In recent years, the frequent occurrence of extreme natural disasters has posed severe threats to the safe and stable operation of distribution networks. Taking the 2021 rainstorm in Henan Province, China, as an example, extreme weather caused faults in over 800 distribution lines, affecting more than 980,000 people and resulting in significant economic losses. To assess the ability of distribution networks to cope with extreme disasters, the concept of “resilience” has been introduced to describe their capacity to prevent, withstand, and rapidly recover from such disruptive events. Effectively improving the resilience level of distribution networks has become an urgent task worldwide.
The large-scale integration of Distributed Generation (DG) offers new means for enhancing distribution network resilience. Following a large-scale fault, DGs can serve as islanded power sources to continuously supply power to partial loads, reducing the blackout scope and minimizing load loss throughout the disaster event. Currently, most strategies for DG-integrated resilience improvement focus on post-disaster islanding. However, these studies often simplistically treat all DGs as island-capable power sources. In reality, the ability of a DG to operate in islanded mode is significantly influenced by the control strategy of its grid-connected power electronic interface, the on grid inverter.
The control mode of an on grid inverter is primarily divided into two categories: Grid-Following (GFL) and Grid-Forming (GFM). This distinction is crucial for resilience planning. GFL inverters synchronize with the grid using a Phase-Locked Loop (PLL). They act as controlled current sources but cannot provide inertia or frequency support. Consequently, they are unsuitable for operation in an islanded grid lacking a stable frequency reference. In contrast, GFM inverters employ a power synchronization strategy similar to synchronous generators, acting as controlled voltage sources. They can autonomously establish grid voltage and frequency, making them capable of operating in both grid-connected and islanded modes, providing essential power and frequency support.
| Feature | Grid-Following (GFL) Inverter | Grid-Forming (GFM) Inverter |
|---|---|---|
| Operating Characteristic | Controlled Current Source | Controlled Voltage Source |
| Response to Voltage Transient | Output voltage fluctuates, output current remains constant. | Output voltage remains constant, output current fluctuates (potentially large). |
| Applicable Scenarios | Grid-connected mode only. | Grid-connected and Islanded modes. |
| Advantages |
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| Disadvantages |
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The vector diagrams in Figure 3 illustrate the distinct responses of GFL and GFM on grid inverters to a grid voltage transient ($U_g$ to $U’_g$). The GFL inverter maintains a constant current $I$, causing its internal equivalent electromotive force $E$ to jump to $E’$. The GFM inverter maintains a constant internal voltage $E$, resulting in a current transient to $I’$, which carries a risk of overcurrent.
Therefore, a practical resilience enhancement strategy must account for the type of on grid inverter control. Not all DGs can seamlessly form or support an island. This paper proposes a resilience enhancement method for distribution networks that specifically considers the control strategies of DG on grid inverters. The core idea involves a two-stage islanding process: In Stage 1, immediately after a fault severs the connection to the main grid, GFM inverters within the isolated section activate to establish voltage and frequency stability, forming a stable microgrid island. In Stage 2, once the island’s frequency is securely established by GFM units, the GFL inverters (which were disconnected initially) can be safely reconnected to the island. They then provide additional active power support, reducing the power deficit within the island and maximizing the critical load supply, thereby enhancing the overall system resilience.
The proposed framework is built upon reliable distribution automation, sensor, and communication technologies, allowing for accurate monitoring of wind power, PV, load, and tie-line power. Following a large-scale fault, distributed resources can flexibly provide power and frequency support to the system through their on grid inverters based on different control strategies, aiming to minimize the scope and amount of load loss and mitigate the adverse effects of frequency instability caused by unplanned islanding.
Modeling DG Output Considering On Grid Inverter Control Strategy
The output of a DG is constrained by its on grid inverter’s capabilities. A GFL-controlled on grid inverter can operate normally in grid-connected mode, providing active power support ($P_{i,t}$) to the main grid. However, in an islanded mode lacking a stable frequency reference, the GFL inverter becomes unstable and must disconnect. Therefore, for a DG at node $i$ with a GFL on grid inverter, its active and reactive power output in an unstable island is zero. Conversely, a GFM-controlled on grid inverter can operate in both grid-connected and islanded modes, but its output is always limited by its maximum capacity.
We define the relevant sets: $\phi_{DG}$ for all DG nodes, $\phi_{GFL}$ for nodes with GFL inverters, and $\phi_{GFM}$ for nodes with GFM inverters. The output constraints for a DG at node $i$ at time $t$ can be modeled as:
$$0 \leq P_{i,t} \leq x_{i,g} P^{max}_{i,t}, \quad \forall i \in \phi_{DG}$$
$$0 \leq Q_{i,t} \leq x_{i,g} Q^{max}_{i,t}, \quad \forall i \in \phi_{DG}$$
where $P^{max}_{i,t}$ and $Q^{max}_{i,t}$ are the maximum available active and reactive power. The binary variable $x_{i,g}$ indicates the operational availability based on inverter type:
$$x_{i,g} = 1, \quad \forall i \in \phi_{GFM}$$
$$x_{i,g} = 0, \quad \forall i \in \phi_{GFL}$$
This model explicitly captures the fact that GFL-type on grid inverters contribute zero power in an island until frequency stability is provided by other sources (like GFM units).
Resilience Enhancement Model Formulation
Objective Function
The goal is to enhance resilience by minimizing the total active power deficit throughout the disaster event. The objective function is formulated as the integral of the difference between the load profile under normal conditions $l_0(t)$ and the actual supplied load profile $l_1(t)$ during the disaster period from start time $T_s$ to end time $T_f$:
$$\min f = \int_{T_s}^{T_f} (l_0(t) – l_1(t)) dt$$
Constraints
The model must satisfy various operational and safety constraints for both grid-connected and islanded modes.
1. Power Flow Constraints: The system must obey the DistFlow equations for each line $(i,j)$ in the set of connected branches $\Psi_b$:
$$\sum_{i \in f(j)} (P_{ij} – r_{ij} I_{ij,sqr}) = \sum_{i \in s(j)} P_{jk} + P_j$$
$$\sum_{i \in f(j)} (Q_{ij} – x_{ij} I_{ij,sqr}) = \sum_{i \in s(j)} Q_{jk} + Q_j$$
$$P_i = P_{i,G} + P_{i,pv} + P_{i,w} – P_{i,load}$$
$$Q_i = Q_{i,G} + Q_{i,pv} + Q_{i,w} – Q_{i,load}$$
$$U_{j,sqr} = U_{i,sqr} – 2(r_{ij}P_{ij} + x_{ij}Q_{ij}) + I_{ij,sqr}(r_{ij}^2 + x_{ij}^2), \quad \forall (i,j) \in \Psi_b$$
where $f(j)$ and $s(j)$ are sets of upstream and downstream nodes connected to node $j$, $I_{ij,sqr}$ and $U_{i,sqr}$ are squared current and voltage magnitudes, and $r_{ij}$, $x_{ij}$ are line resistance and reactance.
2. Node Voltage and Branch Current Limits:
$$U_{i,min} \leq U_i \leq U_{i,max}$$
$$0 \leq I_{ij} \leq I_{ij,max}$$
3. Line Thermal Limits:
$$-P_{ij,min} \leq P_{ij} \leq P_{ij,max}, \quad ij \in \phi_{line}$$
$$-Q_{ij,min} \leq Q_{ij} \leq Q_{ij,max}, \quad ij \in \phi_{line}$$
4. Connectivity and Radiality Constraints: The post-reconfiguration network must be connected and radial.
$$\sum_{ij \in \Psi_b} \alpha_{ij} = n – 1$$
$$\beta_{ij} + \beta_{ji} = \alpha_{ij}$$
$$\sum_{j=1}^{N} \beta_{ij} = 1$$
$$\beta_{12} = 1$$
where $\alpha_{ij}$ is a binary variable indicating the on/off state of line $ij$, $n$ is the number of branches, $N$ is the total nodes, and $\beta_{ij}$ is a binary variable indicating parent-child relationships in the radial tree.
5. Renewable Generation Output Limits: As defined in the DG model above, and additionally bounded by physical limits:
$$P_{i,min} \leq P_i \leq P_{i,max}, \quad i \in \phi_{ne}$$
$$Q_{i,min} \leq Q_i \leq Q_{i,max}, \quad i \in \phi_{ne}$$
6. Repair Crew Logistics: Constraints governing the repair process of faulted lines in set $F$, with $m$ repair crews available.
$$\alpha_{ij,1} = 0, \quad ij \in F$$
$$\alpha_{ij,t_1} \leq \alpha_{ij,t_2}, \quad \forall t_1 < t_2$$
$$\sum_{ij \in \Psi_b} (\alpha_{ij,t+1} – \alpha_{ij,t}) \leq m$$
7. Island Frequency Security Constraints: This is a critical innovation. For an island $K$ (in the set of all islands $\phi_{land}$), the Rate of Change of Frequency (RoCoF) following a power imbalance $P_{loss,K}$ must be limited to a safe maximum $R_{K,max}$ to prevent instability. The system inertia $H_K$ of the island is calculated from the inertia constants $H_i$ and ratings of constituent generators.
$$R_K = \frac{d f_K}{dt} = \frac{P_{loss,K}}{2 H_K} \leq R_{K,max}, \quad K \in \phi_{land}$$
$$H_K = \frac{\sum_{i \in \phi_K} H_i P_{i,max}}{f_0}$$
Furthermore, the instantaneous power imbalance upon island formation must be constrained to prevent excessive frequency deviation:
$$P_{loss,K} \leq \alpha \sum_{i \in \phi_K} P_i$$
where $\alpha$ is a frequency response factor (e.g., 0.1), $\phi_K$ is the set of nodes in island $K$, and $P_i$ is the output of generator $i$.
Model Linearization and Solution
The non-linear constraint linking $U$, $I$, $P$, and $Q$ is relaxed using a second-order cone relaxation:
$$\left\| \begin{array}{c} 2P_{ij} \\ 2Q_{ij} \\ U_{i,sqr} – I_{ij,sqr} \end{array} \right\|_2 \leq U_{i,sqr} + I_{ij,sqr}, \quad \forall (i,j) \in \Psi_b$$
The disjunctive constraint for voltage drop is linearized using the Big-M method. The overall model, incorporating the distinct behaviors of GFL and GFM on grid inverters, network reconfiguration, repair scheduling, and island frequency security, is solved as a Mixed-Integer Second-Order Cone Programming (MISOCP) problem using commercial solvers like GUROBI.
Case Study and Analysis
The proposed method is validated on a modified IEEE 33-node distribution system. Key system parameters are shown below.
| DG Type | Connection Node | Capacity (kW) | On Grid Inverter Control Type |
|---|---|---|---|
| PV | 7 | 500 | Grid-Forming (GFM) |
| PV | 13 | 300 | Grid-Forming (GFM) |
| PV | 27 | 400 | Grid-Forming (GFM) |
| Wind | 10 | 500 | Grid-Following (GFL) |
| Wind | 16 | 300 | Grid-Following (GFL) |
| Wind | 17 | 200 | Grid-Following (GFL) |
| Wind | 30 | 200 | Grid-Following (GFL) |
| Wind | 33 | 300 | Grid-Following (GFL) |
An extreme event at 08:00 causes faults on six branches (6, 12, 18, 21, 26, 32). Two repair crews are dispatched, each requiring 1 hour per line repair. Three strategies are compared:
- Strategy 1 (Baseline): All DGs disconnect after the fault.
- Strategy 2 (GFM-only): Only DGs with GFM on grid inverters remain connected/islanded; GFL DGs disconnect.
- Strategy 3 (Proposed): Two-stage process: GFM units form stable islands first, then GFL units reconnect to provide additional power support.
The system performance, measured as the total served active load, is plotted over the restoration period. The proposed Strategy 3 consistently maintains the highest load supply. The resilience metric, the total active power deficit in MWh, is calculated for each strategy.
| Strategy | Description | Active Power Deficit (MWh) | Improvement vs. Strategy 1 |
|---|---|---|---|
| 1 | All DG Disconnect | 2.687 | – |
| 2 | GFM DGs Only | 2.227 | ~17.1% Reduction |
| 3 | Proposed Two-Stage | 1.928 | ~28.2% Reduction |
The results clearly demonstrate the effectiveness of the proposed method. Strategy 2 shows that utilizing GFM on grid inverters for islanding significantly reduces power deficit (by ~17%) compared to the no-DG baseline. Strategy 3, which further incorporates the delayed reconnection of GFL on grid inverters after stable island formation, achieves an additional ~11% reduction in deficit compared to Strategy 2, leading to a total improvement of ~28%. This highlights the substantial value of coordinating the different capabilities of GFL and GFM on grid inverters in a resilience-oriented operation strategy.
Conclusion
This paper addresses the distribution network resilience enhancement problem by proposing a method that integrates the control strategies of DG on grid inverters. The key conclusions are:
- The control type of the on grid inverter (Grid-Following or Grid-Forming) fundamentally determines a DG’s capability to support system operation during islanded conditions following a major fault. Any realistic resilience plan must account for this distinction.
- The proposed two-stage islanding strategy—first establishing frequency stability using GFM on grid inverters, then reconnecting GFL on grid inverters for power support—effectively leverages the strengths of both inverter types. This strategy directly mitigates the risk of frequency instability in unplanned islands while maximizing the utilization of available distributed energy resources.
- The formulated optimization model, which includes constraints for island frequency security (RoCoF and instantaneous power imbalance), network reconfiguration, and repair crew logistics, provides a comprehensive tool for minimizing active power deficit during extreme events.
- Case study results on a modified IEEE 33-node system verify the superiority of the proposed method, showing a reduction in active power deficit of approximately 28% compared to a strategy where all DGs disconnect.
The proposed method, centered on the intelligent management of on grid inverter capabilities, is of great significance for reducing load loss after extreme disasters. Future work will focus on integrating more flexibility resources (e.g., energy storage, flexible loads) with DGs for coordinated load restoration to further elevate distribution network resilience levels.