Selection of Reactance Rate for Series Reactors in Capacitor Banks

Introduction

Series reactors (also known as detuned reactors) used with power capacitor banks have been widely proven in power systems worldwide to improve reactive power compensation, reduce line losses, limit capacitor switching inrush currents, and suppress harmonic distortion.

 

The selection of an appropriate reactor reactance rate is critical because harmonic currents are influenced by multiple factors, including grid harmonic sources, system impedance, and capacitor bank parameters. An unsuitable reactance rate may lead to resonance, capacitor overload, overheating, or premature equipment failure.

 

This article explains the principles behind reactance rate selection and provides practical guidance for capacitor bank applications.

 

1. Limiting Capacitor Switching Inrush Current

Capacitor switching inrush current is one of the most common causes of stress on switching devices and capacitor banks. Excessive inrush current can damage contactors, circuit breakers, capacitors, and other power system components.

 

Two types of inrush current typically occur during capacitor bank energization:

Type 1: Single Capacitor Bank Switching

When a standalone capacitor bank is energized, the resulting inrush current is usually within the allowable withstand capability of standard switching equipment. In most cases, no additional current-limiting measures are required.

 

Type 2: Back-to-Back Capacitor Bank Switching

When an additional capacitor bank is switched on while one or more capacitor banks are already connected to the system, a much higher inrush current can occur.

 

Field experience shows that this transient current may reach 20 to 250 times the rated current of the capacitor bank.

The inrush current can be expressed as:

 

Where:

(Q_C) = Capacitor reactive power

(X_L) = Circuit inductive reactance

 

The equation shows that increasing the inductive reactance of the circuit reduces the inrush current. Therefore, installing a properly selected series reactor effectively limits switching surges and protects both capacitors and switching equipment.

 

2. Harmonic Suppression and Reactance Rate Selection

Modern power systems contain a large number of nonlinear loads, such as:

• Variable Frequency Drives (VFDs)
• Rectifiers
• UPS systems
• Arc furnaces
• Renewable energy converters

 

These devices generate harmonic currents that distort the voltage waveform and negatively affect capacitor banks.

 

To improve power quality and protect capacitors, series reactors are commonly installed as harmonic suppression reactors.

 

Impact of Harmonics on Capacitor Banks

A non-sinusoidal waveform consists of a fundamental frequency component plus harmonic frequencies that are integer multiples of the fundamental frequency.

 

In practical power systems, the most significant harmonic orders are:

• 3rd harmonic
• 5th harmonic
• 7th harmonic
• 11th harmonic
• 13th harmonic

 

Among these, the 5th harmonic is usually the dominant component.

 

Consider a system containing only the fundamental voltage and a 5th harmonic voltage component. If the 5th harmonic voltage reaches 26.45% of the rated voltage:

• Capacitor overvoltage reaches approximately 3.4%
• Capacitor overcurrent reaches approximately 65.6%
• Reactive power overload reaches approximately 35%

 

These values clearly demonstrate the severe impact of harmonics on capacitor bank operation.

 

3. Resonance Analysis

The harmonic current can be calculated as:

Where:

• (E_n) = Harmonic voltage
• (X_B) = System impedance
• (X_L) = Reactor reactance
• (X_C) = Capacitor reactance
• (n) = Harmonic order

 

Resonance occurs when:

 

The corresponding resonance conditions:

To avoid resonance and effectively suppress harmonic currents, the following condition must be satisfied:

 

This ensures that the capacitor branch exhibits inductive characteristics at the target harmonic frequency, thereby preventing harmonic amplification.

 

4. Determining the Reactor Reactance Rate

In engineering practice, a safety factor of 1.5 is commonly applied:

 

For 5th harmonic suppression:

The reactance rate (K) is defined as:

where:

(K) = Reactor reactance rate

(X_L) = Fundamental-frequency reactor reactance

(X_C) = Fundamental-frequency capacitor reactance

 

Therefore, a 6% reactance rate effectively detunes the capacitor bank below the 5th harmonic frequency, suppresses 5th-order and higher harmonics, and limits switching inrush current to approximately five times the rated current.

 

5. Standard Reactance Rate Selection Guide

0.1% – 1% Reactance Rate

Application:

• Inrush current limiting only
• No harmonic suppression requirement

 

Typical Use:

• Clean power systems with very low harmonic content
• Short-circuit current limitation

 

4.5% – 6% Reactance Rate

Application:

• Suppression of 5th-order and higher harmonics

 

Typical Use:

• Industrial facilities
• Commercial buildings
• General reactive power compensation systems

 

Most commonly selected reactance rate

12% – 13% Reactance Rate

Application:

• Suppression of 3rd-order and higher harmonics

 

Typical Use:

• Systems with significant 3rd harmonic content
• Special harmonic mitigation projects

 

Applicable System Frequency

• 50 Hz power systems
• 60 Hz power systems

 

Conclusion

Series reactors are an essential component of modern capacitor banks, providing effective protection against switching inrush currents, harmonic distortion, and resonance problems while improving overall power quality and energy efficiency.

 

The reactance rate should always be selected according to actual site conditions and harmonic measurements:

• 6% reactance rate is generally recommended for harmonic suppression and capacitor bank protection.
• 0.2%–1% air-core reactors are suitable when the primary objective is to limit switching inrush current and, to a lesser extent, reduce short-circuit current.
• 12%–13% reactance rates are recommended for applications requiring suppression of significant 3rd-order harmonics.

 

Proper reactor selection ensures reliable operation, extended capacitor service life, improved power factor correction performance, and enhanced power quality throughout the electrical system.