⚡ electrical engineering

A Novel Two-Step Approach for Reactive Power Demand Calculation Using Integrated Voltage Stability Analysis

This paper proposes a novel two-step methodology that integrates Quasi-Dynamic Simulation, Q-V analysis, and dynamic simulation to calculate actual reactive power demand over a full annual period, effectively addressing voltage stability issues and outperforming existing single-simulation optimization approaches.

Original authors: Hassan Abouelgheit, Hendrik Lens

Published 2026-04-29

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CC BY 4.0

Original authors: Hassan Abouelgheit, Hendrik Lens

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the electrical grid as a massive, complex plumbing system. In this system, voltage is the water pressure, and reactive power is the "push" needed to keep that pressure steady, especially when the pipes are long or the demand is high.

For a long time, engineers trying to fix low pressure (voltage issues) have used two different, separate tools:

The Slow-Change Tool: Looking at how pressure drops over a whole year as usage slowly rises and falls.
The Fast-Change Tool: Looking at what happens to pressure in the split second after a pipe bursts (a fault).

The problem is that the world is changing. We are adding more solar and wind power (which are like unpredictable sprinklers) and removing old, heavy generators (which used to act like giant pressure stabilizers). This makes the plumbing system unstable in both the slow and fast ways. Existing methods usually tried to fix one or the other, or they just guessed the best place to put a "pressure booster" (reactive power equipment) to save money.

This paper introduces a new, two-step "back-to-back" approach to calculate exactly how much "push" (reactive power) is needed to keep the lights on and the pressure stable.

Here is how their method works, using simple analogies:

Step 1: The "Year-Long Weather Report" (Long-Term Stability)

Imagine you want to know if your house will flood during the rainy season. Instead of just checking the weather for one hour, you simulate the entire year (8,760 hours) of weather patterns.

The Simulation: The authors ran a computer simulation for a full year, hour by hour.
The Problem: They found specific times and specific locations (buses) where the "water pressure" dropped too low.
The Fix: They didn't just guess. They identified the worst-hit location, calculated exactly how much "push" was needed to bring the pressure back to a safe zone, and added a virtual booster there.
The Loop: They ran the year-long simulation again. If other spots were still low, they found the next worst spot, added another booster, and ran it again. They kept doing this until the pressure was safe for the whole year.
Result: They calculated the total "push" needed to survive the slow, long-term changes in the grid.

Step 2: The "Sudden Storm Test" (Short-Term Stability)

Now that the pressure is stable for the whole year, they ask: "What happens if a tree falls on a power line right now?"

The Simulation: They took the worst moments from Step 1 (the times when pressure was lowest) and simulated sudden accidents, like a short circuit (a pipe bursting) or a generator shutting down.
The Metric (TVI): They used a special ruler called the Trajectory Violation Integral (TVI). Imagine a "safe zone" tunnel for the pressure. If the pressure drops too low or takes too long to recover after a shock, it hits the walls of the tunnel. The TVI measures how hard and how long the pressure hits those walls.
The Fix: If the pressure hit the walls too hard, they ran a quick analysis to see exactly how much extra "push" was needed to keep the pressure inside the safe tunnel during the shock. They added this extra capacity to the specific spots that were struggling.
The Loop: They ran the crash test again to make sure the pressure stayed safe.

The Final Result

By combining these two steps, the authors didn't just guess where to put equipment or optimize for cost. They directly calculated the actual amount of reactive power needed to keep the system safe from both slow, year-long drifts and sudden, fast crashes.

In their test case (a model of a power grid with 39 connection points):

Step 1 identified that two main locations needed boosters to handle the yearly load, requiring about 1,522 Mvar of power.
Step 2 found that during a sudden crash, one specific location needed a massive 2,750 Mvar boost to prevent a voltage collapse.

In short: The paper presents a method that acts like a rigorous stress test. It simulates a whole year to find weak spots, then simulates sudden disasters to see if those spots hold up, and finally calculates the exact amount of "support" needed to ensure the grid never loses pressure, whether the problem is slow or sudden.

1. Problem Statement

The global energy transition toward high penetration of Renewable Energy (RE) and Inverter-Based Resources (IBRs) (e.g., wind and solar) is fundamentally altering power system dynamics. Unlike traditional synchronous generators, IBRs provide variable output and lack inherent inertia, leading to complex reactive power balance issues and voltage instability.

Existing methodologies for Reactive Power Planning (RPP) suffer from several limitations:

Optimization-Centric: Most approaches formulate RPP as an optimization problem focused on minimizing costs or determining equipment sizing/placement, often treating voltage stability merely as a constraint rather than a direct calculation target.
Fragmented Stability Analysis: Current methods typically address either long-term voltage stability (steady-state, slow dynamics) or short-term voltage stability (dynamic, fault-induced) in isolation.
Lack of Direct Demand Calculation: There is a gap in methods that directly calculate the actual reactive power demand required to maintain stability margins across both time scales without relying solely on iterative optimization loops.

The paper aims to bridge this gap by developing a methodology to directly calculate the necessary reactive power compensation to ensure voltage stability under both long-term load variations and short-term fault conditions.

2. Methodology

The authors propose a novel two-step approach that integrates Quasi-Dynamic Simulation (QDS), Q-V analysis, and Root Mean Square (RMS) dynamic simulations in a sequential, iterative framework. The process covers a full annual period (8,760 hours) and utilizes a multi-criteria violation assessment (number, severity, and duration of violations).

Step 1: Long-Term Voltage Stability Assessment

Simulation: A time-series (Quasi-Dynamic) simulation is performed over 8,760 hours.
Violation Detection: System voltages are compared against a pre-defined band (e.g., $V = [0.95, 1.05]$ p.u.). Violations are quantified by frequency ( $f_n$ ), severity ( $\Delta V$ ), and duration ( $t_v$ ).
Prioritization: Critical buses and time steps are identified and ranked based on violation metrics.
Iterative Compensation:
1. A Q-V analysis is performed on the highest-priority bus to determine the reactive power injection ( $\Delta Q$ ) needed to restore voltage to a target level.
2. Compensation equipment is virtually installed at that bus.
3. The QDS is re-run to assess the impact.
4. This loop repeats until all long-term voltage violations are resolved.
Output: The cumulative reactive power demand ( $\Delta Q_{long}$ ) required for long-term stability.

Step 2: Short-Term Voltage Stability Assessment

Input: Uses the results from Step 1, focusing only on critical time steps (e.g., hours with minimum voltage) and the system state after Step 1 compensation.
Contingency Simulation: Dynamic (RMS) simulations are run for specific contingency scenarios (e.g., short-circuit faults combined with generator outages).
Trajectory Violation Integral (TVI): Instead of simple voltage thresholds, the TVI metric is used. TVI quantifies the area between the voltage trajectory and a predefined, exponentially recovering boundary. It captures both the magnitude and duration of post-fault voltage deviations.
Iterative Correction:
1. If TVI limits are violated, a Q-V analysis is performed on the affected bus to calculate the additional reactive power ( $\Delta Q_{short}$ ) needed.
2. Dynamic compensation devices are added, and the RMS simulation is repeated.
3. The process continues until all dynamic voltage deviations are within TVI limits.
Final Verification: A final QDS ensures that the added dynamic compensation does not introduce new long-term violations.

3. Key Contributions

Integrated Framework: Unlike previous works that separate long-term and short-term analysis, this method sequentially integrates both, ensuring that short-term dynamic requirements do not compromise long-term steady-state stability and vice versa.
Direct Demand Calculation: The approach moves away from pure optimization (minimizing cost) to a direct calculation of the required reactive power to meet specific stability margins.
Comprehensive Time-Series Analysis: The methodology evaluates the system over a full year (8,760 hours) rather than single snapshots or typical days, capturing the full spectrum of operational variability.
Advanced Metrics: The use of TVI for short-term stability provides a more robust assessment of dynamic performance than simple voltage magnitude checks, accounting for recovery time and deviation severity.
Iterative Back-to-Back Simulation: The framework employs a "back-to-back" simulation loop (QDS $\to$ Q-V $\to$ RMS $\to$ Q-V) to refine the solution until convergence.

4. Results (Case Study)

The methodology was validated using a modified IEEE 39-bus system with synthetic time-series data for loads and generators.

Step 1 Results (Long-Term):
- Initial analysis identified Bus 04 as the most critical (5,800 violations).
- A Q-V analysis determined a need for 916 Mvar at Bus 04.
- After a second iteration, Bus 08 was identified as the next critical node, requiring 606 Mvar.
- Total Long-Term Demand: 1,522 Mvar distributed across critical buses.
- Observation: The compensation at critical buses improved voltage profiles system-wide, not just locally.
Step 2 Results (Short-Term):
- A contingency (fault on line 09-39 + loss of Generator 03) was simulated.
- TVI analysis revealed significant deviations at Bus 07, which was not the primary focus of Step 1.
- A dynamic compensation device providing 2,750 Mvar was required at Bus 07 to satisfy TVI limits.
- Total Reactive Power Demand: The final solution combined the long-term static compensation and the short-term dynamic compensation.
Outcome: The iterative process successfully eliminated all voltage violations in both the steady-state (QDS) and dynamic (RMS) simulations.

5. Significance and Future Outlook

Practical Applicability: The framework offers a systematic tool for engineers to determine reactive power needs without relying on complex, black-box optimization algorithms. It is flexible enough to incorporate different stability indices (e.g., FVSI, LQP).
Scalability: The authors tested the framework on networks of varying sizes, including systems with over 50 nodes, demonstrating its potential for larger transmission and distribution networks.
Limitations & Future Work:
- The current method calculates demand for every violating bus, which may lead to overestimation of total demand compared to a global optimization approach.
- Real-world constraints (space, regulations) preventing equipment installation at every critical bus are not yet fully modeled.
- Future directions include applying the method to ultra-large systems (>100,000 nodes), developing automated critical bus identification metrics, and integrating sizing/placement optimization to refine the calculated demand.

In conclusion, this paper presents a robust, simulation-driven methodology that directly addresses the reactive power planning challenges posed by modern, renewable-heavy power grids by unifying long-term and short-term stability assessments.