Harmonics Filters

Harmonics Filters

Overview

• Harmonic filters are electrical devices designed to mitigate or eliminate harmonic distortion in power grids.
• They operate in parallel to the load.
• Tuned to specific harmonic frequencies to filter out unnecessary harmonics.
• Allowing only the fundamental frequency (50–60 Hz) to pass through.

Function

The function of harmonic filters is to either:

• Prevent the harmonic current from flowing through the network impedance.
• Reducing or eliminating the harmonic voltage.

Types

• Passive Harmonics Filters
  • Series Filter
  • Parallel Filter
• Active Harmonics Filters
  • Series Active Filter
  • Parallel Active Filter
• Hybrid Harmonics Filters
  • Passive & Active
  • Series & Parallel Active

Passive Harmonics Filters

• Passive harmonic filters are utilized to eliminate harmonics using passive elements like resistors, inductors, and capacitors.
• Although they are easy to install and affordable, they could not function as effectively under different load conditions.
• Used for lower order harmonics filtering.

Active Harmonics Filters

• Active harmonic filters inject compensating currents into system to neutralize harmonic currents generated by loads.
• Compared to passive filters, they are more sophisticated and more expensive.
• Offer more flexibility and adaptability to varying grid conditions.
• Used for higher order harmonics filtering.

Hybrid Harmonics Filters

• Hybrid filters offer a balanced approach between cost-effectiveness and efficiency through integrating passive and active filter technologies.

Resonance in LC Circuit

• Resonance in an LC circuit occurs when the magnitude of inductive reactance and capacitive reactance in the LC circuit becomes equal.
• The frequency at which this occurs is known as resonant frequency.
• During the resonance, the energy will be exchanged between the energy storage elements.

Series LC Resonance

• When $ω = ω<em>0$, $Z</em>{LC} → 0$, $I → I_{max}$.

• $ω = 2πf$

• Resonance Frequency: $f_0 = \frac{1}{2\sqrt{LC}}$

  • Example: L = 100 μH, C = 62.5 nF
  • $f_0 = \frac{1}{2π\sqrt{LC}} = \frac{1}{2π\sqrt{100 \times 10^{-6} \times 62.5 \times 10^{-9}}} = 63,663 Hz$

• Quality factor (unloaded): $Q = \frac{ωL}{R} = \frac{2πf_0L}{R}$

  • Example: R = 5Ω
  • $Q = \frac{2πf_0L}{R} = \frac{2π \times 63663 \times 100 \times 10^{-6}}{5} = 8$

Parallel LC Resonance

• When $ω = ω<em>0$, $Z</em>{LC} → ∞$, $I → 0$

• $ω = 2πf$

• Resonance Frequency: $f_0 = \frac{1}{2\sqrt{LC}}$

  • Example: L = 5.0 μH, C = 50 pF
  • $f_0 = \frac{1}{2π\sqrt{LC}} = \frac{1}{2π\sqrt{5.0 \times 10^{-6} \times 50 \times 10^{-12}}} ≈ 10.07 MHz$

• Quality factor (unloaded): $Q = \frac{ωL}{R} = \frac{2πf_0L}{R}$

  • Example: R = 10.5 Ω
  • $Q = \frac{2πf_0L}{R} = \frac{2π \times 10.07 \times 10^{6} \times 5.0 \times 10^{-6}}{10.5} ≈ 30$

Resonance Common Terms

• Bandwidth: It is the width of the peak which is defined by the distance between the two half power points $ω<em>1$ and $ω</em>2$
  • $Bandwidth = Δω = ω<em>2 - ω</em>1$
• Center frequency: Center frequency is the frequency $ω_0$ at which the current in the circuit is the maximum.
• Q factor: Quality factor or Q factor is a measurement to determine the sharpness of the curve shown in the above figure which is very important to know to design a band pass filter.
  • $Q = \frac{ω<em>0}{Δω} = \frac{ω</em>0}{ω<em>2 - ω</em>1}$
  • For a series RLC circuit, $Q = \frac{ω<em>0L}{R}$. For a parallel RLC circuit, $Q = ω</em>0RC$.

Shunt Passive Filter

• The most common type of passive filter is the single-tuned “notch" filter.
• This is the most economical type and is frequently sufficient for the application.
• The notch filter is series-tuned to present a low impedance to a particular harmonic current and is connected in shunt with the power system. Thus, harmonic currents are diverted from their normal flow path on the line through the filter.

Series Passive Filter

• Inductance and capacitance are connected in parallel and are tuned to provide a high impedance at a selected harmonic frequency and a low impedance at the fundamental frequency.

Third Harmonic Filter (THF)

• The third harmonic filter (THF), usually, is a parallel resonant filter offers a high impedance for the third harmonic current and very low impedance for the fundamental frequency.

• Third Harmonic filter is a parallel resonance circuit connected in series in neutral circuit

• Assume the capacitor value in the previous example $C = 3453.8μF$.

  • $f_0 = \frac{1}{2 * π * \sqrt{L * C}}$
  • $180 = \frac{1}{2 * π * \sqrt{L * 3453.8 * 10^{-6}}}$
  • $L = 0.226mH$

Fifth Harmonic Filter (FHF)

• To design a 3 phase filter to mitigate the fifth harmonics to be connected at load center 480V.

• We need to find the value of the reactive power that the filter will provide or supply.

• Assume the $Q = 300KVAr$

  • $X_c = \frac{V^2}{Q} = \frac{480^2}{100 * 10^3} = 2.304Ω$
  • $X_c = \frac{1}{2 * π * 60 * C}$
  • $C = \frac{1}{2 * π * 60 * X_c} = \frac{1}{2 * π * 60 * 2.304} = 1151.27μF$

• Now we need to find the value of the inductance L. For that we should consider the 3 capacitances connected in star or wye.

  • $X_c = \frac{(480/\sqrt{3})^2}{100 * 10^3} = 0.768Ω$
  • $C = \frac{1}{2 * π * 60 * X_c} = \frac{1}{2 * π * 60 * 0.768} = 3453.8μF$

• Now we need to find the Inductance value to get a filter tuned to fifth harmonics.

• To avoid the situation, the filter will represents as a short circuit in case of there is a fifth harmonics will consider the 4.7th harmonics. The $f_1 = 282Hz$.

  • $282 = \frac{1}{2 * π * \sqrt{L * 3453.8 × 10^{-6}}}$
  • $L = 0.0922mH$

Disadvantages of Passive Filters

• The application of passive filters may cause parallel resonance with the network impedance, over compensation of reactive power at fundamental frequency.
• Poor flexibility for dynamic compensation of different frequency harmonic components.

Active Filters

Active filters provide an effective alternative to the conventional passive filters, also called:

• Switching Compensators
• Active Power Line Conditioner

Active Filters Function

Active filters are able to compensate:

• Current and voltage harmonics.
• Reactive power.
• Regulate terminal voltage.
• Suppress flicker.
• Improve voltage balance in 3Φ system.

Advantages of Active Filter

• Automatically adapts to changes in the network and load fluctuations.
• Not affected by major changes in network characteristics.
• Compensates for several harmonic orders.
• Eliminating the risk of resonance with the network.
• Smaller in size comparing to the passive filter.

Functional Principles of Active Filter

• A typical configuration of Shunt Active Power Filter (SAPF) is shown in the picture.
• SAPF draws current in such a way that the source current which is sum of load current and active filter current becomes sinusoidal.
• $I<em>s = I</em>L + I_c$
  • Where $I<em>s$ is the source current, $I</em>L$ is the load current and $I_c$ is the current drawn by the filter.

Shunt Active Filter

• It is connected in parallel to the distribution supply and injects harmonic current that is equal in magnitude to the load harmonic current but having 180 degree phase shift to cancel out the harmonic load current to make the source current is sinusoidal.

Series Active Filter

• It is connected in series with the distribution through a matching transformer.
• It is less commonly used.
• In general it is used to compensate voltage Harmonic source, unlike the shunt active filter which is used for current compensation

Hybrid Active Filter

• It consists of the combination of the passive and active filter for better performance.
• Another combination of series and shunt active filters, the control of this hybrid filter is very complicated.