# Generation Expansion Planning with Energy Storage Systems Considering Renewable Energy Generation Profiles and Full-Year Hourly Power Balance Constraints

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## Abstract

**:**

_{2}emissions for the coming decades, a complex multi-period mixed integer linear programming (MILP) model needs to be formulated and solved with individual unit characteristics along with hourly power balance constraints. This problem requires huge computational effort since there are thousands of possible scenarios with millions of variables in a single calculation. However, in this paper, instead of finding the globally optimal solutions of such MILPs directly, a simplification process is proposed, breaking it down into multiple LP subproblems, which are easier to solve. In each subproblem, constraints relating to renewable energy generation profiles, charge-discharge patterns of ESSs, and system reliability can be included. The proposed process is tested against Thailand’s power development plan. The obtained solution is almost identical to that of the actual plan, but with less computational effort. The impacts of uncertainties as well as ESSs on GEP, e.g., system reliability, electricity cost, and CO

_{2}emission, are also discussed.

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Literature Review

#### 1.3. Our Contribution

_{2}emissions, of the system have not met acceptable criteria. Therefore, the large-scale multi-period MILP problem can be decomposed into multiple linear programming subproblems. With these separated and simplified models, solutions to the subproblems associated with each period can be easily obtained. Solution for earlier period that satisfy all criteria will then be used as the initial conditions for the subproblem of the next period. With these smaller scale subproblems, hourly power balance constraints with renewable energy generation profiles for a whole subperiod, e.g., 720 h in a month, can be included in the model without too much computational burden. The process will then be repeated from the first until the last period, covering the total planning time horizon. Another benefit of the separation of this decision-making process and optimization model is the ability to incorporate non-linear power system indices calculation. The proposed separation process allows non-linear indices, i.e., LOLE, to be calculated during the decision-making process, instead of being estimated as they are in other optimization models.

## 2. Methodology

#### 2.1. Problem Statement

- The model is deterministic.
- Adequacy of generation capacity can be ensured by exceeded capacity results from reliability constraints.
- The objective of this problem is to create a generation expansion plan that has minimum total electricity cost. Total electricity cost consists of average and levelized investment costs, fuel costs, fixed operation and maintenance costs, and variable operation and maintenance costs.
- The given planning horizon is divided into monthly timeslots.
- The power system is modelled as a conventional system as shown in Figure 1. Only generation and total system load are considered. Transmission elements are neglected.
- The initial generation system prior to the given planning horizon is required.
- Renewable energy penetration is already planned for a whole planning horizon.
- A set of candidate units for generation expansion are given with different technologies, fuels, sizes, and heat rates.
- Operational and short-term characteristics, e.g., ramp rates, minimum up and down times, synchronization and desynchronization time, etc., are neglected in this optimization.
- Only generation system reliability is considered. Transmission system reliability is neglected.
- The individual hourly output power of each generation unit is considered to accurately represent power generation profile of intermittent renewable energy resources. For example, non-dispatchable solar generation units generate varied output power, which changes hourly according to sunlight.
- Electricity demand is represented with a full-year hourly load curve.
- Generation expansion decisions will be made from reliability criteria and hourly power balance criteria.

- The generation units selected from the set of candidates during each timeslot.
- The hourly electricity production of each generation unit in each timeslot.
- The hourly charged and discharged electricity of each ESS unit.

#### 2.2. Mathematical Formulation

#### 2.2.1. Objective Function

_{j,y,m}is number of new units with fuel type f commissioned in month m of year y, IC

_{f,k,y,m}is a variable of installed capacity each individual new unit k with fuel type f (MW), C

_{f,k}is fixed cost per MW of candidate generation unit k with fuel type f (THB/MW), N

_{f,y,m}is number of existing generation unit of fuel type f in moth m of year y, H

_{m}is number of hours in month m, F is number of fuel type f, P

_{f,j,y,m,h}is a variable of power generated by generation unit j, which use fuel type f in hour h of month m of year y (MW), e

_{f,j,y}is variable cost of electricity generated from generation unit j of fuel type f in year y (THB/MWh).

_{f,k}) is a combination of the unit’s investment (Cinv

_{f,k}), fixed operation, and maintenance cost per year (FOMC

_{f,k}), multiplied by the lifetime of the unit (LT

_{f,k}) as shown in (4). All mentioned parameters are constant for each technology of candidate generation unit. Only the fixed costs of additional units are considered in the objective function since the fixed costs of existing units prior to the optimization process are fixed and committed. However, the fixed costs of existing units prior to the optimization process are included in the total cost of electricity generation.

_{f,j,y}) is a combination of each generation unit’s fuel cost, variable operation, and maintenance cost per MWh (VOMC

_{f,j}). A unit’s fuel cost is a combination of the cost of each fuel type (FC

_{f,y}) and the unit’s heat rate (HR

_{f,j}) as shown in (5). Fuel costs each year are different according to the forecasted market price of each fuel. A discount rate (r) is also applied to both fixed and variable costs of the power system as a function of β shown in (2).

#### 2.2.2. Constraints

#### Reliability Constraint

_{f,j,y,m}) above annual peak demand. It is defined as the difference between the total available generation capacity and the annual peak demand (PL

_{y,m}) divided by the peak demand. For Thailand’s generation system, since there are cases of generation units unable to supply power at their installed capacity due to equipment degradation and availability of renewable supply resources, the generation capacity of each unit is equal to the multiplication of its dependable factor (DF

_{f,j}) and installed capacity as shown in (7). Dependable factor can be different each month, especially for hydropower plants where available generation capacity depends on the amount of water in their reservoirs.

_{f,j,y,m})) and load model (load duration curve(LDC

_{y.m})) as shown in (9)

#### Hourly Energy Balance Constraint

_{s,j,y,m,h}and Pch

_{s,j,y,m,h}are variables of self-power supplied by ESS type s unit j in hour h of month m of year y (MW), η

_{dch,s,j}and η

_{ch,s,j}are the ESS unit’s discharging and charging efficiency (%) and L

_{y,m,h}is load of hour h in month m of year y (MW).

#### Energy Storage System Operating Constraint

_{s,j,y,m,h}is stored energy in ESS type s unit j at hour h of month m in year y, SOC

_{min,s,j}and SOC

_{max,s,j}is minimum and maximum state of charge of ESS type s unit j.

#### Fuel Mix Ratio Constraint

_{f,y,m}is fuel ratio of fuel type f in year y (%).

#### CO_{2} Emissions Constraint

_{2}emission constraints are set to limit the environmental impact of electricity generation (18).

_{f}is emission factor of fuel type f (kgCO

_{2}/Btu) and ε

_{y,m}is maximum average CO

_{2}emission of year y (kgCO

_{2}/MWh).

#### Power Generation Upper Bound and Lower Bound

#### 2.3. Simplification Process

#### 2.3.1. The Concept of Simplification

- Separate each month into multiple timeslots within the planning horizon to reduce the number of variables in a single calculation. By doing this, multiple MILP models will be used instead of a single multi-period MILP. Thus, multiple problems need to be iteratively solved and the optimal solution of the previous timeslot will be used as the initial condition of the next.
- Separate generation expansion decisions from the MILP model. By doing this, the MILP model will be reduced to a linear programming model. Reliability constraints can also be removed from the linear programming model. However, a reliability index still needs to be calculated separately for generation expansion decisions. The remaining linear programming model in each specific month m of year y will be used for unit commitment problem and energy dispatch, which provides decision-making indices that will be subsequently used for generation expansion decisions.
- Generation expansion decisions shall be made by comparing candidate generation units’ levelized average cost of electricity. With objective function shown in (1), adding generation units with the cheapest levelized average cost, considering the aforementioned constraints, still leads to near-optimal solutions for generation expansion planning, even if a full-scale optimization model is not used.

#### 2.3.2. A Slack Generation Unit

- Availability: always available
- Generating capacity: larger than peak demand of considered timeslot
- Unit cost: much more than the most expensive unit
- Fuel type and CO
_{2}emissions: unspecified fuel type, no emission factor

#### 2.3.3. Simplified Model

_{2}emission index with planning constraints.

_{i}is individual probability of outage capacity state i, and t

_{LDC}(O

_{i}) is duration of the load loss due to the outage capacity O

_{i}(hr).

#### 2.3.4. LOLE Calculation with ESS

_{LDC}(O

_{i}) will be changed to t

_{LDC’}(O

_{i}). Thus, the obtained LOLE will represent the impact of ESS in the generation system. In case there are 2 or more ESS units, the method presented in Section 2.3.4 shall be done for every ESS unit before LOLE calculation.

#### 2.3.5. Candidate Generation Capacity Selection

- the system reserve margin is lower than the planning criteria, or
- system LOLE is higher than the planning criteria, or
- there is no optimal solution provided by linear programming, (in this case the slack generation units will be dispatched, instead).

_{2}emissions. The selection process is shown in (39).

## 3. Case Study and Simulation Results

#### 3.1. Planning Constraints

- Planning horizon: 2013–2030
- Existing generation system as of December 2012 used as initial power generation system.
- Consider reserve margin as reliability criteria. Reserve margin of the system shall not fall below 16%
- Renewable energy source penetration in this plan is set in advance according to Thailand’s alternative energy development plan: AEDP 2012-2021 [34].
- Average CO
_{2}emission limited to 0.5 kgCO_{2}/kWh within planning horizon. - Fuel used in electricity generation classified into ten types:
- Bituminous
- Diesel
- Bunker oil
- Import coal
- Natural gas
- Import hydro
- Lignite
- Import HVDE
- Nuclear
- Renewable

- Maximum fuel mix ratio in 2030 of natural gas is 70% and bituminous is 13%

#### 3.2. System Demand

#### 3.3. Fuel Cost

#### 3.4. Generation System

#### 3.4.1. Generation Units in Generation Expansion Planning

#### 3.4.2. Generation Unit Modeling

- Renewable energy generation units with generation profiles:

- 2.
- Peak cutting generation units:

- 3.
- Dispatchable generation units:

- 4.
- Energy storage systems:

#### 3.5. Result and Discussion

#### 3.5.1. Verification of the Results from the Proposed Method

_{2}emission of Case 1 and Case 2 are shown in Figure 8. From Figure 8, reserve margin of Case 1 and Case 2 are mostly exactly the same, but slightly different in 2026 and 2027. Considering LOLE, since LOLE in this study is calculated monthly, annual LOLE can be obtained by accumulation of LOLE of 12 previous months. Case 1 has better reliability index since the new generation units in Case 1 are commissioned earlier compared to those of Case 2. However, both of them satisfy the requirement that LOLE must be less than one day per year. Thus, considering reserve margin and LOLE as the generation expansion decision-making indices, Case 1 and Case 2 provide almost the same result.

_{2}emission of Case 1 is also slightly higher than that of the Case 2 from 2025 to 2027. They are caused by the differences in commissioning sequence of additional generation unit as described earlier.

#### 3.5.2. Generation Expansion Planning with Uncertainty

_{2}emission are shown in Figure 10. respectively. It can be seen that the results obtained from using only forecasted data are a bit different from their corresponding expected values. They are just close to each other, but not exactly the same value, even though they are calculated from the symmetric joint probability distribution shown in Table 3.

#### 3.5.3. Generation Expansion Planning with ESS

_{2}emission of both cases are almost equal since energy supplied from BESS is generated from generation units in the system with the same average CO

_{2}emission. However, due to loss in BESS, average CO

_{2}emission of Case 3 is slightly higher than that of the Case 2.

#### 3.5.4. Computational Cost

## 4. Conclusions

_{2}emissions. These constraints can vary each season or each year, allowing more flexibility in long term generation expansion planning. Furthermore, with less computation time, it allows uncertainties to be taken into consideration. Multiple GEP using different assumptions with corresponding probabilities can be solved. The impact of installation of ESSs on system reliability can also be obviously seen in the LOLE.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Indices | |

f | fuel type |

h | hour in considering month |

i | State of capacity outage O_{i} |

j | existing generation unit and ESS in current planning horizon |

k | new generation unit added into current planning horizon |

m | month in planning horizon |

s | ESS type |

y | year in planning horizon |

Parameters | |

Cinv_{j,k} | investment capital cost of generation unit k which use fuel type f (THB/MW) |

C_{f,k} | fixed cost per MW of candidate generation unit k which use fuel type f (THB/MW) |

Crate_{s,j} | c-rate of ESS type s unit j (MW/MWh) |

DF_{f,j} | dependable factor of generation unit j of fuel type f (%) |

e_{f,j,y} | variable cost of electricity generated from generation unit j of fuel type f in year y (THB/MWh) |

EF_{f} | emission factor of fuel type f (kgCO_{2}/Btu) |

E_{s,j,y,m,h} | stored energy in ESS type s unit j at hour h month m year y (MWh) |

FC_{f,y} | fuel cost of fuel type f in year y (THB/Btu) |

FOMC_{f,k} | Fixed operation and maintenance cost of generation unit k which use fuel type f (THB/MW/year) |

FOR_{f,j,y,m} | forced outage rate of generation unit j which use fuel type f of month m of year y (%) |

H_{m} | number of hours in month m, i.e., 744 h in January, 720 h in April |

HR_{f,j} | heat rate of generation unit j that use fuel type f (Btu/MWh) |

LDC_{y,m} | Load duration of month m of year y |

LOLE | loss of load expectation (day/year) |

LT_{f,k} | lifetime of new generation unit k which use fuel type f (year) |

L_{y,m,h} | load of hour h in month m of year y (MW) |

N_{f,y,m} | number of existing generation unit of fuel type f in month m of year y |

N_{s,y,m} | number of existing ESS unit of type s in month m of year y |

N_{f,y,m} | number of new generation unit of fuel type f added in the system in month m of year y |

O_{i} | Outage capacity i (MW) |

Pch_{s,j,max} | maximum internal power input (charge state) of ESS of type s unit j (MW) |

Pch_{s,j,min} | minimum internal power input (charge state) of ESS of type s unit j (MW) |

Pdch_{s,j,max} | maximum internal power output (discharge state) of ESS of type s unit j (MW) |

Pdch_{s,j,min} | minimum internal power output (discharge state) of ESS of type s unit j (MW) |

P_{f,j,max} | maximum power output of generation unit j that use fuel type f (MW) |

P_{f,j,min} | minimum power output of generation unit j that use fuel type f (MW) |

p_{i} | individual probability of outage capacity state i |

PL_{y,m} | peak load of month m of year y (MW) |

PSch_{s,j,max} | maximum system power input (charge state) of ESS unit j (MW) |

PSdch_{s,j,max} | maximum system power output (discharge state) of ESS unit j (MW) |

r | discount rate (%) |

RM | reserve margin (%) |

SOC_{max,s,j} | maximum state of charge of ESS type s unit j (%) |

SOC_{min,s,j} | minimum state of charge of ESS type s unit j (%) |

t_{LDC}(O_{i}) | duration of the load loss due to the outage capacity O_{i} (hr) in load duration curve (LDC) |

t_{LDC’}(O_{i}) | duration of the load loss due to the outage capacity O_{i} (hr) in modified load duration curve (LDC’) |

VOMC_{f,j} | variable operation and maintenance cost of generation unit j of fuel type f (THB/MWh) |

δ_{f,y,m} | fuel ratio of fuel type f in year y (%) |

ε_{y,m} | maximum average CO_{2} emission of year y (kgCO_{2}/MWh) |

η_{ch,s,j} | charging efficiency of ESS type s unit j (%) |

η_{dch,s,j} | discharging efficiency of ESS type s unit j (%) |

Variable | |

IC_{f,k,y,m} | Installed capacity of candidate generation unit k which use fuel type f commissioned in month m of year y (MW) |

Pch_{s,j,y,m,h} | Self-power absorbed by ESS type s unit j in hour h of month m of year y (MW) |

Pdch_{s,j,y,m,h} | Self-power supplied by ESS type s unit j in hour h of month m of year y (MW) |

P_{f,j,y,m,h} | Power generated by generation unit j which use fuel type f in hour h of month m of year y (MW) |

## Appendix A

Fuel Type | Number (Unit) | Total Capacity (MW) | Lifetime (Years) | Heat Rate (Btu/kWh) |
---|---|---|---|---|

bituminous | 8 | 2376.00 | 25–30 | 8300–9100 |

diesel | 1 | 4.40 | 25 | 10,400 |

oil | 2 | 320.00 | 21–30 | 8300–10,400 |

import coal | - | - | - | - |

import HVDC | 1 | 300.00 | 25 | - |

import hydro | 5 | 2104.60 | 25–50 | - |

Lignite | 10 | 2180.00 | 30–39 | 10,600–11,500 |

natural gas | 65 | 21,796.30 | 20–31 | 6800–10,300 |

nuclear | - | - | - | - |

renewable | N/A | 4684.10 | 21–50 | - |

PHS | 1 | 500.00 | 50 | - |

Fuel Type | Total Cap. (MW) | Lifetime (Years) |
---|---|---|

hydro | 2967.98 | 25–50 |

solar | 303.03 | 25 |

wind | 249.90 | 25 |

biomass | 1028.60 | 21–25 |

biogas | 110.20 | 25 |

waste | 22.40 | 25 |

geothermal | 2.00 | 25 |

Year | Bituminous | Diesel | Oil | Import Coal | Import Hydro | Lignite | Natural Gas | PHS |
---|---|---|---|---|---|---|---|---|

2013 | 1186.00 | |||||||

2014 | 3436.90 −1052.00 | |||||||

2015 | 982.00 | 3056.90 −1175.10 | ||||||

2016 | 270.00 | 491.00 | 1370.80 −478.20 | |||||

2017 | 270.00 | 900.00 −494.00 | 500.00 | |||||

2018 | 659.00 | 720.90 −680.50 | ||||||

2019 | 800.00 | −5.00 | 1220.00 | 724.80 −180.00 | ||||

2020 | 90.00 −1521.00 | |||||||

2021 | 300.00 | 1080.90 −200.00 | ||||||

2022 | 300.00 | 1084.80 −150.00 | ||||||

2023 | 300.00 | 1980.00 −2863.00 | ||||||

2024 | −270.00 | 300.00 | 1980.90 −360.00 | |||||

2025 | −90.00 | 300.00 | 1084.8 −2330.00 | |||||

2026 | 300.00 | 1080.00 | ||||||

2027 | 300.00 | 1980.90 −2617.00 | ||||||

2028 | 250.00 | 300.00 | 1804.80 −1289.00 | |||||

2029 | 250.00 | 300.00 | −270.00 | 900.00 | ||||

2030 | 250.00 | 300.00 −126.00 | −270.00 | 0.90 |

Year | Small Hydro | Solar | Wind | Biomass | Biogas | Waste |
---|---|---|---|---|---|---|

2013 | 19.20 | 375.80 | 14.00 | 574.50 | - | 56.00 |

2014 | 0.50 | 181.10 | 263.60 | 206.80 | 1.20 | 12.80 |

2015 | 51.80 | 191.10 | 302.90 | 180.50 | 2.30 | 22.80 |

2016 | 5.20 | 130.10 | 163.10 | 175.30 | 2.30 | 32.80 |

2017 | 22.00 | 130.10 | 163.10 | 175.30 | 2.30 | 41.80 |

2018 | 23.60 | 130.00 | 7.40 | 184.50 | 2.40 | 41.80 |

2019 | 3.50 | 151.00 | 117.80 | 179.80 | 2.40 | 41.80 |

2020 | 4.70 | 151.00 | 8.20 | 234.00 −8.00 | 2.50 | 41.90 |

2021 | 1.50 | 201.00 | 8.60 | 186.00 | 2.50 | 41.90 |

2022 | 1.30 | 220.10 | 9.00 | 53.70 | 2.50 | 1.90 |

2023 | 3.50 | 220.10 | 19.50 | 32.80 | 2.60 | 1.90 |

2024 | 2.20 | 220.10 | 9.90 | 38.60 −49.80 | 2.60 | 1.90 |

2025 | 3.30 | 220.00 | 10.40 | 21.20 −56.00 | 2.60 | 2.00 |

2026 | 1.00 | 221.00 | 11.00 | 16.80 −5.00 | 2.70 | 2.00 |

2027 | 12.00 | 220.10 | 61.50 | 16.90 −7.00 | 2.70 | 2.00 |

2028 | 17.30 | 221.00 | 12.10 | 14.40 −103.00 | 2.80 | 2.00 |

2029 | 1.00 | 223.00 | 22.70 | 14.50 | 2.80 | 2.00 |

2030 | 1.00 | 230.00 | 43.30 | 14.70 −20.00 | 2.80 | 2.10 |

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Capacity Outage (MW) | Capacity Available (MW) | State Probability |
---|---|---|

O_{1} | Installed capacity—O_{1} | p_{1} |

O_{2} | Installed capacity—O_{2} | p_{2} |

$\vdots $ | $\vdots $ | $\vdots $ |

O_{i} | Installed capacity—O_{i} | p_{i} |

$\vdots $ | $\vdots $ | $\vdots $ |

O_{N} | Installed capacity—O_{N} | p_{N} |

Generation Unit | Fuel Type | Capacity (MW) | Lifetime (years) | Heat Rate (Btu/kWh) | Remark |
---|---|---|---|---|---|

Coal fired thermal | Bituminous | 800 | 30 | 8650 | Unlimited |

Combined cycle | Natural gas | 900 | 25 | 6800 | Unlimited |

Nuclear | Nuclear | 1000 | 60 | 10,950 | Unlimited |

Parameters | % of Forecasted Load (Associated Probability) | |||
---|---|---|---|---|

97% (0.25) | 100% (0.5) | 103% (0.25) | ||

% of solar power generation(associated probability) | 90% (0.25) | 0.0625 | 0.125 | 0.0625 |

100% (0.5) | 0.125 | 0.25 | 0.125 | |

110% (0.25) | 0.0625 | 0.125 | 0.0625 |

Type | C-Rate (MW/MWh) | Charging Efficiency (%) | Discharging Efficiency (%) | Minimum State of Charge (%) | Maximum State of Charge (%) |
---|---|---|---|---|---|

PHS | 0.125 | 86.6% | 86.6% | 0.0% | 100.0% |

BESS | 1 | 97.5% | 97.5% | 10.0% | 90.0% |

Year | Results for Section 3.5.1 | Results for Section 3.5.2 | ||
---|---|---|---|---|

Case 1 | Case 2 (w/Forecasted) | Case 2 Min | Case 2 Max | |

2015 | (4) NG 900 MW | |||

2021 | (1) NG 900 MW | (4) NG 900 MW | ||

2022 | (6) Coal 800 MW (6) NG 900 MW | (4) NG 900 MW | ||

2023 | (1) NG 900 MW | (3) Coal 800 MW (3) NG 900 MW (4) NG 900 MW | (3) Coal 800 MW (3) NG 900 MW (4) NG 900 MW | (3) Coal 800 MW (3) NG 900 MW (4) NG 900 MW |

2024 | (6) NG 900 MW | |||

2025 | (6) Coal 800 MW (6) NG 900 MW | (4) NG 900 MW | (4) NG 900 MW | (4) NG 900 MW (4) NG 900 MW |

2026 | (6) Nuclear 1000 MW (6) NG 900 MW | (3) Nuclear 1000 MW (4) Coal 800 MW | (3) Nuclear 1000 MW (4) NG 900 MW | (4) Nuclear 1000 MW |

2027 | (6) Nuclear 1000 MW | (3) Nuclear 1000 MW (4) NG 900 MW | (3) Nuclear 1000 MW (4) Coal 800 MW | (3) Nuclear 1000 MW (4) Coal 800 MW (4) NG 900 MW |

2028 | (1) Coal 800 MW | (3) Coal 800 MW (4) NG 900 MW | (4) NG 900 MW | (3) Coal 800 MW (4) NG 900 MW |

2029 | (6) NG 900 MW | |||

2030 | (1) NG 900 MW | (3) NG 900 MW (4) NG 900 MW | (3) Coal 800 MW (4) NG 900 MW | (3) NG 900 MW (4) NG 900 MW |

Total | 11,600 MW | 11,600 MW | 9800 MW | 13,400 MW |

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## Share and Cite

**MDPI and ACS Style**

Diewvilai, R.; Audomvongseree, K. Generation Expansion Planning with Energy Storage Systems Considering Renewable Energy Generation Profiles and Full-Year Hourly Power Balance Constraints. *Energies* **2021**, *14*, 5733.
https://doi.org/10.3390/en14185733

**AMA Style**

Diewvilai R, Audomvongseree K. Generation Expansion Planning with Energy Storage Systems Considering Renewable Energy Generation Profiles and Full-Year Hourly Power Balance Constraints. *Energies*. 2021; 14(18):5733.
https://doi.org/10.3390/en14185733

**Chicago/Turabian Style**

Diewvilai, Radhanon, and Kulyos Audomvongseree. 2021. "Generation Expansion Planning with Energy Storage Systems Considering Renewable Energy Generation Profiles and Full-Year Hourly Power Balance Constraints" *Energies* 14, no. 18: 5733.
https://doi.org/10.3390/en14185733