Charging Incentive Design with Minimum Price Guarantee for Battery Energy Storage Systems to Mitigate Grid Congestion

Abstract

The large-scale integration of renewable energy sources (RESs) has raised concerns regarding grid congestion in Japan. Battery energy storage systems (BESSs) can mitigate congestion by adjusting charging schedules; however, BESS owners basically prioritize market arbitrage, which may not be aligned with congestion mitigation. This paper proposes a charging incentive design to guide arbitrage-oriented BESS charging toward time periods that are effective for grid congestion mitigation. The system operator predicts congested hours and ensures that BESS owners can purchase electricity at the lowest daily market price. This design intends to shift the BESS charging time towards congestion periods. Because market prices tend to decline during congestion periods, the proposed method reduces the operator’s financial burden while encouraging congestion-mitigating charging behavior. Numerical simulations using a simplified Japanese east-side power system model demonstrate that the proposed method reduced the congestion mitigation costs by 3.86% and curtailed the RES output by 3.89%, compared to using no incentive method (current operation in Japan). Furthermore, additional payments to BESS owners accounted for only around 7% of the resulting cost savings, indicating that the proposed method achieved lower overall system operating costs.

1. Introduction

To achieve a decarbonized society, the large-scale introduction of renewable energy sources (RESs) is progressing in energy transmission and distribution systems. In Japan, the goal is to increase the share of renewable energy generation by 36–38% by 2030 [1]. However, the introduction of RESs can cause congestion on transmission and distribution lines [2]. If such congestion occurs, there are concerns regarding renewable energy output curtailment and an increase in operational costs due to congestion mitigation measures. To further promote renewable energy as the main power source, it is essential to avoid congestion by utilizing various resources within the power system.

As a measure to mitigate power system congestion, previous studies have proposed operational management systems that utilize battery energy storage systems (BESSs) [3,4,5]. These systems typically adopt a scheme in which the surplus electricity from RESs is stored in a BESS, thereby mitigating the increase in power flow through transmission lines caused by renewable energy generation. In Japan, the number of BESS interconnection applications increased by approximately 2.1 times over nine months [6]. Accordingly, congestion mitigation approaches that utilize BESSs are considered effective in Japan.

An important factor in utilizing BESSs to mitigate congestion is to match the BESS charging periods with the time periods during which congestion occurs. In Japan, entities that are independent of the system operator (BESS owners) own many BESSs. Consequently, the BESS charge/discharge schedule is, in principle, determined by the BESS owner rather than by the system operator. When BESS owners aim to earn revenue through the day-ahead market, they are expected to operate the BESS in an arbitrage manner, charging during low-price periods and discharging during high-price periods, to maximize the price arbitrage profits [7,8]. Generally, a tendency for co-occurrence exists between day-ahead market prices and the timing of congestion caused by RESs [9]. This is because prices decrease in the day-ahead market, and congestion is often driven by the same factor—an increase in renewable energy generation. Therefore, even arbitrage operations aimed solely at profit maximization can provide a congestion mitigation effect. However, during low-demand periods or holidays, there are cases where the day-ahead market price remains at its minimum for extended periods, including periods with no congestion [10]. In such cases, arbitrage operations that consider only market prices may not necessarily result in BESS charging during hours when congestion occurs. These circumstances highlight the need for an incentive framework that encourages BESS charging to match congestion periods.

Several previous studies have sought to balance the economic operation of BESSs with the mitigation of power system constraints. References [11,12] proposed model predictive control (MPC) strategies designed to simultaneously mitigate congestion in microgrids and maximize the self-consumption of storage operators co-located with photovoltaic (PV) systems. Their findings demonstrate a reduction in peak power flows while considering economic aspects, such as self-consumption maximization and degradation prevention. Similarly, references [13,14] presented a control method for islanded and port microgrids that enhance RES utilization and limit BESS degradation. Reference [15] proposed a multi-objective BESS control method based on dynamic programming, which aims to maximize self-consumption, absorb supply–demand fluctuations, and avoid congestion for BESSs co-located with PV systems. Reference [16] proposed a real-time decentralized control method for multiple BESSs in distribution networks, targeting voltage violation and line congestion mitigation. To prevent excessive charging and discharging, their method incorporates a reference value for the state of charge (SOC) in the objective function and imposes a penalty for deviations. Reference [17] investigated operational strategies for renewable–battery hybrid power plants to maximize revenues under transmission congestion. The study emphasizes that, in areas with high RES penetration, battery charging can absorb local surplus RES generation. Furthermore, Reference [18] introduced a framework for congestion management that considers distributed generation and market price uncertainties through resource control, such as BESSs and electric vehicles (EVs). In this framework, the distribution system operator (DSO) determines the optimal scheduling of each resource and provides financial compensation as an incentive for end users. However, these studies did not sufficiently address the motivation of BESS owners to incorporate congestion-aware BESS operations, nor did they thoroughly explore the design of specific incentive mechanisms to support this behavior.

Meanwhile, several studies have proposed approaches that provide compensation to BESS owners for mitigating grid constraints through participation in electricity markets. Reference [19] introduced a framework in which demand-side resources, such as RESs and BESSs, that contribute to congestion relief are procured via a “congestion management market”. This market is designed to utilize the available local resources to mitigate grid congestion at the minimum possible cost. Similar concepts, referred to as local flexibility markets, were proposed and evaluated in references [20,21]. Furthermore, Reference [22] proposed a new market pricing mechanism using Security-Constrained Optimal Power Flow (SCOPF) to utilize a BESS to reduce renewable energy curtailment owing to grid congestion. Reference [23] presents the design of a Locational Marginal Price (LMP)-based multi-settlement market (MSM) that considers demand response (DR) and BESS participation. The MSM connects the day-ahead and real-time markets to reduce the price volatility risks in the real-time market for BESS owners. The authors indicate that DR and BESSs’ participation in such markets contribute to price suppression and congestion relief. Additionally, reference [24] proposed a novel control method using Incentive-Based Grid Access Requests (IBGAR) to balance supply and demand while maintaining high cost-efficiency and respecting the comfort and privacy of resource owners, such as BESS owners. In this framework, the aggregators determine incentives based on electricity prices and grid constraints. Reference [25] explored the promotion of BESS charge/discharge shifting through incentive designs linked to electricity prices, confirming a reduction in the generation costs and peak demand under six different electricity market scenarios. References [26,27] investigated optimal BESS scheduling methods that leverage the feed-in tariff (FIT) scheme to absorb PV output fluctuations and mitigate mismatches between generation and demand. Moreover, reference [28] proposes a coordinated TSO-DSO operational planning framework for day-ahead and real-time markets, aiming to achieve effective congestion management in liberalized electricity markets. Under this scheme, BESS owners benefit from the clear and direct valuation of upward and downward flexibility provided by system operators, thereby improving the transparency in the flexibility market. Moreover, reference [29] introduces a novel market design in which BESSs serve as providers of flexible ramping products (FRPs) to alleviate grid constraints. Unlike conventional FRP markets, this scheme positions BESSs as price makers, and no revenue is awarded for unaccepted bids. These market-based congestion mitigation frameworks are useful because they motivate BESS owners to contribute to grid constraint relief. However, as pointed out in references [30,31], the feasibility of BESS operations to mitigate grid constraints, including congestion, is highly dependent on the market design. If the compensation for contributing to congestion relief is insufficient, BESS owners may refrain from participating in the market because of a lack of profitability. Conversely, if the compensation is excessively high, additional payments to BESS owners may increase the overall system operating costs. Therefore, it is necessary to establish a framework that encourages BESS charging during congestion periods and avoids excessive incentive payments, which would lead to increased social costs.

To balance these two aspects, it would be effective to design charging incentives based on the co-occurrence tendency between congestion periods and day-ahead market prices. As the day-ahead market prices tend to be low during congestion periods, matching BESS charging with such periods can benefit BESS owners who aim to maximize their arbitrage profits. Therefore, if the system operator can provide prior assurance that charging will be possible at a low cost, specifically during congestion periods, the BESS charging behavior can be effectively guided without the need for substantial additional compensation, such as significant discounts on charging costs.

This paper proposes a charging incentive design method for BESSs aimed at congestion mitigation based on the co-occurrence tendency between congestion periods and day-ahead market prices. Specifically, the proposed framework involves the system operator forecasting congestion periods in advance and guaranteeing that transactions during such periods are conducted at the minimum target-day market price. The system operator compensates for the difference between the actual and minimum market prices. A comparison between the proposed method and the leading studies is summarized in

Table 1. A comparison between the proposed method and references [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29].

References	[11,12,13,14,15,16]	[17]	[18]	[19,20,21,22,23,24,25,26,27,28,29]	Proposed Method
Benefits for BESS owners	Self-consumption and battery degradation are incorporated into output control	Revenue maximization	Financial compensation	Market revenue	Lowest price guarantee
Reliable utilization of BESSs for grid constraint mitigation	✓	-	✓	-	✓
Motivation of BESS owners to contribute to grid constraint mitigation	-	-	✓	✓	✓
Avoiding excessive additional payments to BESS owners	✓	✓	-	-	✓

. The proposed method outperforms conventional approaches by effectively guiding BESS owners to charge during congestion periods, without the need to precisely estimate incentive levels that match the congestion mitigation cost savings. This is possible because the proposed method is expected to offer the following benefits to BESS owners and system operators:

✓

For BESS owners, improvements in both profitability and price predictability can be expected via charging shifts as the most cost-effective charging periods are identified in advance;

✓

For system operators, as the market prices during congestion periods tend to be at their lowest, the additional payment required to compensate BESS owners (i.e., the difference between the market and minimum prices) can be minimized.

To evaluate the effectiveness of the proposed method, numerical simulations were conducted using an extended version of the IEEJ EAST 10-machine O/V system model [32], in which RESs and BESSs are introduced. As a benchmark, a comparison was performed with a method that did not provide charging incentives to the BESS. The validity of the proposed approach was assessed based on three criteria: the congestion mitigation cost, renewable energy curtailment, and additional payments to storage operators on the target day.

The main contributions of this study can be summarized as follows.

• A novel incentive design method is proposed to guide BESS charging for congestion mitigation by leveraging the alignment between day-ahead market prices and congestion periods.
• The proposed method aims to balance two potentially conflicting objectives, namely promoting BESS charging during congestion periods and avoiding increased social costs due to excessive incentives, offering benefits to both BESS owners and system operators.
• Congestion management simulations based on a Japanese power system model confirm that the proposed method reduces both the congestion mitigation costs and renewable energy curtailment compared to the case without incentives. Furthermore, the additional payments to BESS owners under the proposed scheme were smaller than the corresponding reduction in the congestion mitigation costs, demonstrating a net decrease in the total system operating costs.

The remainder of this paper is organized as follows. Section 2 defines and formulates the grid congestion management and BESS charge/discharge scheduling concepts adopted in this study. Section 3 describes the proposed incentive design method for BESS charging based on the co-occurrence tendency between day-ahead market prices and congestion periods. In Section 4, the effectiveness of the proposed method is evaluated through numerical simulations. Finally, Section 5 concludes the paper.

2. Definition of Grid Congestion Management

In this study, grid congestion management is defined as the day-ahead operational process whereby the system operator evaluates potential transmission bottlenecks based on submitted operation plans and performs the rescheduling of generator outputs to ensure network feasibility and efficiency. An overview of the congestion management problem considered in this study is shown in Figure 1. For each submitted operation plan, the system operator conducts a DC power flow analysis to check whether any transmission line exceeds its thermal capacity or whether nodal imbalances are anticipated. If any such violations are found, output rescheduling is performed. In the DC-OPF formulation, generator outputs excluding BESS units—whose operation schedules are pre-determined as described in Section 2.1—are adjusted to resolve the anticipated congestion. This study focuses on the sequence of processes ranging from the formulation and submission of next-day operation plans by BESS owners to congestion management and day-ahead market price calculations by the system operator [33]. In this framework, market prices are calculated for each bus as the LMPs. On the day prior to operation, each power producer, including BESS owners, independently forecasts the LMPs for the following day and formulates an operation plan accordingly. These plans are then submitted to the system operator. The system operator performs a power flow analysis based on the submitted plans to determine whether congestion is expected in the next day’s grid operation. If congestion is anticipated, the system operator performs output rescheduling for individual generators. In the actual power supply on the target day, all generators and BESSs adhere to the revised schedules determined by the system operator during the pre-operation coordination process. Moreover, the market price for each bus is calculated for each period and published as the LMP. Each power producer earns revenue based on the LMP as the electricity unit selling price. This section explains the formulation of BESS operation plans, as well as the modeling of congestion management and LMP calculation within this framework.

2.1. BESS Operation Planning

To maximize the arbitrage profits, BESS owners are generally expected to determine their operation plans through a two-step procedure: (i) forecasting the next day’s LMP and (ii) optimizing the charge/discharge schedule based on the forecast results. In Step (i), each BESS owner constructs a forecasting model using actual operational data from the past month and forecasts the LMP for the next day at 30 min intervals. In Step (ii), based on the forecast results, the operator optimizes the BESS charge/discharge schedule to maximize the arbitrage revenue for the next day. In this optimization problem, the decision variable vector at bus $k$ at time $t$ is defined as follows:

$$x_{k,t}=\left[P_{k,t}^{\mathrm{D}\mathrm{C}},P_{k,t}^{\mathrm{C}},S_{k,t},{\delta }_{k,t}^{\mathrm{D}\mathrm{C}},{\delta }_{k,t}^{\mathrm{C}},{\delta }_{k,t}^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}},{\delta }_{k,t}^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}},{\delta }_{k,t}^{\mathrm{D}\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}},{\delta }_{k,t}^{\mathrm{D}\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}}\right], \forall k\in \mathcal{K},t\in \mathcal{T},$$

(1)

where $k$ is the bus index; $\mathcal{K}$ is the set of buses; $t$ is the time step index; $\mathcal{T}$ is the set of time step indices; $P_{k,t}^{\mathrm{C}}$ is the BESS charge output at bus $k$ at time $t$; $P_{k,t}^{\mathrm{D}\mathrm{C}}$ is the BESS discharge output at bus $k$ at time $t$; $S_{k,t}$ is the BESS SOC at bus $k$ at time $t$; ${\delta }_{k,t}^{\mathrm{C}} \mathrm{a}\mathrm{n}\mathrm{d} {\delta }_{k,t}^{\mathrm{D}\mathrm{C}}$ are binary variables indicating the BESS charging and discharging states at bus $k$ at time $t$, respectively; ${\delta }_{k,t}^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}} \mathrm{a}\mathrm{n}\mathrm{d} {\delta }_{k,t}^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}}$ are binary variables indicating the start and stop of charging at bus $k$ at time $t$, respectively; and ${\delta }_{k,t}^{\mathrm{D}\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}} \mathrm{a}\mathrm{n}\mathrm{d} {\delta }_{k,t}^{\mathrm{D}\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}}$ are binary variables indicating the start and stop of discharging at bus $k$ at time $t$, respectively. To maximize the total profit from discharging minus the charging cost during the day, BESS owners are expected to optimize these decision variables according to the following objective function:

$$\underset{x_{k,t}}{\mathrm{Maximize}}\sum _{t\in \mathcal{T}}{\widehat{C}}_{k,t}·\left(P_{k,t}^{\mathrm{D}\mathrm{C}}-P_{k,t}^{\mathrm{C}}\right), \forall k\in \mathcal{K},$$

(2)

where ${\widehat{C}}_{k,t}$ is the predicted LMP at bus $k$ at time $t$. In this optimization, the charge/discharge schedule is determined while imposing the BESS operational constraints. First, the SOC at each time step is updated according to the following constraint:

$$S_{k,t}=S_{k,t-1}+{\displaystyle \frac{∆t}{B_k}}\left(P_{k,t}^{\mathrm{C}}{\delta }_{k,t}^{\mathrm{C}}·{\eta }_k^{\mathrm{C}}-P_{k,t}^{\mathrm{D}\mathrm{C}}{\delta }_{k,t}^{\mathrm{D}\mathrm{C}}·{\displaystyle \frac{1}{{\eta }_k^{\mathrm{D}\mathrm{C}}}}\right),\forall k\in \mathcal{K},t\in \mathcal{T},$$

(3)

where $∆t$ is the time step interval; $B_k$ is the BESS capacity at bus $k$; and ${\eta }_k^{\mathrm{C}} \mathrm{a}\mathrm{n}\mathrm{d} {\eta }_k^{\mathrm{D}\mathrm{C}}$ are the BESS charging and discharging efficiencies at bus $k$, respectively. To enable continuous BESS charge and discharge operations, constraints on the initial and terminal SOC values are imposed as follows:

$$S_{k,1}=S_k^{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}},\forall k\in \mathcal{K},$$

(4)

$$S_{k,48}\ge S_k^{\mathrm{e}\mathrm{n}\mathrm{d}},\forall k\in \mathcal{K},$$

(5)

where $S_k^{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}$ is the initial BESS SOC at bus $k$, and $S_k^{\mathrm{e}\mathrm{n}\mathrm{d}}$ is the minimum terminal BESS SOC at bus $k$. Additionally, the BESS output is subject to upper and lower limits on its output power, which are expressed by the following constraints:

$$0\le P_{k,t}^{\mathrm{C}}\le {\overline{P}}_{k,t}^{\mathrm{C}}·{\delta }_{k,t}^{\mathrm{C}},\forall k\in \mathcal{K},t\in \mathcal{T},$$

(6)

$$0\le P_{k,t}^{\mathrm{D}\mathrm{C}}\le {\overline{P}}_{k,t}^{\mathrm{D}\mathrm{C}}·{\delta }_{k,t}^{\mathrm{D}\mathrm{C}},\forall k\in \mathcal{K},t\in \mathcal{T},$$

(7)

where ${\overline{P}}_{k,t}^{\mathrm{C}} \mathrm{a}\mathrm{n}\mathrm{d} {\overline{P}}_{k,t}^{\mathrm{D}\mathrm{C}}$ are the charging and discharging power upper limits at bus $k$ at time $t$, respectively. The above constraints imply that, when the charge or discharge flag is set to zero, the corresponding charging or discharging output variable must also be zero. To prevent simultaneous charging and discharging, the charging and discharging flags must not take a value of unity simultaneously, as represented below:

$${\delta }_{k,t}^{\mathrm{C}}+{\delta }_{k,t}^{\mathrm{D}\mathrm{C}}=1,\forall k\in \mathcal{K},t\in \mathcal{T}.$$

(8)

To reflect changes in operation status, the charging and discharging start/stop flags are set to 1 when a transition occurs from the previous time step, as defined by the following constraints:

$${\delta }_{k,t}^{\mathrm{C}}-{\delta }_{k,t-1}^{\mathrm{C}}={\delta }_{k,t}^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}-{\delta }_{k,t}^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}},\forall k\in \mathcal{K},t\in \mathcal{T},$$

(9)

$${\delta }_{k,t}^{\mathrm{D}\mathrm{C}}-{\delta }_{k,t-1}^{\mathrm{D}\mathrm{C}}={\delta }_{k,t}^{\mathrm{D}\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}-{\delta }_{k,t}^{\mathrm{D}\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}},\forall k\in \mathcal{K},t\in \mathcal{T}.$$

(10)

In the above equations, to avoid simultaneous charging or discharging starts and stops, the corresponding flags are restricted from being set to 1 simultaneously, as specified below:

$${\delta }_{k,t}^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}+{\delta }_{k,t}^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}}\le 1,\forall k\in \mathcal{K},t\in \mathcal{T},$$

(11)

$${\delta }_{k,t}^{\mathrm{D}\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}+{\delta }_{k,t}^{\mathrm{D}\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}}\le 1,\forall k\in \mathcal{K},t\in \mathcal{T}.$$

(12)

Finally, to limit the frequency of charge operations, the number of charge activations is constrained as follows:

$$\sum _{t\in \mathcal{T}}{\delta }_{k,t}^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}\le n_k^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}},\forall k\in \mathcal{K},$$

(13)

where $n_k^{\mathrm{C}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}$ is the maximum number of charging starts allowed for the BESS at bus $k$.

2.2. Grid Congestion Management and LMP Calculation

After each power producer submits its day-ahead generation plan, the system operator verifies whether congestion is expected to occur at each time step via power flow calculations. If congestion is identified, the system operator controls the generator outputs to mitigate it. In this study, the output control of thermal and renewable energy generators for congestion mitigation is simulated using a DC Optimal Power Flow (DC-OPF) model to minimize the total system operating cost. Let $P_t=\left(P_{1,t},P_{2,t},\dots \right)$ represent the active power output vector of all generators (including the BESS outputs determined in Section 2.1 at time $t$, and ${\theta }_t=\left({\theta }_{1,t},{\theta }_{2,t},\dots \right)$ represent the voltage phase angle vectors at each bus. Then, the DC-OPF problem can be formulated as follows:

$$\underset{P_t,{\theta }_t}{\mathrm{mini}\mathrm{mize}}\sum _{t\in \mathcal{T}}f\left(P_t,{\theta }_t\right),$$

(14)

$$\mathrm{s}.\mathrm{t}.$$

$$G\left(P_t,{\theta }_t\right)=0,\forall t\in \mathcal{T},$$

(15)

$$H\left(P_t,{\theta }_t\right)\le 0,\forall t\in \mathcal{T},$$

(16)

where $f\left(P_t,{\theta }_t\right)$ is a scalar function representing the total generation cost of the system; $G\left(P_t,{\theta }_t\right)$ is the equality constraint vector, corresponding to the power flow equations at each bus and each time step; and $H\left(P_t,{\theta }_t\right)$ is the inequality constraint vector, including the generator output limits and transmission line capacity constraints at each time step. In this case, the Lagrangian function $L$ corresponding to Equations (14)–(16) can be expressed using the Lagrange multipliers $\lambda$ for the equality constraints in Equation (15) and $\mu$ for the inequality constraints in Equation (16) as follows:

$$L\left(P_t,{\theta }_t,\lambda ,\mu \right)=f\left(P_t,{\theta }_t\right)+\lambda G\left(P_t,{\theta }_t\right)+\mu H\left(P_t,{\theta }_t\right).$$

(17)

Accordingly, the LMP at each bus can be calculated as the marginal increase in the Lagrange function corresponding to a unit increase in the corresponding demand as follows [34]:

$$C_{k,t}={\displaystyle \frac{\partial L\left(P_t,{\theta }_t,\lambda ,\mu \right)}{\partial P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}}={\displaystyle \frac{\partial f}{\partial P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}}+\lambda {\displaystyle \frac{\partial G}{\partial P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}}+\mu {\displaystyle \frac{\partial H}{\partial P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}},\forall k\in \mathcal{K},t\in \mathcal{T},$$

(18)

where $C_{k,t}$ and $P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}$ are the LMP and active power load at bus $k$ and time $t$, respectively. Each power producer earns revenue based on the LMP calculated using Equation (18), which serves as the unit selling price for electricity.

3. Charging Incentive Design with Minimum Price Guarantee for BESSs

In the proposed method, the system operator provides each BESS owner with information on charging incentives prior to the submission of the operation plans (i.e., before 10:00 a.m. on the day before operation), with the aim of utilizing BESS charging for congestion mitigation. An overview of the proposed charging incentive scheme is presented in Figure 2. As can be seen, the provision of charging incentives primarily consists of two steps. First, the system operator forecasts the congestion locations and periods for the following day and designates the lowest-price-guaranteed hours, during which transactions are guaranteed to be settled at the lowest market price of the day. Second, a sensitivity analysis is conducted for transmission lines expected to experience congestion, and the minimum price guarantee is applied only to BESSs connected to buses with high sensitivity to the congested line flow. This is intended to avoid providing excessive incentives to BESSs that do not contribute to congestion mitigation. Next, we describe in detail each step and the calculation method for additional payments resulting from the incentive scheme.

3.1. BESS and Period Identification for Incentive Application

In the proposed method, the system operator forecasts the power flow on each transmission line for the following day in 30 min intervals based on historical operational data. If the predicted power flow exceeds the capacity of any transmission line, the congestion mitigation effect of the BESS charging at each bus and time step is evaluated based on a sensitivity analysis. The aim of the sensitivity analysis is to identify the locations and periods where the application of charging incentives is the most effective in terms of congestion mitigation. Here, the sensitivity is defined as the reduction in transmission line flow resulting from a unit increase in demand at each bus. Specifically, when the demand at bus $k$ increases by $∆P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}$, and the dependent variable vector $X_t$ (including the active power outputs of generators and the voltage phase angles at each bus) changes by $∆X_t$ to satisfy the power flow equations, the following relationship holds:

$$G\left(X_t+∆X_t,P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}+∆P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}\right)=0,\forall k\in \mathcal{K},t\in \mathcal{T}.$$

(19)

A first-order Taylor expansion of Equation (19) around the operating point ($X_t, P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}$) yields the following linear approximations:

$${\displaystyle \frac{\partial G}{\partial X_t}}·∆X_t+{\displaystyle \frac{\partial G}{\partial P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}}·∆P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}=0,\forall k\in \mathcal{K},t\in \mathcal{T},$$

(20)

$${\displaystyle \frac{\partial X_t}{\partial P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}}={\displaystyle \frac{∆X_t}{∆P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}}=-{\left({\displaystyle \frac{\partial G}{\partial X_t}}\right)}^{-1}·{\displaystyle \frac{\partial G}{\partial P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}},\forall k\in \mathcal{K},t\in \mathcal{T}.$$

(21)

Accordingly, the sensitivity of bus $k$ with respect to power flow $F_{m,t}$ on transmission line $m$ at time $t$, denoted as ${\alpha }_{k, m, t}$, can be formulated as follows:

$$\begin{array}{c}{\alpha }_{k, m, t}=-{\displaystyle \frac{∆F_{m,t}}{∆P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}}=-{\displaystyle \frac{\partial F_{m,t}}{\partial X_t}}·{\displaystyle \frac{\partial X_t}{\partial P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}}\hfill \\ =-{\displaystyle \frac{\partial F_{m,t}}{\partial X_t}}·\left\{-{\left({\displaystyle \frac{\partial G}{\partial X_t}}\right)}^{-1}·{\displaystyle \frac{\partial G}{\partial P_{k,t}^{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}}\right\}, \forall k\in \mathcal{K},m\in \mathcal{M},t\in \mathcal{T},\hfill \end{array}$$

(22)

where $m$ is the transmission line index, $\mathcal{M}$ is the set of transmission lines, and $∆F_{m,t}$ is the change in power flow on transmission line $m$ at time $t$. A larger positive sensitivity value indicates that the BESS charging (i.e., increased demand) at bus $k$ is more effective at reducing the power flow on a congested transmission line. Conversely, when the calculated sensitivity is small or negative, BESS charging at bus $k$ does not contribute to congestion mitigation. Therefore, in the proposed method, the sensitivity of each bus’s BESS with respect to the congested line is calculated at each time step, and lowest-price-guaranteed hours are assigned to the time periods in which the sensitivity exceeds a predefined threshold $\epsilon$. This process is formulated as follows:

$${\alpha }_{k,t}^{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=\sum _{m\in \mathcal{M}}{\alpha }_{k, m, t}{\delta }_{m,t},\forall k\in \mathcal{K},t\in \mathcal{T},$$

(23)

$${\delta }_{k,t}^{\mathrm{L}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{s}\mathrm{t}}=\left\{\begin{array}{c}1 \mathrm{if} {\alpha }_{k,t}^{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\ge \epsilon \\ 0 \mathrm{otherwise}\end{array}\right.,\forall k\in \mathcal{K},t\in \mathcal{T},$$

(24)

where ${\alpha }_{k,t}^{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ is the total sensitivity of the BESS at bus $k$ and time $t$ with respect to all congested transmission lines; ${\delta }_{m,t}$ is a congestion flag for transmission line $m$ at time $t$ (binary variable; equals 1 if congestion occurs); and ${\delta }_{k,t}^{\mathrm{L}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{s}\mathrm{t}}$ is the lowest-price-guaranteed flag for bus $k$ at time $t$ (binary variable; equals 1 if the guarantee is applied). To consider the possibility of congestion on multiple transmission lines, the total sensitivity of each bus with respect to all congested lines is calculated using Equation (23). Threshold $\epsilon$ must be determined in advance by the system operator, and it serves as a parameter that determines which buses, based on their sensitivity levels, are eligible for incentive application.

3.2. Additional Payment Cost Calculation

After the generation plans or charge/discharge schedules are submitted by each power producer, the system operator verifies whether congestion is expected to occur at each time step. If necessary, the operator curtails the output of the relevant generators and calculates the LMPs, as described in Section 2. Once the LMPs are finalized, the system operator compensates the BESS owners located at the buses where the lowest price guarantee is applied. As illustrated in Figure 3, the additional payment corresponds to the difference between the market price and the lowest price of the target day and is calculated as follows:

$$A_k=\sum _{t\in \mathcal{T}}{\delta }_{k,t}^{\mathrm{L}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{s}\mathrm{t}}·\left(C_{k,t}-{\underset{\_}{C}}_k\right)·P_{k,t}^{\mathrm{C}},\forall k\in \mathcal{K},$$

(25)

where $A_k$ is the additional payment to the BESS at bus $k$, and ${\underset{\_}{C}}_k$ is the lowest market price at bus $k$ on the target day.

The effectiveness of the proposed method can be characterized by its ability to simultaneously guide the BESS charging behavior and avoid excessive incentive payments. When the lowest-price-guaranteed hours are designated, BESS owners are assured that they can charge their BESS at the lowest price during these periods. Therefore, as illustrated in Figure 2, BESS owners aiming to maximize the arbitrage revenue are expected to schedule charging within the guaranteed hours. Furthermore, because the market prices in congested areas within the network often reach their lowest values during congestion periods, the proposed method can contribute to suppressing social cost increases by minimizing the additional payments required.

4. Numerical Simulations

4.1. Simulation Settings

To evaluate the effectiveness of the proposed method, numerical simulations were conducted using a tested model based on the IEEJ EAST 10-machine O/V system model, in which RESs and grid-connected BESSs are integrated [32]. The numerical simulation model used in this study is shown in Figure 4. This model represents a simplified bulk power system in Japan’s Tohoku (Area 1) and Tokyo (Area 2) areas. The RESs and BESS are connected to buses 1–9, as shown in Figure 4. The demand at each bus and the generation output from the RESs were simulated by proportionally allocating the total electricity demand and the total solar and wind generation recorded in the Tokyo area during the FY2022–FY2023 period to each bus [35]. The demand ratio at buses 10–12 relative to buses 1–9 was set according to the original EAST 10-machine O/V model. Regarding the BESSs, the contracted grid-scale BESS capacity in the Tokyo area as of the end of June 2024 (990 MW) was uniformly allocated to nine buses [36]. The initial and terminal BESS SOC were both set to 50%, and the maximum number of charging starts per day was limited to one. The generation outputs of G1–G10 before congestion management were calculated by solving a DC-OPF that excluded the transmission line capacity constraints from Equations (14)–(16). In response to the additional integration of RESs and to maintain a supply–demand balance, G2, G3, and G5 (as shown in Figure 4) were removed from the model. Furthermore, the minimum output levels of the remaining generators were set to half of those defined in the original EAST 10-machine O/V system model. The generation costs for each generator were set based on the fuel, operation, and maintenance costs according to the generator type, as reported in References [37,38]. The generation cost of G7 (nuclear power) and the BESS was assumed to be 0 JPY/kWh, whereas that of the RESs was set to 0.01 JPY/kWh. The operational capacity of the transmission lines forming the loop network in Area 2 was set to 10,441 MW. This setting is based on congestion forecasts for the Tokyo area in FY2029, which indicate that three transmission lines with voltage levels of 154 kV or higher are expected to experience congestion exceeding 25 MW [39]. In the numerical model used in this study, Lines 1–3, as shown in Figure 4, experienced congestion throughout FY2023, with maximum congestion levels of 25, 35, and 512 MW, respectively. The operational capacity of all other transmission lines followed the settings of the original IEEJ EAST 10-machine O/V system model.

In this study, congestion management simulations were conducted for 12 representative days, one for each month of FY2023. These representative days were selected as the lowest-demand days during which congestion caused by RESs was more likely to occur. The maximum congestion observed on each transmission line during these days is presented in Figure 5, which shows only the lines where congestion occurred. As can be seen, transmission congestion is observed on ten out of the 12 representative days. To evaluate the effectiveness of the proposed method, two benchmark scenarios were introduced for comparison. The first was a case in which a BESS was installed but no charging incentives were provided (referred to as the “No Incentive” case). The second was a reference case where no BESS was integrated into the system (referred to as the “No BESS” case). The benefits of the proposed method were assessed by comparing the output curtailment results under these scenarios. The evaluation was based on three key indicators: the congestion mitigation cost, the total amount of renewable energy curtailment required to mitigate congestion, and additional payments to BESS owners.

Each BESS owner is assumed to independently predict the LMP to maximize the arbitrage profit for the following day. Additionally, in the proposed method, it is necessary for the system operator to predict the periods during which congestion is expected to occur. To simulate both the LMP prediction by BESS owners and the congestion prediction in the proposed method, the XGBoost algorithm, a variant of the gradient boosting method, was utilized [40].

Table 2. Setup of XGBoost algorithm for the prediction of LMPs and grid congestion.

Content	Settings
Inputs (explanatory variables)	Total RES generation output and demand on the target day (30 min intervals from 0:00–23:30)
Output	LMP at each bus or power flow at each line on the target day (30 min intervals from 0:00–23:30)
Maximum depth of a tree	3
Number of trees	100
Learning rate	0.1

summarizes the setup of the XGBoost model for the prediction of the LMP and grid congestion. These predictions are assumed to be performed at 12:00 on the day prior to the schedule submission. The model predicts 30-min-interval LMPs and transmission line power flows for the following day. A single model was trained and applied uniformly across all time slots. As explanatory variables, the total RES generation and the demand at each 30 min interval (00:00–23:30) on the target day were used. While these inputs must be predicted in real-world applications, they were assumed to be known here to isolate the performance of the prediction model. Historical data from FY2022, including the actual RES generation, demand, and power flow for each transmission line [35], were used to train the prediction model.

4.2. Simulation Results and Discussion

Figure 6 shows the congestion mitigation cost and the amount of renewable energy curtailment for each method over the evaluation period. These results are based on a threshold value of $\epsilon =0.5$, which was used to determine which buses were eligible for the lowest price guarantee under the proposed method (additional results obtained using different threshold values are provided in Appendix A). As shown in Figure 6, even the comparison method without charging incentives (“No Incentive”) achieves an approximately 14% reduction in both the congestion mitigation cost and renewable energy curtailment compared to the reference method (“No BESS”). This indicates that an arbitrage-based BESS operation, even without explicitly considering congestion timing, can still provide a certain level of congestion mitigation. However, the proposed method, which provides charging incentives to selected BESS units, achieves additional reductions of approximately 3.86% in the congestion mitigation cost and 3.89% in renewable energy curtailment compared with the “No Incentive” case.

Figure 7 shows a comparison between these indicators for each representative day. As can be seen, the proposed method consistently achieves lower congestion mitigation costs and renewable energy curtailment across all representative days compared with both the comparison and reference methods.

To discuss the underlying reasons for these results, a specific example from a representative day in April is examined. Figure 8 shows the power flow on Line 3, illustrating the occurrence of transmission congestion on the selected representative day. As can be seen, significant congestion of up to 191 MW occurred. According to the system operator’s power flow forecasts, the congestion was expected to occur between 9:30 and 12:30. Figure 9 shows the calculated power flow sensitivities of each BESS with respect to the congested line during this period. As can be seen, BESS 5, BESS 6, and BESS 9, located on the sending side of Line 3, exhibit higher sensitivities than the other BESS units. Accordingly, in the proposed method, the lowest-price-guaranteed hours were assigned to BESS 9 from 9:30 to 12:30 because its sensitivity exceeded the threshold (i.e., $\epsilon =0.5$). The resulting power flow changes on Line 3 and the charge/discharge schedule for BESS 9 using the proposed method are shown in Figure 10a,b, respectively. In the proposed method, the charging time of BESS 9 matches with the congestion period, whereas, in the “No Incentive” case, the BESS 9 owner begins charging at 7:30, resulting in a partial mismatch between the charging and congestion periods. To clarify the cause of this mismatch, Figure 11 shows both the LMP forecast devised by the BESS 9 owner and the actual LMP values. As can be seen, the forecasted LMP was expected to reach its minimum at 7:30. However, because system congestion mainly occurs during daytime, charging at 7:30 am did not contribute to congestion mitigation. Meanwhile, the proposed method applied the lowest price guarantee from 9:30 to 12:30 based on the forecasted congestion period, during which the BESS owner was assured the lowest possible charging cost. Consequently, the BESS owner was incentivized to charge during the designated period, matching the charging behavior with the congestion mitigation objective. These findings demonstrate that the proposed incentive scheme effectively encourages BESS charging during critical congestion periods, thereby enhancing the system’s ability to utilize BESSs for congestion relief.

Subsequently, the additional payments given to BESS owners as a result of the charging incentives under the proposed method are shown in Figure 12 and Figure 13. These figures also include the congestion mitigation cost reduction achieved by the proposed method compared with the other method (“No Incentive”). As shown in Figure 12, the additional payments to BESS owners under the proposed method accounted for approximately 7% of the corresponding cost-saving effect. This implies that the proposed method achieved a net reduction of approximately JPY 2.12 million in operational costs. Furthermore, for all representative days, the congestion mitigation cost-saving effect exceeds the additional payments, as shown in Figure 13, demonstrating that the proposed method reduces the operational costs more effectively than in the “No Incentive” case. This result can be attributed to the fact that the LMPs during the lowest-price-guaranteed hours tend to coincide with the lowest price of the day. For example, as shown in Figure 11, during a representative day in April, the LMP from 9:30 to 12:30—all within the lowest-price-guaranteed hours—remained at 0.01 JPY/kWh. Consequently, no additional payments were incurred in this case because the difference between the actual LMP and the guaranteed minimum was zero. These results confirm that the proposed method achieves both objectives: utilizing BESS charging for congestion relief and avoiding increases in social costs owing to incentive payments.

Figure 14 shows the arbitrage profit of the BESS selected for incentive application by the proposed method on each representative day. When the threshold was set to 0.5, only BESS 9 was selected as the target of the charging incentive across all representative days. Accordingly, Figure 12 presents the corresponding charging and discharging revenues of BESS 9. As observed, on all representative days, the arbitrage profit of BESS 9 under the proposed method exceeded that obtained in the “No Incentive” case. In particular, on the representative day in July, the revenue of BESS 9 increased by approximately JPY $109\times {10}^4$ compared to the “No Incentive” case. Note that both methods ceased operation on the representative day in August, as the predicted LMP at BESS 9 lacked sufficient volatility to enable profitable arbitrage.

Figure 15 shows the predicted LMP of BESS 9 on the representative day in July, while Figure 16 illustrates its charging and discharging schedules on the same day. In this case, the predicted LMP remains relatively stable throughout the day. As a result, under the comparison method (“No Incentive”), arbitrage opportunities are limited due to charging and discharging losses. Consequently, charging occurs only during the 8:30–9:30 period, when a temporary drop in the predicted LMP is expected. By contrast, the proposed method applies a lowest price guarantee to BESS 9 from 8:30 to 14:30. This increases the potential for arbitrage profit, resulting in a longer charging duration compared to the “No Incentive” case. These results confirm that the proposed method improves the price predictability and enhances the arbitrage profitability for BESS owners through the application of the lowest price guarantee.

5. Conclusions

This paper proposes a charging incentive design method for grid-connected BESSs aimed at congestion mitigation while considering the interests of both system operators and BESS owners. The proposed method utilizes the co-occurrence tendency between congestion periods and market prices. Specifically, the system operator designates “lowest-price-guaranteed hours” during time slots when congestion is expected. During these periods, BESS owners are allowed to charge the lowest daily price. Consequently, the proposed method naturally guides BESS operators, who aim to maximize their arbitrage revenues, to schedule charging during congestion periods. Furthermore, because market prices tend to fall to their minima during congestion events caused by RESs, the proposed method can suppress increases in additional payment costs from the system operator to BESS owners. Numerical simulation results based on a model representing a standard Japanese power system demonstrate that the proposed method reduces both the congestion mitigation costs by 3.86% and the curtailment of renewable energy by 3.89%, relative to the “No Incentive” method (current operation scheme in Japan). Moreover, the additional payments required under the proposed method represented only about 7% of the resulting cost savings, indicating that the proposed method achieves lower overall system operating costs.

The main limitation of this study is the assumption of perfect prediction in power flow by system operators. If congestion periods are predicted inaccurately, the market prices may not fall to the expected minimum levels, potentially resulting in increased compensation payments. Moreover, the accuracy of congestion forecasting is highly influenced by input conditions such as weather. For instance, under cloudy conditions, fluctuations in the RES output become more pronounced, making it difficult to accurately predict the magnitude and timing of congestion events. To address this challenge, it is essential to establish a framework that accounts for the uncertainty in the next-day congestion levels and determines whether the charging incentive should be applied accordingly. Future research should evaluate how forecasting errors during congestion periods affect the congestion mitigation costs, renewable energy curtailment, and additional payments. Overall, the findings of this study support the effective integration of renewable energy and BESSs by providing a practical and cost-efficient congestion management scheme.