Energy storage is a flexible component in modern distribution systems. Energy storage integration into smart distribution networks can enhance power supply and accommodation capabilities (Wang et al., 2021; Sun et al., 2024), facilitate load leveling (Calero et al., 2023; Wang et al., 2024), and optimize the operation of distribution networks (Liu et al., 2021; Tur, 2020). Therefore, investigating the optimal configuration of energy storage contributes to the efficient and low-carbon operation of distribution networks.

There has been extensive research on the optimal configuration of energy storage in distribution networks. Zhao et al. (2024) proposed an energy storage planning method based on the adaptive alternating direction method of multipliers, which improves the accommodation capability of renewable energy and reduces operational costs. Feng et al. (2024) introduced energy storage planning that considers demand response, resulting in lower operating costs and increased system flexibility. Chen et al. (2024) formulated the planning decisions for the locations and capacities of energy storage, ensuring economic operation of the system and enhancing its resilience to catastrophic weather events. Li et al. (2023) proposed an energy storage system planning method that considers multiple uncertainties, enhancing the local consumption level of renewable energy. Muqbel et al. (2022) introduced a budget-constrained planning model for distributed energy storage in unbalanced distribution networks, which effectively improves system economics. Abdeltawab and Mohamed (2022) proposed an energy storage planning method for profitability maximization, effectively reducing system upgrade costs. Zhu et al. (2023) found that appropriately configuring energy storage in high-penetration distribution networks can balance the intermittency of renewable energy power and improve system economics. Santos et al. (2022) proposed a dynamic distribution system reconfiguration technique with energy storage integration, which effectively reduces the system’s energy demand and carbon emissions. Jiang et al. (2021) introduced an optimal configuration method for both stationary and mobile energy storage in distribution networks, ensuring economic operation and power supply reliability. Sun et al. (2023) presented a two-layer planning method for energy storage in response to large-scale distributed photovoltaic integration, significantly enhancing the total supply capability (TSC) and accommodation capability of the distribution network. Wu et al. (2018) analyzed the impact of energy storage integration on power supply capability and found that properly configuring energy storage within the distribution network can increase the TSC.

In summary, it is found that the proper integration of energy storage can effectively enhance the TSC of distribution networks. However, existing research on energy storage optimization primarily focuses on increasing the TSC. In reality, the complete power supply capability of a distribution network under various load and distributed generation (DG) distributions is not solely defined by TSC but rather by a TSC curve (Xiao et al., 2018; 2021; 2022), of which the TSC represents only a small portion. On the other hand, research on the TSC curve of distribution networks that include energy storage has not yet been studied, leaving the quantification of the complete power supply capability in such networks unaddressed. Additionally, no studies have explored the optimization of energy storage integration in distribution networks based on the TSC curve, which means there is currently no effective method to determine the energy storage configuration that can enhance the complete power supply capability of the system based on the TSC curve.

To effectively address the aforementioned challenges, this paper proposes a novel method for optimizing energy storage configuration in distribution networks with a focus on enhancing power supply capability. The main contributions are as follows: (1) Introduced a TSC curve model for distribution networks with integrated energy storage, which provides a quantitative assessment of the complete power supply capability in distribution networks; (2) Proposed an energy storage optimal configuration method aimed at enhancing the TSC curve, which identifies critical components and effectively determines the optimal energy storage configuration, thereby fully enhancing the power supply capability of the distribution network.

The rest of this paper is organized as follows. Section 2 introduces the TSC curve model of distribution networks with energy storage. The optimal configuration method of energy storage for enhancing the TSC curve in distribution networks is presented in Section 3. The case study is presented in Section 4. Finally, the conclusion is drawn in Section 5.

The TSC curve is defined as a curve composed of the total load of all secure boundary points in ascending order (Xiao et al., 2018; 2021; 2022). A secure boundary point is a secure operating point with criticality. The criticality means that any minor load increase is bound to insecurity (Xiao et al., 2018; 2021; 2022). The physical meaning of the TSC curve is the complete power supply capability range of a distribution network that satisfies security constraints. It represents the complete load supply capability of the distribution network under various load and DG distributions.

The TSC curve model with integrated energy storage is formulated in Equation 1. L TSC = i , Val W LB , i Val W LB , i ≤ Val W LB , i + 1 Val W LB , i = ∑ k = 1 n S LB , k i ∈ 1 , 2 , 3 . . . (1) where L _TSC represents the TSC curve, the power supply capability Val( W _LB,i ) of an operating point is defined as the total load, S _LB,k is the apparent power of the load node k, and i is the serial number of the sampling point.

The security constraints satisfied by the TSC curve are formulated in Equations 2–5. A secure boundary point lies on the security boundary of Equation 2. W B , i = W LB , i W DGB , i = S LB , 1 , S LB , 2 , . . . , S LB , n T S DGB , 1 , S DGB , 2 , . . . , S DGB , h T ∈ B B = β j | j = 1 , 2 , 3 . . . (2) where W _B,i is the secure boundary point composed of W _LB,i and W _DGB,i , W _LB,i represents the apparent power vector of the load node, W _DGB,i represents the apparent power vector of the DG node, S _DGB,h denotes the apparent power of the DG node h, B represents the set of all security boundaries, and β _DG,j is the j-th security boundary.

The secure boundary point satisfies the criticality constraint of Equation 3. This constraint means that all load variables are subject to equality constraints, which are ensured by the summation of coefficients of load variables in equality constraints being greater than zero. Equation 3 includes both reverse and forward power flow constraints. Specifically, the equality constraints indicate that the forward power flow of a component has reached its capacity, while the inequality constraints ensure that the power flow does not exceed this capacity. Equality constraints imply that once the forward power flow of a component reaches its capacity, any load cannot be further increased. In this paper, a component that reaches its forward power flow capacity under equality constraints is defined as a critical component. Identifying critical components is crucial for the optimal configuration of energy storage. β j = W B , i 1 + s ( b 11 S LB , 1 + . . . + b 1 n S LB , n + b 1 n + 1 S DGB , 1 + . . . + b 1 n + h S DGB , h + b 1 n + h + 1 S ESSB , 1 + . . . + b 1 n + h + k S ESSB , k ) = c 1 … … 1 + s ( b l 1 S LB , 1 + . . . + b ln S LB , n + b l n + 1 S DGB , 1 + . . . + b l n + h S DGB , h + b l n + h + 1 S ESSB , 1 + . . . + b l n + h + k S ESSB , k ) = c l − c l + 1 ≤ 1 + s b l + 1 1 S LB , 1 + . . . + b l + 1 n + h S DGB , h + . . . + b l + 1 n + h + k S ESSB , k < c l + 1 … … − c m ≤ 1 + s b m 1 S LB , 1 + . . . + b m n + h S DGB , h + . . . + b m n + h + k S ESSB , k < c m b 11 + b 21 + . . . + b l 1 > 0 , … … , b 1 n + b 2 n + . . . + b ln > 0 (3) where l is the number of equality constraints, m is the total number of equality and inequality constraints, b _ln is coefficients with values of 0 or 1, s is the network loss coefficient, and c _l is the capacity of the l-th component (branch or electrical device).

Equation 4 represents the power constraint of energy storage. The energy storage power is the minimum of the power control system (PCS)-constrained power and state of charge (SOC)-constrained power. Noted that “max” indicates the selection of the minimum absolute value from the non-positive numbers, since both quantities on the right-hand side of the S _ESS,d expression are non-positive. S ESSB , i = ϒ S ESS , d + 1 − ϒ S ESS , c   ϒ = 0  or  1 S ESS , d = max S ESS , d PCS , T ESS , N Q S O C min − Q S O C t Δ t λ ESS η ESS , d S ESS , c = min S ESS , c PCS , T ESS , N Q S O C max − Q S O C t Δ t λ ESS η ESS , c (4) where S ESSB , i denotes the power of energy storage connected to node i, ϒ is a binary variable, S ESS , d is the discharging power of energy storage, S ESS , c is the charging power of energy storage, S ESS , d PCS is the maximum discharging power limits of the PCS, S ESS , c PCS is the maximum charging power limits of the PCS, T ESS , N is the energy capacity of the energy storage, Q S O C min is the minimum values of the SOC, Q S O C max is the maximum values of the SOC, Δ t is the charging and discharging time of the energy storage, η ESS , c is the charging efficiencies of the energy storage, η ESS , d is the discharging efficiencies of the energy storage, λ ESS is the power factor of the energy storage when connected to the distribution network.

Equation 5 indicates that all secure boundary points satisfy the voltage constraints. Δ U − ≤ Δ U % ≤ Δ U + (5) where Δ U is the voltage offset vector at nodes, Δ U − is the minimum voltage offset, and Δ U + is the maximum voltage offset. In China’s low-voltage distribution network, the national standard specifies that the maximum and minimum values of Δ U are +7% and −7%, respectively.

Note that the proposed TSC curve model is applicable in scenarios with high DG penetration. The reasons are as follows: A significant feature of distribution networks with high DG penetration is the occurrence of reverse power flow, where power flows from the feeder back to the network. In the proposed TSC curve model, both forward and reverse power flow constraints are included in Equation 3. This indicates that the model allows power flow reversal in distribution networks with abundant DG resources.

The differences between the proposed TSC curve model and existing models are as follows: The proposed TSC curve model takes into account energy storage as a flexible component, incorporating the power constraints of energy storage. It quantifies the complete power supply capability range of an active distribution network with integrated energy storage, which helps guide the optimal configuration of energy storage in the distribution network to improve system efficiency. However, the existing models (Xiao et al., 2018; 2021; 2022) do not consider energy storage and are not applicable to active distribution networks with integrated energy storage.

The proposed optimal configuration of energy storage aimed at enhancing the TSC curve is illustrated in Figure 1 and involves three steps: 1) Identify the critical component; 2) Develop a preliminary configuration scheme for energy storage integration into the distribution network based on the critical component; 3) Determine the optimal configuration of energy storage to enhance the TSC curve.

Step 1: Identify the critical component

As defined in Section 2, critical components are those in the distribution network where the forward power flow first reaches its capacity limit, at which point any load cannot be increased. The critical components are characterized by the fact that they include all downstream load nodes and the fewest possible DG nodes. This characteristic allows for the identification of critical components in any given distribution network.

Step 2: Develop a preliminary configuration scheme for energy storage integration into the distribution network based on the critical component

Based on the critical components, the nodes in the distribution network are divided into downstream and upstream nodes relative to the critical components. Downstream nodes are those located downstream of the critical component, while upstream nodes are those located upstream. Downstream refers to the direction from the substation transformer toward the end of the feeder, and upstream refers to the direction from the feeder end back toward the substation transformer.

N_S = {N₁, … ,N _k } denotes the upstream nodes of the critical component, and N_X = {N _k+1, … ,N _q } denotes the downstream nodes of the critical component. N _k represents the kth node in the distribution network, and q is the total number of nodes.

To effectively enhance the power supply capability of the distribution network, the preliminary configuration scheme involves integrating energy storage at the downstream nodes of the critical components rather than at the upstream nodes.

Step 3: Determine the optimal configuration of energy storage to enhance the TSC curve

After determining the preliminary configuration scheme for energy storage, it is necessary to calculate the TSC curve and its indices for the network with integrated energy storage. Then, the impact of different configuration schemes on enhancing power supply capability is compared. Finally, the optimal energy storage configuration that provides the most significant improvement in power supply capability is selected. The process includes the following steps:

Step 3.1: Calculate the TSC curve and its indices for distribution networks with integrated energy storage.

First, identify the secure boundary points from the sampled operating points that satisfy the criticality constraint of Equation 3. Then, solve the voltage offset for each secure boundary point with the power flow solver OpenDSS, thus determining the effective secure boundary points that satisfy the voltage constraints of Equation 5. (3)

Plot the TSC curve

Calculate the total load Val W LB , i for effective secure boundary points using Equation 1, then plot the TSC curve by arranging Val W LB , i in ascending order. (4)

Calculate the TSC curve indices

The maximum power supply capability is TSC (Xiao et al., 2018; 2021; 2022). The average power supply capability is TSC ¯ . The minimum power supply capability is TSC_min.

Step 3.2: Determine the optimal configuration scheme of energy storage by comparing the performance of different schemes in enhancing power supply capability.

Compare the TSC curves and its indices for different energy storage configuration schemes in the same figure and table. Select the configuration scheme with the highest TSC curve and the largest indices as the optimal configuration scheme of energy storage, as this configuration scheme offers the greatest comprehensive power supply capability.

In this section, the IEEE 33-node distribution network is used to verify the effectiveness of the proposed method. First, the TSC curve of the case is calculated, and then the optimal configuration scheme of energy storage is determined based on the TSC curve.

To address the planning of energy storage in the distribution network, this paper introduces a TSC curve model for the distribution network with integrated energy storage and proposes an optimal configuration method for energy storage aimed at enhancing power supply capability. The main conclusions are summarized as follows: (1)

The proposed TSC curve model quantifies the complete power supply capability of the distribution network with integrated energy storage as a TSC curve rather than a single TSC value.

To determine effectively the configuration scheme for integrating energy storage into the distribution network is of significant value for enhancing the system’s power supply capability and flexibility. The proposed method contributes to the secure, efficient, and clean low-carbon operation of the distribution network. As the computation of the TSC curve encompasses all possible load and DG distributions, it can effectively cover all the load and DG variations. The limitations of the proposed method in practical applications are as follows: The applicability of the proposed method to large-scale distribution networks is limited because the method requires a time-consuming sampling process when calculating the TSC curve. In the future, the energy storage planning of distribution networks, considering electric vehicles, the N-1 security constraints, and weather conditions on DG output power will be studied.