Introduction

The rapid growth of renewable energy sources particularly wind power is playing a pivotal role in diversifying energy generation and reducing dependence on fossil fuels. In Ethiopia, the increasing integration of wind energy into the national 230 kV transmission grid represents a promising advancement toward sustainable development. However, this transition introduces considerable technical challenges, with voltage stability emerging as one of the most critical concerns. The inherently intermittent and variable nature of wind power can lead to system reliability issues, particularly under high penetration scenarios where fluctuations in wind generation heighten the risk of voltage collapse and reduce loadability margins1.

To mitigate these challenges, this study proposes the deployment of a Static Var Compensator (SVC), a type of Flexible AC Transmission System (FACTS) device, to enhance voltage stability within the transmission network2. The proposed approach utilizes Continuation Power Flow (CPF) analysis via the Power System Analysis Toolbox (PSAT) in MATLAB to identify weak buses and determine the system’s maximum loadability under varying operational conditions. The methodology is initially validated on the IEEE 57 standard test bus system a widely recognized benchmark in power system studies before being applied to Ethiopia’s 230 kV transmission network. A comparative analysis is performed between the uncompensated system and the SVC-compensated case to assess improvements in voltage profiles and overall system stability. This introduction, together with the design methodology, provides a coherent and technically grounded foundation for the proposed solution. Globally, the rising demand for sustainable and clean energy has accelerated the integration of renewable energy particularly wind into conventional power systems3. Despite its environmental benefits, wind power’s inherent intermittency presents significant operational challenges, with voltage instability being a critical issue, especially in weak or sparsely meshed networks4.

Overview of the Ethiopian electric power system

The Ethiopian national grid infrastructure includes 132KV, 230 kV and 400 kV high-voltage transmission lines, forming the backbone of long-distance electricity delivery. Strategic developments in recent years have included the construction of 400 kV cross-border interconnectors with Sudan, Djibouti, and Kenya key components of regional power integration under the Eastern Africa Power Pool (EAPP) initiative.

The Ethiopian electric power sector is primarily managed by two key institutions: Ethiopian Electric Power (EEP), which is responsible for electricity generation and high-voltage transmission, and Ethiopian Electric Utility (EEU), which oversees power distribution, sales, and medium- to low-voltage transmission networks. Additionally, the Ethiopian Energy Authority (EEA) operates under the sector’s regulatory framework, tasked with developing and enforcing effective regulations, directives, and technical standards to ensure reliability and sustainability in the industry. According to EEP data from May 2021, Ethiopia’s total installed power generation capacity was 4,473.9 MW, with 90.63% of the electricity generated from hydropower, while the remaining 9.37% came from other sources such as wind, solar, and thermal energy.

Notable wind farms include Ashegoda (120 MW), Adama I (51 MW), Adama II (153 MW), and Aysha (120 MW). These renewable energy projects mark significant milestones in Ethiopia’s transition toward a sustainable energy future. However, the growing penetration of variable wind generation presents operational challenges, particularly in the 230 kV transmission network, which is critical for inter-regional power delivery. Fluctuations in wind power output can impose voltage stability concerns, making the integration of advanced grid support technologies increasingly essential for ensuring reliable system performance and long-term planning5.

Related work

Voltage stability is a critical concern in modern power systems, especially in developing grids with increasing penetration of intermittent renewable energy sources such as wind. Various studies highlight the vulnerability of voltage profiles in wind-dominated networks5. In6, the authors investigated the impact of wind generation on system voltage stability under different load conditions. Similarly, in7 the authors analyzed voltage collapse scenarios resulting from fluctuating wind outputs and identified weak buses in the grid that are more prone to instability.

Flexible AC Transmission Systems (FACTS) have been widely adopted to enhance voltage stability, increase power transfer capability, and mitigate instability in high-voltage networks. Static Var Compensators (SVC), in particular, provide dynamic reactive power support. in8 the authors demonstrates how SVCs improve voltage stability margins in wind-integrated systems.

One of the primary tools used for voltage stability assessment is the Continuation Power Flow (CPF) method. It allows tracing the full P-V curve, determining the maximum loading point before voltage collapse and determines the weak buses. In9 the author pioneered the CPF technique for voltage stability analysis, showing that it offers better convergence near the bifurcation point compared to traditional Newton-Raphson methods. CPF has since been widely adopted for assessing system loadability and critical bus voltages in both academic and utility settings.

In10 introduced PSAT as an open-source MATLAB-based platform supporting CPF, time-domain simulation, and control design. Its modularity and flexibility have made it a preferred tool in academic research for simulating renewable-integrated systems. Utilized PSAT to model wind farms integrated into weak grids, providing insights into dynamic behavior and voltage collapse patterns. Its CPF capabilities make it a preferred tool for academic and preliminary grid studies in sub-Saharan African contexts4.

PSAT used to determine the load flow of an IEEE 14 Bus system. It has been determined that the systems load flow analysis enhanced power quality and voltage stability by integrating renewable energies11. IEEE 9 bus system is also used for integrating various FACTS devices to improve voltage sustainability12.Furthermore, in13 the author proposed the use of FACTS devices and grid reconfiguration as potential solutions to improve voltage profiles under high renewable integration.

In14, the authors presented a probabilistic reliability assessment for wind-dominated networks, showing that grid reinforcements and voltage control devices significantly reduce outage risks. The work analyzed contingency criteria to assess the resilience of wind-integrated transmission systems.

Numerous strategies have been proposed for voltage stability enhancement, ranging from optimal placement of FACTS devices to coordinated control methods. In15, a fuzzy logic controller was implemented for SVC to dynamically respond to voltage dips. Another study in16 explored the hybrid use of SVC and capacitor banks to manage voltage profiles under heavy load and wind variability conditions.

From the literature review, it is observed that the IEEE 57-bus system has not been utilized for the integration of a Wind Farm and SVC. In previous studies, this test system was primarily used for load flow analysis only. Therefore, in this work, a Wind Farm combined with an SVC is integrated into the Ethiopian 230 kV transmission network is conducted to enhance voltage stability. This research seeks to contribute to:

  1. a)

    Innovatively integrates a Wind Farm and SVC into the test system, serving as a benchmark for voltage stability studies.

  2. b)

    Model the IEEE 57 Bus system with the integration of Wind and SVC to validate the actual Ethiopian 230 kV transmission network.

  3. c)

    Investigate the impact of integrating wind farms with SVC on the voltage stability of the grid, offering practical insights into mitigating voltage instability issues resulting from high wind power penetration.

  4. d)

    The study employs Continuation Power Flow analysis in the Power System Analysis Toolbox (PSAT) environment to assess voltage stability margins and identify weak buses under different operating conditions.

Proposed methodology

Modelling of wind turbine

A 1.5 MW doubly Fed Induction Generator (DFIG) is used for this study. The mechanical output power for a constant wind flow in aerodynamic system is expressed in Eq. (1)12.

$${P_w}=\frac{\rho }{2}{c_p}(\lambda ,\beta ){A_R}v_{w}^{3}$$
(1)

Where, AR is Swept area, Cp is power coefficient, p is air density, β is pitch angle, λ is tip speed ratio, and vw is wind Speed17.

\(\begin{gathered} {\text{The power coefficent }}{c_p}(\lambda ,\beta ){\text{ }}is{\text{ a function of the tip speed ratio and the pitch angle }}\beta . \hfill \\ {\text{The tip speed ratio (}}\lambda ){\text{ is defined as the ratio of the turbine speed }} \hfill \\ {\text{at the tip of the rotor (Vu) to the axial wind speed (Vw) in equation (2)}}{\text{.}} \hfill \\ \end{gathered}\)

$$\lambda =\frac{{{v_u}}}{{{v_w}}}=\frac{{{r_R}{\omega _T}}}{{{v_w}}}$$
(2)

Where rR is the rotor radius and ωt is turbine rotational speed.

DFIG in d-q reference frame

The stator and rotor voltages equation in synchronous reference frame are computed in Eqs. (3) and (4) respectively17.

$$\begin{gathered} {v_{ds}}={R_s}{i_{ds}}+\frac{{d{\psi _{ds}}}}{{dt}} - {\omega _s}{\psi _{qs}} \hfill \\ {v_{qs}}={R_s}{i_{qs}}+\frac{{d{\psi _{qs}}}}{{dt}}+{\omega _s}{\psi _{ds}} \hfill \\ \end{gathered}$$
(3)
$$\begin{gathered} {v_{dr}}={R_r}{i_{dr}}+\frac{{d{\psi _{dr}}}}{{dt}} - ({\omega _s} - {\omega _r}){\psi _{qr}} \hfill \\ {v_{qr}}={R_r}{i_{qr}}+\frac{{d{\psi _{qr}}}}{{dt}}+({\omega _s} - {\omega _r}){\psi _{dr}} \hfill \\ \end{gathered}$$
(4)

Where, v, I, ѱ are voltage, current and flux linkage respectively. Subscripts d, q, s, r, ωs, and ωr are stands for direct, quadrature, stator, rotor, synchronous speed and rotor speed respectively. Figure 1 shows the DFIG based wind turbine integrated to the electrical grid system.

Fig. 1
figure 1

Doubly fed induction generator (DFIG) based wind turbine integrated to the network13.

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Figure 1 illustrates DFIG wind turbine. The stator is directly connected to the grid, while the rotor is linked to a back-to-back voltage source converter through slip rings.

Wind speed scenarios

Wind generation profiles were modeled for three wind speed scenarios under weak and strong grid conditions.

  • Low Wind Speed (Vw = 5 m/s): Reduced wind power output (30% rated capacity).

  • Medium Wind Speed (Vw = 10 m/s): Nominal generation (70% rated capacity).

  • High Wind Speed (Vw = 15 m/s): Full rated power generation (100%).

System description

A significant number of wind farms are currently interconnected with the 230 kV transmission network of the Ethiopian power system. The integration of large-scale wind energy can introduce voltage stability challenges, particularly under system disturbances or in weak grid regions. This study examines the impact of wind farm integration on voltage stability and proposes the deployment of a Static Var Compensator (SVC) to improve voltage stability. The analysis is conducted using Continuation Power Flow (CPF) within the Power System Analysis Toolbox (PSAT). The proposed system includes the Ashegoda Wind Farm, which has an installed capacity of 120 MW. Figure 2 illustrates the Ashegoda Wind Farm integrated Ethiopian power network, 230 kV transmission lines. This network forms the basis for evaluating voltage stability enhancements through the optimal placement of SVCs.

Fig. 2
figure 2

120 MW Ashegoda wind Farm in Ethiopia18.

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Ethiopia, with an estimated population of 120 million and a landmass of approximately 113 million hectares, is a Horn of Africa Nation located between 33° and 48° east longitude and 3° to 8° north latitude. The country’s transmission grid currently includes two international interconnections one with the Republic of Djibouti and another with Sudan. The primary transmission voltage levels in Ethiopia are 400 kV, 230 kV, and 132 kV. This study focuses on the 230 kV network for voltage stability analysis and enhancement.

Due to the complexity of modeling and analysing large-scale interconnected power systems, and the localized nature of bus voltage behaviour, only the 230 kV transmission network is considered. To develop the test network, data including nameplate specifications of substations and power plants, as well as the ratings of lumped loads and transformers, were collected and converted into per-unit values using a base power of 100 MVA and a base voltage of 230 kV. The Ethiopian transmission grid of 230 KV single line diagram is depicted in13.

SVC Model

  1. a)

    SVC Reactive power model.

The reactive power provided by the SVC is typically controlled to either absorb or supply reactive power based on the voltage at the wind farm connection point. The reactive power for SVC and TCR is computed using Eqs. (6) and (7)20.

$${\rm Q_{SVC} = V_{wind-farm.}(V_{ref-}V_{wind-farm)}}$$
(5)

Where, QSVC is the reactive power injected by the SVC, Vwind-farm is the voltage at the wind farm bus, Vref is the reference voltage set by the SVC controller. The SVC adjusts its reactive power to maintain the voltage level at the wind farm bus within acceptable limits according to IEEE standards (0.95–1.05 p.u.).

  1. b)

    Thyristor- Controlled reactor (TCR) model.

The TCR part of the SVC controls the inductive reactive power and is modeled as,

$$\:{\text{Q}}_{\text{T}\text{C}\text{R}}=\:\frac{{\text{V}}_{\text{w}\text{i}\text{n}\text{d}-\text{f}\text{a}\text{r}\text{m}}^{2}}{\text{X}\text{T}\text{C}\text{R}}$$
(6)

Where, XTCR is the reactance of the TCR, which depends on the firing angle \(\:\alpha\:\).The reactance XTCR can be varied as

$$\:{X}_{TCR}\:\:=\:\frac{{X}_{mass}}{1-\text{c}\text{o}\text{s}\left(\alpha\:\right)}$$
(7)

The Firing angle \(\:\alpha\:\) adjusts based on the voltage deviation from the reference voltage.

Continuation power flow (CPF) analysis

The Continuation Power Flow (CPF) algorithm is an advanced extension of the conventional power flow method, built upon the Newton-Raphson technique. It is particularly useful when the Jacobian matrix of the power flow equations becomes singular at the voltage stability limit, known as the saddle-node bifurcation (SNB) point.

Fig. 3
figure 3

Continuation Power Flow Processes18.

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CPF is designed to trace the Voltage-Loading Factor (PV) curve under progressively increasing load conditions, allowing accurate analysis even beyond the SNB point. Unlike traditional methods, CPF can fully capture the entire PV curve and determine the maximum loadability limit, which corresponds to the SNB point. The algorithm is fundamentally based on bifurcation theory, which characterizes the behavior of power systems near critical operating points.

The Continuation Power Flow (CPF) method employs a predictor-corrector technique to trace the system’s response to increasing load, as illustrated in Fig. 314. In the prediction step (from Point A to B), a tangent vector is computed to estimate the next operating point based on a specified load increase pattern. This estimated solution is then refined in the correction step (B to C) using the Newton-Raphson load flow method17. The process is repeated predicting the next solution (C to D) using a new tangent vector and correcting it (D to E) with each step incrementally increasing the system load.

Simulation model of the IEEE 57 bus systems

The bus system model is designed in the PSAT simulink library in MATLAB software as shown in Fig. 4. In this model, there are 79 lines, 17 transformers, 57 buses with 4 generators, and 42 loads. The data used for simulation of the IEEE 57 standard bus system model are taken from21.

Fig. 4
figure 4

Simulation Diagram of the IEEE 57 bus system model with DFIG and SVC.

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Voltage stability assessment for the base case

The network diagram of the IEEE 57-bus case study system is shown in Fig. 4. Two parameters are used to investigate the voltage stability of the system in this study. The first is the Maximum Loading Factor (MLF), which is designated as λmax and the second is the corresponding Megawatt Margin (MWM), Pmarg. which is the difference between the critical (maximum) scalable active power demand (Pmax) and the total base case active power demand (Pbase). The maximum loading factor can be obtained from the active load demand expression in terms of λ, which is given in Eq. (8)16.

$$\rho (\lambda )={\rho _{base}}(1+\lambda )$$
(8)

At maximum loading factor can be obtained from the active load demand expressed in Eq. (9)18.

$${\rho _{\hbox{max} }}={\rho _{base}}(1+{\lambda _{\hbox{max} }})$$
(9)

Thus, the maximum loading factor λmax and the megawatt margin, pmarg are expressed in Eq. (10)

$${\lambda _{\hbox{max} }}=(\frac{{{\rho _{\hbox{max} }}}}{{{\rho _{base}}}}) - 1$$
$${\rho _{m\arg .}}={\rho _{\hbox{max} }} - {\rho _{base}}$$
(10)

For any change in the operating condition of the grid from the base case scenario, the percentage change in the MWM gives an indication of the impact of such change on the voltage stability of the system. The percentage change in the MWM is thus expressed in Eq. 11 as19.

$$\Delta {\rho _{m\arg .(\% )}}=\left( {\frac{{{\rho _{m\arg .}}}}{{{\rho _{m\arg .bus}}}} - 1} \right) \times 100\%$$
(11)

Parameter values

Wind Energy Resource and Static Var Compensator parameters are shown in Table 1.

Table 1 Parameter values of DFIG and SVC.
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Simulation results and discussion

Simulation result without wind farm integration (base Case)

In this section, the performance of the IEEE 57-bus system is analysed under base case condition. The primary objective is to establish a reference scenario against which the impacts of renewable integration particularly wind farms can be evaluated. The system is simulated using the defined load configurations. Figure 5 shows the voltage magnitude across all buses of IEEE57.

Fig. 5
figure 5

voltage profile of IEEE 57 Standard Bus system.

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The CPF analysis technique can used to select the weak buses. The weak buses according to Fig. 4 are bus 17, 18, 25, 26, 28, 35, and 52 with a voltage magnitude of 0.9, 0.756, 0.80, 0.899, 0.84, and 0.856 respectly. We can observe from the figure that several buses, which is operating near or below the lower acceptable voltage limit (0.95 p.u.), which highlights the need for voltage support or compensation measures. Figure 6 shows the network visualization diagram. PSAT uses network visualization in conjunction with CPF to graphically illustrate Bus voltages across the system as load increases. The red color illustrates the weakest bus.

Fig. 6
figure 6

Network visualization.

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Simulation result with wind farm

The IEEE 57-bus system is re-evaluated by integrating a wind farm with a generation capacity of 120 MW. The wind farm is connected to the weakest bus (Bus 18) to assess its impact on voltage stability, system losses, and reactive power sharing. This simulation scenario aims to analyze how the incorporation of renewable energy affects the overall network performance. Figure 7 shows the voltage profile of IEEE 57 Bus system with 120 MW wind farm.

Fig. 7
figure 7

Voltage profile of IEEE 57 Bus system with Wind.

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You can clearly see from Fig. 7 that the voltage improvement at several buses especially those that were previously under-voltage indicating the stabilizing effect of wind integration. However, bus 25, bus 52, and bus 53 are below the lower voltage limits which need to be improved.

Simulation result with wind farm and SVC

This simulation considers the IEEE 57-bus system integrated with wind farm and SVC. The objective is to analyze how the addition of SVC enhances the voltage stability and capabilities beyond what the wind farm alone provides. Figure 8 illustrates the voltage profile with 120 MW Wind Farm and SVC integration. The integration of large-scale wind energy introduces voltage stability challenges, particularly under varying wind conditions and increased load demand. To address these issues, the installation of a Static Var Compensator (SVC) was proposed. The selection of the optimal bus for SVC placement was based on voltage magnitude analysis, reactive power sensitivity, and Continuation Power Flow (CPF) studies. Among several weak buses, Bus 25 was selected due to its critical role in system voltage support and its significant improvement in voltage stability when an SVC was applied.

Fig. 8
figure 8

Voltage profile of IEEE 57 Bus system with Wind + SVC.

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The voltage levels as shown in F.g 9, have significantly improved after integrating SVC. All the bus voltages are within the voltage magnitude limit (between 0.95 p.u and 1.05p.u).

Comparisons of voltage profile and power loss

Figure 9; Table 2 show a structured summary of power flow results comparison for the IEEE 57-Bus System under three operating scenarios: base case, with wind and with wind and SVC respectively.

Fig. 9
figure 9

Voltage profile comparison.

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In Fig. 10, the voltage is significantly restored with SVC within the range of (0.95–1.05 p.u.). SVC improves both the voltage profile and then stability margin across the network.

Table 2 Comparison of power losses using continuation power flow with and without wind and wind & SVC.
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Table 2 illustrates a notable reduction in both active and reactive power losses, demonstrating the efficiency gains from wind integration in the IEEE 57-bus system. Wind integration alone leads to higher losses due to poor voltage regulation and inefficient flow paths. Adding an SVC partially restores the system efficiency by compensating reactive power, stabilizing voltages, and optimizing power flow. The real power loss for the base case is 20.3 MW. It is increased to 24.7 MW using wind farm integration into the base case. This is due to the intermittent nature of wind source resulting in voltage fluctuation, which can increase power loss. By introducing SVC controller, the real power loss is decreased from 24.7 MW to 17.1 MW. Therefore, we can summarize that the incorporation of wind with SVC controllers is very essential to minimize power losses and improve the system’s power reliability and stability.

Stability margin analysis via continuation power flow (CPF)

Figure 10 demonstrates the bar chart comparing the voltage stability margin (VSM) across different scenarios.

Fig. 10
figure 10

voltage stability margin comparison.

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In the base case, the maximum loading factor (λ) is 1.2, indicating that the system can support up to 120% of the base load before voltage collapse occurs. At this loading condition, the minimum bus voltage at critical buses drops to 0.85 p.u., placing the weakest bus below the acceptable stability threshold. This suggests that while the system is moderately stable under normal conditions, it becomes vulnerable under high loading scenarios.

With wind farm integration, the maximum loading factor (λ) is at 1.3, but the minimum bus voltage improves slightly to 0.88 p.u. This improvement is due to the additional real power supplied by the wind farms, resulting in a 3% increase in Voltage Stability Margin (VSM). Although there is a marginal enhancement in system performance, it is not sufficient to ensure stable operation under heavily stressed conditions. When both wind farms and SVCs are integrated, the maximum loading factor increases to 1.40, and the minimum bus voltage rises significantly to 0.95 p.u., representing a 17% improvement in VSM. In this configuration, the SVC provides dynamic reactive power support, substantially enhancing voltage stability and improving the system’s ability to withstand higher load demands.

Voltage stability improvements under different wind speed levels and grid strength conditions, both with and without SVC

Table 3 shows the simulation results based on various scenarios of wind speed (Low, Medium, High) and grid strength (Weak Grid and Strong Grid) for the study:

Table 3 Comparison of maximum loadability and minimum bus voltage under different Scenarios.
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From Table 3, the maximum loadability improves in all scenarios with the inclusion of the SVC. The minimum bus voltage is consistently higher with SVC, indicating enhanced voltage stability. The improvement is more pronounced under weak grid and high wind scenarios, where the system is more stressed. Tables 4 and 5 illustrate the simulation results for weak and strong grid conditions respectively without and with SVC.

Table 4 Simulation results for weak grid conditions (Without and with SVC).
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Table 5 Simulation results for strong grid conditions (Without and with SVC).
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Conclusion

This study has thoroughly investigated the voltage stability performance of the Ethiopian 230 kV transmission network with the integration of a Wind Farm and Static Var Compensator (SVC) using Continuation Power Flow (CPF) analysis in PSAT. The analysis was based on the IEEE 57-bus system model, adapted to reflect the characteristics of the Ethiopian grid. The results demonstrated that the integration of wind energy without appropriate voltage support can lead to a reduction in voltage stability margin, particularly at weak buses. However, the coordinated deployment of an SVC significantly improved the voltage profile and enhanced the system’s ability to withstand increased loading conditions. CPF analysis revealed a noticeable increase in the critical loading point (λmax) when the SVC was integrated alongside the Wind Farm, confirming its effectiveness in mitigating voltage collapse. Moreover, the identification and placement of the SVC at a strategically selected weak bus ensured optimal reactive power support and stabilization of voltage across the network. The findings highlight the importance of incorporating FACTS devices like SVCs when integrating large-scale renewable energy sources into transmission systems, particularly in developing power systems like Ethiopia’s. In conclusion, this research provides valuable insights for system planners and policymakers on the need for reactive power compensation strategies to maintain voltage stability in renewable-integrated power networks.