two days constraints, using nonlinear programming.
Melo et al. [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... ]	Load duration curve with 12 levels	CARTHER optimizes VRE expansion by MILP. It optimizes conventional generating units to meet the residual load.
Basu [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 https://doi.org/10.1080/15325008.2020.17... ]	Monthly resolution	Capacity expansion is optimized by monthly balance demand using mixed integer nonlinear programming.
EPE [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... ,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... ]	Three load levels per month	Optimizes capacity expansion with peak constraint by MILP.
Paes et al. [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... ]	Three load levels per month	Optimize capacity expansion with peak constraint and greenhouse gas emissions cost using MILP.
B: Short-term planning
FAST2 [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/... ]	Full year at hourly resolution	Calculates system dispatch and required upward and downward ramping capabilities.
InFLEXion [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/... ]	Full year at hourly resolution	System operation is optimized. The results are used to assess potential flexibility shortfalls in different situations.
C: Longand short-term planning
Koltsaklis and Georgiadis [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... ]	One day per month with hourly resolution	Capacity expansion and system operation are optimized with thermal units’ shut-down cost, using MILP.
Flores-Quiroz et al. [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... ]	13 representative weeks with hourly resolution	Optimize capacity expansion and system operation with thermal units’ shut-down cost, using MILP. They spent 15 days to solve the problem using decomposition.
Luz and Moura [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.... ]	Two days with hourly resolution	Capacity expansion and system operation with battery system are optimized, using multi-objective programming.
Karimianfard [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... ]	Three days with hourly resolution	Capacity expansion and system operation are optimized using reformulationand-decomposition approach.
English et al. [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 https://doi.org/10.1016/j.renene.2019.07... ]	Resolution 32 time slices	Capacity expansion is optimized using four demand periods per day, with flexibility constraints.
D: Longand short-term planning with full year
IRENA [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/... ]	Full year at hourly resolution	IRENA FlexTool performs capacity expansion and system operation using linear programming.
Gils et al. [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... ]	Full year at hourly resolution	REMix energy system model performs capacity expansion and system operation using linear programming.
Felix and Vila [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... ]	Full year at hourly resolution	Renewable energy capacity expansion and transmission for a microgrid using Gurobi in Peru.
Deane et al. [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.... ]	Full year at hourly resolution	Optimizes capacity expansion and system operation using a heuristic two-stage approach.
Proposed model	Full year at hourly resolution	Optimizes capacity expansion and system operation using a single level formulation with MILP. Reservoir level is optimized.

Symbol	Description	Symbol	Description
h	Index for hydropower	R	Set of units r
H	Set of new hydropower h	RoR_new RoR_ex	Set of new and existing run-of-river
h_step	Duration (hours) of the time periods	ReS_new ReS_ex	Set of new and existing hydroelectric with reservoir
i_u	Discount rate	t	Time step index
l	Index for transmission line	T	Set of time steps t
life_u	lifetime	th	Index for thermal power plant
n	Index for node	TH	Set of thermal power plant
N	Set of nodes n	u	Index for unit type
N_n	Set of nodes n2 with a line to node n	U	Set of units u
r	Index for non-dispatchable renewable energy

Symbol	Description	Symbol	Description
α	Minimum reserve energy (%)	INV_u,n	Investment cost of new units (USD/MW)
c_n^curtail	Penalty cost for curtailment of VRE (USD/MWh)	L_n,t	Hourly demand (MW)
c_u^emission	Emission costs (USD/MWh)	OPEX_h	OPEX of hydropower (USD/yr)
c_u,n^fixed_O&M	Annual fixed O&M costs of units (USD/MW/yr)	P_l,n,n2^Max	Maximum investment in transfer capacity between nodes (MW)
c_u,n^fuel	Variable O&M costs of units (USD/MWh)	P_u,n^Max	Maximum investment in generation (MW)
c_n^{Loss_capacity}	Penalty cost for insufficient capacity (USD/MW)	P_n^Max,curta	Maximum Curtailment allowable (MW)
c_n^loss_load	Penalty cost for loss of load (USD/MWh)	P_n^Max,loss	Maximum loss of load allowable (MW)
CAPEX_h	Investment cost of hydropower h (USD)	P_l,n,n2^Min	Minimum investment in transfer capacity between nodes (MW)
CF_r,n,t	Capacity factor for renewable energy (dimensionless)	P_u,n^Min	Minimum investment in generation (MW)
CRF_u	CRF based on lifetime and interest rate i	P_l,n,n2^old	Transfer capacity between nodes initially installed (MW)
E_h,n^max	Maximum energy storage capacity (MWh)	P_u,n^old	Power initially installed (MW)
G_u,n^min	Minimum generation (MWh)	t2	Window of time that RoR units can reallocate water in the reservoir
G_h,n,t^nat	Natural inflow of the hydro (MWh)	tl	Transmission loss (%)
INV_l,n,n2	Investment cost of transfer capacity between nodes (USD/MW)

Symbol	Description	Symbol	Description
b_h	Binary variable of investment {0,1}	E_h,n,t	Energy stored in hydropower h (MWh)
c_t^curtail	Penalty cost for curtailment of VRE (USD/h)	E_h,n,t-1	Energy stored in hydropower h, at previous time period
c_t^emission	Emission costs of thermal units (USD/h)	G_r,n,t	Auxiliary variable for R set (MW)
c^fixed_hidro	Annual O&M costs with hydropower (USD)	G_u,n,t	Variable of generation for H and Th set (MW)
c^fixed_O&M	Annual O&M costs in new units (USD)	IN_n2,n,t	Variable of imports of energy from node n2 to node n (MW)
c_t^fuel	Fuel costs of thermal units (USD/h)	OUT_n,n2,t	Decision variable of export of energy from node n to node n2 (MW)
c^inv	Annualized investment in new units (USD)	P_l,n,n2	Variable of investment in transfer capacity between nodes (MW)
c^inv_hidro	Annualized investment in new hydropower (USD)	P_u,n	Variable of investment in generation (MW)
c^inv_trans	Annualized investment in new transmission line (USD)	P_n,t^curtail	Variable to indicate Curtailment possibility (MW)
c^{loss_capacity}	Penalty cost for the maximum insufficient capacity (USD)	P_n^loss	Variable to insufficient capacity (MW)
c_t^loss_load	Penalty cost for loss of load (USD/h)	P_n,t^loss	Variable of loss of load (MW)

Unit Type	Fuel cost/MWh	Fixed cost/kW	Investment cost/kW	CO₂+NO_x+ SO_x cost/MWh	Lifetime	Interest %		Capacity by node (MW)				Maximum investment by node (MW)
Unit Type	Fuel cost/MWh	Fixed cost/kW	Investment cost/kW	CO₂+NO_x+ SO_x cost/MWh	Lifetime	Interest %		S	SE	NE	N	S	SE	NE	N
Coal	24	159	2100	26	25	8	1577		158	1303	544	-	-	-	-
CCGT¹ 1 Combined Cycle Gas Turbine.	71	84	1000	17	20	8	1411		5675	1379	1175	-	-	-	-
OCGT² 2 Open Cycle Gas Turbine.	92	96	800	7	20	8	0		2658	2007	1448	-	-	-	-
Nuclear	5	66	5000	-	30	8	0		1990	0	0	-	-	-	-
Sugarcane	-	90	1200	-	20	8	541		1e4	878	107	-	-	-	-
Biomass	-	120	1500	-	20	8	1102		1388	496	383	-	-	-	-
Biogas	-	163	1531	-	20	8	12		155	0	2.4	-	-	-	-
Urban waste	-	276	4000	-	20	8	0		28.2	0	0	-	-	-	-
Wind	-	55	918	-	20	8	2022		0	14800	0	1e5	0	1e5	0
PV	-	39	82	-	20	8	8		923	2128	5	7000	4e5	1e5	4e5
SHP³ 3 Small Hydro.	-	65	1531	-	30	8	2005		3950	143.4	0	4700	1e4	800	0

Hydro type	Minimum generation (%)	Minimum storage (%)	Initial reservoir level (%)	Capacity by node (MW)
Hydro type	Minimum generation (%)	Minimum storage (%)	Initial reservoir level (%)	S	SE	NE	N	S	SE	NE	N
ReS	10	20	70	8231	14878	4023	10818	14247	1.5e5	37178	10619
RoR	10	-	-	6700	29808	8731	25850	-	-	-	-

Name	Type	Node	Fixed $/kW	Inv. Cost/kW	Cap. (MW)	Storage cap. (GWh)	Life-time	IR %
Name	Type	Node	Fixed $/kW	Inv. Cost/kW	Cap. (MW)	Storage cap. (GWh)	Life-time	IR %	Maranhão	ReS	SE	129	1939	125	2647	30	8
Mirador	ReS	SE	129	2082	80	1230	30	8
Buriti Queimado	ReS	SE	129	3122	142	1800	30	8
Formoso	ReS	SE	129	2204	342	1981	30	8
Apertados	RoR	S	129	1857	139	-	30	8
Santo Antônio	RoR	S	106	1429	84.3	-	30	8
Itapiranga	RoR	S	106	1653	724.6	-	30	8
Saudade	RoR	S	129	1939	61.4	-	30	8
Telêmaco Borba	RoR	S	106	1612	118	-	30	8
Paranã	RoR	SE	129	1959	90	-	30	8
Itaguaçu	RoR	SE	106	1510	92	-	30	8
Porto Galeano	RoR	SE	106	1673	81	-	30	8
Jatobá	RoR	NE	129	1878	1650	-	30	8
Tabajara	RoR	N	129	1980	400	-	30	8
Castanheira	RoR	N	153	2510	140	-	30	8

Scenario	Hydro	Wind	PV + DG	Bio.	Coal	Gas
Scenario	Hydro	Wind	PV + DG	Bio.	Coal	Gas	2020¹	65.2	8.8	1.7	9.1	4.7	8.3
ZDeficit	33.6	13.0	18.2	32.8	1.2	0.7
COPEE²	53.7	11.3	16.1	9.3	3.3	3.6
GILS³	47.0	26.0	18.0	9.0	-	-
NEP⁴	36.0	37.0	17.5	2.2	0.0	5.7

Brasil

Brasil

Generation and Transmission Expansion Planning with Full-year Hourly Power Balance

Abstract

HIGHLIGHTS

GRAPHICAL ABSTRACT