How to design harmonic filters for large power systems

Introduction

Electrical loads can be divided into linear and non-linear loads. A linear load is one which draws a sinusoidal current when subjected to a sinusoidal voltage as shown in Fig 1 (a). A pure resistance, capacitance, inductance or a combination of these elements forms a linear load. 

A non-linear load draws a non-sinusoidal current, when subjected to a sinusoidal voltage as shown in Fig 1(b). 

Linear loads draw currents that are proportional to applied voltages for example incandescent lighting, heating and motor loads. Non-linear loads draw currents only a part of the voltage cycle and introduce harmonics.
Any non-sinusoidal current can be mathematically resolved into a series of sinusoidal components (Fourier series). The first component is called the fundamental component and the remaining components whose frequencies are integral multiples of the fundamental frequency are known as harmonics. In India, the fundamental frequency is 50 Hz. Hence, 2nd harmonic will have a frequency of 100 Hz, 3rd harmonic will have 150 Hz and so on. A diagrammatic representation of the various harmonics of a non-sinusoidal current is shown in Fig 1(c). Here, f1 = fundamental frequency, f5 = Fifth harmonic, f7 = Seventh harmonic, f11 = Eleventh harmonic. 

It can be understood that design and installation of the harmonic filters shall result in improvement in power quality, improvement in power factor (pf) and reduction in KVA demand from the supply side. This will in turn result in reduction in fixed charges in electricity bill and incentive from DISCOM if pf > 0.95. In our design we shall consider a first order shunt type tuned passive harmonic filter of 400 kVAr rating which is capable of eliminating 5th order harmonic currents. The separate harmonic filters shall be required to be connected in parallel to filter out harmonic frequencies of higher orders.

Why do we need to design filters?

A harmonic rich environment is said to exist when the percentage of non-linear loads in a power system becomes greater than 20% of the connected load. 
Harmonic filters are connected in a power system at the income of load supply bus to improve power factor by supplying reactive power to inductive loads of the power distribution system and elimination of harmonic currents. 
But use of the capacitors in a harmonic rich environment is not safe due to the fact that parallel resonance conditions can occur i.e. magnitude of capacitive reactance of power capacitors and inductive reactance of the source can tend to become equal. If such resonance occurs at a frequency near to that present in source current, current amplification takes place. A circuit representation of this phenomenon is shown in the next figure.

This current amplification will result in overloading of power capacitors i.e. the capacitors drawing more than rated current and harmonic distortion of voltage waveform. This condition can cause premature failure of the power capacitors. This condition can also cause total harmonic distortion (THD) in the power system to become more than permissible limits. This is not good for the health of power system equipment.
Hence, it becomes essential to design a harmonic filter which is helpful in improvement in power factor of power system, controlling harmonic current amplification and to limit harmonic currents in power systems.
The typical impedance characteristic of shunt type tuned passive harmonic filter is shown in fig-4(b). fr is the tuning frequency of the filter. Below fr, the filter impedance is capacitive in nature. Above fr, the filter impedance is inductive in nature. 

To achieve above requirements, a first order shunt type tuned passive filter is suitable and economical for large power system applications. This type of filter is suitable for power systems of more than 500 kVA, where harmonic frequencies of the order of 5th and above are dominant.
Types of Harmonic Filters
Shunt type first order tuned passive harmonic filters
The passive filters are typically used in power systems with loads more than 500 kVA.  The passive filter consists of a series circuit of resistor reactor and capacitor (RLC), which is connected in parallel to the connected loads of the power system, as shown in Fig-3a. Harmonic currents generated by non-linear loads are filtered out by this filter by providing a low impedance path compared to total impedance of source for a particular order of harmonic frequency for which it is tuned, thereby reducing the amount of harmonic current that flows into the power system. Also, power factor is improved based on reactive power fed by the harmonic filter.
Active Harmonic Filters or active harmonic conditioners
These filters are mostly used in power systems with loads less than 500kVA. This type of filter is shown in fig ‚Äì 3(b). Active filters employ power electronics. They are installed either in series or in parallel with the nonlinear load to provide the harmonic currents required by nonlinear load. Active filters are most suitable when more than one type of non-linear load is present i.e. UPS, VFD, rectifiers, inverters etc. The active filters feed the harmonic current of a particular order required by the non-linear loads, so that the harmonic current of this order is eliminated from the supply current. 

Is = Source current
Iact = Current injected by active filter
Ihar = Harmonic current generated by nonlinear load
Hybrid Filters
A type of filter combines both passive and active filters for power systems with loads more than 500kVA. It has the advantages of the previous two types of filters and covers different power and performance levels. This type of filter is shown in fig-3(c).

How to design a first order shunt-type tuned passive harmonic filters?
In our study we are considering the design of a harmonic filter of 400 kVAr. For this large power system the most simple and suitable harmonic filter is first order shunt type tuned passive harmonic filter. 3 phase connection diagram of such type of filter is shown in Fig 4. This is a common design of shunt type passive harmonic filters. In this design of harmonic filters, it is tuned for elimination of 5th order harmonic current i.e. 250 Hz and power factor improvement from pf1 to pf2. 

% of harmonic current of a particular order being filtered out is dependent upon the quality factor of the harmonic filter. Higher the quality factor, higher will be the % of harmonic current of a particular order being filtered out. Value of quality factor is dependent upon filter elements namely resistance, inductance and capacitance. For 5th order filter with quality factor (Q5) of 10, % of harmonic current being filtered out is 51.2%. For a quality factor of 30, this % is 87.28. For a quality factor of 50, this % is 94.48. For a quality factor of 100, this % is 98.66. Hence, as the quality factor increases, performance of the filter improves. For a high quality harmonic filter, the value of quality factor must be in between 50 to 100. 
Let us assume following parameters for designing a high quality first order shunt type tuned passive harmonic filter.
Let us assume ‚Äì 
Line to line voltage at terminals of harmonic filter (VLL) = 415 V
Line to neutral voltage at terminals of harmonic filter (VPH) =   415 V/1.732 = 239.6 V
Is = Current from source side
IL = Current flowing to connected loads
IF = Current flowing through harmonic filter
Reactive power of harmonic filter (Qhf) = 400 kVAr
Order of harmonic frequency (h) = 5
Fundamental frequency (f) = 50 Hz
Quality factor (Q5) = 100
Z5 = Impedance of harmonic filter. 
XC5 = Reactance of power capacitor C5
XL5 = Reactance of inductor L5
R5 = Resistance of harmonic filter
Initial pf (pf1) = 0.8 
final pf (pf2) = 0.98
Active power demand of power system  = P kW
Reactive power requirement of connected loads before use of harmonic filter = Q1 kVAr
Reactive power requirement of connected loads after installation of harmonic filter = Q2 kVAr
Apparent power requirement of connected loads before use of harmonic filter = A1 kVA
Apparent power requirement of connected loads after use of harmonic filter = A2 kVA
Now, let us calculate the parameters of the passive harmonic filter
Impedance of the filter is given by:
Z5 = {R5 + j (hXL5 – XC5/h)}
XC5 = V2phh2/{Qhf(h2 – 1)}
C5 = 1/(XC5 * 2πf) = {Qhf(h2 -1)}/{V2ph h22πf } [Eq.(1)]
XL5 = XC5/h2 
L5 = XL5/2πf = XC5/(h22πf) = V2ph/{Qhf(h2 – 1)2πf} [Eq (2)]
R5 = XL5/Q5  = XC5/(h2Q5 )  = V2ph/{Qhf(h2 ‚Äì 1)Q5} [Eq.(3)]
From Eq. (1) ‚Äì 
C5 = {Qhf(h2 -1)}/{V2ph h22πf } = (400*24)/{(239.6)2 *2523.1450}
C5 = 0.0213 F
From Eq. (2) ‚Äì 
          L5 = V2ph/{Qhf(h2 ‚Äì 1)2œÄf} = (239.6)2/(40010002423.1450)
L5 = 1.904 * 10-5 H 
L5 = 19.04 µH
From Eq. (3) –
R5 = V2ph/{Qhf(h2 – 1)Q5} = (239.6)2/(400100024100)
R5 = 5.9810-5 ‚Ѷ 
R5 = 59.8 µΩ
Now, it can be understood that installation of harmonic filter shall provide two fold advantage. First advantage is annual savings in electricity bill due to improvement in power factor and second advantage is improvement in power quality of power system parameters thereby enhancement in life & performance of power system equipment. 
The aforesaid description shall create awareness among consumers about the importance of power quality and power factor improvement by installation of harmonic filters. 
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