Incentive Determination for Demand Response Considering Internal Rate of Return

Abstract

The rapid expansion of renewable energy sources has led to increased instability in the power grid of Jeju Island, leading to the implementation of the plus demand response (DR) system, which aims to boost electricity consumption during curtailment periods. However, the frequency of curtailment owing to the increased utilization of renewable energy is outpacing the implementation of plus DR, highlighting the need for additional resources, such as energy storage systems (ESS). High initial investment costs have been the primary hindrance to the adoption of ESS by DR-participating companies but have not been fully considered in earlier studies on DR incentive determination. Therefore, this study proposes an algorithm for calculating appropriate incentives for plus DR participation considering the investment costs required for ESS. Based on actual load data, incentives are determined using an iterative mixed-integer programming (MIP) optimization method that progressively adjusts the incentive level to address the overall nonlinearity arising from both the multiplication of variables and the nonlinear characteristics of the internal rate of return (IRR), ensuring that the target IRR is achieved. A case study on the impact of factors such as IRR, ESS costs, and fluctuations in electricity rates on incentive calculations demonstrated that plus DR incentives required to achieve IRR targets of 5%, 10%, and 15% have increased linearly from 142.2 KRW/kWh to 363.0 KRW/kWh, confirming that the appropriate incentive level can be effectively determined based on ESS investment costs and target IRR. This result could help promote ESS adoption among DR companies and plus DR participation, thereby enhancing power grid stability.

1. Introduction

Globally, the utilization of wind and solar power is rapidly growing in response to the urgent need to combat climate change [1]. Jeju Island in South Korea serves as a prime example of this escalating trend. The Island has committed to achieving 100% of its electricity demand through renewable energy sources (RES) by 2030 under its “Carbon-Free Island 2030” (CFI 2030) initiative [2], and as of 2023, it has already reached a significant milestone, with RES generation facilities accounting for 71.6% of its total generation capacity [3]. This rapid expansion of its RES capacity is driven by favorable climatic conditions, a robust high-voltage direct current (HVDC) link to mainland South Korea for supply variability management, and strong policy support under the CFI 2030 initiative. However, the high proportion of RES generation has led to instability in the power system, inevitably resulting in forced output control [4]. System operators in the country are authorized to curtail renewable energy output to maintain grid stability, particularly on Jeju Island, where limitations are imposed by its semi-isolated grid structure. In 2023, Jeju Island experienced 181 instances of RES curtailment over 120 days [3], a trend that is expected to persist as the proportion of RES continues to increase [4].

To address RES curtailment, the Island implemented the plus demand response (DR) system in March 2021 [5]. Unlike conventional demand reduction DR systems, plus DR encourages participants to increase their electricity consumption voluntarily during periods of output control by providing incentives to consumers based on the amount of additional electricity that they use [6]. This system aims to enhance the integration of RES into the power grid by effectively utilizing surplus renewable energy. In 2021, when plus DR was introduced, a plus DR performance of approximately 20 MWh was observed; in the first half of 2023, that value increased to 430 MWh [7]. However, owing to the high rate of increase in RES and the resulting amount of curtailment, the effect of increased electricity consumption should be further enhanced. This challenge is not unique to Jeju Island but is also prevalent in mainland power systems, underscoring the importance of refining the plus DR system to address this issue effectively.

DR is a crucial measure for enhancing the flexibility and stability of a power system by adjusting consumers’ electricity consumption patterns to balance supply and demand [8,9]. This also contributes to reducing the investment costs for transmission and distribution lines [10]. To further enhance the benefits of DR, the use of energy storage systems (ESS) as a valuable resource has been explored in various research studies [11]. ESS can change the timing of energy consumption by storing surplus energy and discharging it when necessary [11], thereby mitigating supply–demand mismatches caused by the variability and uncertainty of RES through rapid charging and discharging [12,13]. A study by Yang et al. [14] proposed a spatial–temporal pricing strategy based on EV group price response to maximize operator revenue and enhance DR. Zou et al. [15] proposed a peer-to-peer energy trading framework utilizing adaptive robust stochastic optimization to address energy uncertainties, highlighting its potential to enhance network flexibility within DR strategies. Z. Wang et al. [16] proposed a DR operation strategy in which a residential ESS is shared between consumers and distribution system operators (DSO) in response to energy price fluctuations and distribution network congestion. This approach resulted in electricity bill reductions for consumers and economic benefits for DSOs by reducing peak demand and delaying distribution network investment costs. Bitaraf and Rahman [17] presented a method for minimizing the output curtailment of wind turbines by utilizing an ESS as a DR resource. However, despite the numerous advantages of using ESS as a DR resource, high initial investment costs remain a significant obstacle to private adoption [18]. Therefore, to facilitate the integration of ESS into the power system, a direct compensation scheme that reduces economic burdens and maximizes the effects of DR is essential [19].

DR can be broadly categorized into price-based DR (PBDR) and incentive-based DR (IBDR) [20]. PBDR can adjust the load by motivating consumers to shift their electricity consumption from peak to off-peak hours through systems such as time-of-use (TOU) pricing [21]. However, while this approach can reduce market energy costs and mitigate supply-side risks [22], it may lead to new peak loads as consumption patterns change [23]. Consequently, relying solely on PBDR may not fully ensure benefits for both suppliers and customers, thus requiring complementary measures to be considered [23]. On the other hand, IBDR involves participants voluntarily adjusting their loads and receiving direct economic incentives from utilities as compensation [21]. This method enables utilities to effectively manage loads during specific periods and encourages active consumer engagement in DR through incentives [24]. By incentivizing customer participation with direct compensation, IBDR can optimize benefits for both suppliers and customers, addressing operational challenges in the power grid [25]. Therefore, IBDR can be effectively deployed in various scenarios; however, it would require specific design and operational strategies to enhance its efficacy [26].

To enhance the effectiveness of IBDR, an appropriate incentive level should be established [27]. Several studies have been conducted on this topic [28,29,30]. A study by Farahani et al. [28] analyzed the effects of DR based on different incentive levels and observed that the effectiveness of DR increases as the incentive level increases. Lu and Hong [29] proposed an IBDR program within a smart grid that utilizes reinforcement learning and deep neural networks to calculate incentives based on real-time electricity demand predictions to determine the optimal incentives that DR service providers should offer to customers. Y. Wang et al. [30] proposed a point-based IBDR mechanism that assigns points based on residents’ electricity consumption patterns, which can be accumulated and exchanged for electricity bill discounts or various products. Their study was designed to optimize incentives by considering consumer reward utilization behavior and maximizing the revenue and power stability of the load aggregator. However, these studies focused primarily on general loads, and not on ESS, as DR resources, potentially limiting the effects of DR.

Owing to the high initial investment costs of ESS, appropriate compensation policies are necessary to motivate their adoption [19]. Companies looking to invest in ESS should utilize economic analysis methods, such as net present value (NPV), to assess the profitability of their investments [31]. This not only helps companies gauge the return on investment from ESS adoption but also aids governments in determining suitable compensation levels. Silvestri and De Santis [32] proposed a load-shifting-based DR program aiming to reduce peak power, reduce costs, and decrease carbon emissions by utilizing solar power and ESS for corporate environmental, social, and governance (ESG) management. Their study involved calculating incentives based on load shifting and DR program participation rates and conducting economic evaluations using the NPV and internal rate of return (IRR). However, their study failed to account for ESS investment costs when calculating incentives, incorporating these costs only during economic evaluations. On the other hand, Astriani et al. [33] considered ESS costs using the NPV to calculate incentives. Their study proposed a method in which a microgrid operator with an ESS provides incentives to DR-participating customers. Incentives were calculated by allocating a percentage of the microgrid owner’s profits toward DR incentives while also considering the wear-and-tear costs of ESS and the NPV of the microgrid owner’s profits. However, similar to the previous study, this approach did not fully consider the initial investment costs of ESS. Instead, both studies relied on load data from specific short periods, failing to capture annual variations in electricity consumption. Consequently, limitations in long-term economic evaluations and practical profitability analyses were observed.

To address these shortcomings, this study introduces an algorithm for determining appropriate incentive levels for plus DR participation, considering the investment costs of the ESS’s power conversion system (PCS) and battery. Through the use of actual load data over a year to reflect annual load variability, realistic DR incentives can be calculated. Through economic evaluations using the NPV and IRR, we identified suitable incentive levels that enable private companies with ESS installation to ensure economic feasibility. This study presents a novel approach to addressing the challenges posed by nonlinearity in incentive estimation using the IRR. By employing iterative mixed-integer programming (MIP) optimization, which focuses on minimizing the electricity costs for DR participants, we linearize the problem. The process starts with setting an initial incentive level, and the incentive is iteratively adjusted based on the resulting IRR from cash flows until the target IRR is achieved, thus effectively determining the required incentive level. Additionally, by incorporating the potential future reduction in ESS costs when calculating incentive levels, companies can strategically assess the optimal timing for investments by anticipating potential cost-saving benefits. Furthermore, incentives are determined by analyzing fluctuations in electricity rates, which are known to affect profitability, enabling companies to assess the profitability of their DR participation based on various factors. The proposed DR incentive model, which calculates incentives per kWh, can be effectively applied to regions implementing comparable DR programs. This algorithm enables the government to establish suitable incentive levels, whereas companies can clearly evaluate the anticipated economic advantages of implementing ESS. This study found that plus DR incentives needed to achieve IRR targets of 5%, 10%, and 15% ranged from 142.2 KRW/kWh to 363.0 KRW/kWh, demonstrating a linear increase with higher IRR targets, with a total load increase of 27 MWh, reducing curtailment.

The remainder of this paper is organized as follows. Section 2 outlines the optimization model and the methodology for calculating incentives. Section 3 presents a demonstration of the proposed model using a case study via a simulation. Finally, Section 4 concludes the paper.

2. Problem Formulation

2.1. DR Strategy

In the domestic electricity market, RES producers generate revenue by selling generated energy. However, if the operator anticipates or observes an imbalance in power supply and demand owing to surplus RES generation, they may implement output control on the RES or execute plus DR for DR participants. A strategy for DR execution is illustrated in Figure 1. Utilities provide an incentive, $X_{Pdr}$, to plus DR participants based on the increase in electricity consumption during the DR execution period. In this framework, the market operator determines the $X_{Pdr}$ that the utility will give to DR participants with ESS. The DR participant pays the utility a cost $C^{grid}$ for electricity consumption, excluding the customer baseline load (CBL). If the DR participant receives a DR signal from the market operator and engages in DR, the utility pays $X_{Pdr}$ to the DR participant. This increase is calculated using the hourly CBL; the plus DR execution period typically occurs during daytime hours when output control is most frequent. Charging the ESS during this period helps balance power system supply and demand, thereby mitigating RES curtailment. The incentive for plus DR is determined as the amount granted per kWh of increased electricity consumption. Consequently, these incentives are designed to empower DR participants to contribute to maintaining power system stability and minimizing the loss of RES generation.

2.2. Modeling Objective Function

This study aims to determine the incentive for a company investing in ESS to achieve a reasonable rate of return through participating in plus DR. Accordingly, we assess the economic feasibility through optimal ESS scheduling when a company participates in plus DR. The objective function is as follows:

$$\min \left\{\sum _{d=1}^D\sum _{t=1}^T\left(P_{d,t}^{grid}\ast C_{d,t}^{TOU}\right)+\sum _{m=1}^M\left(P_{peak}^{grid} \ast C_{base}^{TOU}\right)-\sum _{d=1}^D\sum _{t=1}^T\left(P_{d,t}^{grid}-P_{d,t}^{CBL}\right)\ast X_{Pdr}\ast U_{d,t}^{Pdr}\right\}$$

(1)

The total annual cost for the electricity user, calculated as shown in Equation (1), is defined as the company’s electricity charges minus the incentives from DR participation. Herein, $P_{d,t}^{grid}$ denotes the amount of electricity consumed by the company participating in DR from the utility, paid through the TOU tariff $C_{d,t}^{TOU}$. Additionally, the company incurs a cost based on its maximum power (kW), with the corresponding basic charge paid as $P_{peak}^{grid} \ast C_{base}^{TOU}$.

The incentive obtained from increased electricity consumption is expressed as $\left(P_{d,t}^{grid}-P_{d,t}^{CBL}\right)\ast X_{Pdr}\ast U_{d,t}^{Pdr}$, where $P_{d,t}^{CBL}$ denotes the hourly CBL of the company and $X_{Pdr}$ represents the incentive per kWh for the load increase. As shown in Equation (1), treating $X_{Pdr}$ as a decision variable introduces nonlinearity due to the multiplication between variables. Additionally, determining $X_{Pdr}$ requires both the NPV and IRR to be considered. This direct incorporation of financial metrics into the objective function and constraints also creates nonlinearity, complicating the optimization process. To address this challenge, we employ an iterative MIP optimization where $X_{Pdr}$ is adjusted based on the IRR calculated from the optimization results. The detailed methodology and solution process are discussed in Section 2.5. Meanwhile, $U_{d,t}^{Pdr}$ denotes a binary set representing the periods of load increase; it assumes a value of one and zero during DR and non-DR periods, respectively. Depending on this value, a load increase occurs during the specified periods, and incentives are awarded, whereas during the remaining periods, a strategy is implemented to minimize the company’s electricity charges.

2.3. Modeling DR Customers

Constraints have been established for the power flow of a company participating in DR programs and the operation of ESS. The constraints related to the power utilization of the company are defined in Equations (2)–(4), whereas the constraints regarding the ESS operation are outlined in Equations (5)–(10).

$$P_{d,t}^{grid}=P_{d,t}^{Load}+P_{d,t}^{char}-P_{d,t}^{dis}$$

(2)

$$P_{peak}^{grid}\ge P_{d,t}^{CBL}\ast U_{d,t}^{Pdr}+P_{d,t}^{grid}\ast (1-U_{d,t}^{Pdr})$$

(3)

$${S^{max}\ast S_{rate}^{min}\le S}_{d,t}\le S^{max}\ast S_{rate}^{max}$$

(4)

$$S_{d,t}=S_{d,t-1}+P_{d,t}^{char}\ast \eta -P_{d,t}^{dis}/\eta$$

(5)

$$S_{d,1}=S_{d,24}=S^{max}\ast S_{rate}^{init}$$

(6)

$$0\le P_{d,t}^{char}\le P_{PCS}^{max}\ast u_{d,t}^{char}$$

(7)

$$0\le P_{d,t}^{dis}\le P_{PCS}^{max}\ast u_{d,t}^{dis}$$

(8)

$$u_{d,t}^{char}+u_{d,t}^{dis}\le 1$$

(9)

$$u_{d,t}^{dis}\le 1-U_{d,t}^{Pdr}$$

(10)

The power balance condition is presented in Equation (2), indicating that a company’s daily TOU demand equals its supply. The right-hand side is expressed as the sum of the company’s existing load $P_{d,t}^{Load}$ and the ESS charging power $P_{d,t}^{char}$ minus the ESS discharging power $P_{d,t}^{dis}$, resulting in the power drawn from the utility, which is represented as $P_{d,t}^{grid}$. To calculate the basic charge, the peak value of power purchases must be determined. However, a company’s peak demand may increase as the load increases. In this case, the increased load is accounted for based on the CBL, not on the company’s actual power consumption, when determining the peak. This is defined in Equation (3). During DR execution, when $U_{d,t}^{Pdr}=1$, $P_{d,t}^{grid}$ is deactivated, and the peak is calculated based on $P_{d,t}^{CBL}$. In the remaining periods, when $U_{d,t}^{Pdr}=0$, $P_{d,t}^{CBL}$ is deactivated, and the peak is calculated based on the company’s power consumption, $P_{d,t}^{grid}$. Through this method, the company’s peak demand throughout the year is determined.

The state of charge (SoC) of an ESS is represented as $S_{d,t}$. The range of $S_{d,t}$ is defined in Equation (4) as being within $S^{max}\ast S_{rate}^{min}$ and $S^{max}\ast S_{rate}^{max}$, which represent the minimum and maximum operating ranges of the SoC, respectively. The relationship between $S_{d,t}$ and ESS charging and discharging, considering the efficiency $\eta$, is defined in Equation (5). Additionally, Equation (6) ensures that the ESS capacity remains constant at the beginning and at the end of each day. The ranges of ESS charging and discharging power per day and period are defined in Equations (7) and (8), respectively, ensuring that the capacity of the PCS is not exceeded. To prevent simultaneous charging and discharging, the same time-series binary variables $u_{d,t}^{char}$ and $u_{d,t}^{dis}$ are multiplied. Equation (9) further ensures that simultaneous charging and discharging cannot occur. Furthermore, if ESS discharging occurs during periods requiring an increase in load, Equation (2) dictates that the power demand decreases. To prevent this scenario, Equation (10) is defined using the binary set $U_{d,t}^{Pdr}$. Therefore, ESS discharging during these periods is prevented, and ESS charging or operation is disabled.

2.4. Economic Analysis with NPV and IRR

In this study, we determined the appropriate incentive levels by considering the NPV and IRR during the incentive calculation. The NPV evaluates whether the projected cash flows of a project exceed the initial investment cost when evaluated at the present time. It is defined as the sum of the present values of all cash flows occurring over the entire project period, discounted using a specific discount rate r [34], as shown in Equation (11). The IRR, on the other hand, is utilized to assess the profitability of a project. It is the discount rate that equates the present value of future cash flows to the initial investment cost, making the NPV zero. If the IRR exceeds the target rate of return, the investment is deemed profitable; if it falls below the target, it is considered insufficiently profitable.

$$NPV=\sum _{n=1}^N{\displaystyle \frac{C{F}_n}{{\left(1+r\right)}^n}}$$

(11)

Therefore, the company’s cash flows are defined such that the NPV and IRR are considered. Accordingly, the NPV is calculated as follows:

$${CF}_n=I_n+C_n^{grid}-C_{ini}^{grid} ,$$

(12)

$$NPV=\sum _{n=1}^N{\displaystyle \frac{C{F}_n}{{\left(1+IRR\right)}^n}}-C_{tot}^{ESS}=0 .$$

(13)

The company’s cash flows are evaluated by comparing them with those before ESS investment. In Equation (12), $I_n$ represents the total DR incentives received by the company in year n, $C_n^{grid}$ denotes the total electricity charges incurred by the company over n years, and $C_{ini}^{grid}$ denotes the total electricity charges incurred by the company before the ESS investment. Furthermore, $C_{tot}^{ESS}$ represents the ESS investment cost, which includes the costs per capacity of the PCS and battery. The ESS investment cost is assumed to be fully incurred during the first year, without any financing or loans. Accordingly, the company’s cash flow in year n is defined as ${CF}_n$, with the NPV and IRR determined based on these cash flows as shown in Equation (13).

2.5. Iterative MIP Optimization

This study aims to determine the plus DR incentive $X_{Pdr}$ by considering the IRR. However, nonlinearity occurs when calculating the incentive in the objective function Equation (1) owing to the multiplication between the two decision variables, $X_{Pdr}$ and $P_{d,t}^{grid}$. Additionally, including Equation (13) as a constraint introduces further nonlinear problems in this process of deriving $X_{Pdr}$ that satisfies the IRR, as ${CF}_n$ depends on the result of Equation (1). This complexity makes it challenging to directly derive $X_{Pdr}$. To address this issue, an iterative MIP optimization was implemented. The iterative optimization process is shown in the flowchart in Figure 2. In the initial step of the optimization algorithm, an initial value is set for $X_{Pdr}$, and objective function optimization is performed based on this value. Using the cash flows derived from the optimization results, the IRR is calculated using Equation (13). To achieve the desired target rate of return, adjustments are made to $X_{Pdr}$ by incrementing or decrementing a small value (α) and then re-optimizing using the updated $X_{Pdr}$. This iterative process continues until the IRR reaches the target value, at which point the final $X_{Pdr}$ is determined as the incentive to be awarded to DR participants. This optimization method aims to enhance the effectiveness of the DR program by offering reasonable incentives to participants while ensuring economic benefits for the company.

3. Case Study and Results

3.1. Simulation Conditions

This paper presents a model for determining incentives to ensure the profitability of plus DR participants, considering the investment costs associated with ESS. To validate the proposed model, daily scheduling simulations were conducted using D = 365 and T = 24. The NPV calculations considered a period of N = 15 years, with an incentive increment α set to 0.05 KRW/kWh during the iterative optimization process. Additionally, the DR execution time $U_{d,t}^{Pdr}$ was assumed to be from 12:00 to 15:00 based on the curtailment times during spring and autumn seasons in Jeju Island. The simulation conditions for this study were as follows.

3.1.1. Customer’s TOU Pattern and Load Pattern

The electricity rates for power purchased by DR-participating companies from the utility based on the industrial TOU tariff provided by the Korean utility are shown in Figure 3a, reflecting 2024 data [35]. The tariff periods were categorized as off-peak from 22:00 to 07:00, mid-peak from 09:00 to 15:00, and peak-load from 16:00 to 21:00. On Saturdays, the peak-load period applied the mid-peak rate, whereas on Sundays and public holidays, the peak-load period applied the off-peak rate.

The corporate load pattern in the proposed model is based on the actual TOU load patterns, with the company’s load pattern shown in Figure 3b to illustrate seasonal variations and differences in electricity consumption between weekdays and weekends. This load pattern represents data for a single DR-participating company, derived from the actual annual load data of one company.

3.1.2. ESS Operating Conditions

The operational characteristics of the ESS under simulation conditions are listed in

Table 1. ESS operating conditions.

Symbol	Parameter	Value
$S^{max}$	Battery Spec	200 kWh
$P_{PCS}^{max}$	PCS Spec	44 kW
$S_{rate}^{min}, S_{rate}^{max}$	Operating zones	10%, 90%
$S_{rate}^{init}$	Initial capacity rate	10%
η	Efficiency	90%

. The ESS battery capacity was determined based on the consumption, whereas the PCS capacity was calculated based on the battery capacity, determined from the efficiency and operational range to ensure operation during the DR operating hours. Furthermore, the charging and discharging efficiencies η of the PCS were assumed to be 90%, with the SoC operational range set between 10% and 90% of the battery capacity ($S^{max}$), maintaining a 10% SoC at the beginning and end of operation.

3.1.3. ESS Installation Costs

A major cost for companies participating in DR programs is the investment cost of the ESS. Based on the assumption in Section 2, the company’s ESS investment cost was paid in advance when calculating the incentives. The lifespan of the ESS was assumed to be 15 years, aligning with the cash flow period N. The costs per capacity for the PCS and battery were considered. The equipment costs accounted for in the simulation are listed in

Table 2. Cost of ESS.

Symbol	Parameter	Value
$C_{tot}^{BAT}$	Cost per kWh	0.46 M KRW
$C_{tot}^{PCS}$	Cost per kW	0.47 M KRW
$C_{tot}^{ESS}$	Total Cost	117 M KRW

, based on data published by the National Renewable Energy Laboratory (NREL) [36].

3.2. Case Study and Simulation Result

Based on the aforementioned simulation conditions, we determined the plus DR incentive by considering the ESS investment cost and IRR.

3.2.1. Incentive Variations Based on IRR

In determining appropriate incentive levels for DR participation, it is essential to account for the varying return expectations of companies. To assess the economic feasibility of DR participation under different financial scenarios, this study selected IRR targets of 5%, 10%, and 15% [37,38].

The incentives for IRRs of 5%, 10%, and 15% are shown in Figure 4, whereas the differences in electricity consumption and electricity bills before and after ESS installation are presented in

Table 3. Simulation results before and after ESS installation.

Separation	Without ESS (Traditional)	After ESS Installation
Electricity bill (M KRW)	300.9	294.5
Peak (kW)	463.872	424.248
Amount of energy consumed (MWh)	1966.9	1984.3
DR participation through ESS (MWh)	-	27.0
Total ESS cost (M KRW)	-	115.4

.

Based on the simulation results, ESS installation decreased the electricity bill from 300.9 million KRW to 294.5 million KRW, with the peak load decreasing from 463.872 kW to 424.248 kW. However, the total electrical energy consumption increased slightly from 1966.9 MWh to 1984.3 MWh. The total investment cost of the ESS was 115.4 million KRW. ESS installation resulted in an additional 27 MWh of load through plus DR. The total incentive received by the DR participant corresponds to the increased load multiplied by the incentive rate presented in Figure 4.

As shown in Figure 4, the DR incentive linearly increased as IRR increased. This trend can be attributed to a strategic approach of actively charging the ESS during DR execution hours to maximize incentives, thereby directly correlating the incentive increase with an increase in IRR. Additionally, despite applying optimization strategies to minimize electricity costs outside DR execution hours, we verified that a substantial incentive, equivalent to the peak-load tariff levels in spring and autumn, was necessary to achieve an IRR of 5%.

A comparison between the pre-ESS installation load of the DR participant and the optimized load, based on days with seasonal peak loads, is shown in Figure 5. The dotted line represents the existing load, whereas the solid line represents the new load of the company, reflecting the optimal ESS schedule.

As shown in Figure 5a,c, during the plus DR execution period from 12:00 to 15:00, the load increased owing to the charging of the ESS. However, after 16:00, when the DR ended, a strategy was implemented to minimize utility power purchases by discharging the stored energy. In conclusion, during the DR periods, the total electricity consumption increased compared to that in the period before the ESS installation. Conversely, as shown in Figure 5b,d, the overall peak load was reduced when the power demand was considerably suppressed between 14:00 and 17:00. This reduction in peak load resulted in lower basic charges, demonstrating the economic benefits of reducing electricity costs even when DR is not executed.

In summary, while ESS scheduling is optimized to maximize efficiency during both DR execution and non-execution periods, the required incentive level exceeds the peak load tariff levels of the TOU rates in spring and autumn. This suggests that to break even and secure a minimum profit, the DR incentive must be set above peak-load tariff levels, clearly indicating the required level to ensure profitability and encourage ESS adoption.

3.2.2. Incentive Variations with Decreasing ESS Investment Costs

In Section 3.2.1, we compared the results of ESS installation with a baseline scenario without ESS, showing that ESS installation reduces curtailment and peak load. However, the high incentive levels required for profitability made this approach less feasible under current conditions. With advancements in ESS technology and the scale of production expanding, the investment costs of ESS are continuously decreasing [36]. This improvement in economic feasibility for ESS participation in DR programs impacts the incentives necessary to ensure the profitability of ESS investment projects. The changes in ESS investment costs and corresponding DR incentives, calculated based on the annual cost reduction trends of PCS and batteries predicted by the NREL, are shown in Figure 6 [36]. The ESS costs considered were projected from 2022 to 2050. The analysis in Section 3.2.1, comparing incentive levels across IRR targets of 5%, 10%, and 15%, demonstrated a linear increase in incentives with higher IRR targets. Based on this trend, an IRR target of 10%, as the midpoint value among the IRR targets compared in Section 3.2.1, was chosen for further analysis.

The simulation results indicate that the required DR incentives generally decreased as the ESS investment costs decreased. However, the reduction rates of the ESS costs and DR incentives were inconsistent. Until 2025, both ESS costs and DR incentives decreased at comparable rates. However, after 2025, the decrease in DR incentives appears to be greater than the decrease in ESS costs. From 2022 to 2025, ESS costs decreased by approximately 22.4%, whereas DR incentives decreased by approximately 38.4%. During this period, the reduction rates of the ESS costs and DR incentives were approximately 1.7 times higher than those of the ESS costs, indicating a difference in the rates of decrease between the two variables. However, from 2025 to 2050, the ESS costs decreased by an additional 39.8%, whereas the DR incentives decreased by approximately 95.2%, which highlights the significantly larger decrease in DR incentives. This can be attributed to the continuous decrease in ESS costs, which reduces the initial investment burden and enhances the economic feasibility of participating in DR programs. Consequently, the effect of reducing electricity costs through ESS operation increased, leading to a decreased reliance on DR incentives. If ESS costs decrease by approximately 40% from current levels, only minimal or no DR incentives would be required to achieve profitability.

3.2.3. Incentive Variations Based on TOU Rates

TOU tariffs are systems designed to efficiently manage power demand by applying different electricity rates depending on the time of the day [39]. Changes in TOU tariffs directly influence the economic feasibility of DR programs utilizing ESS, potentially altering the level of incentives required for DR participation. The demand and energy charges for each TOU tariff category are listed in

Table 4. TOU rates.

Class		Demand Charge (KRW/kW)	Energy Charge (KRW/kWh)
			Period	Month
				6–8	3–5 9–10	11–2
A	1	7220	Off-peak	92.8	92.8	99.8
			Mid-peak	145.7	115.3	145.9
			Peak-load	227.8	146.0	203.4
	2	8320	Off-peak	87.3	87.3	94.3
			Mid-peak	140.2	109.8	140.4
			Peak-load	222.3	140.5	197.9
	3	9810	Off-peak	86.4	86.4	93.7
			Mid-peak	139.6	108.5	139.8
			Peak-load	209.9	132.2	186.7
B	1	6630	Off-peak	95.9	95.9	102.9
			Mid-peak	151.1	119	149.3
			Peak-load	179.3	128.8	166.3
	2	7380	Off-peak	92.1	92.1	99.1
			Mid-peak	147.3	115.2	145.5
			Peak-load	175.5	125	162.5
	3	8190	Off-peak	90.4	90.4	97.5
			Mid-peak	145.6	113.6	143.8
			Peak-load	173.9	123.3	160.9

[35]. Simulations were conducted by applying these tariffs to previously assumed simulation conditions. Notably, Class A tariffs have higher rates compared with those for Class B within the same subclass, with higher subclass numbers corresponding to lower energy charges. The incentive values calculated from the simulation results are shown in Figure 7, with calculations based on a target IRR of 10%.

The simulation confirmed that the equilibrium between basic charges and energy charges within the TOU tariff structure significantly influences the economic viability of DR programs utilizing ESS. In tariff categories A-1 and B-1, characterized by low basic charges and high energy charges, the energy cost-saving impact is significant. However, the basic charge-saving effect resulting from peak power reduction is limited, necessitating higher levels of DR incentives. Conversely, in tariff categories A-3 and B-3, where basic charges are high and energy charges are low, the basic charge-saving effect due to peak power reduction is significant. However, the energy cost-saving effect is minimal, requiring a moderate level of DR incentives. Notably, in tariff category A-2, where basic charges and energy charges are balanced, ESS can maximize both energy cost-saving and basic charge-saving effects, resulting in the lowest required level of DR incentives. This underscores the critical importance of balancing basic and energy charges for the economic feasibility of ESS operation.

Therefore, when designing DR incentives according to TOU tariffs, the interrelationship between the basic and energy charges must be comprehensively considered. Simply having a high energy charge or basic charge alone does not necessarily reduce the required DR incentive level. The synergy between these tariff components is pivotal in optimizing the efficiency of DR programs and enhancing economic benefits to participants. This analysis is poised to enhance the effectiveness of DR programs and facilitate the determination of appropriate incentive levels.

4. Conclusions

This study proposed an algorithm to calculate the appropriate incentive level for plus DR participation, considering the investment cost associated with the ESS. By utilizing real load data, we have incorporated annual load variability and conducted an economic feasibility analysis using metrics such as the NPV and IRR. This study used iterative MIP optimization to linearize the nonlinear characteristics of the IRR, which is a metric for evaluating the profitability of investments. By employing iterative MIP optimization, the algorithm proposed in this study minimizes electricity costs for DR participants while iteratively adjusting incentives to achieve the target IRR, effectively linearizing the nonlinearity in incentive estimation. This methodology provides DR-participating companies with a comprehensive understanding of the potential profitability associated with ESS adoption while also assisting governmental entities in establishing suitable incentive structures to promote corporate engagement. Moreover, this model could contribute to refining policy frameworks to support the broader adoption of DR programs and ESS investments, fostering long-term sustainability in the energy sector. Our proposed algorithm demonstrated its effectiveness in determining appropriate incentives based on ESS costs and desired rates of return. Notably, the required incentive level decreases as the ESS costs decrease, with an approximate 40% reduction in ESS costs potentially leading to an approximately 95% decrease in the required incentive level. Furthermore, the balance between basic and energy charges in the TOU tariff structure significantly influences the economic feasibility of ESS operations. This underscores the importance for companies to strategically evaluate tariff structures when selecting TOU plans to maximize economic benefits through ESS adoption and DR participation.

Despite the potential benefits, the high initial investment cost of ESS remains a key barrier to adoption by DR-participating companies. To overcome this challenge, we recommend that governments implement supportive policies, such as offering appropriate levels of DR incentives, tax incentives, and financial assistance for ESS investments.

Future research endeavors should focus on conducting detailed economic evaluations that account for operational costs such as ESS depreciation and maintenance expenses, as well as consider various consumer profiles across different industrial sectors, accounting for factors such as ESS capacity, placement, and long-term electricity price volatility. Moreover, the economic feasibility should be evaluated using models that incorporate power market volatility, load uncertainties for the enhanced robustness of DR strategies, and uncertainties related to RES curtailment. These aspects will be key areas of focus for future research initiatives.