A vast number of communities in rural South Africa still have limited access to electricity, where access by grid extension is not feasible [1]. This is a common occurrence in other rural areas and is not limited to South Africa [2][3]. Energy access is increasingly being delivered through grid-tied and off-grid infrastructure [4]. Mini-grids (MG) are one of the solutions for providing reliable and sustainable electricity to rural communities [5][6]. Mini-grids can be defined as decentralized collective systems of electricity supply [7]. Islanded operation in mini-grids is critical for rural electrification, where access to a reliable grid connection is limited [8]. During high-impact events, the resilience of the islanded mini-grid ensures a sustainable power supply [9]. Along with grid extension and standalone systems, mini-grids are a crucial technical solution for delivering cost-effective, high-quality power to people in need of electricity access [10][11]. In such systems, a Capacitor Coupled Substation (CCS), combined with a Controllable Network Transformer (CNT), can play a crucial role in managing load-supply balance and maintaining system stability during grid disconnection [12][13]. The proposed model ensures minimal voltage fluctuations during the transition to an islanded state. While CCS and CNT are established technologies, their combined application using the proposed grid status function G(t) for high-power rural tapping is a unique contribution that addresses the specific transient challenges of large-scale solar integration in isolated areas. This paper aims to provide an efficient strategy for controlling power flow and voltage stability in such islanded systems using mathematical modelling and algorithmic optimization.

To efficiently control the power flow during islanding, an algorithm is proposed to balance the active and reactive power across the CCS and CNT while ensuring voltage stability.

The results presented the observation of the modelled system during the islanding scenario. The main focus of this study is the observation of the main voltage deviations at the load during islanding. The results are in Figure 3Figure 3.

Figure 3. CCS red phase voltage signal statistics.

The model results presented in Figure 3Figure 3 show the tapped voltage at 1.137 × 10 e⁴, which is the desired V_tap. The RMS value of 1.137 × 10⁴ V shown in Figure 3Figure 3 represents the stabilized tapped voltage. This confirms that the control system maintains the voltage within the standard ±5%permissible fluctuation limits Δ V required by utility reference standards, ensuring equipment safety during the 1.1 s islanding event.

This result is further presented in a waveform in Figure 4.

Figure 4. CCS Voltage: Load switched at 1 second.

The resulting transients during switching are given by:

When:

Load CB closes at 0.8 s, the resulting transient effect of inrush current is given by:

Mini-grid CB closes at 0.91 s, resulting in synchronization transient given as:

Minigrid CB opens at 0.95 s, resulting in power fluctuations given by:

Minigrid CB closes at 0.99 s, resulting in a residual charge transient given by:

When the main grid CB opens at 1.1 s (shown in Figure 5Figure 5), there is a transient effect resulting from a power dip and frequency shift, and given by:

where:

I s t e a d y - s t a t e = Final steady-state current

I t r a n s i e n t = Initial transient current

α = R 2 L = Damping factor

ω d = 1 L C − α 2 = Damped natural frequency

ϕ = Phase angle

The Grid Control System (GCS) is achieved by implementing a GCS that uses control logic for the CB operations.

A State flow or MATLAB Function Block can be used for CB operations. The state definition on the state flow or the MATLAB Function Block is as presented in Table 4.

Table 4. State definitions in state flow.

When using MATLAB Block Functions, the CB operation is based in time and power availability. The logic is as follows (See Table 5):

Table 5. CB Logic using MATLAB Function Block

The final sequence results in the expected system behaviour as presented in Table 6.

Table 6. Simulation and expected behaviour.

With the mathematics representation given as:

Main Grid Breaker:

Mini-Grid Breaker:

Load Breaker:

The voltage measurements are given by Figures 4-12.

Figure 5. Load voltage measurement.

Figure 6. Load parameters: MG supplying power.

Where each figure representation is:

Figure 5Figure 5: The voltage measured at the load.Figure 6Figure 6: Graphical representation when MG supplies power.Figure 7Figure 7: Load voltage when the MG supplies zero power.Figure 8Figure 8: Graphical representation of Figure 8Figure 8.Figure 9Figure 9: MG when zero power is generated.Figure 10Figure 10: MG when power is generated.Figure 11Figure 11: MG voltage when power is generated.Figure 12Figure 12: Base Tapped voltage when CCS is used.

Figure 7. Load parameters when no MG supply.

Figure 8. Load parameters when no MG power.

Figure 9. Mini-grid parameters with no generation.

Figure 10. MG when generating.

Figure 11. MG voltage.

Figure 12. Tapped voltage.

The transient phenomena identified throughout the simulation reflect the critical nature of load management during the islanding process. When the load CB closes at 0.8 seconds, a significant inrush current is generated as expected, characterized by the exponential rise defined by the function:

This inrush can lead to temporary voltage fluctuations that may impact sensitive electrical equipment. The observations during the minigrid operations (with CB closing and opening at 0.91 s, 0.95 s, and again at 0.99 s) highlight the importance of synchronization in maintaining stable voltage levels. The synchronization transient, captured by:

Indicates that careful control of the minigrid’s output is necessary to prevent abrupt voltage shifts, which could destabilize the entire system. These transients need to be considered in the design of control strategies that enforce a seamless transition into and out of islanding operation. Additionally, the significant effects of power fluctuations when the minigrid CB opens at 0.95 s highlight the necessity for robust energy management strategies. In the absence of power from the minigrid, the subsequent drop in system stability must be adequately addressed by reactive power support or by strategically designed energy storage systems. The Grid Control System (GCS), executed through MATLAB function blocks and state flow diagrams, is integral in coordinating the dynamic response of the system. The use of state definitions for managing the main grid and minigrid breakers ensures systematic operations, which are critical during the transition states. The control logic effectively allows for the necessary responses to changes in the electrical environment, such as disconnecting the load in scenarios of no minigrid generation after 1.1 seconds. The results from the CB logic reveal the robustness of the control algorithms, providing a foundation for automating responses based on power availability and operational conditions. However, future improvements could include real-time analytics and machine learning techniques to enhance predictive capabilities, thus minimizing delays during critical events. The data portrayed in Figures 4-12 shed light on system stability under varying operational conditions. When the minigrid supplies power, the load parameters show stable voltage levels, indicative of successful integration with the existing grid structure. Conversely, the parameters under conditions of no supply show the changes in load behaviour, emphasizing the uncertain balance that occurs during islanding. The simulated transient behaviours, such as the inrush current, align with the theoretical bidirectional power flow models established in [12] and [13], providing indirect validation of the simulation’s accuracy in the absence of site-specific field data. Although this study utilizes a static 500 kVA load, the control algorithm incorporates a proportional gain k in the CNT adjustment formula

V C N T = V C N T − k ( Δ V ) to ensure the system’s robustness against varying load demands.

This study provides important insights into microgrid behaviour under islanding conditions, with particular emphasis on voltage stability and control system performance. The simulation results highlight the dynamics of load voltage deviation during the transition from grid-connected to islanded operation. Overall, the findings demonstrate the need for improved control strategies, continuous system monitoring, and proactive energy management to enhance system resilience. Increasing the monitoring resolution and appropriately tuning system time constants may further reduce adverse transient effects on the load. The use of MATLAB function blocks also supports model flexibility, allowing for easier modification and scalability in future studies. Further research is required to deepen the understanding of these transient dynamics and to optimize control strategies for more advanced grid configurations. In addition, the integration of advanced voltage regulation methods, CCS-CNT systems, and smart grid technologies, such as automatic voltage regulators, predictive load forecasting, and real-time communication between grid components, is recommended to further improve voltage stability and system robustness during islanding.