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	$$C(n^2-1)$$

Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Use nominal values to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources. One of these sources is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Examples

Scalar Control in Matrix Converter-Fed Induction Machine Drive

Control the rotor speed in a matrix converter-fed induction machine drive by using the scalar V/f control method. To generate three-phase voltage with reference frequency, the controller maintains a constant voltage-to frequency ratio though scalar V/f control. A three-phase voltage source with fixed amplitude and frequency feeds the induction machine through a three-phase matrix converter. The matric converter is controlled using third harmonic injection Venturini modulation with unity input displacement factor. The induction machine operates in both motoring and generating modes. The Scopes subsystem contains scopes that allow you to see the simulation results.

• Open Model

Ports

Conserving

~ — Composite three-phase port

electrical

Electrical conserving port representing the three phases of the three-phase block. For more information, see Three-Phase Ports.

Dependencies

To enable this port, set the Electrical connection parameter to Composite three-phase ports.

a — Phase a of three-phase system

electrical

Electrical conserving port associated with the phase a of the three-phase block.

Dependencies

To enable this port, set the Electrical connection parameter to Expanded three-phase ports.

b — Phase b of three-phase system

electrical

Electrical conserving port associated with the phase b of the three-phase block.

Dependencies

To enable this port, set the Electrical connection parameter to Expanded three-phase ports.

c — Phase c of three-phase system

electrical

Electrical conserving port associated with the phase c of the three-phase block.

Dependencies

To enable this port, set the Electrical connection parameter to Expanded three-phase ports.

Parameters

Electrical connection — Whether to model composite or expanded three-phase ports

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

Since R2026a

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.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	port_option
Values:	"ee.enum.threePhasePort.composite" (default) | "ee.enum.threePhasePort.expanded"

Rated reactive power — Reactive power

100e6 V*A (default) | positive scalar

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

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

4160 V (default) | positive scalar

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

Rated frequency — Rated frequency

60 Hz (default) | positive scalar

Fundamental frequency, in Hz.

Quality factor — Quality factor

10 (default) | positive scalar

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.

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) | positive scalar

Tuned frequency for the filter, in Hz.

Dependencies

To enable this parameter, set Filter type to Band-pass filter, single-tuned, High-pass filter, second-order, or High-pass filter, C-type.

Tuned frequency 1 — First tuned frequency

7 * 60 Hz (default) | positive scalar

First tuned frequency, in Hz.

Dependencies

To enable this parameter, set Filter type to Band-pass filter, double-tuned.

Tuned frequency 2 — Second tuned frequency

11 * 60 Hz (default) | positive scalar

Second tuned frequency, in Hz. The value of this parameter must be greater than the value of the Tuned frequency 1 parameter.

Dependencies

To enable this parameter, set Filter type to Band-pass filter, double-tuned.

Extended Capabilities

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

Version History

Introduced in R2019b

R2026a: The Modeling option parameter has changed

The Modeling option parameter has been replaced with the Electrical connection parameter. You can now also set this parameter value programmatically by using the set_param function.

If you created a model containing this block in an earlier release, the software now automatically sets the value of the Electrical connection parameter to the previous value of the Modeling option parameter.