Day-Ahead PV Generation Scheduling in Incentive Program for Accurate Renewable Forecasting

Abstract

Photovoltaic (PV) power can be a reasonable alternative as a carbon-free power source in a global warming environment. However, when many PV generators are interconnected in power systems, inaccurate forecasting of PV generation leads to unstable power system operation. In order to help system operators maintain a reliable power balance, even when renewable capacity increases excessively, an incentive program has been introduced in Korea. The program is expected to improve the self-forecasting accuracy of distributed generators and enhance the reliability of power system operation by using the predicted output for day-ahead power system planning. In order to maximize the economic benefit of the incentive program, the PV site should offer a strategic schedule. This paper proposes a PV generation scheduling method that considers incentives for accurate renewable energy forecasting. The proposed method adjusts the predicted PV generation to the optimal generation schedule by considering the characteristics of PV energy deviation, energy storage system (ESS) operation, and PV curtailment. It then maximizes incentives by mitigating energy deviations using ESS and PV curtailment in real-time conditions. The PV scheduling problem is formulated as a stochastic mixed-integer linear programming (MILP) problem, considering energy deviation and daily revenue under expected PV operation scenarios. The numerical simulation results are presented to demonstrate the economic impact of the proposed method. The proposed method contributes to mitigating daily energy deviations and enhancing daily revenue.

1. Introduction

In recent years, South Korea has been implementing a 2050 carbon-neutral strategy and a renewable energy 3020 plan, resulting in a substantial increase in renewable energy generation. In particular, photovoltaic (PV) generation has experienced significant growth. However, inaccurate forecasting of PV generation can negatively affect the stability of the power system and lead to congestion problems in power lines [1,2,3].

In order to mitigate the problems caused by energy deviations in PV generation, South Korea has introduced an incentive program beginning in 2021. The incentive program promotes efficient and stable power system operation by mitigating renewable energy volatility and reducing associated costs. This incentive program rewards renewable energy resources that can provide fewer energy deviations [4]. It encourages energy deviation reduction through more accurate self-forecasting of PV generators and the use of ancillary resources within the PV site. From the perspective of resources that achieve accurate forecasting, they can receive an additional benefit of approximately 5% of the energy market price.

PV generators typically offer their forecasted PV output as part of their generation schedule without making additional adjustments. In this situation, PV sites may try to increase their revenue by improving the performance of their forecasting model. However, there are inherent limitations to achieving significant improvement due to the fundamentally uncertain nature of weather. Therefore, assuming that the forecasting accuracy is already high enough, additional energy deviation mitigation measures are needed.

In order to mitigate energy deviation, energy storage system (ESS) operation and PV curtailment can be considered. First, by establishing an appropriate ESS operational strategy, it is possible to mitigate energy deviation [5], resulting in increased incentive revenues [6,7]. For PV sites with ESS, if actual PV power exceeds the forecast threshold eligible for incentives, the incentive level can be increased by reducing the energy deviation through ESS operation [8]. However, there may be a limitation in reducing the energy deviation due to the physically limited capacity of ESS [9]. In addition, ESS can charge during higher market prices and discharge during lower market prices to mitigate energy deviations [10], which will reduce revenue from the energy market.

Alternatively, power curtailment can mitigate the energy deviation by limiting power output by setting an upper limit [11,12,13]. In contrast to ESS operation, power curtailment does not require installation investment, as the curtailment is controlled within the generator. However, power curtailment can only control unidirectional energy deviations that exceed the predicted power generation by setting output limits. Additionally, curtailing power can decrease revenue from the energy market.

Both ESS and curtailment can mitigate energy deviations and increase incentives. On the other hand, they can reduce revenues from electricity sales in the energy market [14]. In general, increasing power generation is profitable when market prices are high. However, there are instances where it may be more advantageous to forgo a portion of the generation revenue in exchange for higher incentives. PV sites should make an optimal generation schedule to enhance both the generation revenue and incentives simultaneously through co-optimization. For the day-ahead market, the generation schedules of PV sites should be based on the predicted PV output. However, in real-time operations, PV output will differ from the predicted PV output, and this uncertainty makes it hard to determine the generation schedule that brings the highest revenues.

Numerous studies have been conducted on day-ahead scheduling to enhance the profitability of PV sites. In a study by Rashidizadeh-Kermani [15], the proposed optimal scheduling strategy has mainly focused on maximizing electricity sales revenue but has not considered mitigation of energy deviation while considering incentives. Maximizing sales revenue can lead to an increase in energy deviation, potentially resulting in a penalty. As a result, when considering incentives, it is important to additionally consider mitigating energy deviations. Ko et al. [16] proposed an ESS operation strategy that considers incentives. However, the operational range of the PV generator is not extended by strategically adjusting the generation schedule. Extending the operational range through generation schedule adjustment is crucial because it allows for considering the energy deviation characteristics of each generator. Perez et al. [10] and Saez-De-Ibarra et al. [17] mitigated penalties by reducing PV energy deviations and enhancing economic benefits. However, the consideration of incentives is excluded. It is a reasonable attempt to increase the economic benefits by mitigating penalties, but the economic benefits can be further maximized by additionally considering incentives. Ding et al. [18] formulated the optimal ESS scheduling to maximize daily revenue for arbitrage purposes. The formulation includes penalties, although incentives are not considered.

Many countries are imposing penalties or reward programs to mitigate renewable energy deviations. Also, in Korea, incentives are provided to encourage accurate forecasting and generation of PVs as an initial step to deal with PV generation as a dispatchable energy source. Despite the numerous studies proposing various scheduling strategies to maximize revenue for PV sites, their methods are not expected to maximize PV revenues in the electricity market, where newly introduced revenues can be obtained by minimizing energy deviations. In electricity markets introducing incentive programs, such as in Korea, PV sites should schedule their generation resources by considering both electricity market revenue and incentive returns. Considering that incentives arise by reducing energy deviations, it is required to simultaneously schedule ESS operation and PV curtailment to reduce the energy deviations of PV sites while ensuring that market revenue does not decrease significantly.

The main objective of this paper is to determine the optimal generation schedule for PV sites in the day-ahead market, considering the incentive program for accurate renewable energy forecasting. In order to maximize the revenue from generation sales and incentives simultaneously in the uncertain situation arising from PV forecast errors, a scenario-based stochastic optimization is proposed. The paper presents PV curtailment scheduling and ESS operation scheduling methods that can maximize both revenues in all statistically possible PV scenarios from the predicted PV generation. The constraints associated with PV curtailment and ESS operation are considered, and the PV scheduling problem with the incentive program is formulated and transformed into the mixed-integer linear programming (MILP) problem. The expected incentives, total revenue, and energy deviation are calculated based on the optimal PV schedule that has been derived.

The paper is organized as follows: Section 2 introduces the renewable energy incentive program in South Korea and the concept of adjusting the PV schedule based on PV curtailment and ESS operation. Section 3 presents the optimization model for PV scheduling and describes the linearization method. Section 4 analyzes the results numerically. Finally, Section 5 summarizes the study’s conclusions.

2. PV Generation Scheduling Problem in the Incentive Program

2.1. Renewable Energy Incentive Program

In the day-ahead market of Korea, PV sites forecast their PV generation and schedule their net output for market offerings. In order to reduce energy deviations from PV generation, incentives are provided when the difference between actual output and the generation schedule is lower than a certain level [19].

For a given time step t, the energy deviation can be calculated as follows:

$$e_t=\frac{\left|{output}_t-a_t\right|}{CAP}\times 100\%$$

(1)

where $e_t$ is the energy deviation at time $t$, ${output}_t$ is the actual net PV generation, $a_t$ is the scheduled net PV generation at time $t$, and $CAP$ is the capacity of the PV generator. At each time step, the actual output is compared to the generation schedule to calculate the energy deviation and determine the incentive unit price. The unit price of the incentive is determined on an hourly basis, which means that if the energy deviation at any given time is greater than 8%, no incentives will be available at that time. In addition, if the daily average energy deviation is greater than 8%, that PV site will not qualify for the incentive.

PV generation can be variable depending on weather conditions, but it is possible to adjust net PV generation by curtailing PV output or using ancillary resources, including energy storage systems. Therefore, the net PV generation can be calculated as follows:

$${output}_t={PV}_t-{curt}_t-{ess}_{chg,t}+{ess}_{dis,t}$$

(2)

where ${PV}_t$ is the PV generation at time $t$, ${curt}_t$ is the PV curtailment at time $t$, and ${ess}_{chg,t}$ and ${ess}_{dis,t}$ are ESS charge and discharge amount at time $t$, respectively.

The net PV generation is scheduled and offered to the energy market one day in advance. Depending on the energy deviation, the incentives are provided as follows:

$$I_d=\sum _{t=1}^{24}{output}_t\times i_t$$

(3)

where $I_d$ is the daily incentives, and $i_t$ is an incentive unit price at time $t$. Figure 1 shows the incentive unit price that is changed depending on the energy deviation.

In order to maximize the revenue of the PV site in the incentive program, optimized net generation scheduling is required, considering the ESS operation and curtailment based on the given scheduled PV output.

2.2. PV Curtailment and ESS Operation

Generation schedules can have a significant impact on the PV site’s daily revenue. Therefore, the PV site should strategically schedule its generation, including ancillary resources. Typically, PV generators offer their PV generation as a generation schedule without any adjustments. However, strategically modifying the generation schedule before submission has the potential to increase incentives.

Figure 2 shows a concept of adjusting the generation schedule based on PV curtailment and ESS operation to maximize incentives. The PV scenarios are examples of under-forecasted and over-forecasted for the following day. Two PV scenarios lie outside the permissible range for energy deviation in the incentive program; both scenarios are ineligible for incentives.

Considering the characteristics of PV energy deviation, the generation schedule can be adjusted to be lower than forecasted PV generation in day-ahead scheduling. In this situation, it is necessary to consider as many PV scenarios as possible to incorporate the characteristics of the energy deviation. Subsequently, in real-time operation, ESS discharge can be performed for generation levels below the range of energy deviation eligible for incentives, and PV curtailment and ESS charging are performed for generation levels above the range. In general, PV curtailment can reduce electricity sales revenue. However, mitigating the energy deviation by considering incentives can increase revenues. Indeed, operating ESS or curtailing PV alone can mitigate energy deviation. However, the proposed method is expected to enhance the flexibility of PV operation during real-time operation by expanding the controllable output range.

In the scheduling problem, the main objective is maximizing the economic benefit from MP and incentives. In order to maximize the total revenue, ESS charging is likely to occur more frequently than PV curtailment to mitigate errors. In this situation, PV curtailment will reduce the daily power generation sales revenue. In addition, the ESS discharge may occur even when MP is low to mitigate the energy deviation, reducing daily power generation sales revenue. Therefore, it requires optimized ESS operation, PV curtailment, and a strategically adjusted generation schedule. Considering these simultaneously makes it possible to maximize the economic benefit from MP and incentives efficiently.

3. Modeling of the PV Generation Scheduling Problem

3.1. Formulation of PV Generation Scheduling Problem

This paper proposes a method to determine the optimal PV generation schedule based on characteristics of energy deviation, ESS operation, and PV curtailment. The main objective is to maximize the economic benefit from MP and incentives.

Assuming that there are s PV scenarios, Equation (2) related to calculating the net PV generation is modified as follows:

$${output}_t^s={PV}_t^s-{curt}_t^s-{ess}_{chg,t}^s+{ess}_{dis,t}^s$$

(4)

where $s$ is the number of PV scenarios.

The PV curtailment should be determined to be less than PV generation and should not be negative. The physical constraint related to PV curtailment can be expressed as follows:

$$0 \le {curt}_t^s \le {PV}_t^s$$

(5)

An hourly PV curtailment rate can be calculated as follows:

$$r_t^s=\frac{{curt}_t^s}{{PV}_t^s}\times 100\%$$

(6)

where $r_t^s$ is the hourly PV curtailment rate, which varies by scenario and time.

The constraint related to the state of charge (SOC) of ESS can be expressed as follows:

$${soc}_t^s={soc}_{t-1}^s+{\eta }_{chg}\times {ess}_{chg,t}^s-\frac{{ess}_{dis,t}^s}{{\eta }_{dis}}$$

(7)

where ${soc}_t^s$ is an indicator of the remaining capacity of the ESS at the time $t$ for scenario $s$, ${\eta }_{chg}$ and ${\eta }_{dis}$ are charging and discharging efficiencies of the ESS, respectively. Equation (7) updates the SOC based on the ESS charge and discharge from the previous time step to the current time step.

$${ess}_{chg,t}^s\le {PCS}_{max}\times o_t^s$$

(8)

$${ess}_{dis,t}^s\le {PCS}_{max}\times (1-o_t^s)$$

(9)

where ${PCS}_{max}$ is the capacity of the power conversion system (PCS) of the ESS, and $o_t^s$ is a binary variable that distinguishes between the charging and discharging operations of the ESS. Equations (8) and (9) restrict the ESS operation to charging or discharging during each time step.

The physical constraints related to ESS operation can be expressed as follows:

$$0\le {ess}_{chg,t}^s\le {PV}_t^s$$

(10)

$$0\le {soc}_t^s\le {SOC}_{max}$$

(11)

$$0\le {ess}_{chg,t}^s$$

(12)

$$0\le {ess}_{dis,t}^s$$

(13)

where ${SOC}_{max}$ is the maximum storage capacity of ESS. Equation (10) restricts the ESS to prevent charging beyond the PV generation. Equation (11) imposes a physical constraint by setting the maximum ESS storage capacity as an upper bound for all scenarios and time steps. In addition, it assumes that the values of ${ess}_{chg,t}^s$ and ${ess}_{dis,t}^s$ are positive.

The energy deviation considering scenarios can be calculated by modifying Equation (1) as follows:

$$e_t^s=\frac{\left|{output}_t^s-a_t\right|}{CAP}\times 100\%$$

(14)

where $a_t$ is a decision variable of the MILP model. By optimally adjusting the generation schedule to cover all scenarios, the energy deviation is moved within the available range for incentives.

The incentive unit price in Figure 1 can be generalized as follows:

$$i_t^s=\left\{\begin{array}{c}\begin{array}{c}{u}_1,\\ u_2,\end{array}\\ \begin{array}{c}\begin{array}{c}⋮\\ u_k,\end{array}\\ \begin{array}{c}⋮\\ u_K\end{array}\end{array}\end{array} \begin{array}{c}\begin{array}{c}0\%\le e_t^s\le E_1\\ \begin{array}{c}{E}_1<e_t^s\le E_2\\ ⋮\end{array}\end{array}\\ \begin{array}{c}{E}_{k-1}<e_t^s\le E_k\\ \begin{array}{c}⋮\\ E_{K-1}<e_t^s\le 100\%\end{array}\end{array}\end{array}\right.$$

(15)

where $u_k$ is the incentive unit price, $E_{k-1}$ and $E_k$ are the lower and upper limits of the energy deviation range corresponding to the incentive unit price. A parameter $K$ divides the energy deviation (0~100%) into $K$ intervals, which is the number of intervals in which the energy deviation is accumulated. The user can set parameters $K$ according to the incentive program.

The PV site’s daily revenue consisted of energy market sales revenue, renewable energy certificates (REC) revenue, and incentives. The REC can be received when energy is generated from renewable energy sources. The optimization problem to maximize the expected daily revenue of the PV site can be formulated as follows:

$$\underset{a_t}{\mathit{maximize}}\sum _{s=1}^S{p}^s\sum _{t=1}^T{output}_t^s\times ({MP}_t+{\alpha }_{pv}\times REC+i_t^s)$$

(16)

where $p^s$ is the probability of occurrence for the PV scenario $s$, ${MP}_t$ is the market price at time $t$, which remains constant regardless of the scenarios, ${\alpha }_{pv}$ is the REC weight of the PV generator, $REC$ is the unit price of REC, $i_t^s$ is the incentive unit price at time $t$ for the PV scenario $s$, $S$ is the number of PV scenarios that can be considered, and $T$ represents 24 h.

MP revenue can be calculated by multiplying the net PV generation, considering ESS operation and PV curtailment by the hourly MP. Moreover, expected MP revenue can be calculated by considering the probability of occurrence. The REC weight can be changed according to the type and regulation of PV generator installation for each energy source. The REC weight and REC unit price have the same constant value for all scenarios, which remains constant at all times. Therefore, these constants do not affect the determinants in the optimization problem-solving process.

3.2. Linearization of the PV Generation Scheduling Problem

The generalized incentive unit price in Equation (15) has a nonlinear structure, making it impossible to solve the nonlinear constraint in the MILP model. Therefore, to formulate the scheduling problem as a MILP model, a new variable is introduced as follows:

$$e_t^s=\sum _{k=1}^K{e}_{t,k}^s$$

(17)

where $e_{t,k}^s$ is a fragmented energy deviation of the $k$-th interval when dividing the $e_t^s$ into $K$ intervals. Equation (17) allows $e_t^s$ to be divided into $K$ intervals since $e_{t,k}^s$ is accumulated to satisfy $e_t^s$.

$$e_{t,k}^s\le (E_k-E_{k-1})\times w_{t,k}^s$$

(18)

$$w_{t,k}^s\le w_{t,k-1}^s$$

(19)

where $w_{t,k}^s$ is a binary variable indicating in which of the $k$-th energy deviation $e_{t,k}^s$ is to be accumulated. Equation (18) restricting the value determination of $e_{t,k}^s$ for each interval to within an interval size $E_k-E_{k-1}$ using a binary variable $w_{t,k}^s$. Equation (19) allows $w_{t,k}^s$ to increase sequentially for $k$, and through Equation (18), $e_{t,k}^s$ can be increased sequentially for $k$ accordingly.

Ultimately, the incentive unit price $i_t^s$ is determined based on the energy deviation as follows:

$$i_t^s={\sum }_{k=1}^K(u_k-u_{k-1})\times w_{t,k}^s$$

(20)

Figure 3 shows an example of applying the linearization method to determine the incentive unit price considering the energy deviation. If the first interval is defined as ranging from 0% to 6%, the second interval as 6% to 8%, and the third interval as 8% to 100%, then if the percentage of forecast error is 7%, $e_{t,1}^s$, $e_{t,2}^s$, and $e_{t,3}^s$ will have values of 6%, 1%, and 0%, respectively. In addition, to maximize $i_t^s$, $w_{t,1}^s$, $w_{t,2}^s$, and $w_{t,3}^s$ will have values of 1, 1, and 0, respectively.

In order to linearize the calculation of incentive revenue, ESS operation, and PV curtailment are both set to zero within the portion of incentive revenue calculation. Therefore, by multiplying the PV generation by the incentive unit price determined in Equation (20), Equation (16) can be modified in the mixed integer linear optimization model as follows:

$$\underset{a_t}{\mathit{maximize}}{\sum }_{s=1}^S{p}^s{\sum }_{t=1}^T{output}_t^s\times ({MP}_t+{\alpha }_{pv}\times REC)+({PV}_t^s\times i_t^s)$$

(21)

A linearization process is required because Equation (14) contains a nonlinear structure due to the absolute value. Therefore, it can be expressed in the mixed integer linear optimization model as follows [20]:

$$-e_t^s\le \frac{{output}_t^s-a_t}{CAP}\times 100\%$$

(22)

$$\frac{{output}_t^s-a_t}{CAP}\times 100\%\le e_t^s$$

(23)

The formalized scheduling problem has the objective function of Equation (21) and can be defined as a mixed integer linear optimization problem with Equations (4)–(13), (17)–(20) and (22)–(23) as constraints.

3.3. PV Scenario Generation

In this paper, PV scenarios are generated using a normal distribution. The forecasted PV generation is used as the mean, and the energy deviation for each generation forecast level is used as the standard deviation.

$${PV}_t^s ~ ({PV}_t^f,{\left({\sigma }_t\right)}^2)$$

(24)

where ${PV}_t^f$ is a forecasted PV generation at time $t$, ${\sigma }_t$ is a standard deviation of the energy deviation of PV generation at time $t$, which represents the standard deviation of the energy deviation for each level of forecasted power generation. The ${\sigma }_t$ can be expressed as follows:

$${\sigma }_t=\left\{\begin{array}{c}\begin{array}{c}{\sigma }_{\left(1\right)}, b_{\left(1\right)}\le {PV}_t^f<b_{\left(2\right)} \\ \begin{array}{c}{\sigma }_{\left(2\right)}, b_{\left(2\right)}\le {PV}_t^f<b_{\left(3\right)} \\ \begin{array}{cc}⋮ & ⋮ \end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{c}{\sigma }_{\left(n\right)}, b_{\left(n\right)}\le {PV}_t^f<b_{(n+1)}\\ \begin{array}{cc}⋮ & ⋮ \end{array}\end{array}\\ {\sigma }_{\left(N\right)}, b_{\left(N\right)}\le {PV}_t^f<b_{(N+1)}\end{array}\end{array}\right.$$

(25)

where $b_{\left(n\right)}$ is the PV generation boundary in the $n$-th interval, and ${\sigma }_{\left(n\right)}$ is the standard deviation of the energy deviation in the set of conditions. PV generation scenarios can be generated by separately calculating the standard deviations of the energy deviation for different forecasted output ranges.

Assuming that the PV scenarios follow a normal distribution, the probability of occurrence in each scenario can be calculated as follows:

$$p^s=\frac{1}{S}$$

(26)

where $s$ is the number of scenarios. The randomly generated scenarios from the probability distribution in Equation (24) are applied to the ${PV}_t^s$ in Equations (4), (5) and (10).

4. Numerical Results

4.1. Test CASE

In this study, the generation schedule that maximizes the daily revenue of PV sites in Hadong, South Korea, is simulated using hourly PV generation data from 2021. The PV generator capacity in Hadong is 300 kW, and the ESS storage capacity is 30 kW. The PCS capacity of the ESS is 7.5 kW, allowing continuous operation for up to 4 h. The ESS charging and discharging efficiency is 95%, and the SOC is assumed to reset to 50% every 24 h [21].

The incentive unit price is used based on Korean renewable energy incentives. Since the REC unit price has the same value for all times and scenarios, it does not affect the decision variables. As a result, daily REC revenue is excluded from the scheduling problem. The Korean hourly market price data in 2021 is used for simulation [22].

4.2. Result of PV Generation Scheduling Problem

The analysis focused on the daily revenue for the PV generator while considering both power generation sales revenue and incentives.

Table 1. Construction of cases for daily revenue comparison.

	Case 1	Case 2	Case 3	Case 4	Case 5
Generation schedule ($a_t$)	Forecasted PV (${PV}_t^f$)	Decision variable ($a_t$)	Decision variable ($a_t$)	Decision variable ($a_t$)	Decision variable ($a_t$)
PV curtailment	Excluded	Excluded	Included	Excluded	Included
ESS operation	Excluded	Excluded	Excluded	Included	Included

shows five cases for the simulation study of the proposed method. Case 1 was designed for revenue comparison by excluding the decision variable and applying the predicted PV generation as the generation schedule. The others were designed so that the ESS and PV curtailment are included or excluded. Subsequently, the results of the scheduling problem were compared and analyzed to assess their impact on the daily revenue.

The PV scenarios forecasted PV generation and hourly MP remained consistent for all case simulations. Moreover, the ESS operation is observed irrespective of PV generation levels, while PV curtailment is primarily observed during periods of high PV generation. Therefore, the scheduling problem results were compared for each case when a day with high PV generation was observed. Hourly MP on such a day is shown in Figure 4, indicating that the MP is low during lunchtime when high levels of PV generation are expected. Conversely, the MP is high during the evening when low levels of PV generation are expected.

Figure 5 shows thirty PV scenarios generated based on the forecasted PV generation. This paper does not aim to make predictions but uses a simple forecasting algorithm. It uses actual output data from the same time period seven days ago as a forecasted output, assuming that past output will appear as it is. The PV scenarios between 11:00 and 15:00 observed substantially higher values than the forecasted output.

Figure 6 shows the results of the scheduling problem for each case. Case 1 was the benchmark for comparing the economic revenue of all cases. In this case, the generation schedules remained the same as the forecasted PV generation. In case 2, the generation schedules increased between 11:00 and 15:00. During this time, the MP was low, and the PV scenarios appeared higher than the forecasted PV generation. This adjustment was a strategy to reduce the upward energy deviation by adjusting the generation schedules upward. In case 3, the generation schedules increased between 12:00 and 14:00 compared to case 1 but decreased compared to case 2. This adjustment resulted from a strategy that reduced the upward energy deviation by adjusting the generation schedules upward. In case 4, the generation schedules were similar to case 1 between 12:00 and 14:00 but decreased compared to case 2. This strategy reduced the upward energy deviation through the ESS charging operation and decreased the generation schedules to reduce the downward energy deviation. In addition, the generation schedules increased by the amount of ESS discharge for all scenarios during 20:00 and 21:00 when the MP was high. In case 5, the generation schedules increased between 12:00 and 13:00 compared to case 4. During this time, the MP was low, and the PV scenarios were higher than the forecasted PV generation. Despite the simultaneous implementation of ESS charging and PV curtailment, the generation schedules were increased due to sufficient PV generation.

Figure 7 shows the results of the SOC of ESS simulation for case 4. Among the thirty PV generation scenarios, twenty-three scenarios involved charging during low MP hours from 09:00 to 16:00 to maximize MP revenues. In contrast, the remaining seven scenarios involved discharging during low MP hours from 08:00 to 12:00, indicating a strategy to reduce energy deviation and maximize incentive revenues.

Figure 8 shows the SOC results of the ESS simulation for case 5. Eighteen of the thirty PV generation scenarios included charging during low MP hours from 10:00 to 16:00 to maximize MP revenues. In contrast, the remaining twelve scenarios involved discharging during low MP hours from 07:00 to 14:00, indicating a strategy to reduce energy deviation and maximize incentive revenues. Compared to case 4, case 5 showed a more active ESS operation as it could simultaneously perform both ESS operation and PV curtailment, allowing a more comprehensive range of generation adjustments to maximize daily revenues.

Figure 9 shows the simulation results of PV curtailment for case 3. PV curtailment occurred in only fifteen of thirty scenarios, with ten scenarios having a curtailment rate of 1% or greater and the remaining five having a curtailment rate of less than 1%. In contrast to ESS operation, PV curtailment is infrequent because it can reduce daily MP revenues and does not occur in all scenarios. In addition, the hours in which PV curtailment occurs is a time period in which the increase of incentives due to a reduction in energy deviation is greater than the reduction in MP revenue.

Figure 10 shows that in case 5, PV curtailment occurred in only seven out of thirty scenarios, three of which had a curtailment rate of 1% or more, while the remaining four scenarios had a curtailment rate of less than 1%. It infers that case 3 is more frequent and has a higher curtailment rate than case 5. It is attributed to case 5’s ability to perform both ESS operation and PV curtailment, while case 3 uses only PV curtailment to adjust the output to energy deviation reduction.

4.3. Result of the Revenue of the PV Site

The daily revenue of the PV site was analyzed for one year in all cases.

Table 2. Results of calculating the expected daily incentive and total revenue for a date with a high level of PV generation.

	Case 1	Case 2	Case 3	Case 4	Case 5
Expected daily incentive	$5.894 (0.00%)	$6.082 (3.19%)	$6.297 (6.83%)	$6.459 (9.58%)	$6.536 (10.89%)
Expected daily total revenue	$96.017 (0.00%)	$96.206 (0.20%)	$96.345 (0.34%)	$96.700 (0.71%)	$96.743 (0.76%)

,

Table 3. Results of calculating the expected daily incentive and total revenue for a date with a medium level of PV generation.

	Case 1	Case 2	Case 3	Case 4	Case 5
Expected daily incentive	$3.554 (0.00%)	$3.582 (0.75%)	$3.610 (1.56%)	$3.624 (1.96%)	$3.624 (1.96%)
Expected daily total revenue	$55.077 (0.00%)	$55.104 (0.04%)	$55.119 (0.08%)	$55.593 (0.94%)	$55.593 (0.94%)

and

Table 4. Results of calculating the expected daily incentive and total revenue for a date with a low level of PV generation.

	Case 1	Case 2	Case 3	Case 4	Case 5
Expected daily incentive	$1.882 (0.00%)	$1.891 (0.52%)	$1.896 (0.75%)	$1.903 (1.14%)	$1.903 (1.14%)
Expected daily total revenue	$29.216 (0.00%)	$29.225 (0.03%)	$29.227 (0.04%)	$29.551 (1.15%)	$29.551 (1.15%)

present the expected daily revenue of the PV site, including selected dates of high, medium, and low levels of PV generation, respectively. On days with high PV generation levels, the expected revenue from incentives for case 5 increased by approximately 10% compared to case 1, resulting in a daily revenue increase of 0.76%. Similarly, on days with low PV generation levels, compared to case 1, the expected revenue from incentives for case 5 increased by 1.14%, resulting in a daily revenue increase of 1.15%. These results indicate that the proposed generation scheduling method can improve the daily income of PV sites, regardless of PV generation levels. The results of case 1 and case 2 demonstrate that adjusting the schedule by considering the characteristics of PV energy deviation can increase incentives compared to submitting the predicted power generation without changes. Generally, PV curtailment can reduce power generation revenues. However, the results of case 3 demonstrate that incentives can be increased, despite PV curtailing, by adjusting the schedule simultaneously. Furthermore, in case 5, consideration of PV curtailment and ESS operation can increase the daily total revenue.

4.4. Result of the Energy Deviation of the PV Site

The frequency of occurrence of energy deviation was analyzed for each scenario and case on a date with a high level of PV generation. Figure 11 shows the frequency of the occurrence of energy deviations. In order to maximize the revenue from incentives, most cases occurred with an energy deviation of 5–6% or less compared to case 1. Among the cases, case 5 had the highest frequency of occurrence in the 5–6% range and the lowest frequency in the 7–8% range. These results show the outcome of efforts to reduce the energy deviation by less than 6% to maximize the revenue from the incentive. In case 2, the frequency of occurrence in the range of 7–8% was higher than that of other cases. As case 2 only allows for adjustment of the generation schedule and does not include ESS operation or PV curtailment, it aims to increase the probability of benefit from the incentive, even if only slightly. The frequency of occurrence of case 5 in the range of energy deviation of 3–4% was the lowest among all cases. It aims at improving the revenue from MP within the energy deviation rate of 6%, which can qualify for the incentive, even if the frequency of occurrence of energy deviation changes by 5–6%. It demonstrates that if the unit price of the incentive program was designed in a step function, the optimal scheduling result was often determined at the point of the unit price changes. In other words, if the energy deviation exceeds 8%, whether the value is large or small, it will be reduced to 8% or less to receive the incentive. However, it should be noted that even if the energy deviation had been determined to be less than 5%, it may have increased within 5–6%. Therefore, when designing an incentive or penalty program, it seems that it is significant to consider the effect of the unit price.

5. Conclusions

This paper proposed a generation scheduling method for PV sites in the day-ahead market, considering incentives for accurate renewable forecasting. The proposed method formulated the incentive calculation and transformed the day-ahead PV scheduling problem into the MILP form. The optimized generation schedule is determined based on energy deviation characteristics, ESS operation, and PV curtailment. Actual PV generation data was used to analyze daily revenues over one year. The proposed method was found to enhance the expected daily revenues by about 0.7 to 1.1%, regardless of the PV generation levels. Additionally, the proposed method mitigates energy deviation by less than 6% to maximize revenue from the incentive. As a result, the proposed method is expected to have the potential to enhance the expected revenue of PV sites, contribute to the stable operation of the power system, and facilitate the rational expansion of renewable energy deployment. Future research will involve not only generating scenarios based on varying levels of prediction error, considering the characteristics of each generator, but also expanding the proposed bidding method. This expansion will focus on determining generation schedules for the participation of virtual power plants in energy markets.