7.1 Passive damping of filter

#### 7.1.1 Type I filter

In LCL filter, the damping can be achieved by simply adding series resistance in series with capacitor C. It is obvious that large value of damping resistance (Rd) gives large damping. But damping is effective around the resonance point only [15]. Above the resonance point, damping weakens. Also, the large value of resistance causes higher losses (Figure 17).

Harmonic Resonance Analysis for Wind Integrated Power System and Optimized Filter Design DOI: http://dx.doi.org/10.5772/intechopen.89167

Figure 17. Type I LCL filter.

b<sup>1</sup> ¼ 0 b<sup>0</sup> ¼ 0

Figure 16 shows the frequency response of LCL filter together with PI controller. It is clear from Eq. (29) and from Figure 16 that the PI controller increases the order of filter, so the frequency response of passive filter gets changed by the

The design criterion for filter design should comply with the regulatory requirement. As per IEEE 519-1992 standard, the current harmonics for weak grid condition (Isc/IL) should be less than 0.3%. The ripple is caused by pulse width modulated signal. Output voltage varies from zero level to DC voltage level (Vdc). The modulated wave causes ripple in the current, which can be reduced by proper selection of output filter parameters. Typical L-C-L filter is used in most of the inverter. The L1-C-L2 filter has three unknowns. The selection of these parameters depends on various factors. Grid condition is one of them. The strength of the grid decides the effectiveness of filters. Typical grid impedance varies from 5 to 8% with X/R ratio in

The switching frequency decides the ripple level and ripple frequency. Generally, inverter switching frequency remains in the range of 3–5 kHz. The ripple current is reduced either by increasing switching frequency or by using passive filter at the inverter/converter output. Higher switching frequency is selected to reduce the ripple current at the generation point, but it adversely affects the converter (IGBT) losses [14]. The second option is to use large inductor at the output of converter, but this not only incurs high cost but also increases the core losses. Typically 20% ripple current is expected in the output current. Keeping this in

controller action.

7. Optimised filter design

Wind Solar Hybrid Renewable Energy System

the range of 7–10 [13].

power.

80

7.1 Passive damping of filter

causes higher losses (Figure 17).

7.1.1 Type I filter

consideration, the inductor L1 is given by [7]

<sup>L</sup><sup>1</sup> <sup>¼</sup> <sup>1</sup> 8 x

Vdc ΔIL fsw ¼ 1 8 x

The capacitor rating is selected such that the reactive power of capacitor is neither too high nor too low. Higher reactive power demands more power from converter, which causes more loss in reactor L1 and also more loss in converter switches. A lower value of capacitor will increase the inductor size. So, the capacitor is selected so that the reactive power should be in the range of 15–20% of the rated

C ¼ 0:15x

Pr ω V<sup>2</sup> r

In LCL filter, the damping can be achieved by simply adding series resistance in series with capacitor C. It is obvious that large value of damping resistance (Rd) gives large damping. But damping is effective around the resonance point only [15]. Above the resonance point, damping weakens. Also, the large value of resistance

Vdc 0:2 Irated fsw

(30)

(31)

Impedance of Type I LCL filter with damping resistance is given by

$$Z\_o = \frac{a\_4s^4 + a\_3s^3 + a\_2s^2 + a\_1s^1 + a\_0s^0}{b\_2s^2 + b\_1s^1 + b\_0s^0} \tag{32}$$

where

$$a\_4 = L\_{\mathcal{g}} L\_1 C^2$$

$$a\_3 = L\_1 C^2 (R\_d + R\_{\mathcal{g}})$$

$$a\_2 = L\_{\mathcal{g}} R\_d C + L\_1 C$$

$$a\_1 = L\_{\mathcal{g}} + C R\_d R\_{\mathcal{g}}$$

$$a\_0 = R\_{\mathcal{g}}$$

$$b\_2 = L\_{\mathcal{g}} C$$

$$b\_1 = (R\_{\mathcal{g}} + R\_d) C$$

$$b\_0 = \mathbf{1}$$

Frequency response of LCL filter with damping resistor is given in Figure 18. The grid parameters are Lg = 0.212 mH and Rg = 0.0095 Ohm, whereas the filter parameters are L1 = 0.450 mH, L2 = 0.300 mH and C = 270 uF. The damping resistance is varied from 0.05 to 0.8 Ohm. It is clear from the plot that the response of impedance is similar to inductive impedance. The notch is observed at the resonant frequency, which can be dampened by resistor in series with capacitor.

Figure 18. Nyquist plot of Type I LCL filter.

The gain margin is �40 dB and phase margin is around 120°. So, as per the Nyquist criterion, the filter response is very stable.
