Recovery Strategy of Distribution Network Based on Power Supply Capability Assessment of Local Area Configured with Energy Gateway

Abstract

The growing integration of DG enhances distribution network resilience, but existing centralized fault recovery strategies face critical limitations: excessive computational burdens on DCs and the insufficient utilization of local control capabilities, particularly with large-scale DG deployments. Current studies often fail to balance computational efficiency and dynamic recovery coordination between centralized and decentralized resources. To address the issue, a hierarchical control architecture is proposed that involves collaboration between the DC and LA energy gateways. By dynamically quantifying LA PSC through net power feasibility analysis, the framework optimizes network reconfiguration (DC level) and decentralized DG scheduling (gateway level). Validated on a modified IEEE 45-bus system, the strategy restored 7 MWh (4:00 fault) and 5 MWh (10:00 fault) of load, outperforming static methods by 26.9× in the mid-day case. While effective in urban grids, rural DG-sparse areas require future integration of mobile storage. The work balances centralized coordination and decentralized execution, offering a scalable resilience solution for modern networks.

1. Introduction

The increasing frequency of extreme weather events, coupled with the rapid integration of DG, has underscored the critical need for resilient power distribution networks. Recent blackouts, such as the 2021 Texas winter storm [1], the 2022 Taiwan outage [2], and the 2023 Pakistan grid collapse [3], have exposed vulnerabilities in conventional grid recovery strategies. These events highlight a pressing challenge: traditional centralized fault recovery mechanisms struggle to balance computational efficiency with the dynamic coordination required in modern grids enriched with DG, including PV technologies, ESSs, and NBSUs. While DG offers significant potential for post-blackout recovery [4], its large-scale deployment introduces complexities in resource coordination, network reconfiguration, and real-time decision making, necessitating innovative solutions to enhance grid resilience.

Existing research has explored various approaches to address these challenges. Centralized optimization frameworks, such as those proposed in [5,6,7], rely on DCs to coordinate all DG technologies and switches. However, these methods suffer from exponential computational growth as DG penetration increases, leading to impractical solving times during emergencies. Decentralized strategies, such as microgrid-based islanding [6] and layered architectures [7], mitigate computational burdens but often sacrifice global optimality or require complex boundary adjustments. Recent advancements in flexibility modeling, including Thevenin equivalents [8] and projection-based feasible regions [9], aim to simplify multi-region coordination. However, high-dimensional constraints and redundant security conditions [10,11] limit their scalability. Furthermore, while studies like [12] emphasize operator interaction in regional energy systems, they overlook the autonomous capabilities of local controllers. A critical gap persists in harmonizing centralized oversight with decentralized execution, particularly in dynamically assessing local PSCs to enable efficient resource allocation.

The concept of TSC [13,14,15,16,17,18,19] has been widely adopted for contingency analysis, yet its application to DG-rich networks remains limited. For instance, Xu et al. [18] evaluated PSC under reliability constraints but did not integrate real-time DG variability. Similarly, Silva et al. [20] proposed TSO-DSO flexibility estimation but omitted hierarchical control mechanisms. Recent work by Chen et al. [16] optimized load ability curves but relied on static models incompatible with dynamic restoration phases. These limitations underscore a fundamental research question: How can distribution networks achieve computationally efficient, scalable recovery while fully leveraging localized DG capabilities during blackouts? This question branches into sub-problems: (1) how to decouple centralized and decentralized control tasks to reduce DC computational burdens; (2) how to dynamically quantify and utilize LA-specific PSC for optimal net power planning; and (3) how to ensure seamless coordination between network topology adjustments and DG scheduling?

Motivated by these challenges, this paper proposes a hierarchical recovery strategy grounded in PSC assessment. Our work diverges from prior studies by introducing a two-tier architecture, where DCs optimize high-level network topology and net power plans, while energy gateways at LAs autonomously schedule DG based on locally feasible regions. This approach builds on the umbrella constraint reduction framework [11] and integrates advancements in linearized mixed-integer programming [21]. Notably, we extend the concept of TSC to DG-dominated LAs, enabling dynamic PSC quantification through reactive power decoupling, a novel contribution that addresses the rigidity of traditional TSC models [22,23,24]. Additionally, we incorporate insights from recent studies on hybrid AC/DC microgrid resilience [25], which emphasize the role of localized control in mitigating communication failures.

The remainder of this paper is organized as follows: Section 2 details the hierarchical control architecture; Section 3 formalizes the PSC assessment methodology; Section 4 presents the recovery strategy; Section 5 validates the approach through simulations; Section 6 analyzes the achievements of this work; and Section 7 describes the main results achieved in quantitative and qualitative forms and adds the weaknesses of the proposed methodology, existing limitations, and possible future research. By bridging the gap between centralized optimization and decentralized execution, this work advances the state of the art in grid resilience, offering a scalable solution for DG-rich urban networks.

2. Hierarchical Control Architecture

2.1. The Subsection of the Distribution System Equipped with Energy Gateways

The distribution system illustrated in Figure 1 consists of multiple areas, each equipped with an energy gateway, where the DC serves as the central control point, managing switches and DG technologies by communicating with DTUs, FTUs, and the respective energy gateway for each LA. The energy gateway serves as a communication interface between the DC and the LA it serves. When the DC sends commands to alter switches, the network topology undergoes changes, facilitated by the collaboration between DTUs and FTUs. The energy gateway of each LA generates schedules for DG based on the commands received from the DC. This ensures the efficient operation and output of DG within each LA. The system configuration enables effective communication, control, and coordination, thereby guaranteeing a reliable power supply to the loads in the network. The hardware configuration of energy gateways is detailed in

Table 1. Hardware configuration of LAs.

The Components of a LA	Configuration
GPU running	1.2 GHz (Cortex-A71)
Internal memory	150 MB
Storage	4 GB
Operating system	Armv71 GNU/Linux

, and the communication protocol complies with the IEC 60870-5-104 standard [26].

2.2. The Information-Sharing Framework of a Distribution System Equipped with Energy Gateways

The information-sharing framework in Figure 2 is a key component of the distribution system, involving the DC, gateways, and clients. The DC collects dates from gateways to assess the LAs’ PSCs and design SRPs after blackouts, designing their net power plans.

Post-blackout, gateways collect historical data, real-time information, and power forecasts from clients. This dataset is used to calculate parameters for the DC, enabling informed decisions on SRP implementation. Gateways implement DC-provided SRPs and schedule DG within LAs.

3. Power Supply Capability Assessment of LAs

Assuming B PVs, C ESSs, and E NBSUs operate within the LA, the NBSUs managed by the same energy gateway start to generate energy simultaneously.

3.1. PSC Method of LAs

The PSC of LAs transmitted from gateways to the DC is represented by parameter set D, defined as follows:

$$\mathit{D}=\{p_{i,1}^L,p_{i,2}^L,\cdots ,p_{i,T}^L,q_{i,1}^L,q_{i,2}^L,\cdots ,q_{i,T}^L,{\zeta }_{i,1}^{PV},{\zeta }_{i,2}^{PV},\cdots ,{\zeta }_{i,T}^{PV},E_i^{ESS,Char},E_i^{ESS,Dis}\},$$

(1)

The method to calculate each element in set D is as follows:

$${\zeta }_{i,t}^{PV}=({\displaystyle \sum _{b=1}^B{S}_{i,b}^{PV}{\zeta }_{i,t,b}^{PV}})/({\displaystyle \sum _{b=1}^B{S}_{i,b}^{PV}})$$

(2)

$$E_i^{ESS,Char}={\displaystyle \sum _{\mathrm{c}=1}^C{E}_{i,c}^{ESS,Char}}$$

(3)

$$E_i^{ESS,Dis}={\displaystyle \sum _{c=1}^C{E}_{i,c}^{ESS,Dis}}$$

(4)

3.2. Parameters Stored in DC

When developing SRPs, the DC should rely on locally stored parameters, calculated as follows:

$$S_i^{PV}={\displaystyle \sum _{b=1}^B{S}_{i,b}^{PV}}$$

(5)

$$S_i^{ESS}={\displaystyle \sum _{c=1}^C{S}_{i,c}^{ESS}}$$

(6)

$$S_i^{NBSU}={\displaystyle \sum _{e=1}^E{S}_{i,e}^{NBSU}}$$

(7)

$$S_{i,\min }^{ESS}=\min \{S_{i,1}^{ESS},S_{i,2}^{ESS},\cdots ,S_{i,C}^{ESS}\}$$

(8)

$$p_i^{NBSU,down}=\min \{p_{i,1}^{NBSU,down},p_{i,2}^{NBSU,down},\cdots ,p_{i,E}^{NBSU,down}\}$$

(9)

$$p_i^{NBSU,up}=\min \{p_{i,1}^{NBSU,up},p_{i,2}^{NBSU,up},\cdots ,p_{i,E}^{NBSU,up}\}$$

(10)

$$T_i^{NBSU}=\max \{T_{i,1}^{NBSU}, T_{i,2}^{NBSU}, \cdots ,T_{i,E}^{NBSU}\}$$

(11)

$$p_i^{NBSU,in}=({\displaystyle \sum _{e=1}^E{T}_{i,e}^{NBSU}{p}_{i,e}^{NBSU,in}})/T_i^{NBSU}$$

(12)

3.3. The Feasible Regions of $p_{i,t}$/$q_{i,t}$ Defined by PSC of LAs

A DC uses feasible regions with smaller dimensions and fewer constraints, defined by LA PSCs, for centralized control. These regions are:

$${\Omega }^{DC,net}=\left\{(p_{i,t},q_{i,t})\left|s.t.Equation(13)\right.\right\}$$

$$-0.31(S_i^{PV}+S_i^{ESS}+S_i^{NBSU})\le q_{i,t}+q_{i,t}^L\le 0.31(S_i^{PV}+S_i^{ESS}+S_i^{NBSU})$$

(13a)

$$p_{i,t}+p_{i,t}^L=p_{i,t}^{PV}+p_{i,t}^{ESS}+p_{i,t}^{NBSU}$$

(13b)

$$0\le p_{i,t}^{PV}\le X_{i,t-1}{\zeta }_{i,t}^{PV}{S}_i^{PV}$$

(13c)

$$-S_{i,\min }^{ESS}\le p_{i,t}^{ESS}\le S_{i,\min }^{ESS}$$

(13d)

$$\begin{array}{cc}-E_i^{ESS,Char}\le \Delta t{\displaystyle \sum _{t=1}^d{p}_{i,t}^{ESS}}\le E_i^{ESS,Dis}& 1\le d\le T\end{array}$$

(13e)

$$-{\mu }_{i,t}^{NBSU}M\le t_i^{NBSU}-t\le \left(1-{\mu }_{i,t}^{NBSU}\right)M$$

(13f)

$$-{\phi }_{i,t}^{NBSU}M\le t_i^{NBSU}+T_i^{NBSU}-t\le \left(1-{\phi }_{i,t}^{NBSU}\right)M$$

(13g)

$${\mu }_{i,t}^{NBSU}-{\phi }_{i,t}^{NBSU}\le X_{i,t}$$

(13h)

$$0\le p_{i,t}^{NBSU}-({\phi }_{i,t}^{NBSU}-{\mu }_{i,t}^{NBSU})p_i^{NBSU,in}\le {\phi }_{i,t}^{NBSU}{S}_i^{NBSU}$$

(13i)

$$\left({\phi }_{i,t}^{NBSU}-1\right)M-p_i^{NBSU,down}\le p_{i,t+1}^{NBSU}-p_{i,t}^{NBSU}\le \left(1-{\phi }_{i,t}^{NBSU}\right)M+p_i^{NBSU,up}$$

(13j)

3.4. The Actual Feasible Regions of DG in LAs

Ignoring ESS charge/discharge losses, the feasible range for DG’s actual PSC within LAs is defined as:

$${\Omega }^{LA}=\left\{(p_{i,t},q_{i,t})\left|s.t.Equation(14),Equation(15),Equation(16),Equation(17)\right.\right\}$$

$$p_{i,t}={\displaystyle \sum _{b=1}^B{p}_{i,t,b}^{PV}}+{\displaystyle \sum _{c=1}^C{p}_{i,t,c}^{ESS}}+{\displaystyle \sum _{\mathrm{e}=1}^E{p}_{i,t,e}^{NBSU}}-p_{i,t}^L$$

(14a)

$$q_{i,t}={\displaystyle \sum _{b=1}^B{q}_{i,t,b}^{PV}}+{\displaystyle \sum _{c=1}^C{q}_{i,t,c}^{ESS}}+{\displaystyle \sum _{\mathrm{e}=1}^E{q}_{i,t,e}^{NBSU}}-q_{i,t}^L$$

(14b)

$$-\sqrt{2}{S}_{i,b}^{PV}\le p_{i,t,b}^{PV}\pm q_{i,t,b}^{PV}\le \sqrt{2}{S}_{i,b}^{PV}$$

(15a)

$$-S_{i,b}^{PV}\cos {\phi }_{\max }\le q_{i,t,b}^{PV}\le S_{i,b}^{PV}\cos {\phi }_{\max }$$

(15b)

$$0\le p_{i,t,b}^{PV}\le X_{i,t-1}{\zeta }_{i,t,b}^{PV}{S}_{i,b}^{PV}$$

(15c)

$$-\sqrt{2}{S}_{i,c}^{ESS}\le p_{i,t,c}^{ESS}\pm q_{i,t,c}^{ESS}\le \sqrt{2}{S}_{i,c}^{ESS}$$

(16a)

$$-S_{i,c}^{ESS}\cos {\phi }_{\max }\le q_{i,t,c}^{ESS}\le S_{i,c}^{ESS}\cos {\phi }_{\max }$$

(16b)

$$-S_{i,c}^{ESS}\le p_{i,t,c}^{ESS}\le S_{i,c}^{ESS}$$

(16c)

$$\begin{array}{cc}-E_{i,c}^{ESS,Char}\le \Delta t{\displaystyle \sum _{t=1}^d{p}_{i,t,c}^{ESS}}\le E_{i,c}^{ESS,Dis}& 1\le d\le T\end{array}$$

(16d)

$$-\sqrt{2}{S}_{i,e}^{NBSU}\le p_{i,t,e}^{NBSU}\pm q_{i,t,e}^{NBSU}\le \sqrt{2}{S}_{i,e}^{NBSU}$$

(17a)

$$-S_{i,e}^{NBSU}\le q_{i,t,e}^{NBSU}\le S_{i,e}^{NBSU}$$

(17b)

$$-{\mu }_{i,t,e}^{NBSU}M\le t_{i,e}^{NBSU}-t\le \left(1-{\mu }_{i,t,e}^{NBSU}\right)M$$

(17c)

$$-{\phi }_{i,t,e}^{NBSU}M\le t_{i,e}^{NBSU}+T_{i,e}^{NBSU}-t\le \left(1-{\phi }_{i,t,e}^{NBSU}\right)M$$

(17d)

$${\mu }_{i,t,e}^{NBSU}-{\phi }_{i,t,e}^{NBSU}\le X_{i,t}$$

(17e)

$$0\le p_{i,t,,e}^{NBSU}-({\phi }_{i,t,e}^{NBSU}-{\mu }_{i,t,e}^{NBSU})p_{i,e}^{NBSU,in}\le {\phi }_{i,t,e}^{NBSU}{S}_{i,e}^{NBSU}$$

(17f)

$$\left({\phi }_{i,t,,e}^{NBSU}-1\right)M-p_{i,e}^{NBSU,down}\le p_{i,t+1,e}^{NBSU}-p_{i,t,e}^{NBSU}\le \left(1-{\phi }_{i,t,e}^{NBSU}\right)M+p_{i,e}^{NBSU,up}$$

(17g)

where ${\phi }_{\max }$ is the upper limit of the power factor angle of PVs and ESSs, and the value of $\cos {\phi }_{\max }$ is 0.31.

Proof. 

The Net Power Plans Formulated by a DC All Can Be Implemented by Las. □

The transformation from Equations (14)–(17) to Equation (15) is outlined here, emphasizing that Equation (15) is a sufficient condition for Equations (14)–(17), i.e., ${\Omega }^{\mathrm{D}\mathrm{C},\mathrm{n}\mathrm{e}\mathrm{t}}$⊆${\Omega }^{\mathrm{L}\mathrm{A},\mathrm{n}\mathrm{e}\mathrm{t}}$.

Detailed derivations of the feasible regions are provided in Appendix A.

4. The Recovery Strategy of a Distribution Network

The recovery strategy of a distribution network includes an upper-level DC model and lower-level LA energy gateway models. The upper-level model determines the dynamic network topology and the net power plants, whereas the lower-level model schedules DG.

4.1. The Upper-Level Model for a DC

4.1.1. Objective Function

The objective function F₁, defined in Equation (18), calculates the post-blackout load saved and switch operating costs.

$$F_1={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^N{X}_{i,t}{C}_i{p}_{i,t}^L}}-{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^N{\displaystyle \sum _{t=1}^T\left|b_{ij,t}-b_{ij,t-1}\right|}}}$$

(18)

4.1.2. Constraints of Network Topology

The locations of tie lines and switches in the distribution network form the structural foundation for topology modifications. Only lines equipped with switches can be disconnected or connected, as shown in Equation (19). The linear relationships between the connectivity matrix and the network adjacent matrix, established in [21], are shown in Equations (20)–(26):

$$b_{ij,t}=a_{ij}\cdot b_{ij,t}$$

(19)

$$h_{ij1,t}=b_{ij,t}$$

(20)

$$h_{{ijk}_{\max },t}=g_{ij,t}$$

(21)

$$k_{\max }=2+{\log }_2\left(N-1\right)$$

(22)

$$1<k\le k_{\max }$$

(23)

$$\begin{array}{cc}(h_{ijk,t}-1)M+\epsilon \le {\displaystyle \sum _{q=1}^N{c}_{ij(k-1)q,t}}\le h_{ijk,t}M& i\le j\end{array}$$

(24)

$$h_{ijk,t}=h_{jik,t}$$

(25)

$$-c_{ij(k-1)q,t}M\le 2-h_{iq(k-1),t}+h_{qj(k-1),t}\le (1-c_{ij(k-1)q,t})M$$

(26)

where nonlinear constraints arising from integer–binary multiplications are converted using the linearized factors h_ijk,t and c_ijkq,t, as shown in Equations (24)–(26).

The restored island is radial, with the number of tie lines equal to twice the number of LAs minus 2, derived from the undirected graph’s relationship, as shown in Equations (27)–(30):

$$x_{i,t}={\displaystyle \sum _{j=1}^N{b}_{ij,t}}-1$$

(27)

$$\left(X_{i,t}-1\right)M\le {\displaystyle \sum _{j=1}^N{y}_{ij,t}}-2{\displaystyle \sum _{j=1}^N{g}_{ij,t}}+2\le \left(1-X_{i,t}\right)M$$

(28)

$$\left(g_{ij,t}-1\right)M\le y_{ij,t}-x_{j,t}\le \left(1-g_{ij,t}\right)M$$

(29)

$$-g_{ij,t}M\le y_{ij,t}\le g_{ij,t}M$$

(30)

where x_i,t is the connected tie line number of LA i at time t; y_ij,t are linearized factors used to linearize the multiplication of binary and integer variables, as expressed in Equation (28) to (30).

4.1.3. Constraints of Tidal Flow

It is necessary to ensure that system i can restore LA j, as shown in Equations (31)–(33), before computing the power flow.

$$\left(g_{ij,t}-1\right)M\le G_{ij,t}-p_{j,t}\le \left(1-g_{ij,t}\right)M$$

(31)

$$-g_{ij,t}M\le G_{ij,t}\le g_{ij,t}M$$

(32)

$$(X_{i,t}-1)M\le {\displaystyle \sum _{j=1}^N{G}_{ij,t}}\le X_{i,t}M$$

(33)

For the restored LAs, the inflow power is equal to the outflow power, as shown in Equation (34).

$$\left\{\begin{array}{c}(X_{i,t}-1)M\le p_{i,t}-{\displaystyle \sum _{j=1}^N{P}_{ij,t}}\le (1-X_{i,t})M\\ (X_{i,t}-1)M\le q_{i,t}-{\displaystyle \sum _{j=1}^N{Q}_{ij,t}}\le (1-X_{i,t})M\end{array}\right.$$

(34)

The LA with the largest net power within the system is selected as the balanced node for power flow calculation, as shown in Equations (35) and (36). The voltage drop rule is shown in Equation (37).

$$(A_{ij,t}-1)M+\epsilon \le G_{ii,t}-G_{ij,t}\le A_{ij,t}M$$

(35)

$$-(N-1+A_{ii,t}-{\displaystyle \sum _{j=1}^N{A}_{ij,t}})M\le U_{i,t}^{sqr}-X_{i,t}{U}_N^{sqr}\le (N-1+A_{ii,t}-{\displaystyle \sum _{j=1}^N{A}_{ij,t}})M$$

(36)

$$\left(b_{ij,t}-1\right)M\le U_{i,t}^{sqr}-U_{j,t}^{sqr}-{\displaystyle \frac{P_{ij,t}{R}_{ij}+Q_{ij,t}{X}_{ij}}{2}}\le \left(1-b_{ij,t}\right)M$$

(37)

The power flowing between two unconnected LAs is 0, as shown by Equation (38). The net power coming from the unrecovered LAs is 0, as shown by Equation (39).

$$\left\{\begin{array}{c}-b_{ij,t}M\le P_{ij,t}\le b_{ij,t}M\\ -b_{ij,t}M\le Q_{ij,t}\le b_{ij,t}M\end{array}\right.$$

(38)

$$\left\{\begin{array}{c}-X_{i,t}M\le P_{ij,t}\le X_{i,t}M\\ -X_{i,t}M\le Q_{ij,t}\le X_{i,t}M\end{array}\right.$$

(39)

4.1.4. Constraints of Voltage Limit

In restored LAs, bus voltages remain within the specified range; for unrecovered LAs, voltages are 0, as shown in Equation (40).

$$X_{i,t}{U}_{\min }^{sqr}\le U_{i,t}^{sqr}\le X_{i,t}{U}_{\max }^{sqr}$$

(40)

The dynamic network topology and net power of LAs are determined by the upper-level model for a DC based on Equation (41).

$$\left\{\begin{array}{l}\max imize:\left(18\right)\\ subjectto:\left(13\right),\left(19\right)–\left(40\right)\end{array}\right.$$

(41)

4.2. The Lower-Level Models for LA Energy Gateways

The objective function F2, defined in Equation (42), calculates the total cost of DG. The charging and discharging costs of ESSs differ, as indicated by Equations (43)–(45). Lower-level models schedule DG for LA energy gateways based on Equation (46).

$$F_2={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^N({\alpha }^{PV}{p}_{i,t,b}^{PV}+C_{i,t,c}^{ESS}+{\alpha }^{NBSU}{p}_{i,t,e}^{NBSU})}}$$

(42)

$$({\eta }_{i,t,c}^{ESS}-1)M\le p_{i,t,c}^{ESS}\le {\eta }_{i,t,c}^{ESS}M$$

(43)

$$({\eta }_{i,t,c}^{ESS}-1)M\le C_{i,t,c}^{ESS}-{\alpha }^{ESS,Dischar}{p}_{i,t,c}^{ESS}\le (1-{\eta }_{i,t,c}^{ESS})M$$

(44)

$$-{\eta }_{i,t,c}^{ESS}M\le C_{i,t,c}^{ESS}-{\alpha }^{ESS,Char}{p}_{i,t,c}^{ESS}\le {\eta }_{i,t,c}^{ESS}M$$

(45)

$$\left\{\begin{array}{l}\min imize:\left(42\right)\\ subjectto:\left(14\right)–\left(17\right),\left(43\right)–\left(45\right)\end{array}\right.$$

(46)

5. Numerical Evaluation

5.1. Case Study

The proposed optimization is tested on a modified 45-bus 10 kV urban distribution network. The IEEE 45-bus model was selected for its standardized representation of 10 kV urban distribution networks, ensuring comparability with prior studies. Its topology aligns with real-world radial structures and mixed-load profiles, while modifications enable testing under high DG penetration. The model’s dynamic switch configurations and adjustable parameters effectively validate the hierarchical control architecture’s adaptability to fault recovery and network reconfiguration.

The transformers in the urban distribution network include two 110 kV transformers with a capacity of 50,000 kVA. The system comprises three ESSs, four PV power stations, and two diesel generators from NBSUs. The schematic of the network is shown in Figure 3.

Table 2. Details of the PV power stations.

Bus No.	Voltage Level	Installed Capacity (kW)
20	10 kV	260
23	10 kV	260
28	380/220 V	2800
38	10 kV	1000

,

Table 3. Details of the ESSs.

Bus No.	${\mathit{E}}_{\mathit{i},\mathit{c}}^{\mathit{E}\mathit{S}\mathit{S},\mathit{D}\mathit{i}\mathit{s}}$ (kWh)	${\mathit{E}}_{\mathit{i},\mathit{c}}^{\mathit{E}\mathit{S}\mathit{S},\mathit{C}\mathit{h}\mathit{a}\mathit{r}}$ (kW)	${\mathit{S}}_{\mathit{i},\mathit{c}}^{\mathit{E}\mathit{S}\mathit{S}}$ (kW)
25	1450	50	500
27	2320	80	800
37	1450	50	200

and

Table 4. Details of the NBSUs.

Bus No.	${\mathit{S}}_{\mathit{i},\mathit{e}}^{\mathit{N}\mathit{B}\mathit{S}\mathit{U}}$ (kW)	${\mathit{p}}_{\mathit{i},\mathit{e}}^{\mathit{N}\mathit{B}\mathit{S}\mathit{U},\mathit{i}\mathit{n}}$ (kW)	${\mathit{p}}_{\mathit{i},\mathit{e}}^{\mathit{N}\mathit{B}\mathit{S}\mathit{U},\mathit{u}\mathit{p}}$ (kW/h)	${\mathit{p}}_{\mathit{i},\mathit{e}}^{\mathit{N}\mathit{B}\mathit{S}\mathit{U},\mathit{d}\mathit{o}\mathit{w}\mathit{n}}$ (kW/h)	${\mathit{T}}_{\mathit{i}}^{\mathit{N}\mathit{B}\mathit{S}\mathit{U}}$ (h)
36	360	6.4	360	360	0.5
44	80	0.8	80	80	0.5
45	400	7.2	400	400	0.5

list the installed DG technologies, including PV power stations, NBSUs, and ESSs, respectively.

Table 5. Details of the lines.

Start Bus	Termination Node	Total Line Length (m)	Line Model	Conductor Section (mm2)
1	2	420	YJV22-8.7/15-3*300	300
2	3	226	JKLYJ-10/185	185
3	4	138	JKLYJ-10/185	185
3	20	130	JKLYJ-10/185	185
20	21	180	JKLYJ-10/185	185
21	22	170	JKLYJ-10/185	185
22	23	280	JKLYJ-10/185	185
4	5	145	JKLYJ-10/185	185
5	6	——	——	——
6	7	136	JKLYJ-10/185	185
7	8	150	JKLYJ-10/185	185
8	9	162	JKLYJ-10/185	185
9	10	——	——	——
10	11	700	JKLYJ-10/185	185
11	12	160	JKLYJ-10/185	185
12	13	153	JKLYJ-10/185	185
13	14	——	——	——
14	15	102	JKLYJ-10/185	185
15	16	505	JKLYJ-10/185	185
16	17	——	——	——
17	18	105	JKLYJ-10/185	185
18	19	170	YJV22-8.7/15-3*300	300
1	24	196	YJV22-8.7/15-3*300	300
24	25	148	YJV22-8.7/15-3*300	300
24	26	120	YJV22-8.7/15-3*300	300
24	27	92	YJV22-8.7/15-3*300	300
24	28	116	YJV22-8.7/15-3*300	300
24	29	370	YJV22-8.7/15-3*300	300
29	30	150	YJV22-8.7/15-3*300	300
29	31	375	YJV22-8.7/15-3*300	300
29	32	150	YJV22-8.7/15-3*300	300
32	33	802	YJV22-8.7/15-3*300	300
32	34	120	YJV22-8.7/15-3*300	300
32	35	806	YJV22-8.7/15-3*300	300
35	36	132	JKLYJ-10/185	185
36	37	150	JKLYJ-10/185	185
37	38	132	JKLYJ-10/185	185
38	39	——	——	——
39	40	180	JKLYJ-10/185	185
40	41	233	JKLYJ-10/185	185
41	42	160	JKLYJ-10/185	185
42	43	——	——	——
43	44	155	JKLYJ-10/185	185

Note: In Table 5, ‘3*300’ means ‘three conductors, with a single section of 300 mm²’.

presents the details of the 10 kV lines assuming a fault on the tie line between buses 12 and 13, causing a power outage from 6:00 to 14:00.

5.2. Results and Discussion

The effectiveness and adaptability of the proposed hierarchical recovery strategy were validated through comprehensive simulations on a modified IEEE 45-bus urban distribution network. Two distinct fault cases—occurring at 4:00 and 10:00—were analyzed to evaluate the method’s performance under varying operational conditions.

5.2.1. Case 1: Fault at 4:00

A five-hour outage commencing at 4:00 tested the strategy’s ability to coordinate ESSs, NBSUs, and power stations during low solar availability. The dynamic SRP, as shown in Figure 4 and Figure 5, restored an additional 7 MWh of load through phased recovery actions. During the initial phase (4:00–4:30), ESSs prioritized power supply to critical loads while simultaneously initiating NBSUs, enabling the restoration of LAs 29–42 within 30 min. Subsequent load surges at 6:00 temporarily disrupted service in LAs 39–42; however, increased PV output by 7:00 allowed these areas to be re-energized. By 8:30, dynamic network reconfiguration mitigated outages in LAs 6–18 and 24–28, demonstrating the method’s adaptability to fluctuating demand. Energy contributions were quantified as follows: NBSUs provided 34.1% (25.7 MWh) of the restored energy, ESSs contributed 28.5%, and PV systems accounted for 37.4%, reducing load shedding by 18% during peak sunlight hours.

5.2.2. Case 2: Fault at 10:00

This case evaluated the method’s responsiveness to mid-day operational challenges characterized by higher solar irradiance and dynamic load profiles. The dynamic SRP, as shown in Figure 6 and Figure 7, restored 5 MWh of load, with PV systems contributing 54.7% and NBSUs contributing 41.1%. Real-time adjustments to solar irradiance variations (10:00–13:00) enabled ESSs to compensate for declining PV output, preventing load interruptions. In contrast, the static SRP, as shown in Figure 8, which relies on predefined DG output profiles and rigid network topologies, achieved only 0.186 MWh of restored energy, failing to adapt to PV generation fluctuations and load demand shifts. The dynamic approach’s ability to integrate real-time environmental data and adjust topology accordingly resulted in a 26.9-fold improvement over the static method, underscoring its superiority in dynamic environments.

These results highlight its robustness across diverse fault cases, system scales, and DG penetration levels.

6. Discussion

The hierarchical recovery strategy demonstrates significant advancements in computational efficiency, dynamic coordination, and multi-resource synergy, positioning it as a transformative solution for modern distribution networks. A critical analysis of the 10:00 fault scenario reveals the algorithm’s ability to outperform static approaches through real-time adaptability. While the static SRP assumes fixed DG outputs and network configurations, the dynamic SRP continuously updates PSC boundaries based on real-time data. For instance, during the 10:00–13:00 period, PV generation fluctuated by ±30% due to transient cloud cover. The dynamic method maintained restored energy stability with less than 5% deviation by adjusting the ESS discharge rates and NBSU startup sequences. In contrast, the static SRP, constrained by rigid PSC assumptions, experienced a 22% increase in load-shedding events, highlighting its inability to respond to real-time variability.

In the 10:00 fault scenario, it achieved 5 MWh of restored energy—26.9 times higher than the static SRP—while maintaining computation times under 34 s. This efficiency enables real-time implementation in large-scale networks, a critical requirement for grid resilience. However, limitations persist in DG-sparse rural networks, where conservative PSC boundaries may reduce restored energy by 15%. Integrating mobile ESSs or demand response mechanisms could mitigate this issue. Additionally, prolonged communication outages (>10 min) between gateways and the dispatch center degrade the performance to islanded modes, lowering restored energy by 28%. Future work could explore edge computing architectures to enhance fault tolerance

In conclusion, this strategy bridges the gap between computational efficiency and dynamic adaptability, offering a scalable solution for DG-rich distribution networks. Its ability to outperform static and centralized methods across diverse fault scenarios positions it as a critical tool for enhancing grid resilience. Future research may explore hybrid AC/DC microgrid integration or probabilistic load forecasting to further refine its robustness under uncertainty.

7. Conclusions

The hierarchical recovery strategy proposed in this paper has achieved remarkable results in enhancing the resilience of distribution networks. Quantitative outcomes demonstrate that the strategy successfully restored 7 MWh of load in the event of a 4:00 fault and 5 MWh in the case of a 10:00 fault. When compared to static methods, the dynamic approach showcased a 26.9-fold improvement in the mid-day scenario. Notably, during the 10:00 fault, the dynamic strategy restored 5 MWh of load, with PV systems contributing 54.7% and NBSUs contributing 41.1%. The strategy also exhibited exceptional adaptability to fluctuating solar irradiance and dynamic load profiles, maintaining restored energy stability with less than 5% deviation by adjusting the ESS discharge rates and NBSU startup sequences.

Qualitatively, the strategy effectively bridges the gap between centralized coordination and decentralized execution, offering a scalable solution for modern distribution networks with high penetration of DG. It dynamically quantifies the PSC of LAs through net power feasibility analysis, thereby optimizing network reconfiguration at the DC level and decentralized DG scheduling at the gateway level. This approach not only enhances computational efficiency but also fully leverages localized DG capabilities during blackouts, thereby improving the overall resilience of the grid.

However, the strategy also has some weaknesses and limitations. While it performs exceptionally well in urban grids with high DG penetration, it faces challenges in rural areas with sparse DG deployment. In such cases, the strategy may require the integration of mobile energy storage systems to enhance its effectiveness. Additionally, the strategy assumes reliable communication between energy gateways and the dispatch center. Prolonged communication outages can degrade the system’s performance, reducing the restored energy by 28% as the system reverts to islanded modes. In DG-sparse rural networks, conservative PSC boundaries may result in a 15% reduction in restored energy. Future research directions could include the integration of mobile energy storage, edge computing architectures, hybrid AC/DC microgrid integration, probabilistic load forecasting, and demand response mechanisms to further enhance the strategy’s effectiveness and applicability.