Contingency-Based Reactive Power Injection for Proactive Voltage Collapse Mitigation in Heavily Loaded Networks: A Case Study in a Heavily Loaded Transmission Network

Contingency-Based Reactive Power Injection for Proactive Voltage Collapse Mitigation in Heavily Loaded Networks: A Case Study in a Heavily Loaded Transmission Network

Published by : http://www.ijert.org

International Journal of Engineering Research & Technology (IJERT)

ISSN: 2278-0181

Vol. 14 Issue 10, October – 2025

Ganashree Gt, Ankitha C, Vaishnavi M

Department of Electrical and Electronics Engineering SJB Institute of Technology, Bengaluru, India

AbstractModern electric power systems are increasingly vulnerable to instability due to rising demand, integration of intermittent renewable resources, and limited transmission expansion. Voltage collapse remains one of the most severe threats, with historical blackouts underscoring its economic and societal impact. This report provides a comprehensive technical discussion on methodologies for voltage stability assessment, com-parative review of Voltage Stability Indices (VSIs), contingency analysis frameworks, corrective actions during emergencies, and advanced optimization approaches such as CurrentVoltage (IV) formulation and Branch-Parameter Continuation Power Flow (BCPF). A particular focus is given to strategies mitigating Fault-Induced Delayed Voltage Recovery (FIDVR) through dynamic reactive compensation and STATCOM deployment. Future re-search directions include smart grid adaptation, DSM integra-tion, renewable impacts, uncertainty handling, and EV charging effects.

Index TermsVoltage Collapse, Contingency Analysis, Reac-tive Power, FACTS, STATCOM, Voltage Stability Indices, IV Formulation, FIDVR

1. INTRODUCTION

   Modern electric power systems are operating closer to their stability limits than ever before. This trend is driven by a confluence of factors, including the steady increase of electric loads from economic and population growth, the large-scale integration of intermittent renewable energy sources, and mar- ket pressures that prioritize economic efficiency over building extensive new transmission infrastructure [1]. Operating in this stressed state increases the grids vulnerability, where even minor disturbances can trigger significant instability, potentially leading to cascading outages. Power system voltage stability refers to the networks ability to maintain acceptable voltage levels at all buses under both normal operating con-ditions and after being subjected to a disturbance. A failure to do so can lead to voltage collapse, a severe form of instability characterized by a progressive and uncontrollable decline in voltage. The consequences of such events are severe, as demonstrated by historical blackouts, including the Tokyo blackout of 1987, which affected 2.8 million consumers for over three hours, and the widespread outages across North America and Europe in 2003. These incidents underscore

   the profound economic and societal costs associated with grid instability[1]. The primary causes of voltage instability include imbalances between power generation and demand, an inadequate supply of reactive power, and the sudden tripping of key components like transmission lines or generators. A particularly critical modern challenge is the phenomenon of Fault-Induced Delayed Voltage Recovery (FIDVR). FIDVR is largely driven by the proliferation of induction motor loads, such as those in air conditioning units, which draw significant reactive power during the voltage recovery period following a fault. This massive, sudden demand can overwhelm the local systems reactive power reserves, stalling voltage recovery and potentially leading to collapse. This report provides a comprehensive overview of the engineering strategies used to ensure grid reliability against these threats. It details the methodologies for assessing voltage stability, performing con- tingency analysis to identify critical threats, and implementing effective emergency control actions. The following sections begin by establishing the fundamental methods for stability assessment, which form the basis for all subsequent protective and corrective measure [1].

2. METHODOLOGIES FOR VOLTAGE

   STABILITY ASSESSMENT

   Continuous and accurate voltage stability monitoring is a strategic imperative for the secure operation of any power sys- tem. Effective assessment provides the foundational situational awareness required to deploy preemptive measures before instability occurs and to execute rapid, targeted corrective actions during an emergency. This section outlines the core techniques used to evaluate a systems stability posture.

   1. Steady-State Analysis

      • P-V and Q-V curves: The use of active power-voltage (P- V) and reactive power-voltage (Q-V) curves are fun- damental tools for static voltage stability analysis. By plotting the change in voltage at a bus in response to a gradual increase in either active (P) or reactive (Q) power, these curves reveal the systems stability margins and its

        Published by :

        International Journal of Engineering Research & Technology

        proximity to the nose of the curve, which represents the point of voltage collapse. While invaluable for planning studies, generating these curves requires multiple power flow solutions and demands comprehensive knowledge of the power system beyond its operational states, making them computationally intensive for real-time applications.

        Fig. 1. Typical PV curve illustrating the voltage collapse point (nose point) beyond which the system becomes unstable.

        • V-Q Analysis:V-Q analysis serves as a benchmark methodology for calculating the reactive power margin, or Qmin, at a specific bus. This is achieved by modeling a fictitious synchronous condenser at the bus of interest and plotting its reactive power output as its scheduled voltage is varied. A positive margin indicates the maximum amount of additional reactive power the bus can support before collapse, signifying a stable condition. Conversely, a negative margin indicates a reactive power deficiency, meaning the bus is already in a state of voltage collapse and requires external reactive support to recover.

   2. Identification of Vulnerable Areas

   Voltage collapse rarely occurs across an entire system simultaneously; it typically originates in specific, vulnerable areas. Identifying these weak parts of the grid is crucial for targeted monitoring and reinforcement.

   • Weak buses/areas: These are the buses or regions within the power system that are most susceptible to initiating a voltage collapse, often due to being heavily loaded or distant from generation and reactive power sources. A common method for identifying these areas involves systematically increasing the reactive power load at each bus until a stability limit is reached. The buses that can sustain the smallest increase are identified as the weakest.

   • Voltage Control Areas (VCAs): To manage stability more effectively, a large network can be subdivided into Voltage Control Areas. A VCA is defined as a sub-region of the grid within which local reactive power resources are most effective for voltage control. This concept recognizes that transferring reactive power over long distances is inefficient and often ineffective. By

     International Journal of Engineering Research & Technology (IJERT)

     ISSN: 2278-0181

     Vol. 14 Issue 10, October – 2025 partitioning the system into VCAs, operators can as-sess reactive power adequacy on a regional basis and iplement more targeted and efficient control actions.

     These assessment methods provide a high-level view of system stability. To quantify the proximity to collapse in a more computationally efficient manner, engineers rely on specialized measurement tools known as Voltage Stability Indices[2].

     Fig. 2. Representation of Voltage Control Areas (VCAs) in a large transmis- sion network for localized stability management.

3. COMPARATIVE REVIEW OF VOLTAGE

   STABILITY INDICES (VSIS)

   Voltage Stability Indices (VSIs) are essential tools for quantifying a systems proximity to voltage collapse. These scalar indices, typically ranging from 0 (no-load/stable) to 1.0 (collapse point), are computationally efficient, making them suitable for both offline planning studies and online monitoring applications. An ideal VSI should exhibit a near- linear, predictable response as the system approaches collapse, providing system operators with a clear, real-time metric of grid stress that enables timely intervention[4].

   1. Classification

      VSIs can be broadly classified based on the system variables used in their formulation:

      • Line-variable based:Derived from power flow and pa- rameters of a single transmission line.

      • Bus-variable based:Derived from voltage and power injection data at a specific bus.

      • Jacobian-based:Derived from the full system power flow Jacobian matrix. While Jacobian-based indices offer high accuracy in pinpointing the exact collapse threshold, their computational complexity and the need for frequent recalculation make them unsuitable for real-time assess- ment, especially in large-scale systems. Consequently, line- based VSIs (LVSIs) are often preferred for online monitoring and as objective functions in optimization problems due to their computational efficiency and their ability to identify both weak lines and buses[5].

        Published by :

        International Journal of Engineering Research & Technology

   2. Modern Stability Assessment Index (MSAI)

      The documented limitations of traditional LVSIs particularly their common failure to account for line resistance and shunt admittance as detailed in Table 1necessitated the development of a more robust metric. The Modern Stability Assessment Index (MSAI) was engineered to address these specific shortcomings. By being derived from the exact transmission line model (using ABCD parameters), MSAI inherently incorporates all physical line characteristics, including the very resistance (R) and shunt admittance (Y) that indices like LQP, NVSI, and VSLI neglect, leading to their documented inaccuracies. This comprehensive formulation makes the MSAI universally applicable across short, medium, and long transmission lines, providing a more reliable and precise measure of stability.

   3. Performance Summary

   • Superior:Indices such as MSAI, NCPI, and MVSI con- sistently demonstrate superior and more reliable perfor- mance. They accurately predict voltage collapse under diverse loading conditions, including variations in active, reactive, and apparent power.

   • Poor: In contrast, indices like LQP and NVSI exhibit poor performance due to their complete neglect of line resistance, which can introduce significant errors in col-lapse prediction. Indices such as Lmn and FVSI are only effective in scenarios dominated by reactive power vari-ations and fail when active power loads are significant.

   • Best for VCA: Within the specific context of Voltage Control Areas (VCAs), the Sensitivity Factor Index (SFI) was identified as the best-performing index for identify-ing the most critical contingencies, offering the highest accuracy for this targeted application.

4. CONTINGENCY ANALYSIS

   Contingency analysis is a cornerstone of secure power system operation. Its purpose is to systematically predict the impact of unforeseen equipment outagessuch as the loss of a transmission line or a generator (an N-1 contingency)on the grid. By simulating a list of credible contingencies, operators can identify the most severe threats to system stability and prepare to mitigate them. Partitioning the network into Voltage Control Areas (VCAs) makes this large-scale analysis more manageable and effective by localizing the assessment of im-pacts and the deployment of required reactive power resources.

   1. Ranking Process

      Given the vast number of potential outages in a large power system, analyzing every possibility in detail is computationally prohibitive. Therefore, a two-stage process is employed:

      1. Screening: This initial stage involves quickly evaluating a long list of credible contingencies to filter out the benign ones and identify a smaller, more manageable subset of potentially harmful events.

      2. Ranking: The screened contingencies are then analyzed more thoroughly. A performance index, such as a highly

         International Journal of Engineering Research & Technology (IJERT)

         ISSN: 2278-0181

         Vol. 14 Issue 10, October – 2025

         accurate Voltage Stability Index ((VSI), is used to cal-culate the severity of each outage. The contingencies are then ranked from most to least severe based on this index[6].

         Fig. 3. Flowchart of contingency analysis and ranking process for voltage stability assessment.

   2. Application

   To ensure that contingency analysis reveals genuine sta-bility risks, the simulations are typically performed under pre- stressed system conditions. Running an analysis on a lightly loaded, base-case scenario may not expose underlying vulnerabilities. Therefore, a common practice is to apply a pre-determined load increase. Case studies confirm that advanced VSIs are highly effective tools for this process. Indices such as MSAI, NCPI, and SFI have been shown to successfully identify and correctly rank the most severe line and genera-tor outages. This provides operators with reliable, predictive insights, allowing them to understand which potential failures require the most urgent attention and proactive planning. Once a critical contingency and its potential for instability are identified, the focus shifts to implementing solutions through corrective actions.

5. CORRECTIVE ACTIONS FOR EMERGENCY

   CONTROL

   The primary objective of emergency control actions is to rapidly restore the system to a normal operating state following a disturbance. These measures are designed to remove the immediate danger of component damage, prevent a localized issue from escalating into a cascading failure, and mitigate widespread outages. Corrective actions are most effective when applied within the Voltage Control Area (VCA) where the instability originates, reinforcing the importance of the VCA identification discussed earlier.

   1. Generation Re-dispatch and Load Shedding

      Generation re-dispatch and load shedding are two of the primary control actions available to operators during an emer- gency. Re-dispatch involves adjusting the power output of online generators to alleviate overloads and support voltage[7]. Load shedding is a last-resort but critical measure used to prevent a system-wide collapse when other controls are insuffi-cient. By intentionally disconnecting a portion of the electrical

      Published by : http://www.ijert.org

      International Journal of Engineering Research & Technology (IJERT)

      ISSN: 2278-0181

      Vol. 14 Issue 10, October – 2025

      load, operators can restore the balance between generation and demand. A common automated scheme is Under-Voltage Load Shedding (UVLS), which trips loads when voltage falls below a predfined threshold. However, while a fundamental last resort, the operational delays inherent in many UVLS schemes pose a significant risk when confronting fast- developing phe-nomena like FIDVR, which can lead to collapse before the shedding action is completed.

   2. Dynamic Reactive Compensation

   Dynamic VAR sources provide immediate, fast-acting volt- age support in the critical moments following a contingency. Flexible AC Transmission System (FACTS) devices are the primary technology used for this purpose.

   • SVC: An SVC is a shunt-connected device that can rapidly inject or absorb reactive power by controlling a set of thyristor-switched capacitors and reactors. It effectively acts as a controllable shunt susceptance.

   • STATCOM: Voltage-source converter injecting VARs, maintains current even at low voltages, ideal for miti-gating FIDVR.

6. ADVANCED FRAMEWORKS FOR STABILITY MANAGEMENT

   The complexity and speed of modern grid emergencies ne- cessitate advanced computational frameworks that can analyze a developing situation and optimize corrective actions in near real-time. These frameworks leverage advanced mathematical techniques to find feasible and effective solutions under im- mense pressure.

   1. IV Formulation

      The Current-Voltage (IV) formulation is an advanced op- timization framework for determining emergency control ac- tions like generation re-dispatch and load shedding.

      • Advantage: Its main benefit is the linearization of the network power flow equations. In the IV domain, the re- lationship between bus current injections and bus voltages is linear, which allows for highly efficient and scalable computation. This makes the IV formulation well-suited for analyzing very large systems where traditional non-linear power flow methods would be too slow.

      • Challenge: The primary challenge of the IV formulation lies in the non-convex transformation from currents and voltages back to active and reactive power (p,q), which is necessary to enforce generation limits and load con-straints. To manage this, two approximation strategies are used:1. First- Order Taylor Expansion: This approach creates a linear approximation of the power constraints around a known operating point. It is computationally fast but may introduce errors. 2. Robust Inner Approxi-mation: This is a more conservative method that defines a convex feasibility domain for currents and voltages. It guarantees that any solution found within this domain is also a feasible solution for the original non-convex problem, ensuring robustness at the cost of potential over-conservatism.

   2. FIDVR Mitigation Strategy

      Addressing the complex challenge of Fault-Induced Delayed Voltage Recovery (FIDVR) requires a multi-stage strategy that combines both steady-state and dynamic analysis to design an effective solution.

      1. Screen contingencies with margin criteria:The pro-cess begins by screening for contingencies that violate established stability margin criteria. Using P-V and Q-V analysis, engineers identify N-1 contingencies that result in a post-contingency power margin below a required threshold (e.g., the WECC requirement of a ¿5

      2. Analysis of Unsolvable Contingencies:For the most severe outages, standard power flow calculations may fail to converge, indicating a likely voltage collapse. In these cases, Branch-Parameter Continuation Power Flow (BCPF) is used. BCPF is a powerful technique that numerically traces a solution path from a solvable pre- contingency state to the post-contingency state, allowing engineers to analyze the systems behavior up to the precise point of collapse even when a standard power flow solution does not exist.

      3. Optimal Placement of VAR Compensation:Once vul-

   nerable areas are identified, sensitivity analysis is used to determine the most effective locations for installing dynamic VAR sources like STATCOMs. The Participa- tion Factor, derived from the Y-V curve generated by BCPF, quantifies the impact of a reactive power injection at each bus, identifying the locations that will provide the greatest stability benefit[8-9].

   Fig. 4. Multi-stage framework for Fault-Induced Delayed Voltage Recovery (FIDVR) mitigation using STATCOM activation and reactive power injection to enhance voltage stability.

   Published by : http://www.ijert.org

   International Journal of Engineering Research & Technology (IJERT)

   ISSN: 2278-0181

   Vol. 14 Issue 10, October – 2025

7. CONCLUSION AND FUTURE DIRECTIONS

Ensuring power system voltage stability in the face of increasing operational stress requires a multi-faceted approach that integrates accurate, real-time assessment with rapid and optimized corrective actions. As this report has detailed, the challenge has evolved from simple static analysis to a complex interplay of steady-state and dynamic phenomena, demanding more sophisticated tools and strategies. The key findings highlight the superiority of modern Voltage Stability Indices, such as MSAI for general monitoring and SFI for VCA-specific analysis, in providing accurate and computationally efficient insights into system stress and contingency sever-ity. In terms of emergency response, a combination of last-resort measures like load shedding and proactive dynamic VAR compensation from FACTS devices like STATCOMs is critical. The effectiveness of these responses can be maximized through advanced computational frameworks, including the IV formulation for scalable optimization and the BCPF-driven methodology for comprehensively designing solutions to dy-namic challenges like FIDVR. Ultimately, a successful stabil-ity management program relies on the seamless integration of these advanced assessment, analysis, and control strategies.

Future research directions:

• Integration with DSM for load-side stability support.

• Smart grid adaptation with DERs and storage.

• Renewable impact-tailored stability metrics.

• Robust indices under uncertainty.

• EV charging influence on local/system voltage.

REFERENCES

1. Paramasivam, M.; Salloum, A.; Ajjarapu, V.; Vittal, V.; Bhatt, N.B.; Liu, S. Dynamic optimization based reactive power planning to mitigate slow voltage recovery and short term voltage instability. IEEE Trans. Power Syst. 2013, 28, 38653873. [CrossRef]

2. Glavic, M.; Novosel, D.; Heredia, E.; Kosterev, D.; Salazar, A.; Habibi- Ashrafi, F.; Donnelly, M. See it fast to keep calm: Real-time voltage control under stressed conditions. IEEE Power Energy Mag. 2012, 10, 4355. [CrossRef]

3. Williams, B.R.; Schmus, W.R.; Dawson, D.C. Trans-mission voltage recovery delayed by stalled air condi-tioner compressors. IEEE Trans. Power Syst. 1992, 7, 11731181. [CrossRef]

4. Taylor, L.Y.; Hsu, S.M. Transmission voltage recovery following a fault event in the Metro Atlanta area. In Proceedings of the Power Engineering Society Sum-mer Meeting, Seattle, WA, USA, 1620 July 2000; pp. 537542.

5. North American Electric Reliability Corporation. Tech-nical Reference Paper Fault-Induced Delayed Voltage Re-covery; North American Electric Reliability Corporation: Princeton, NJ, USA, 2009.

6. Alaqeel, T.A.; Almohaimeed, S.A.; Suryanarayanan, S. A review of air conditioning motor loads stalling on voltage recovery in the saudi electric grid. In Proceedings of the Power Symposium (NAPS), Morgantow, WV, USA,1719 September 2017; pp. 16.

7. DeLeon, J.D.; Taylor, C.W. Understanding and solving short-term voltage stability problems. In Proceedings of the PowerEngineeringSociety SummerMeeting, Chicago, IL,USA,21 25July2002; Volume2, pp.745752.

8. Lu, N.; Yang, B.; Huang, Z.; Bravo, R. The system im-pact of air conditioner under-voltage protection schemes. In Proceedings of the Power Systems Conference and Exposition, Seattle, WA, USA, 1518 March 2009; pp. 18.

9. Shaffer, J.W. Air conditioner response to transmission faults. IEEE Trans. Power Syst. 1997, 12, 614621. [CrossRef]