Energy Storage Mix Optimization Based on Time Sequence Analysis Methodology for Surplus Renewable Energy Utilization

Abstract

Increasing the proportion of carbon-free power sources, such as renewable energy, is essential for transitioning to a zero-carbon power system. However, when the rate of grid expansion and flexibility cannot match the rate of renewable energy increase, surplus energy is the result. Surplus energy can be discarded through curtailment or stored and utilized when required. The optimal equipment configuration of the storage system should be determined based on the surplus energy characteristics. This study proposes an optimal energy storage mix configuration method by considering long-term forecasts of surplus energy in the South Korean renewable energy supply and power grid expansion plan. The surplus energy by time slot is comprehensively analyzed considering renewable energy power output, power demand, and power system operation constraints. We calculate the required power and energy of storage devices. Furthermore, we construct a long-term optimal energy storage mix using surplus energy generation patterns and technical and economical characteristics of storage technologies. The total cost minimization was considered as the objective function, comprising three elements: initial construction, equipment replacement, and loss costs for charging and discharging. We propose a time sequence analysis (TSA) method that enables chronological analysis from the starting year to the final target year. The TSA method provides an energy storage mix configuration roadmap that can utilize surplus energy for various years over the entire period, considering the annual increase in surplus energy and commercialization timing of each storage technology. We compare the difference between our proposed TSA method and the method that analyzes only the final target year to validate the superiority of this methodology.

1. Introduction

In South Korea and globally, the rate of increase in the proportion of renewable energy is expected to gradually accelerate for the construction of future carbon-neutral power systems [1,2].

The Korean government plans to increase the share of renewable energy to 70.8%, while reducing the share of thermal power generation to 0% by the early phase-out of thermal power generation [3]. This change in the Korean power generation mix can result in decreased flexibility in the power system operation. This is because renewable energy has no control infrastructure yet, and the implementation of output control infrastructure is planned mainly for large-scale renewable energy power plants after 2035.

When the percentage of renewable energy increases above a certain threshold, the power generation at certain periods exceeds the power demand, resulting in the curtailment of renewable generation. This curtailed renewable energy output is called surplus energy [4].

Minimizing surplus energy is crucial as its increase renders the achievement of carbon reduction goals difficult and hinders the operation efficiency of power systems [5].

Various energy storage systems (ESSs) and energy conversion technologies can be used to utilize surplus renewable energy without discarding it [6,7,8,9,10,11,12].

In the case of an increase in the proportion of renewable energy, various technologies must be optimally configured to minimize the generation of surplus energy, which is called the optimal energy storage mix (ESM) [13,14,15,16].

Many studies have been conducted to examine the need for optimal capacity of energy storage devices. However, most studies target energy storage devices to reduce volatility in conjunction with renewable energy generation complexes or energy storage devices to increase the operational flexibility of micro-grids [4,5,6,7,8,9,10,11,12,13,14,15,16,17].

The method used to analyze the optimal ESM is shown in Figure 1. First, the surplus renewable energy (SE_Y) for the initial year (Y = 0) is calculated, followed by an annual surplus energy analysis, which considers renewable energy expansion plan, output pattern by time slot, maximum power demand increase forecast, power demand pattern by time, and minimum power output constraints. The amount, duration, and generation cycle of surplus renewable energy are calculated annually and used as input for the optimal ESM analysis.

Next, we propose a method to analyze the optimal ESM for each unit time slot until the final analysis target year, using the time sequence analysis (TSA) methodology. The TSA methodology can minimize the total cost incurred during the entire period by repeating the optimal ESM analysis for each unit time slot until the final analysis target year. This method considers the changes in surplus energy, timing of technology commercialization, changes in equipment investment costs, and ESM equipment configuration of the previous period for each unit time slot.

We include the analysis results of the optimal ESM based on the 2050 Carbon-Neutrality Scenario for South Korea in a case study to validate the efficacy of our proposed method. Further, we compare the differences in the optimal ESM analysis results for 2050 based on the applicability of the TSA method.

The remainder of this paper is organized as follows. A detailed explanation of the method used to analyze surplus energy that results from the increase in the proportion of renewable energy is described in Section 2. Section 3 describes the method used for analyzing the optimal ESM. Section 4 presents the analysis results of the ESM based on the 2050 Carbon-Neutrality Scenario in South Korea. Finally, Section 5 concludes the paper.

2. Estimation of Surplus Renewable Energy in Future Carbon-Neutral Power Systems

2.1. Method of Surplus Renewable Energy Estimation

Surplus renewable energy refers to the amount of renewable generation that exceeds the limit that can be accommodated in the power system. Surplus energy is calculated as shown in Figure 2. First, the Gross Load (GL_T) and renewable generation (RG_T) for each time slot are input to calculate the Net Load (NL_T) for each time slot; subsequently, RG_T is subtracted from GL_T. Next, the minimum generation level constraint (MG_T) of the power system is calculated. MG_T for each time slot was calculated considering the system’s minimum inertia requirement and the constraint on the operational generation reserve requirement. Thus, for each time slot, no surplus energy existed when NL_T was greater than or equal to MG_T. However, the difference between the two values (NL_T–MG_T) became the surplus energy generation for that time slot when the reverse situation occurred. The surplus energy for each time slot of that year was calculated by repeating this process until the final time slot (T_max).

2.2. Method of Net Load Calculation

Net Load refers to the Gross Load minus the renewable generation, which signifies the power demand that must be supplied by central generation plants.

$${\mathit{NL}}_t={\mathrm{GL}}_t-{\mathrm{RG}}_t$$

(1)

• NL_t: Net Load per time slot (GW)
• GL_t: Gross Load per time slot (GW)
• RG_t: Renewable energy generation per time slot (GW)

In this study, the Gross Load for each time slot of the analysis target year was created by creating a normalized load pattern with the maximum value set to 1.0 using historical load data from a previous year (2018) when the renewable generation ratio was at most 2%. This was then multiplied by the maximum demand forecast for the analysis target year.

$${\mathrm{GL}}_t=\frac{L_t^{2018}}{L_{\mathit{peak}}^{2018}}\times L_{\mathit{peak}}$$

(2)

• GL_t: Gross Load per time slot (GW)
• L_t²⁰¹⁸: Load historical data per time slot for 2018 (GW)
• L_peak²⁰¹⁸: Peak load historical data for 2018 (GW)
• L_peak: Peak load forecast data for the analysis target year (GW)

The renewable generation was calculated by multiplying the generator capacity by the time slot power output pattern for solar and wind power. The time slot power output pattern for solar and wind power was obtained by normalizing historical generation data with the maximum value set to 1.0.

$$\begin{gathered} {\mathit{RG}}_t=\left({\mathit{PVP}}_t\times {\mathit{Cap}}_{\mathit{PV}}\right)+\left({\mathit{WP}}_t\times {\mathrm{Cap}}_{\mathit{wind}}\right) \\ =\left(\frac{{\mathit{PVG}}_t}{{\mathit{PVG}}_{\mathit{max}}}\times {\mathit{Cap}}_{\mathit{PV}}\right)+\left(\frac{{\mathit{WG}}_t}{{\mathit{WG}}_{\mathit{max}}}\times {\mathrm{Cap}}_{\mathit{wind}}\right) \end{gathered}$$

(3)

• RG_t: Renewable energy generation per time slot (GW)
• PVP_t: PV generation pattern per time slot
• WP_t: Wind generation pattern per time slot
• Cap_PV: PV generation capacity (GW)
• Cap_Wind: Wind generation capacity (GW)
• PVG_t: Solar power output per time slot (GW)
• PVG_max: Maximum solar power output (GW)
• WG_t: Wind power output per time slot (GW)
• WG_max: Maximum wind power output (GW)

2.3. Method of Minimum Generation Constraint Calculation

The minimum generation constraint (MG_T) for each time slot varies based on different factors depending on the characteristics of the power system. In the case of the South Korean power system, which is independent of those of neighboring countries, we calculated MG_T by considering the system’s minimum inertia requirement and the operational generation reserve requirement.

First, the proportion of synchronous generators decreases as the proportion of renewable generation increases, thereby reducing the inertia provided to the power system and potentially leading to instability. To maintain system stability, a certain level of inertia should be ensured at all times by requiring the minimum number of operating synchronous generators. The minimum generation constraint required to maintain the system’s minimum inertia is calculated by multiplying the minimum continuous operating output for each generator by the minimum number of generators that must operate. The minimum generation constraint related to the minimum inertia requirement for each time slot is calculated as follows.

The minimum number of operating generators (NG_t) required to satisfy the critical inertia requirement for each time slot is calculated using Equation (4).

$${\mathit{NG}}_t^{\mathit{CI}\mathit{\_}\mathit{min}}=\frac{{\mathit{CI}}_t}{{\mathit{GC}}_{\mathit{average}}\times {\mathit{IC}}_{\mathit{average}}}$$

(4)

• NG_t^CI_min: Minimum number of operating generators per time slot required to maintain the minimum inertia (units)
• CI_t: Critical inertia; minimum inertia requirement per time slot (GWs)
• GC_average: Average generation capacity (GW)
• IC_average: Average generation inertia constant (sec)

The minimum generation constraint required to secure the critical inertia is calculated using Equation (5).

$${\mathit{SGO}}_t^{\mathit{CI}\mathit{\_}\mathit{min}}={\mathit{NG}}_t^{\mathit{CI}\mathit{\_}\mathit{min}}\times {\mathit{GC}}_{\mathit{average}}\times {\mathit{GO}}_{\mathit{average}}^{\mathit{min}}$$

(5)

• SGO_t^CI_min: Minimum generation constraint per time slot required to maintain the minimum inertia (GW)
• NG_t^CI_min: Minimum number of operating generators per time slot required to maintain the minimum inertia (units)
• GC_average: Average generation capacity (GW)
• GO_average^min: Average minimum level of generation output (%).

The operational reserve power requirement must adapt to the variability in the generation and load. Short-term power supply instability and frequency stability deterioration can occur in the power system in the case of insufficient operational reserve power. The output adjustment capability of operating generators must be maintained higher than the operational reserve power requirement to maintain a short-term power supply in the power system. The minimum generation constraint related to the operational reserve power requirement for each time slot is calculated using Equation (6).

$${\mathit{NG}}_t^{\mathit{SR}\mathit{\_}\mathit{min}}=\frac{{\mathit{MSR}}^{\mathit{min}}+{\mathit{NL}}_t}{{\mathit{GC}}_{\mathit{average}}\times (1-\frac{{\mathit{RSR}}_{\mathit{average}}}{100})}$$

(6)

• NG_t^CI_min: Minimum number of operating generators per time slot required to maintain the operational reserve power (units)
• MSR^min: Minimum required operational reserve power (minimum spinning reserve) (GW)
• NL_t: Net Load per time slot (GW)
• GC_average: Average generator capacity (GW)
• RSR_average: Average operational reserve power provision ratio per generator (%)

The minimum generation constraint required to secure the minimum operational reserve power is calculated using Equation (7).

$${\mathit{SGO}}_t^{\mathit{SR}\mathit{\_}\mathit{min}}={\mathit{NG}}_t^{\mathit{SR}\mathit{\_}\mathit{min}}\times {\mathit{GC}}_{\mathit{average}}\times {\mathit{GO}}_{\mathit{average}}^{\mathit{min}}$$

(7)

• SGO_t^SR_min: Minimum generation constraint per time slot required to maintain the operational reserve power (GW)
• NG_t^SR_min: Minimum number of operating generators per time slot required to maintain the operational reserve power (units)
• GC_average: Average generator capacity (GW)
• GO_average^min: Average minimum level of generation output (%)

As shown in Equation (8), the greater of the two minimum generation constraints calculated for each time slot is determined as the minimum generation constraint for that time slot and is considered in the calculation of surplus energy.

$${\mathit{SGO}}_t^{\mathit{min}}=\mathit{MAX}\left({\mathit{SGO}}_t^{\mathit{CI}\mathit{\_}\mathit{min}},{\mathit{SGO}}_t^{\mathit{SR}\mathit{\_}\mathit{min}}\right)$$

(8)

• SGO_t^min: Minimum generation constraint per time slot (GW)
• SGO_t^CI_min: Minimum generation constraint per time slot required to maintain the minimum inertia (GW)
• SGO_t^SR_min: Minimum generation constraint per time slot required to maintain the operational reserve power (GW)

2.4. Method of Surplus Renewable Energy Calculation

When the Net Load is less than the minimum generation constraint of the power system, surplus energy is the result. Therefore, suppose the Net Load is less. In that case, the difference between the calculated Net Load and the minimum generation constraint for each time slot is considered as the surplus energy for that time slot, as shown in Equation (9).

$${\mathit{NL}}_t<{\mathit{SGO}}_t^{\mathit{min}} \Rightarrow {\mathit{SE}}_t={\mathit{NL}}_t-{\mathit{SGO}}_t^{\mathit{min}}$$

(9)

• SE_t: Surplus energy per time slot (MW)
• NL_t: Net Load per time slot (MW)
• MG_t: Minimum generation constraint per time slot (MW)

3. Energy Storage Mix Optimization

3.1. Time Sequence Analysis (TSA) Method

The TSA method formalizes the optimization problem (cost minimization) for each time step, as shown in Figure 3 by updating and applying the input information at each time step to determine the optimal solution stepwise. The formulation of the optimization problem remains the same in this method; however, the inputs, such as peak load, renewable generation capacity, available storage technology candidates, and technological and cost characteristic information, are updated at each time step. Once the initial ESM (Storage Mix_initial) information is input, the optimal ESM (Storage Mix_#1) is determined through optimization, which influences the optimization problem for the next ESM (Storage Mix_#2) in the next time step. This process is repeated until the final time step, and the cost is calculated for each step.

The cost of each step is then calculated as the sum of the present values according to Equation (10).

$${\mathrm{COST}}_{\mathit{NPV}}={\sum }_{T=0}^n\frac{{\mathrm{COST}}_T}{{(1+r)}^T}$$

(10)

• COST_NPV: Net current value of the total cost over the entire period (hundred million KRW)
• COST_T: Cost per unit time (T) (hundred million KRW)
• r: Discount rate (%)

The TSA method is used for the following reasons.

➀

It efficiently resolves long-term equipment investment optimization problems. To resolve the entire long-term ESM optimization problem, the scale and complexity of the problem become enormous; thus, it is more efficient to divide the problem into set unit time slots and sequentially determine the optimal solution.

➁

It considers the commercialization timing of target storage technology options. Currently, Li-ion batteries are the only energy storage technology that has been commercialized. The remaining technologies are currently under development, and the timing of their commercialization may vary based on various factors, such as the speed of technological development and economic feasibility. Therefore, the TSA method is applied to treat the commercialization timing of the target energy storage technology as an exogenous variable, not as an optimization target.

➂

It considers changes in characteristics and costs of storage technologies for each step. In the long term, changes in characteristics and costs of storage technologies can occur owing to technological development and environmental changes. The TSA method is used to appropriately apply these changes for each step and to optimize the entire period.

3.2. Formulation of the Optimization Problem for Each Period

Because this optimization problem aims to derive an ESM that can utilize all surplus renewable energy, the benefits from using the surplus renewable energy are not included in the formulation.

The formulation for each time step’s optimization problem is similar, as shown in Equation (11). The objective function is defined as the total cost minimization (COST), which is the sum of three costs: investment cost for new equipment (IC), replacement cost for existing equipment (RC), and charging–discharging loss cost (LC).

$$\mathrm{Minimize} {\mathrm{COST}}_Y={\mathrm{IC}}_Y+{\mathrm{RC}}_Y+{\mathrm{LC}}_Y$$

(11)

• COST_Y: Total cost in year Y (hundred million KRW)
• IC_Y: Investment cost incurred to install new ESSs in year Y (hundred million KRW)
• RC_Y: Replacement and maintenance costs for the existing ESSs in year Y (hundred million KRW)
• LC_Y: Charging–discharging loss cost in year Y (hundred million KRW)

The detailed calculations for the cost items are as follows.

$${\mathit{IC}}_Y={\sum }_{I=1}^{N_{\mathit{storage}}}\left\{\left({\mathit{CAP}}_{I,\mathit{new}}^{\mathit{power}}\times P_I^{\mathit{power}}\right)+\left({\mathit{CAP}}_{I,\mathit{new}}^{\mathit{energy}}\times P_I^{\mathit{energy}}\right)\right\}$$

(12)

$${\mathit{RC}}_Y={\sum }_{I=1}^{N_{\mathit{storage}}}\left\{{\sum }_{Y=1}^{y-1}\left({\mathit{CAP}}_{I,Y}^{\mathit{power}}\times \frac{{\mathit{NC}}_{I,Y}}{{\mathit{LT}}_I^{\mathit{power}}}\times P_I^{\mathit{power}}\right)+{\sum }_{Y=1}^{y-1}\left({\mathit{CAP}}_{I,Y}^{\mathit{energy}}\times \frac{{\mathit{NC}}_{I,Y}}{{\mathit{LT}}_I^{\mathit{energy}}}\times P_I^{\mathit{energy}}\right)\right\}$$

(13)

$${\mathit{LC}}_Y={\sum }_{I=1}^{N_{\mathit{storage}}}\left\{{\mathit{CAP}}_I^{\mathit{power}}\times {\mathit{NC}}_I\times \left(1-\frac{{\mu }_I}{100}\right)\times P_Y^{\mathit{electricity}}\right\}$$

(14)

• IC_Y: Investment cost incurred to install new ESSs in year Y (hundred million KRW)
• RC_Y: Replacement and maintenance costs for the existing ESSs in year Y (hundred million KRW)
• LC_Y: Charging–discharging loss cost in year Y (hundred million KRW)
• CAP_I,new^power: New power (PCS) equipment capacity for the I-th technology in the analysis year (MW)
• P_I^power: Installation cost for new power (PCS) equipment for the I-th technology (hundred million KRW/MW)
• P_I^energy: Installation unit cost for new energy (cell) equipment for the I-th technology (hundred million KRW/MWh)
• CAP_I,Y^power: Power (PCS) equipment capacity for the I-th technology in year Y (MW)
• CAP_I,Y^energy: Energy (cell) equipment capacity for the I-th technology in year Y (MWh)
• NC_I,Y: Number of charging and discharging cycles for the I-th technology in year Y (Cycles)
• LT_I^power: Lifespan of power (PCS) equipment for the I-th technology (Cycles)
• LT_I^energy: Lifespan of energy (cell) equipment for the I-th technology (Cycles)
• μ_I: Charging and discharging loss rates for the I-th technology (%)
• P_Y^electricity: Price of electricity in year Y (KRW/kWh)

We considered the minimum energy storage equipment requirement and maximum possible new equipment capacity for each time step as inequality constraints. Moreover, the minimum energy storage equipment requirement constraint was considered separately for the power-conversion-system (PCS) and ESS capacities.

$${\sum }_{Y=0}^{y-1}{\sum }_{I=1}^{N_{\mathit{storage}}}{\mathit{CAP}}_{I,Y}^{\mathit{power}}+{\sum }_{I=1}^{N_{\mathit{storage}}}{\mathit{CAP}}_{I,\mathit{new}}^{\mathit{power}}\ge {\mathit{CAP}}_y^{{\mathit{power}}_{\mathit{req}}}$$

(15)

$${\sum }_{Y=0}^{y-1}{\sum }_{I=1}^{N_{\mathit{storage}}}{\mathit{CAP}}_{I,Y}^{\mathit{energy}}+{\sum }_{I=1}^{N_{\mathit{storage}}}{\mathit{CAP}}_{I,\mathit{new}}^{\mathit{energy}}\ge {\mathit{CAP}}_y^{{\mathit{energy}}_{\mathit{req}}}$$

(16)

• CAP_I,Y^power: Power (PCS) equipment capacity for the I-th technology in year Y (MW)
• CAP_I,new^power: New power (PCS) equipment capacity for the I-th technology in the analysis year (MW)
• CAP_I,Y^energy: Energy (cell) equipment capacity for the I-th technology in year Y (MWh)
• CAP_I,new^energy: New power (PCS) equipment capacity for the I-th technology in the analysis year (MW)
• CAP_Y^power_req: Required power (PCS) equipment capacity in the analysis year (MW)
• CAP_Y^energy_req: Required energy (cell) equipment capacity in the analysis year (MWh)

The capacity of the PCS is referred to as the power capacity and that of the ESS is referred to as the energy capacity in this study.

Furthermore, we considered the power and energy capacities that can be newly constructed at each time step, as shown in the following equations. This is because the physical capacity of the equipment that can be constructed is limited, and this constraint can be input considering the construction conditions.

$${\sum }_{I=1}^{N_{\mathit{storage}}}{\mathit{CAP}}_{I,\mathit{new}}^{\mathit{power}} \le {\mathit{CAP}}_{I,y}^{{\mathit{power}}_{\mathit{max}}}$$

(17)

$${\sum }_{I=1}^{N_{\mathit{storage}}}{\mathit{CAP}}_{I,\mathit{new}}^{\mathit{energy}} \le {\mathit{CAP}}_{I,y}^{{\mathit{energy}}_{\mathit{max}}}$$

(18)

• CAP_I,new^power: New power (PCS) equipment capacity for the I-th technology in the analysis year (MW)
• CAP_I,new^energy: New power (PCS) equipment capacity for the I-th technology in the analysis year (MW)
• CAP_I,y^power_max: Maximum installation capacity of new power (PCS) equipment for the I-th technology (MW)
• CAP_I,y^energy_max: Maximum installation capacity of new energy (cell) equipment for the I-th technology (MWh)

4. Case Study

4.1. Estimation of Surplus Renewable Energy

4.1.1. Preconditions and Input Data

We analyzed the medium- and long-term ESM in South Korea using our proposed time-step optimization method, considering Plan A of the 2050 Carbon-Neutrality Scenario. The preconditions for the case study are as follows.

(1)

Comparative analysis scenarios:

S1: ESM analysis via TSA for 2025, 2030, 2035, 2040, 2045, and 2050

S2: ESM analysis via simple optimization for 2050

(2)

Electricity demand: The pattern of the gross electricity demand by time slot was normalized using the power demand pattern of 2018 when the proportion of renewable generation was less than 2%. The peak demand as shown in

Table 1. Annual electricity peak demand forecast of Korean power system.

Year	2025	2030	2035	2040	2045	2050
Peak Demand (GW)	102.5	109.3	116.2	147.8	168.9	211.0

for each year was obtained from the forecasts in South Korea’s 10th Basic Plan for Long-Term Electricity Supply and Demand and the 2050 Carbon-Neutrality Scenario [1,2,3].

(3)

Renewable generation: Solar and wind power were considered for renewable generation. The generation pattern by time slot was created using the actual generation output data from 2021. We created generation output patterns by time slot for each month to consider the characteristics of the renewable generation output by season. The capacity of the renewable energy generation equipment as shown in

Table 2. Annual renewable generation capacity forecast of Korean power system.

Year	2025	2030	2035	2040	2045	2050
Renewable Generation Capacity (GW)	34.7	65.8	94.6	261.5	372.7	595.3

was obtained from South Korea’s 10th Basic Plan for Long-Term Electricity Supply and Demand and the 2050 Carbon-Neutrality Scenario [1,2,3].

(4)

Critical inertia requirement: Although studies on the characteristics of the South Korean power system are yet to be conducted for critical inertia, we used the critical inertia level of 320 GW, as suggested in the 10th Basic Plan for Long-Term Electricity Supply and Demand, considering the frequency stability. The critical inertia suitable for the South Korean power system must be determined in future studies.

(5)

Minimum reserve power requirement: The minimum reserve power requirement can vary depending on changes in the proportion of renewable energy in the future; however, we used 1.7 GW, which is the sum of the frequency control and primary reserve power, as the minimum reserve power requirement based on the current reserve power standard. The Power Pool Rule (Grid Code) of the Korean power system divides the operational reserve power into four categories. The minimum requirement for securing the total reserve power is 4.5 GW (including 700 MW for frequency control, 1000 MW for primary reserve, 1400 MW for secondary reserve, and 1400 MW for alternative reserve). Among them, the minimum reserve power requirement was considered as 1.7 GW, which is the sum of the frequency control and primary reserve and is a spinning reserve [18].

(6)

Other matters: For calculating surplus energy, 1.0 GW was used as the equipment capacity of a standard thermal power generator, and the inertia constant was set to 5 s. In addition, the minimum stable output level of the generator was considered as 80% (nuclear power plant), 70% (coal-fired power plant), and 40% (gas-turbine power plant) of the rated capacity.

4.1.2. Calculation of Net Load

Using the method presented in Section 2.2, we calculated the Net Load by time slot in five-year intervals from 2025 to 2050; the results are shown in

Table 3. Statistics for analysis results of the Gross and Net Loads.

Year	Gross Load (MW)			Net Load (MW)
	Max	Min	Average	Max	Min	Average
2025	102,484	45,301	71,457	96,986	29,880	65,889
2030	109,300	48,314	76,210	101,467	20,521	64,507
2035	116,158	51,345	80,992	106,416	10,728	63,792
2040	147,772	65,320	103,035	132,125	−66,295	70,155
2045	168,848	74,636	117,730	149,939	−120,144	81,998
2050	211,000	93,268	147,121	186,193	−227,842	104,369

.

The negative Net Load is calculated from 2040, which means that the amount of renewable energy generated increases compared to the power demand at some times. The hourly Net Load patterns for April 2030 and April 2050 are shown in Figure 4 and Figure 5, respectively. By comparing these two graphs, a substantial decrease in Net Load was observed during the daytime in 2050 owing to an increase in solar energy generation.

The graph in Figure 4 shows that the Net Load is lowered to less than 50,000 MW (green) during the daytime and is more than 50,000 MW (blue) after sunset and before sunrise. However, the graph in Figure 5 shows that the Net Load is lowered to a negative value during the day and is approximately 100,000 to 50,000 MW after sunset and before sunrise, respectively.

4.1.3. Minimum Generation Output Constraint

Using the method presented in Section 2.3, we calculated the minimum generation output constraint by time slot in five-year intervals from 2025 to 2050; the results are shown in

Table 4. Analysis results of minimum generation output constraint.

Year	Minimum Generation Output Constraint (MW)
	Max	Min	Average
2025	59,018	38,542	42,182
2030	59,406	36,913	40,275
2035	61,676	36,548	40,120
2040	71,701	34,245	41,766
2045	76,739	32,525	42,688
2050	83,816	28,533	42,832

.

The minimum generation output constraint patterns by time slot for April 2030 and April 2050 are shown in Figure 6 and Figure 7, respectively. By comparing these two graphs, a substantial decrease in the minimum generation output constraint was observed during the daytime in 2050 owing to a decrease in Net Load.

4.1.4. Estimation of Surplus Renewable Energy

Using the method presented in Section 4.1, we calculated the surplus energy for each time slot in five-year intervals from 2025 to 2050; the results of the total surplus energy for each year are shown in Figure 8.

We used heat maps to analyze the characteristics of the surplus renewable energy by time slot throughout the year. The heat maps for the magnitude of the surplus renewable energy generated from 2030 to 2050 are shown in Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13. The heat map chart was created using a visualization tool (R program, ggpolt) to intuitively observe the results of the renewable energy surplus power calculation model.

The X-axis of the heat maps represents days and months, whereas the Y-axis represents time. The surplus energy generated by the time slot is distinguished by the color of each cell, which is categorized as per the legend at the top of the heat map. The characteristics of the surplus renewable energy generation are summarized as follows.

➀

It begins after 2030 and sharply increases from 2040.

➁

Before 2035, it occurs only on holidays, when power demand is low; however, after 2040, it also occurs on weekdays.

➂

Surplus renewable energy has a high concentration during daytime hours in spring and autumn, when solar generation increases, and power demand is low.

4.1.5. Energy Storage Capacity Requirement

We used the calculation results of the surplus energy by time slot to determine the energy storage capacity requirement. Here, we did not define specific energy storage technologies but only calculated the required capacity to utilize all the surplus energy based on the amount and patterns (number of cycles and duration) of the surplus energy. The calculated capacity requirements for energy storage equipment are distinguished by power (GW) and energy (GWh) annually and are shown in Figure 14. According to these analysis results, because the energy storage capacity requirement increases by 100 GWh per year after 2035, 69 GWh after 2040, and 139 GWh after 2045, systematic and efficient investment plans should be established for equipment through optimal ESM analysis.

4.2. Types and Characteristics of Energy Storage Technologies

This study aims to validate the efficacy of the proposed methodology. Owing to the lack of definitive technical characteristic information for various energy storage technologies, we did not classify the technologies in detail. Instead, we divided them into short-term, medium-term, and long-term storage technologies for ESM analysis.

Owing to the absence of a formal distinction between short term, medium term, and long term in Korea, we divided them into four categories and assumed the characteristics of each technology, as listed in

Table 5. Classification of the technical characteristics of energy storage systems.

	Short Term	Medium Term	Long Term
Rated output discharging duration (h)	3	5	8
Unit capacity (PCS/CELL)	100 MW/300 MWh	300 MW/1500 MWh	500 MW/4000 MWh
Designed lifespan (PCS/CELL)	1000/400 Cycles	1000/2000 Cycles	1000/5000 Cycles
Charging and discharging efficiency (%)	90	50	40
Year of Commercialization	Already commercialized	2030	2035

[19,20,21,22,23], which provides the input data of the optimization problem for composing the optimal Energy Storage Mix.

Our proposed methodology can consider more technological alternatives. This is contingent upon the availability of information.

We considered the commercialization timing of each storage technology as follows: short term (already commercialized), medium term (by 2030), and long term (by 2035).

We assumed the initial equipment investment and replacement costs for each technological alternative, as listed in

Table 6. Investment * and replacement costs of the energy storage system.

	2025	2030	2035	2040	2045	2050
Short term (PCS/CELL)	1.00/4.00	0.99/3.92	0.98/3.84	0.97/3.76	0.96/3.69	0.95/3.62
Medium term (PCS/CELL)	-	0.99/3.00	0.98/2.85	0.97/2.71	0.96/2.57	0.95/2.44
Long term (PCS/CELL)	-	-	0.98/2.00	0.97/1.84	0.96/1.69	0.95/1.56

* Units: PCS—100 million KRW/MW; CELL—100 million KRW/MWh.

. For PCS, we assumed the same investment cost for all the technologies. For CELL, we used recent battery energy storage system (BESS) equipment investment records for the short term and assumed lower investment costs for the medium term and long term compared to the short term. Information on investment costs for each storage technology varies by country and region; thus, a suitable environmental cost evaluation is required.

To predict the change in the unit price of investments in storage devices in the long term, the effect of the learning curve was considered in this study. The learning curve is a concept that quantifies the effect of lowering the price as the demand for the product increases. In the case of CELL, the annual price drop was assumed as 0.4% in the short term, 1.0% in the medium term, and 1.6% in the long term. For PCS, we assumed the same annual unit-price drop of 0.2% for all the technologies. However, this assumption is very subjective, and research on more reasonable assumptions is needed. Table 6 shows the results of CELL and PCS price forecasts, considering this assumption of an annual price decline. These price forecast values were used as input data for optimization problems.

Although additional information other than the aforementioned storage technology alternatives can be considered, we only consider the essential technical and cost characteristics for our analysis.

4.3. Energy Storage Mix Optimization (2023–2050)

4.3.1. ESM Analysis Results Based on TSA

The TSA results enable us to establish annual ESM plans that satisfy the yearly storage device (power and energy) capacity requirements, shown in Figure 14, while minimizing costs. These results are shown in Figure 15, Figure 16, Figure 17 and Figure 18.

First, the annual PCS equipment capacity was analyzed, as shown in Figure 15. Until 2035, the calculated capacity is considerably large compared to the storage capacity requirement. This is because we calculated the capacity of the PCS according to the unit capacity after determining the capacity of the cell.

The percentages of storage technologies (power and PCS) by year are shown in Figure 16 and

Table 7. Percentages of storage technologies (power and PCS) by year.

	2025	2030	2035	2040	2045	2050
Short term (GW)	14.9 (100%)	14.9 (69.2%)	14.9 (52.1%)	14.9 (14.9%)	20.3 (13.3%)	30.2 (11.8%)
Medium term (GW)	-	6.6 (30.8%)	6.6 (23.1%)	31.3 (31.2%)	46.7 (30.6%)	75.6 (29.5%)
Long term (GW)	-	-	7.1 (24.8%)	54.2 (54.0%)	85.7 (56.1%)	150.6 (58.7%)
Total (GW)	14.9	21.6	28.7	100.5	152.7	256.4

. Only short-term technologies exist in 2025; thus, this period entirely consists of short-term technology. Medium- and long-term technologies were applied as candidates by 2030 and 2035, respectively, and we analyzed the optimal equipment composition. Based on the results, the composition was 52.1% (short term), 23.1% (medium term), and 24.8% (long term) in 2035. The proportion of long-term technologies gradually increased, and by 2050, the composition was 11.8% (short term), 29.5% (medium term), and 58.7% (long term).

The annual cell equipment capacity was analyzed, as shown in Figure 17. These results are in good agreement with the storage device capacity requirement calculations in Figure 14. This is because we calculated the cell equipment capacity based on the storage device (energy) capacity requirements according to the calculation results of the surplus renewable energy.

The percentages of storage technologies (energy and cell) are shown in Figure 18 and

Table 8. Percentages of storage technologies (energy and cell) by year.

	2025	2030	2035	2040	2045	2050
Short term (GWh)	42.8 (100%)	42.8 (56.3%)	42.8 (32.2%)	42.8 (6.8%)	59.0 (6.0%)	88.7 (5.3%)
Medium term (GWh)	-	33.2 (43.7%)	33.2 (25.0%)	156.7 (24.7%)	233.5 (23.9%)	378.0 (22.6%)
Long term (GWh)	-	-	56.9 (42.8%)	433.8 (68.5%)	685.5 (70.1%)	1204.5 (72.1%)
Total (GWh)	42.8	76.0	132.9	633.3	977.9	1671.2

. Only short-term technologies exist in 2025; thus, this period entirely consists of short-term technologies. Medium- and long-term technologies were applied as candidates by 2030 and 2035, respectively, and we analyzed the optimal equipment composition. Based on the results, the composition was 32.2% (short term), 25.0% (medium term), and 42.8% (long term) in 2035. The proportion of long-term technologies gradually increased; the composition was 5.3% (short term), 22.6% (medium term), and 72.1% (long term) by 2050.

The yearly and cumulative costs for the aforementioned ESM are shown in Figure 19. The proportions of the three components of the annual costs (IC, RC, and LC) are shown in Figure 20. As shown in Figure 8, surplus renewable energy was predicted to increase significantly after 2040. Consequently, the energy storage equipment capacity requirement is also predicted to increase considerably, as shown in Figure 15. Therefore, the proportion of new investment costs (IC) increases from 2040.

When using only short-term storage technologies, the total cumulative cost was 3862 trillion KRW. This was enormous, exceeding 630% of the total cumulative cost of 613 trillion KRW when investing in the optimal ESM proposed in this study. Therefore, when substantial surplus renewable energy is expected, ensuring a reasonable level of cost through the optimal ESM is crucial. The difference between the total cumulative costs when ESSs consist of a combination of short-, medium-, and long-term technologies and when only short-term storage technologies are considered is shown in Figure 21.

4.3.2. ESM Analysis Results and Comparison Based on Single-Year (2050) Optimization

The proposed TSA method can consider the expected utilization of surplus renewable energy throughout the entire period from 2025 to 2050 and the commercialization timing of storage technologies that are yet to be commercialized. We compared the results of the TSA method with those of a method that only considers a specific point in time (single-year analysis). The calculation results of the cumulative PCS equipment capacity from 2025 to 2050 obtained using the TSA method and the PCS equipment capacity composition in 2050 obtained using the single-year analysis method are shown in

Table 9. Comparison of the PCS capacities for the two analysis methods.

	Time Sequence Analysis Result	Snapshot Analysis Result
Short term (GW)	30.2	76.0
Medium term (GW)	75.6	0.0
Long term (GW)	150.6	180.4
Total (GW)	256.4	256.4

and Figure 22.

The calculation results of the cumulative cell equipment capacity from 2025 to 2050 obtained using the TSA method and the cell equipment capacity composition in 2050 obtained using the single-year analysis method are shown in

Table 10. Comparison of the cell capacities for the two analysis methods.

	Time Sequence Analysis Result	Snapshot Analysis Result
Short term (GWh)	88.7	228.0
Medium term (GWh)	378.0	0
Long term (GWh)	1204.5	1443.2
Total (GWh)	1671.2	1671.2

and Figure 23.

Based on the aforementioned comparison results, the TSA method obtained ESM results composed of short-, medium-, and long-term storage equipment because it applied different commercialization times for medium- and long-term storage technologies and considered the annual characteristics of surplus renewable energy. However, the single-year analysis method, which applies to the final analysis target year, obtained ESM results comprising mostly long-term storage technologies with low new investment costs (IC) and short-term storage technologies with small unit capacities.

In other words, the reason the capacity of the medium-term storage facility is “0” in the single-year analysis result is that the investment cost of the long-term storage-facility cell is lower, and the lifespan is longer, as shown in Table 5 and Table 6, respectively. In the case of short-term storage facilities, the investment cost of cells is high, and the lifespan is short; however, the unit capacity is small, and the charging/discharging efficiency is very high compared to the other two technologies. Therefore, approximately 14% of the total capacity is installed.

The ESM comprising the single-year analysis method may be suitable for the surplus energy of the target year; however, it is not suitable for long-term planning because it does not consider the surplus energy generated before the target year and cannot consider situations such as equipment investment and replacement during that period. Further, it is limited because it cannot consider factors such as the commercialization timing or construction period for each type of ESS. These limitations can be overcome using the TSA method, which can assist in establishing more long-term equipment plans.

5. Conclusions

A key method for achieving carbon neutrality in the energy sector is to transition from carbon-emitting to carbon-free and low-carbon generation. Renewable energy expansion is an example of this transition. However, renewable energy expansion must correspond to the hosting capacity of the grid. When renewable energy generation exceeds the grid’s hosting capacity, the result is surplus renewable energy, leading to renewable energy curtailment. Plans to utilize energy storage technologies to efficiently manage this surplus renewable energy without curtailment are underway.

ESSs require substantial investment; therefore, a large energy surplus can be uneconomical, and the required technical characteristics for efficient energy storage vary with the generation characteristics of the surplus energy. Consequently, ESM analysis must determine the optimal energy storage equipment composition in the long term. Previous studies have applied the single-year analysis method, which analyzes the ESM for a single target year.

However, this is not suitable for long-term plans as it considers neither surplus energy generated before the target year nor situations such as equipment investment, replacement, and charging–discharging losses during that period. Moreover, because only short-term ESS, such as BESS, have been commercialized to date, they are not suitable for optimal ESM analysis that considers the commercialization timing of future technologies and the surplus energy generation situation.

We propose the TSA method, which considers the surplus renewable energy generation situation before the target year and reflects the commercialization timing and technical characteristics of various ESS.

Using data from the 9th Basic Plan for Long-Term Electricity Supply and Demand as well as the 2050 Carbon-Neutrality Scenario, we projected the surplus renewable energy from 2025 to 2050 and analyzed the optimal ESM at five-year intervals using the TSA method. We compared the investment costs of utilizing surplus energy with the currently commercialized short-term BESS, as well as the results of the TSA and existing methods that only considered a specific point in time (single-year analysis).

In Section 4.3.2, the ESM optimization results of the proposed TSA method and the single-year analysis method are compared.

Since the TSA method minimizes costs for the entire period and the single-year analysis method only minimizes costs for 2050, the costs of the two methods cannot be directly compared. Simply comparing the installation investment cost according to the composition of ESM in 2050 shows that the investment cost of the TSA method is a total of KRW 360,656 billion, and the investment cost of the single-year analysis method is KRW 331,582 billion.

As shown in Table 9 and Table 10 and Figure 22 and Figure 23, the ESM optimization in 2050 obtained using the single-year analysis method resulted in the ESM configuration (long-term (86%) and short-term (14%) cell capacities) for short-term and long-term storage facilities. However, this result does not take into account the effects of short- and medium-term energy storage devices installed before 2035, that is, before long-term energy storage devices became commercially available. However, in the case of the TSA method, as shown in Figure 17 and Figure 19, ESM can be optimized step by step by considering the timing of the commercialization of energy storage devices, and the results of the ESM optimization in 2050 were derived from long-term (72.1%) and short-term (5%) cell capacities.

The proposed TSA-based ESM composition method could comprehensively consider the surplus renewable energy situation according to future increases in renewable energy and the commercialization timing of ESS. This advantage is crucial for establishing long-term equipment plans and can provide useful information for the establishment of medium- and long-term ESS development strategies.

The results for predicting the long-term renewable energy surplus power and analyzing the annual optimal ESM obtained using the proposed TSA methodology were different from the results obtained using the single-year analysis of the final-year ESM, as described above. In this paper, we do not argue that one of these two ESMs is correct. However, we argue that important considerations for analyzing long-term ESM are the timing of the storage technology commercialization and the impact on ESM in the previous analysis year.

Further studies on optimal ESM composition methods by considering the transmission network topology and including ESM in the long-term transmission-network facility expansion plan will be conducted in the future. The results of these studies are expected to be used to not only establish a long-term transmission network expansion plan but also determine the optimal commercialization target time of medium-term and long-term energy storage technologies.