Passive Harmonic Filter (Three-Phase)

Harmonic current filter

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Libraries:
Simscape / Electrical / Passive

Description

The Passive Harmonic Filter (Three-Phase) block suppresses system harmonic currents and decreases voltage distortion by providing low-impedance paths for the harmonics. At the rated frequency, the passive shunt filters are capacitive and provide reactive power, which can improve electrical power factor.

Each of the four models for the block corresponds to an option for the Filter type parameter:

• Band-Pass Filter, Single Tuned

• Band-Pass Filter, Double Tuned

• High-Pass Filter, Second-Order

• High-Pass Filter, C-type

Band-Pass Filter, Single Tuned

At the tuned frequency, LC resonance occurs and the impedance of the filter reaches its minimum, which equals the value of the resistance.

The filter tuned frequency is defined by this equation:

$$f_1=n{f}_0=\frac{1}{2\pi \sqrt{LC}},$$

where f₁ and f₀ are the tuned and fundamental frequency, n is the harmonic order of the tuned frequency, L is the inductance and C is the capacitance.

The quality factor is defined as the ratio between the inductive or capacitive reactance at the tuned frequency and the resistance, as described by this equation:

$$Q_f=\frac{X_{LN}}{R}=\frac{X_{CN}}{R},$$

where:

• R is the resistance.

• XLN is the impedance of the inductor at the tuned frequency $$X_{LN}=2\pi f_{1}L.$$

• XCN is the impedance of the capacitor at the tuned frequency $$X_{CN}=\frac{1}{2\pi f_{1}C}.$$

Higher quality factor values result in sharper frequencies. However, this produces high-power dissipation at the base frequency due to a relative low resistance.

The rated reactive power is given by:

$$Q_r=\frac{V^2}{X_{C0}-X_{L0}}=\frac{V^2}{X_{C0}-\frac{X_{C0}}{n^2}}=\frac{V^2}{X_{C0}}\frac{n^2}{n^2-1}$$

where Q_r is the rated reactive power for one phase and V is the branch voltage in root mean square.

Band-Pass Filter, Double Tuned

A double-tuned filter has two tuned frequencies, f₁ and f₂, where $$f_1=n_1{f}_0$$ and $$f_2=n_2{f}_0.$$

The double-tuned filter comprises a series LC and a parallel RCL circuit, each tuned at frequencies f_s and f_p, close to the mean geometric frequency of f₁ and f₂, which are represented by the equation:

$$f_m=\sqrt{f_1{f}_2}=\sqrt{f_s{f}_p},$$

where

$$f_s=\frac{1}{2\pi \sqrt{LC}}$$

$$f_p=\frac{1}{2\pi \sqrt{L_2{C}_2}}.$$

The quality factor of this filter is defined as the quality factor of the parallel R and L elements at the mean geometric frequency, f_m:

$$Q_f=\frac{R}{2\pi f_m{L}_2}.$$

High-Pass Filter, Second-Order

The second order high-pass filter shunts a large percentage of the harmonics at and above the tuned frequency. The filter is designed to have a flat impedance for high-order harmonics.

The tuned frequency is described by this equation:

$$f_1=n{f}_0=\frac{1}{2\pi \sqrt{LC}}.$$

The quality factor is the reciprocal of the band-pass, single-tuned filter:

$$Q_f=\frac{R}{X_{LN}}=\frac{R}{X_{CN}}.$$

The rated reactive power is the same of the band-pass, single-tuned filter:

$$Q_r=\frac{V^2}{X_{C0}-X_{L0}}=\frac{V^2}{X_{C0}-\frac{X_{C0}}{n^2}}=\frac{V^2}{X_{C0}}\frac{n^2}{n^2-1}$$

High-Pass Filter, C-type

Compared to the single-tuned version, the C-type, high-pass filter has lower losses at the fundamental frequency, because the capacitor and inductor are parallel with the resistor.

To prevent fundamental currents from passing through the resistor, the resonance frequency of L₂ and C₂ is tuned to the fundamental frequency:

$$f_0=\frac{1}{2\pi \sqrt{L_2{C}_2}}.$$

The quality factor is calculated using this equation:

$$Q_f=\frac{R}{2\pi f_{0}n{L}_2}.$$

Values of RCL Filter Components

	Single-Tuned	Double-Tuned	Second-Order, High-Pass	C-type, High-Pass
R	$$\frac{1}{2\pi f_{0}C{Q}_f}$$	$$2\pi f_m{L}_2{Q}_f$$	$$2\pi n{f}_{0}L{Q}_f$$	$$Q_f\left(2\pi n{f}_0{L}_2\right)$$
L	$$\frac{1}{C{(2\pi n{f}_0)}^2}$$	$$\frac{V^2}{Q_r\pi f_0\left(n_1^2+n_2^2-2\right)}$$	$$\frac{1}{C{(2\pi n{f}_0)}^2}$$	None
C	$$\frac{Q_r}{2\pi f_0{V}^2}\cdot \frac{n^2-1}{n^2}$$	$$\frac{Q_r}{4\pi f_0{V}^2}\left(\frac{n_1^2-1}{n_1^2}+\frac{n_2^2-1}{n_2^2}\right)$$	$$\frac{Q_r}{2\pi f_0{V}^2}\cdot \frac{n^2-1}{n^2}$$	$$\frac{Q_r}{2\pi f_0{V}^2}$$
L2	None	$$\begin{array}{c}\frac{\left(1-\frac{f_1^2}{f_s^2}\right)\left(1-\frac{f_1^2}{f_p^2}\right)}{C(2\pi f_1{}^2)}\\ where{f}_s=\frac{1}{2\pi \sqrt{LC}},f_p=\frac{f_1{f}_2}{f_s}\end{array}$$	None	$$\frac{1}{C_2{(2\pi n{f}_0)}^2}$$
C2	None	$$\frac{1}{L_2{\left(2\pi f_p\right)}^2}$$	None	$$C(n^2-1)$$

Ports

Conserving

~ — Three-phase voltage

electrical

Expandable three-phase port associated with the voltage.

Parameters

Modeling option — Whether to model composite or expanded three-phase ports

Composite three-phase ports (default) | Expanded three-phase ports

Whether to model composite or expanded three-phase ports.

Composite three-phase ports represent three individual electrical conserving ports with a single block port. You can use composite three-phase ports to build models that correspond to single-line diagrams of three-phase electrical systems.

Expanded three-phase ports represent the individual phases of a three-phase system using three separate electrical conserving ports.

Rated reactive power — Reactive power

100e6 V*A (default)

Reactive power at rated frequency and voltage, in V*A.

Rated voltage (phase-to-phase RMS) — Phase-to-phase RMS Voltage

4160 V (default)

Rated phase-to-phase root mean squared (RMS) voltage, in V.

Rated frequency — Rated frequency

60 Hz (default)

Fundamental frequency, in Hz.

Quality factor — Quality factor

10 (default)

Index of the sharpness of the tuned frequency.

Filter type — Filter model

Band-pass filter, single-tuned (default) | Band-pass filter, double-tuned | High-pass filter, second-order | High-pass filter, C-type

Type of harmonic filter.

Dependencies

The Tuned frequency parameter becomes visible if you select Band-pass filter, single-tuned, High-pass filter, second-order, or High-pass filter, C-type for the Filter type parameter.

If you select Band-pass filter, double-tuned for the Filter type parameter, the Tuned frequency 1 and Tuned frequency 2 parameters become visible.

Filter connection — Connection type

Wye with floating neutral (default) | Wye with neutral port | Wye with grounded neutral | Delta

Type of connection

Tuned frequency — Tuned frequency

5 * 60 Hz (default)

Tuned frequency for the filter, in Hz.

Dependencies

This parameter is visible only when you select Band-pass filter, single-tuned, High-pass filter, second-order, or High-pass filter, C-type for the Filter type parameter.

Tuned frequency 1 — First tuned frequency

7 * 60 Hz (default)

First tuned frequency, in Hz.

Dependencies

This parameter is visible only when you select Band-pass filter, double-tuned for the Filter type parameter.

Tuned frequency 2 — Second tuned frequency

11 * 60 Hz (default)

Second tuned frequency, in Hz.

Dependencies

This parameter is visible only when you select Band-pass filter, double-tuned for the Filter type parameter.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2019b